From 406d2088bf0103d229e1bed8b20aa1392246f9a0 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Wed, 19 Mar 2025 20:59:18 +0000 Subject: [PATCH 01/39] depostulate funext in `foundation.function-extensionality` --- src/foundation.lagda.md | 1 + .../function-extensionality-axiom.lagda.md | 172 ++++++++++++++++++ .../function-extensionality.lagda.md | 124 ++----------- 3 files changed, 188 insertions(+), 109 deletions(-) create mode 100644 src/foundation/function-extensionality-axiom.lagda.md diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index fa5ed4f5b6..9979470954 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -198,6 +198,7 @@ open import foundation.finitely-coherently-invertible-maps public open import foundation.fixed-points-endofunctions public open import foundation.full-subtypes public open import foundation.function-extensionality public +open import foundation.function-extensionality-axiom public open import foundation.function-types public open import foundation.functional-correspondences public open import foundation.functoriality-action-on-identifications-functions public diff --git a/src/foundation/function-extensionality-axiom.lagda.md b/src/foundation/function-extensionality-axiom.lagda.md new file mode 100644 index 0000000000..3335f2bf9d --- /dev/null +++ b/src/foundation/function-extensionality-axiom.lagda.md @@ -0,0 +1,172 @@ +# The function extensionality axiom + +```agda +module foundation.function-extensionality-axiom where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-binary-functions +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.evaluation-functions +open import foundation.implicit-function-types +open import foundation.universe-levels + +open import foundation-core.coherently-invertible-maps +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.retractions +open import foundation-core.sections +``` + +
+ +## Idea + +The +{{#concept "function extensionality axiom" Agda=function-extensionality Agda=funext}} +asserts that [identifications](foundation-core.identity-types.md) of (dependent) +functions are [equivalently](foundation-core.equivalences.md) described as +[homotopies](foundation-core.homotopies.md) between them. In other words, a +function is completely determined by its values. + +Function extensionality is postulated by stating that the canonical map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +from identifications between two functions to homotopies between them is an +equivalence. The map `htpy-eq` is the unique map that fits in a +[commuting triangle](foundation-core.commuting-triangles-of-maps.md) + +```text + htpy-eq + (f ＝ g) ----------> (f ~ g) + \ / + ap (ev x) \ / ev x + ∨ ∨ + (f x ＝ g x) +``` + +In other words, we define + +```text + htpy-eq p x := ap (ev x) p. +``` + +It follows from this definition that `htpy-eq refl ≐ refl-htpy`, as expected. + +## Definitions + +### Equalities induce homotopies + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + htpy-eq : {f g : (x : A) → B x} → f ＝ g → f ~ g + htpy-eq p a = ap (ev a) p + + compute-htpy-eq-refl : {f : (x : A) → B x} → htpy-eq refl ＝ refl-htpy' f + compute-htpy-eq-refl = refl +``` + +### An instance of function extensionality + +This property asserts that, _given_ two functions `f` and `g`, the map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +is an equivalence. + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + instance-function-extensionality : (f g : (x : A) → B x) → UU (l1 ⊔ l2) + instance-function-extensionality f g = is-equiv (htpy-eq {f = f} {g}) +``` + +### Based function extensionality + +This property asserts that, _given_ a function `f`, the map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +is an equivalence for any function `g` of the same type. + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + based-function-extensionality : (f : (x : A) → B x) → UU (l1 ⊔ l2) + based-function-extensionality f = + (g : (x : A) → B x) → instance-function-extensionality f g +``` + +### The function extensionality principle with respect to a universe level + +```agda +function-extensionality-Level : (l1 l2 : Level) → UU (lsuc l1 ⊔ lsuc l2) +function-extensionality-Level l1 l2 = + {A : UU l1} {B : A → UU l2} + (f : (x : A) → B x) → based-function-extensionality f +``` + +### The function extensionality axiom + +```agda +function-extensionality : UUω +function-extensionality = {l1 l2 : Level} → function-extensionality-Level l1 l2 +``` + +## Properties + +### `htpy-eq` preserves inverses + +For any two functions `f g : (x : A) → B x` we have a +[commuting square](foundation-core.commuting-squares-of-maps.md) + +```text + inv + (f = g) ---------> (g = f) + | | + htpy-eq | | htpy-eq + ∨ ∨ + (f ~ g) ---------> (g ~ f). + inv-htpy +``` + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} + where + + compute-htpy-eq-inv : inv-htpy {f = f} {g} ∘ htpy-eq ~ htpy-eq ∘ inv + compute-htpy-eq-inv refl = refl + + compute-inv-htpy-htpy-eq : htpy-eq ∘ inv ~ inv-htpy {f = f} {g} ∘ htpy-eq + compute-inv-htpy-htpy-eq = inv-htpy compute-htpy-eq-inv +``` + +## See also + +- The fact that the univalence axiom implies function extensionality is proven + in + [`foundation.univalence-implies-function-extensionality`](foundation.univalence-implies-function-extensionality.md). +- Weak function extensionality is defined in + [`foundation.weak-function-extensionality`](foundation.weak-function-extensionality.md). +- Transporting along homotopies is defined in + [`foundation.transport-along-homotopies`](foundation.transport-along-homotopies.md). diff --git a/src/foundation/function-extensionality.lagda.md b/src/foundation/function-extensionality.lagda.md index 5633842ad1..7dc5040a43 100644 --- a/src/foundation/function-extensionality.lagda.md +++ b/src/foundation/function-extensionality.lagda.md @@ -1,7 +1,12 @@ # Function extensionality ```agda -module foundation.function-extensionality where +open import foundation.function-extensionality-axiom + +module + foundation.function-extensionality + (funext : function-extensionality) + where ```
Imports @@ -63,75 +68,8 @@ It follows from this definition that `htpy-eq refl ≐ refl-htpy`, as expected. ## Definitions -### Equalities induce homotopies - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - htpy-eq : {f g : (x : A) → B x} → f ＝ g → f ~ g - htpy-eq p a = ap (ev a) p - - compute-htpy-eq-refl : {f : (x : A) → B x} → htpy-eq refl ＝ refl-htpy' f - compute-htpy-eq-refl = refl -``` - -### An instance of function extensionality - -This property asserts that, _given_ two functions `f` and `g`, the map - -```text - htpy-eq : f ＝ g → f ~ g -``` - -is an equivalence. - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - instance-function-extensionality : (f g : (x : A) → B x) → UU (l1 ⊔ l2) - instance-function-extensionality f g = is-equiv (htpy-eq {f = f} {g}) -``` - -### Based function extensionality - -This property asserts that, _given_ a function `f`, the map - -```text - htpy-eq : f ＝ g → f ~ g -``` - -is an equivalence for any function `g` of the same type. - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - based-function-extensionality : (f : (x : A) → B x) → UU (l1 ⊔ l2) - based-function-extensionality f = - (g : (x : A) → B x) → instance-function-extensionality f g -``` - -### The function extensionality principle with respect to a universe level - -```agda -function-extensionality-Level : (l1 l2 : Level) → UU (lsuc l1 ⊔ lsuc l2) -function-extensionality-Level l1 l2 = - {A : UU l1} {B : A → UU l2} - (f : (x : A) → B x) → based-function-extensionality f -``` - ### The function extensionality axiom -```agda -function-extensionality : UUω -function-extensionality = {l1 l2 : Level} → function-extensionality-Level l1 l2 -``` - Rather than postulating a witness of `function-extensionality` directly, we postulate the constituents of a coherent two-sided inverse to `htpy-eq`. The benefits are that we end up with a single converse map to `htpy-eq`, rather than @@ -144,23 +82,23 @@ module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} where - postulate + opaque eq-htpy : f ~ g → f ＝ g + eq-htpy = map-inv-is-equiv (funext f g) is-section-eq-htpy : is-section htpy-eq eq-htpy + is-section-eq-htpy = is-section-map-inv-is-equiv (funext f g) - is-retraction-eq-htpy' : is-retraction htpy-eq eq-htpy + is-retraction-eq-htpy : is-retraction htpy-eq eq-htpy + is-retraction-eq-htpy = is-retraction-map-inv-is-equiv (funext f g) - coh-eq-htpy' : + coh-eq-htpy : coherence-is-coherently-invertible ( htpy-eq) ( eq-htpy) ( is-section-eq-htpy) - ( is-retraction-eq-htpy') - -funext : function-extensionality -funext f g = - is-equiv-is-invertible eq-htpy is-section-eq-htpy is-retraction-eq-htpy' + ( is-retraction-eq-htpy) + coh-eq-htpy = coherence-map-inv-is-equiv (funext f g) module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} @@ -173,12 +111,7 @@ module _ is-equiv-eq-htpy : (f g : (x : A) → B x) → is-equiv (eq-htpy {f = f} {g}) is-equiv-eq-htpy f g = - is-equiv-is-invertible htpy-eq is-retraction-eq-htpy' is-section-eq-htpy - - abstract - is-retraction-eq-htpy : - {f g : (x : A) → B x} → is-retraction (htpy-eq {f = f} {g}) eq-htpy - is-retraction-eq-htpy {f} {g} = is-retraction-map-inv-is-equiv (funext f g) + is-equiv-is-invertible htpy-eq is-retraction-eq-htpy is-section-eq-htpy eq-htpy-refl-htpy : (f : (x : A) → B x) → eq-htpy (refl-htpy {f = f}) ＝ refl @@ -244,33 +177,6 @@ module _ ( is-retraction-eq-htpy (eq-htpy H ∙ eq-htpy K)) ``` -### `htpy-eq` preserves inverses - -For any two functions `f g : (x : A) → B x` we have a -[commuting square](foundation-core.commuting-squares-of-maps.md) - -```text - inv - (f = g) ---------> (g = f) - | | - htpy-eq | | htpy-eq - ∨ ∨ - (f ~ g) ---------> (g ~ f). - inv-htpy -``` - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} - where - - compute-htpy-eq-inv : inv-htpy {f = f} {g} ∘ htpy-eq ~ htpy-eq ∘ inv - compute-htpy-eq-inv refl = refl - - compute-inv-htpy-htpy-eq : htpy-eq ∘ inv ~ inv-htpy {f = f} {g} ∘ htpy-eq - compute-inv-htpy-htpy-eq = inv-htpy compute-htpy-eq-inv -``` - ### `eq-htpy` preserves inverses For any two functions `f g : (x : A) → B x` we have a commuting square From 60a5a24b6c8c184e50731c3a8959f78fe975da2c Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Wed, 19 Mar 2025 21:29:18 +0000 Subject: [PATCH 02/39] add funextaxiom dependencies --- src/category-theory/copresheaf-categories.lagda.md | 1 + .../dependent-products-of-large-precategories.lagda.md | 1 + src/category-theory/dependent-products-of-precategories.lagda.md | 1 + src/category-theory/precategory-of-functors.lagda.md | 1 + src/category-theory/precategory-of-maps-precategories.lagda.md | 1 + src/category-theory/presheaf-categories.lagda.md | 1 + src/category-theory/yoneda-lemma-precategories.lagda.md | 1 + .../based-strong-induction-natural-numbers.lagda.md | 1 + src/finite-group-theory/transpositions.lagda.md | 1 + src/foundation-core/propositions.lagda.md | 1 + src/foundation-core/truncated-types.lagda.md | 1 + src/foundation/axiom-of-choice.lagda.md | 1 + src/foundation/binary-functoriality-set-quotients.lagda.md | 1 + src/foundation/cantors-theorem.lagda.md | 1 + src/foundation/cartesian-products-set-quotients.lagda.md | 1 + src/foundation/category-of-sets.lagda.md | 1 + src/foundation/computational-identity-types.lagda.md | 1 + src/foundation/connected-maps.lagda.md | 1 + src/foundation/connected-types.lagda.md | 1 + src/foundation/contractible-types.lagda.md | 1 + src/foundation/dependent-products-pullbacks.lagda.md | 1 + .../dependent-universal-property-equivalences.lagda.md | 1 + src/foundation/diagonal-maps-of-types.lagda.md | 1 + src/foundation/epimorphisms-with-respect-to-sets.lagda.md | 1 + src/foundation/equivalence-extensionality.lagda.md | 1 + src/foundation/exponents-set-quotients.lagda.md | 1 + src/foundation/functoriality-morphisms-arrows.lagda.md | 1 + src/foundation/functoriality-propositional-truncation.lagda.md | 1 + src/foundation/functoriality-truncation.lagda.md | 1 + src/foundation/homotopy-induction.lagda.md | 1 + src/foundation/injective-maps.lagda.md | 1 + src/foundation/isomorphisms-of-sets.lagda.md | 1 + src/foundation/iterating-functions.lagda.md | 1 + src/foundation/lawveres-fixed-point-theorem.lagda.md | 1 + src/foundation/multivariable-homotopies.lagda.md | 1 + src/foundation/negated-equality.lagda.md | 1 + src/foundation/postcomposition-dependent-functions.lagda.md | 1 + src/foundation/postcomposition-functions.lagda.md | 1 + src/foundation/postcomposition-pullbacks.lagda.md | 1 + src/foundation/precomposition-dependent-functions.lagda.md | 1 + .../precomposition-functions-into-subuniverses.lagda.md | 1 + src/foundation/precomposition-functions.lagda.md | 1 + src/foundation/pullbacks.lagda.md | 1 + src/foundation/set-quotients.lagda.md | 1 + src/foundation/strictly-involutive-identity-types.lagda.md | 1 + src/foundation/symmetric-binary-relations.lagda.md | 1 + src/foundation/transport-along-homotopies.lagda.md | 1 + src/foundation/truncations.lagda.md | 1 + src/foundation/uniqueness-set-quotients.lagda.md | 1 + src/foundation/uniqueness-truncation.lagda.md | 1 + .../univalence-implies-function-extensionality.lagda.md | 1 + src/foundation/universal-property-contractible-types.lagda.md | 1 + .../universal-property-family-of-fibers-of-maps.lagda.md | 1 + src/foundation/universal-property-set-quotients.lagda.md | 1 + src/foundation/vectors-set-quotients.lagda.md | 1 + src/foundation/weak-function-extensionality.lagda.md | 1 + src/foundation/yoneda-identity-types.lagda.md | 1 + src/graph-theory/dependent-products-reflexive-graphs.lagda.md | 1 + src/group-theory/group-actions.lagda.md | 1 + src/group-theory/homomorphisms-generated-subgroups.lagda.md | 1 + src/group-theory/isomorphisms-semigroups.lagda.md | 1 + src/group-theory/monoid-actions.lagda.md | 1 + src/linear-algebra/vectors.lagda.md | 1 + .../precategory-of-metric-spaces-and-isometries.lagda.md | 1 + .../precategory-of-metric-spaces-and-short-functions.lagda.md | 1 + src/modal-type-theory/sharp-codiscrete-types.lagda.md | 1 + .../functoriality-localizations-at-global-subuniverses.lagda.md | 1 + src/orthogonal-factorization-systems/higher-modalities.lagda.md | 1 + src/orthogonal-factorization-systems/open-modalities.lagda.md | 1 + .../precomposition-lifts-families-of-elements.lagda.md | 1 + src/orthogonal-factorization-systems/pullback-hom.lagda.md | 1 + .../types-local-at-maps.lagda.md | 1 + .../uniquely-eliminating-modalities.lagda.md | 1 + ...versal-property-localizations-at-global-subuniverses.lagda.md | 1 + src/set-theory/cantors-diagonal-argument.lagda.md | 1 + src/set-theory/cardinalities.lagda.md | 1 + src/synthetic-homotopy-theory/1-acyclic-types.lagda.md | 1 + src/synthetic-homotopy-theory/acyclic-maps.lagda.md | 1 + .../dependent-universal-property-pushouts.lagda.md | 1 + src/synthetic-homotopy-theory/descent-circle.lagda.md | 1 + .../descent-data-function-types-over-pushouts.lagda.md | 1 + .../functoriality-sequential-colimits.lagda.md | 1 + src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md | 1 + src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md | 1 + src/synthetic-homotopy-theory/multiplication-circle.lagda.md | 1 + .../suspensions-of-propositions.lagda.md | 1 + src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md | 1 + .../universal-property-pushouts.lagda.md | 1 + .../universal-property-sequential-colimits.lagda.md | 1 + src/univalent-combinatorics/coproduct-types.lagda.md | 1 + .../orientations-complete-undirected-graph.lagda.md | 1 + 91 files changed, 91 insertions(+) diff --git a/src/category-theory/copresheaf-categories.lagda.md b/src/category-theory/copresheaf-categories.lagda.md index 2916d3e0b2..f0082a5143 100644 --- a/src/category-theory/copresheaf-categories.lagda.md +++ b/src/category-theory/copresheaf-categories.lagda.md @@ -27,6 +27,7 @@ open import foundation.dependent-pair-types open import foundation.empty-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-cartesian-product-types open import foundation.homotopies diff --git a/src/category-theory/dependent-products-of-large-precategories.lagda.md b/src/category-theory/dependent-products-of-large-precategories.lagda.md index eacb31a0b5..4eacbea052 100644 --- a/src/category-theory/dependent-products-of-large-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-large-precategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.large-precategories open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/category-theory/dependent-products-of-precategories.lagda.md b/src/category-theory/dependent-products-of-precategories.lagda.md index 4ee2a1858a..e4f7e693fb 100644 --- a/src/category-theory/dependent-products-of-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-precategories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.precategories open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/category-theory/precategory-of-functors.lagda.md b/src/category-theory/precategory-of-functors.lagda.md index 1797d461fa..ced04e8ab4 100644 --- a/src/category-theory/precategory-of-functors.lagda.md +++ b/src/category-theory/precategory-of-functors.lagda.md @@ -18,6 +18,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-pair-types open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/category-theory/precategory-of-maps-precategories.lagda.md b/src/category-theory/precategory-of-maps-precategories.lagda.md index 8fc3c449a5..1f5fa95dfd 100644 --- a/src/category-theory/precategory-of-maps-precategories.lagda.md +++ b/src/category-theory/precategory-of-maps-precategories.lagda.md @@ -18,6 +18,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-pair-types open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/category-theory/presheaf-categories.lagda.md b/src/category-theory/presheaf-categories.lagda.md index 1e61775687..ad12b0827f 100644 --- a/src/category-theory/presheaf-categories.lagda.md +++ b/src/category-theory/presheaf-categories.lagda.md @@ -19,6 +19,7 @@ open import category-theory.precategories open import foundation.category-of-sets open import foundation.commuting-squares-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/category-theory/yoneda-lemma-precategories.lagda.md b/src/category-theory/yoneda-lemma-precategories.lagda.md index 0820f19127..1181e89b5f 100644 --- a/src/category-theory/yoneda-lemma-precategories.lagda.md +++ b/src/category-theory/yoneda-lemma-precategories.lagda.md @@ -18,6 +18,7 @@ open import foundation.category-of-sets open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md index 52541dc0ab..d355c01418 100644 --- a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md @@ -17,6 +17,7 @@ open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.empty-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/finite-group-theory/transpositions.lagda.md b/src/finite-group-theory/transpositions.lagda.md index 1900b49eed..ad26d6e6af 100644 --- a/src/finite-group-theory/transpositions.lagda.md +++ b/src/finite-group-theory/transpositions.lagda.md @@ -27,6 +27,7 @@ open import foundation.equivalences open import foundation.equivalences-maybe open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-coproduct-types open import foundation.homotopies diff --git a/src/foundation-core/propositions.lagda.md b/src/foundation-core/propositions.lagda.md index 5aeafc52d4..619887268c 100644 --- a/src/foundation-core/propositions.lagda.md +++ b/src/foundation-core/propositions.lagda.md @@ -9,6 +9,7 @@ module foundation-core.propositions where ```agda open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation-core/truncated-types.lagda.md b/src/foundation-core/truncated-types.lagda.md index fb88b4c3df..32a4282a70 100644 --- a/src/foundation-core/truncated-types.lagda.md +++ b/src/foundation-core/truncated-types.lagda.md @@ -12,6 +12,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/axiom-of-choice.lagda.md b/src/foundation/axiom-of-choice.lagda.md index 26774379b7..de669d3bf0 100644 --- a/src/foundation/axiom-of-choice.lagda.md +++ b/src/foundation/axiom-of-choice.lagda.md @@ -9,6 +9,7 @@ module foundation.axiom-of-choice where ```agda open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-propositional-truncation open import foundation.inhabited-types open import foundation.postcomposition-functions diff --git a/src/foundation/binary-functoriality-set-quotients.lagda.md b/src/foundation/binary-functoriality-set-quotients.lagda.md index 43c1441aa4..991ebbee26 100644 --- a/src/foundation/binary-functoriality-set-quotients.lagda.md +++ b/src/foundation/binary-functoriality-set-quotients.lagda.md @@ -13,6 +13,7 @@ open import foundation.binary-homotopies open import foundation.dependent-pair-types open import foundation.exponents-set-quotients open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-set-quotients open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies diff --git a/src/foundation/cantors-theorem.lagda.md b/src/foundation/cantors-theorem.lagda.md index 499ebf65d6..2f8a1eb125 100644 --- a/src/foundation/cantors-theorem.lagda.md +++ b/src/foundation/cantors-theorem.lagda.md @@ -13,6 +13,7 @@ open import foundation.decidable-subtypes open import foundation.dependent-pair-types open import foundation.double-negation-stable-propositions open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.logical-equivalences open import foundation.negation open import foundation.powersets diff --git a/src/foundation/cartesian-products-set-quotients.lagda.md b/src/foundation/cartesian-products-set-quotients.lagda.md index 7c5319f8da..f016d8c0f7 100644 --- a/src/foundation/cartesian-products-set-quotients.lagda.md +++ b/src/foundation/cartesian-products-set-quotients.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.products-equivalence-relations open import foundation.reflecting-maps-equivalence-relations open import foundation.set-quotients diff --git a/src/foundation/category-of-sets.lagda.md b/src/foundation/category-of-sets.lagda.md index 7089fccb08..7587216503 100644 --- a/src/foundation/category-of-sets.lagda.md +++ b/src/foundation/category-of-sets.lagda.md @@ -27,6 +27,7 @@ open import foundation.dependent-pair-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/foundation/computational-identity-types.lagda.md b/src/foundation/computational-identity-types.lagda.md index dd7b53ac80..5c40b6da91 100644 --- a/src/foundation/computational-identity-types.lagda.md +++ b/src/foundation/computational-identity-types.lagda.md @@ -12,6 +12,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.strictly-right-unital-concatenation-identifications open import foundation.transport-along-identifications open import foundation.univalence diff --git a/src/foundation/connected-maps.lagda.md b/src/foundation/connected-maps.lagda.md index d893f11646..850da31ae8 100644 --- a/src/foundation/connected-maps.lagda.md +++ b/src/foundation/connected-maps.lagda.md @@ -10,6 +10,7 @@ module foundation.connected-maps where open import foundation.connected-types open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction open import foundation.precomposition-dependent-functions diff --git a/src/foundation/connected-types.lagda.md b/src/foundation/connected-types.lagda.md index e7a26ab34e..46c7a67e44 100644 --- a/src/foundation/connected-types.lagda.md +++ b/src/foundation/connected-types.lagda.md @@ -11,6 +11,7 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.diagonal-maps-of-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-truncation open import foundation.inhabited-types open import foundation.propositional-truncations diff --git a/src/foundation/contractible-types.lagda.md b/src/foundation/contractible-types.lagda.md index bfb117148d..fb64cece68 100644 --- a/src/foundation/contractible-types.lagda.md +++ b/src/foundation/contractible-types.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.diagonal-maps-of-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.logical-equivalences open import foundation.subuniverses open import foundation.unit-type diff --git a/src/foundation/dependent-products-pullbacks.lagda.md b/src/foundation/dependent-products-pullbacks.lagda.md index 7c429ce124..63b84f2dce 100644 --- a/src/foundation/dependent-products-pullbacks.lagda.md +++ b/src/foundation/dependent-products-pullbacks.lagda.md @@ -10,6 +10,7 @@ module foundation.dependent-products-pullbacks where open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-function-types open import foundation.identity-types open import foundation.standard-pullbacks diff --git a/src/foundation/dependent-universal-property-equivalences.lagda.md b/src/foundation/dependent-universal-property-equivalences.lagda.md index f9a041351b..e02bb797f2 100644 --- a/src/foundation/dependent-universal-property-equivalences.lagda.md +++ b/src/foundation/dependent-universal-property-equivalences.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.coherently-invertible-maps diff --git a/src/foundation/diagonal-maps-of-types.lagda.md b/src/foundation/diagonal-maps-of-types.lagda.md index b4a0135888..9983e97332 100644 --- a/src/foundation/diagonal-maps-of-types.lagda.md +++ b/src/foundation/diagonal-maps-of-types.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-pair-types open import foundation.morphisms-arrows open import foundation.postcomposition-functions diff --git a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md index f34760598e..85011ac449 100644 --- a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md +++ b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.existential-quantification open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.injective-maps open import foundation.propositional-extensionality diff --git a/src/foundation/equivalence-extensionality.lagda.md b/src/foundation/equivalence-extensionality.lagda.md index 54aad95056..2666bf9f62 100644 --- a/src/foundation/equivalence-extensionality.lagda.md +++ b/src/foundation/equivalence-extensionality.lagda.md @@ -10,6 +10,7 @@ module foundation.equivalence-extensionality where open import foundation.dependent-pair-types open import foundation.dependent-universal-property-equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-systems open import foundation.subtype-identity-principle diff --git a/src/foundation/exponents-set-quotients.lagda.md b/src/foundation/exponents-set-quotients.lagda.md index bfc9888f3c..8290ecd3dd 100644 --- a/src/foundation/exponents-set-quotients.lagda.md +++ b/src/foundation/exponents-set-quotients.lagda.md @@ -12,6 +12,7 @@ module foundation.exponents-set-quotients where open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-set-quotients open import foundation.postcomposition-functions open import foundation.reflecting-maps-equivalence-relations diff --git a/src/foundation/functoriality-morphisms-arrows.lagda.md b/src/foundation/functoriality-morphisms-arrows.lagda.md index a8cdd6b387..8d9b3b82f2 100644 --- a/src/foundation/functoriality-morphisms-arrows.lagda.md +++ b/src/foundation/functoriality-morphisms-arrows.lagda.md @@ -18,6 +18,7 @@ open import foundation.dependent-pair-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-pullbacks open import foundation.homotopies diff --git a/src/foundation/functoriality-propositional-truncation.lagda.md b/src/foundation/functoriality-propositional-truncation.lagda.md index 1c895736c6..a7f70efd6c 100644 --- a/src/foundation/functoriality-propositional-truncation.lagda.md +++ b/src/foundation/functoriality-propositional-truncation.lagda.md @@ -10,6 +10,7 @@ module foundation.functoriality-propositional-truncation where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.logical-equivalences open import foundation.propositional-truncations open import foundation.universe-levels diff --git a/src/foundation/functoriality-truncation.lagda.md b/src/foundation/functoriality-truncation.lagda.md index 92e1760616..86a3aaecad 100644 --- a/src/foundation/functoriality-truncation.lagda.md +++ b/src/foundation/functoriality-truncation.lagda.md @@ -10,6 +10,7 @@ module foundation.functoriality-truncation where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/homotopy-induction.lagda.md b/src/foundation/homotopy-induction.lagda.md index 325ffb7e9c..f2d5add7c9 100644 --- a/src/foundation/homotopy-induction.lagda.md +++ b/src/foundation/homotopy-induction.lagda.md @@ -9,6 +9,7 @@ module foundation.homotopy-induction where ```agda open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-systems open import foundation.universal-property-dependent-pair-types open import foundation.universal-property-identity-systems diff --git a/src/foundation/injective-maps.lagda.md b/src/foundation/injective-maps.lagda.md index 8ab3913353..521e90d66d 100644 --- a/src/foundation/injective-maps.lagda.md +++ b/src/foundation/injective-maps.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.logical-equivalences open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/isomorphisms-of-sets.lagda.md b/src/foundation/isomorphisms-of-sets.lagda.md index db721c44c7..c5f46ffa11 100644 --- a/src/foundation/isomorphisms-of-sets.lagda.md +++ b/src/foundation/isomorphisms-of-sets.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.sets open import foundation.universe-levels diff --git a/src/foundation/iterating-functions.lagda.md b/src/foundation/iterating-functions.lagda.md index 60dafe2242..7c6c17cdaf 100644 --- a/src/foundation/iterating-functions.lagda.md +++ b/src/foundation/iterating-functions.lagda.md @@ -17,6 +17,7 @@ open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.commuting-squares-of-maps diff --git a/src/foundation/lawveres-fixed-point-theorem.lagda.md b/src/foundation/lawveres-fixed-point-theorem.lagda.md index 5432486db4..ab2527c307 100644 --- a/src/foundation/lawveres-fixed-point-theorem.lagda.md +++ b/src/foundation/lawveres-fixed-point-theorem.lagda.md @@ -10,6 +10,7 @@ module foundation.lawveres-fixed-point-theorem where open import foundation.dependent-pair-types open import foundation.existential-quantification open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.propositional-truncations open import foundation.surjective-maps open import foundation.universe-levels diff --git a/src/foundation/multivariable-homotopies.lagda.md b/src/foundation/multivariable-homotopies.lagda.md index 01f1635bf5..01d544c5ba 100644 --- a/src/foundation/multivariable-homotopies.lagda.md +++ b/src/foundation/multivariable-homotopies.lagda.md @@ -14,6 +14,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.equality-dependent-function-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.implicit-function-types open import foundation.iterated-dependent-product-types open import foundation.universe-levels diff --git a/src/foundation/negated-equality.lagda.md b/src/foundation/negated-equality.lagda.md index 96ad3cd6a1..da22f198a4 100644 --- a/src/foundation/negated-equality.lagda.md +++ b/src/foundation/negated-equality.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.negation open import foundation.universe-levels diff --git a/src/foundation/postcomposition-dependent-functions.lagda.md b/src/foundation/postcomposition-dependent-functions.lagda.md index af9cd90fde..d560165ad9 100644 --- a/src/foundation/postcomposition-dependent-functions.lagda.md +++ b/src/foundation/postcomposition-dependent-functions.lagda.md @@ -11,6 +11,7 @@ open import foundation-core.postcomposition-dependent-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/postcomposition-functions.lagda.md b/src/foundation/postcomposition-functions.lagda.md index 2799d76ae4..247b3d1eb1 100644 --- a/src/foundation/postcomposition-functions.lagda.md +++ b/src/foundation/postcomposition-functions.lagda.md @@ -12,6 +12,7 @@ open import foundation-core.postcomposition-functions public open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.postcomposition-dependent-functions open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/postcomposition-pullbacks.lagda.md b/src/foundation/postcomposition-pullbacks.lagda.md index b24c28bb74..255b8b04fd 100644 --- a/src/foundation/postcomposition-pullbacks.lagda.md +++ b/src/foundation/postcomposition-pullbacks.lagda.md @@ -10,6 +10,7 @@ module foundation.postcomposition-pullbacks where open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.standard-pullbacks open import foundation.universe-levels diff --git a/src/foundation/precomposition-dependent-functions.lagda.md b/src/foundation/precomposition-dependent-functions.lagda.md index fef97c901d..f7a092edc9 100644 --- a/src/foundation/precomposition-dependent-functions.lagda.md +++ b/src/foundation/precomposition-dependent-functions.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.dependent-universal-property-equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.commuting-squares-of-maps diff --git a/src/foundation/precomposition-functions-into-subuniverses.lagda.md b/src/foundation/precomposition-functions-into-subuniverses.lagda.md index 8e0a567f55..0e0779dbba 100644 --- a/src/foundation/precomposition-functions-into-subuniverses.lagda.md +++ b/src/foundation/precomposition-functions-into-subuniverses.lagda.md @@ -10,6 +10,7 @@ module foundation.precomposition-functions-into-subuniverses where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.precomposition-functions open import foundation.universe-levels diff --git a/src/foundation/precomposition-functions.lagda.md b/src/foundation/precomposition-functions.lagda.md index 9e48f70cfd..c8216b79b9 100644 --- a/src/foundation/precomposition-functions.lagda.md +++ b/src/foundation/precomposition-functions.lagda.md @@ -12,6 +12,7 @@ open import foundation-core.precomposition-functions public open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.precomposition-dependent-functions open import foundation.sections open import foundation.universe-levels diff --git a/src/foundation/pullbacks.lagda.md b/src/foundation/pullbacks.lagda.md index aa710ea8cd..790d188583 100644 --- a/src/foundation/pullbacks.lagda.md +++ b/src/foundation/pullbacks.lagda.md @@ -20,6 +20,7 @@ open import foundation.equality-cartesian-product-types open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-coproduct-types open import foundation.functoriality-function-types open import foundation.standard-pullbacks diff --git a/src/foundation/set-quotients.lagda.md b/src/foundation/set-quotients.lagda.md index 492fac2246..903b9099cb 100644 --- a/src/foundation/set-quotients.lagda.md +++ b/src/foundation/set-quotients.lagda.md @@ -14,6 +14,7 @@ open import foundation.embeddings open import foundation.equivalence-classes open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.inhabited-subtypes open import foundation.reflecting-maps-equivalence-relations diff --git a/src/foundation/strictly-involutive-identity-types.lagda.md b/src/foundation/strictly-involutive-identity-types.lagda.md index 41d8a10e2d..fe946180d7 100644 --- a/src/foundation/strictly-involutive-identity-types.lagda.md +++ b/src/foundation/strictly-involutive-identity-types.lagda.md @@ -12,6 +12,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.multivariable-homotopies open import foundation.strictly-right-unital-concatenation-identifications open import foundation.univalence diff --git a/src/foundation/symmetric-binary-relations.lagda.md b/src/foundation/symmetric-binary-relations.lagda.md index 7f5a829ff1..9ec5848378 100644 --- a/src/foundation/symmetric-binary-relations.lagda.md +++ b/src/foundation/symmetric-binary-relations.lagda.md @@ -12,6 +12,7 @@ open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.equivalence-extensionality open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.morphisms-binary-relations open import foundation.symmetric-operations open import foundation.universe-levels diff --git a/src/foundation/transport-along-homotopies.lagda.md b/src/foundation/transport-along-homotopies.lagda.md index 577c47c512..8308d97123 100644 --- a/src/foundation/transport-along-homotopies.lagda.md +++ b/src/foundation/transport-along-homotopies.lagda.md @@ -9,6 +9,7 @@ module foundation.transport-along-homotopies where ```agda open import foundation.action-on-identifications-functions open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.homotopy-induction open import foundation.transport-along-higher-identifications open import foundation.universe-levels diff --git a/src/foundation/truncations.lagda.md b/src/foundation/truncations.lagda.md index 9523e78045..d7bed98e65 100644 --- a/src/foundation/truncations.lagda.md +++ b/src/foundation/truncations.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/foundation/uniqueness-set-quotients.lagda.md b/src/foundation/uniqueness-set-quotients.lagda.md index 5fd4913def..f2afbd97e3 100644 --- a/src/foundation/uniqueness-set-quotients.lagda.md +++ b/src/foundation/uniqueness-set-quotients.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.reflecting-maps-equivalence-relations open import foundation.sets open import foundation.subtype-identity-principle diff --git a/src/foundation/uniqueness-truncation.lagda.md b/src/foundation/uniqueness-truncation.lagda.md index 25971b85f3..d8b7fadaa0 100644 --- a/src/foundation/uniqueness-truncation.lagda.md +++ b/src/foundation/uniqueness-truncation.lagda.md @@ -7,6 +7,7 @@ module foundation.uniqueness-truncation where
Imports ```agda +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/univalence-implies-function-extensionality.lagda.md b/src/foundation/univalence-implies-function-extensionality.lagda.md index 8845653a49..a082f8d56b 100644 --- a/src/foundation/univalence-implies-function-extensionality.lagda.md +++ b/src/foundation/univalence-implies-function-extensionality.lagda.md @@ -10,6 +10,7 @@ module foundation.univalence-implies-function-extensionality where open import foundation.dependent-pair-types open import foundation.equivalence-induction open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.postcomposition-functions open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/universal-property-contractible-types.lagda.md b/src/foundation/universal-property-contractible-types.lagda.md index e581cf7ee1..d73ff1f0f2 100644 --- a/src/foundation/universal-property-contractible-types.lagda.md +++ b/src/foundation/universal-property-contractible-types.lagda.md @@ -10,6 +10,7 @@ module foundation.universal-property-contractible-types where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.singleton-induction open import foundation.universe-levels diff --git a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md index a9d2691df4..4a72519240 100644 --- a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md +++ b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md @@ -12,6 +12,7 @@ open import foundation.dependent-pair-types open import foundation.diagonal-maps-of-types open import foundation.families-of-equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.subtype-identity-principle open import foundation.universe-levels diff --git a/src/foundation/universal-property-set-quotients.lagda.md b/src/foundation/universal-property-set-quotients.lagda.md index 10bfbb0310..a4e565199c 100644 --- a/src/foundation/universal-property-set-quotients.lagda.md +++ b/src/foundation/universal-property-set-quotients.lagda.md @@ -17,6 +17,7 @@ open import foundation.epimorphisms-with-respect-to-sets open import foundation.equivalence-classes open import foundation.existential-quantification open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types open import foundation.images diff --git a/src/foundation/vectors-set-quotients.lagda.md b/src/foundation/vectors-set-quotients.lagda.md index 80e0ac123d..57d80affe9 100644 --- a/src/foundation/vectors-set-quotients.lagda.md +++ b/src/foundation/vectors-set-quotients.lagda.md @@ -16,6 +16,7 @@ open import foundation.cartesian-products-set-quotients open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.multivariable-operations open import foundation.products-equivalence-relations open import foundation.raising-universe-levels diff --git a/src/foundation/weak-function-extensionality.lagda.md b/src/foundation/weak-function-extensionality.lagda.md index 0abd8761d5..be33e1492c 100644 --- a/src/foundation/weak-function-extensionality.lagda.md +++ b/src/foundation/weak-function-extensionality.lagda.md @@ -12,6 +12,7 @@ open import foundation.decidable-equality open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation/yoneda-identity-types.lagda.md b/src/foundation/yoneda-identity-types.lagda.md index 9f112941a7..d35e342324 100644 --- a/src/foundation/yoneda-identity-types.lagda.md +++ b/src/foundation/yoneda-identity-types.lagda.md @@ -10,6 +10,7 @@ module foundation.yoneda-identity-types where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.multivariable-homotopies open import foundation.strictly-right-unital-concatenation-identifications open import foundation.transport-along-identifications diff --git a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md index 8ff497e2b5..f0cee7443a 100644 --- a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md @@ -16,6 +16,7 @@ open import foundation.dependent-pair-types open import foundation.equality-dependent-function-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/group-theory/group-actions.lagda.md b/src/group-theory/group-actions.lagda.md index b0648b9beb..4741ac11e3 100644 --- a/src/group-theory/group-actions.lagda.md +++ b/src/group-theory/group-actions.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/group-theory/homomorphisms-generated-subgroups.lagda.md b/src/group-theory/homomorphisms-generated-subgroups.lagda.md index 3f3d1b219b..dfebd1378a 100644 --- a/src/group-theory/homomorphisms-generated-subgroups.lagda.md +++ b/src/group-theory/homomorphisms-generated-subgroups.lagda.md @@ -15,6 +15,7 @@ open import foundation.embeddings open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.propositional-truncations open import foundation.propositions diff --git a/src/group-theory/isomorphisms-semigroups.lagda.md b/src/group-theory/isomorphisms-semigroups.lagda.md index 2c2bb15a9a..bf3a93267a 100644 --- a/src/group-theory/isomorphisms-semigroups.lagda.md +++ b/src/group-theory/isomorphisms-semigroups.lagda.md @@ -14,6 +14,7 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/group-theory/monoid-actions.lagda.md b/src/group-theory/monoid-actions.lagda.md index c1f806f207..0a737b826e 100644 --- a/src/group-theory/monoid-actions.lagda.md +++ b/src/group-theory/monoid-actions.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.endomorphisms open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.sets open import foundation.universe-levels diff --git a/src/linear-algebra/vectors.lagda.md b/src/linear-algebra/vectors.lagda.md index a870ba74c9..63c0566a42 100644 --- a/src/linear-algebra/vectors.lagda.md +++ b/src/linear-algebra/vectors.lagda.md @@ -17,6 +17,7 @@ open import foundation.dependent-pair-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md index 9f8d292f56..ebb8a53618 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md @@ -15,6 +15,7 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md index 1133d2e084..886c4037e5 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md @@ -16,6 +16,7 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/modal-type-theory/sharp-codiscrete-types.lagda.md b/src/modal-type-theory/sharp-codiscrete-types.lagda.md index 0eb4a695fb..82641c2cc8 100644 --- a/src/modal-type-theory/sharp-codiscrete-types.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-types.lagda.md @@ -14,6 +14,7 @@ open import foundation.dependent-pair-types open import foundation.embeddings open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md index 84d0582079..09700257be 100644 --- a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md @@ -16,6 +16,7 @@ open import foundation.equivalences open import foundation.extensions-types-global-subuniverses open import foundation.extensions-types-subuniverses open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.global-subuniverses open import foundation.homotopies diff --git a/src/orthogonal-factorization-systems/higher-modalities.lagda.md b/src/orthogonal-factorization-systems/higher-modalities.lagda.md index b4c0cc95ec..54408c3970 100644 --- a/src/orthogonal-factorization-systems/higher-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/higher-modalities.lagda.md @@ -12,6 +12,7 @@ open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/orthogonal-factorization-systems/open-modalities.lagda.md b/src/orthogonal-factorization-systems/open-modalities.lagda.md index f20203e06c..3de73e9582 100644 --- a/src/orthogonal-factorization-systems/open-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/open-modalities.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.locally-small-types open import foundation.propositions diff --git a/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md index 8b53882043..2292277230 100644 --- a/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md @@ -13,6 +13,7 @@ open import foundation.commuting-squares-of-maps open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/orthogonal-factorization-systems/pullback-hom.lagda.md b/src/orthogonal-factorization-systems/pullback-hom.lagda.md index 4181ff3a64..4b50212f0f 100644 --- a/src/orthogonal-factorization-systems/pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/pullback-hom.lagda.md @@ -17,6 +17,7 @@ open import foundation.equivalences open import foundation.equivalences-arrows open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.functoriality-fibers-of-maps diff --git a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md index 1ebbc9e3de..eaf92b9fa5 100644 --- a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md @@ -19,6 +19,7 @@ open import foundation.equivalences open import foundation.families-of-equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md index 493b2f511f..d0a891d833 100644 --- a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md @@ -13,6 +13,7 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md index a3c2143af4..f6f694955a 100644 --- a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md @@ -15,6 +15,7 @@ open import foundation.equivalences open import foundation.extensions-types open import foundation.extensions-types-global-subuniverses open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.global-subuniverses open import foundation.homotopies diff --git a/src/set-theory/cantors-diagonal-argument.lagda.md b/src/set-theory/cantors-diagonal-argument.lagda.md index b573aa9ab7..61626fbf9b 100644 --- a/src/set-theory/cantors-diagonal-argument.lagda.md +++ b/src/set-theory/cantors-diagonal-argument.lagda.md @@ -18,6 +18,7 @@ open import foundation.dependent-pair-types open import foundation.discrete-types open import foundation.double-negation open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.isolated-elements open import foundation.logical-equivalences diff --git a/src/set-theory/cardinalities.lagda.md b/src/set-theory/cardinalities.lagda.md index 0ab8653a6f..70b7ccbab9 100644 --- a/src/set-theory/cardinalities.lagda.md +++ b/src/set-theory/cardinalities.lagda.md @@ -11,6 +11,7 @@ open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.functoriality-propositional-truncation open import foundation.identity-types open import foundation.large-binary-relations diff --git a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md index 9c3c160c3d..9be4b27b1f 100644 --- a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md @@ -15,6 +15,7 @@ open import foundation.dependent-pair-types open import foundation.diagonal-maps-of-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.inhabited-types open import foundation.injective-maps diff --git a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md index 60423d0894..3bf63f4ed1 100644 --- a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md @@ -22,6 +22,7 @@ open import foundation.epimorphisms open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md index 22394d4c95..c0b9760150 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md @@ -15,6 +15,7 @@ open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/synthetic-homotopy-theory/descent-circle.lagda.md b/src/synthetic-homotopy-theory/descent-circle.lagda.md index 8adc5c7904..bd3ccfe178 100644 --- a/src/synthetic-homotopy-theory/descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle.lagda.md @@ -16,6 +16,7 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md index ac284b320a..35a5f3e58d 100644 --- a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md @@ -17,6 +17,7 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md index e978bc0554..1381dac51b 100644 --- a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md @@ -16,6 +16,7 @@ open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md b/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md index c5706895d6..477236e983 100644 --- a/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md @@ -12,6 +12,7 @@ open import foundation.commuting-squares-of-identifications open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md index bab47be956..06ddbb6917 100644 --- a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md @@ -17,6 +17,7 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md index cb1de4f9ff..e9d9b0982c 100644 --- a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md +++ b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md @@ -10,6 +10,7 @@ module synthetic-homotopy-theory.multiplication-circle where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md index 95d058f84b..a5430e4847 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md @@ -13,6 +13,7 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.existential-quantification open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md index 88c1339d10..7363019965 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md @@ -23,6 +23,7 @@ open import foundation.epimorphisms-with-respect-to-truncated-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md index 06f4082d85..171038972c 100644 --- a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md @@ -20,6 +20,7 @@ open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md index e214baf664..4a4aced8a5 100644 --- a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md @@ -18,6 +18,7 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/univalent-combinatorics/coproduct-types.lagda.md b/src/univalent-combinatorics/coproduct-types.lagda.md index 87603eab3b..4c7fb0ae57 100644 --- a/src/univalent-combinatorics/coproduct-types.lagda.md +++ b/src/univalent-combinatorics/coproduct-types.lagda.md @@ -16,6 +16,7 @@ open import foundation.dependent-pair-types open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-coproduct-types open import foundation.functoriality-propositional-truncation diff --git a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md index 6dd93e951d..bd5ea5ce14 100644 --- a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md +++ b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md @@ -34,6 +34,7 @@ open import foundation.equivalence-extensionality open import foundation.equivalence-relations open import foundation.equivalences open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.functoriality-propositional-truncation From da48fc282896b690c435bfa04fed1c89a4e21f66 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Wed, 19 Mar 2025 22:29:29 +0000 Subject: [PATCH 03/39] remove unused funext imports --- src/category-theory/precategory-of-functors.lagda.md | 1 - src/category-theory/precategory-of-maps-precategories.lagda.md | 1 - src/category-theory/presheaf-categories.lagda.md | 1 - src/foundation-core/propositions.lagda.md | 1 - src/foundation/axiom-of-choice.lagda.md | 1 - src/foundation/binary-type-duality.lagda.md | 1 - src/foundation/cantors-theorem.lagda.md | 1 - src/foundation/connected-types.lagda.md | 1 - src/foundation/continuations.lagda.md | 1 - src/foundation/functoriality-propositional-truncation.lagda.md | 1 - src/foundation/identity-systems.lagda.md | 1 - src/foundation/inhabited-types.lagda.md | 1 - src/foundation/iterating-families-of-maps.lagda.md | 1 - src/foundation/lawveres-fixed-point-theorem.lagda.md | 1 - src/foundation/negated-equality.lagda.md | 1 - .../precomposition-functions-into-subuniverses.lagda.md | 1 - src/foundation/pullback-cones.lagda.md | 1 - src/foundation/set-quotients.lagda.md | 1 - src/foundation/symmetric-binary-relations.lagda.md | 1 - src/foundation/transport-split-type-families.lagda.md | 1 - src/foundation/type-arithmetic-unit-type.lagda.md | 1 - src/group-theory/group-actions.lagda.md | 1 - src/group-theory/monoid-actions.lagda.md | 1 - src/linear-algebra/functoriality-vectors.lagda.md | 1 - .../cauchy-approximations-premetric-spaces.lagda.md | 1 - src/metric-spaces/discrete-premetric-structures.lagda.md | 1 - ...unctor-category-set-functions-isometry-metric-spaces.lagda.md | 1 - .../functor-category-short-isometry-metric-spaces.lagda.md | 1 - .../limits-of-cauchy-approximations-in-premetric-spaces.lagda.md | 1 - .../precategory-of-metric-spaces-and-isometries.lagda.md | 1 - src/modal-type-theory/sharp-codiscrete-types.lagda.md | 1 - .../continuation-modalities.lagda.md | 1 - .../fiberwise-orthogonal-maps.lagda.md | 1 - .../functoriality-localizations-at-global-subuniverses.lagda.md | 1 - .../functoriality-pullback-hom.lagda.md | 1 - .../functoriality-reflective-global-subuniverses.lagda.md | 1 - src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md | 1 - .../reflective-global-subuniverses.lagda.md | 1 - .../reflective-subuniverses.lagda.md | 1 - ...versal-property-localizations-at-global-subuniverses.lagda.md | 1 - src/set-theory/baire-space.lagda.md | 1 - src/set-theory/cantors-diagonal-argument.lagda.md | 1 - src/set-theory/cardinalities.lagda.md | 1 - src/structured-types/pointed-equivalences.lagda.md | 1 - src/structured-types/pointed-homotopies.lagda.md | 1 - src/synthetic-homotopy-theory/1-acyclic-types.lagda.md | 1 - src/synthetic-homotopy-theory/descent-circle.lagda.md | 1 - src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md | 1 - src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md | 1 - src/synthetic-homotopy-theory/multiplication-circle.lagda.md | 1 - src/type-theories/precategories-with-attributes.lagda.md | 1 - src/type-theories/precategories-with-families.lagda.md | 1 - src/univalent-combinatorics/coproduct-types.lagda.md | 1 - src/univalent-combinatorics/locally-finite-types.lagda.md | 1 - 54 files changed, 54 deletions(-) diff --git a/src/category-theory/precategory-of-functors.lagda.md b/src/category-theory/precategory-of-functors.lagda.md index ced04e8ab4..a77bc75a50 100644 --- a/src/category-theory/precategory-of-functors.lagda.md +++ b/src/category-theory/precategory-of-functors.lagda.md @@ -17,7 +17,6 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/category-theory/precategory-of-maps-precategories.lagda.md b/src/category-theory/precategory-of-maps-precategories.lagda.md index 1f5fa95dfd..9967524c0f 100644 --- a/src/category-theory/precategory-of-maps-precategories.lagda.md +++ b/src/category-theory/precategory-of-maps-precategories.lagda.md @@ -17,7 +17,6 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/category-theory/presheaf-categories.lagda.md b/src/category-theory/presheaf-categories.lagda.md index ad12b0827f..40467e0a41 100644 --- a/src/category-theory/presheaf-categories.lagda.md +++ b/src/category-theory/presheaf-categories.lagda.md @@ -18,7 +18,6 @@ open import category-theory.precategories open import foundation.category-of-sets open import foundation.commuting-squares-of-maps -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies diff --git a/src/foundation-core/propositions.lagda.md b/src/foundation-core/propositions.lagda.md index 619887268c..73341db418 100644 --- a/src/foundation-core/propositions.lagda.md +++ b/src/foundation-core/propositions.lagda.md @@ -8,7 +8,6 @@ module foundation-core.propositions where ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.universe-levels diff --git a/src/foundation/axiom-of-choice.lagda.md b/src/foundation/axiom-of-choice.lagda.md index de669d3bf0..338419569b 100644 --- a/src/foundation/axiom-of-choice.lagda.md +++ b/src/foundation/axiom-of-choice.lagda.md @@ -8,7 +8,6 @@ module foundation.axiom-of-choice where ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.functoriality-propositional-truncation open import foundation.inhabited-types diff --git a/src/foundation/binary-type-duality.lagda.md b/src/foundation/binary-type-duality.lagda.md index 20a23bc58d..0365d3b368 100644 --- a/src/foundation/binary-type-duality.lagda.md +++ b/src/foundation/binary-type-duality.lagda.md @@ -10,7 +10,6 @@ module foundation.binary-type-duality where open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.equivalences-spans -open import foundation.function-extensionality open import foundation.function-types open import foundation.multivariable-homotopies open import foundation.retractions diff --git a/src/foundation/cantors-theorem.lagda.md b/src/foundation/cantors-theorem.lagda.md index 2f8a1eb125..a69aefcb83 100644 --- a/src/foundation/cantors-theorem.lagda.md +++ b/src/foundation/cantors-theorem.lagda.md @@ -12,7 +12,6 @@ open import foundation.decidable-propositions open import foundation.decidable-subtypes open import foundation.dependent-pair-types open import foundation.double-negation-stable-propositions -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.logical-equivalences open import foundation.negation diff --git a/src/foundation/connected-types.lagda.md b/src/foundation/connected-types.lagda.md index 46c7a67e44..7b8af429f7 100644 --- a/src/foundation/connected-types.lagda.md +++ b/src/foundation/connected-types.lagda.md @@ -10,7 +10,6 @@ module foundation.connected-types where open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.diagonal-maps-of-types -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.functoriality-truncation open import foundation.inhabited-types diff --git a/src/foundation/continuations.lagda.md b/src/foundation/continuations.lagda.md index 3c7d65926e..9ccca39732 100644 --- a/src/foundation/continuations.lagda.md +++ b/src/foundation/continuations.lagda.md @@ -12,7 +12,6 @@ open import foundation.dependent-pair-types open import foundation.empty-types open import foundation.equality-cartesian-product-types open import foundation.evaluation-functions -open import foundation.function-extensionality open import foundation.logical-equivalences open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-function-types diff --git a/src/foundation/functoriality-propositional-truncation.lagda.md b/src/foundation/functoriality-propositional-truncation.lagda.md index a7f70efd6c..3166bf1b47 100644 --- a/src/foundation/functoriality-propositional-truncation.lagda.md +++ b/src/foundation/functoriality-propositional-truncation.lagda.md @@ -9,7 +9,6 @@ module foundation.functoriality-propositional-truncation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.logical-equivalences open import foundation.propositional-truncations diff --git a/src/foundation/identity-systems.lagda.md b/src/foundation/identity-systems.lagda.md index 9f1f3c9ff0..76c39abcc7 100644 --- a/src/foundation/identity-systems.lagda.md +++ b/src/foundation/identity-systems.lagda.md @@ -9,7 +9,6 @@ module foundation.identity-systems where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation/inhabited-types.lagda.md b/src/foundation/inhabited-types.lagda.md index 93682e4ba5..d53273c06a 100644 --- a/src/foundation/inhabited-types.lagda.md +++ b/src/foundation/inhabited-types.lagda.md @@ -11,7 +11,6 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equality-dependent-function-types -open import foundation.function-extensionality open import foundation.functoriality-propositional-truncation open import foundation.fundamental-theorem-of-identity-types open import foundation.propositional-truncations diff --git a/src/foundation/iterating-families-of-maps.lagda.md b/src/foundation/iterating-families-of-maps.lagda.md index 97b4fa1ce6..d0f5296399 100644 --- a/src/foundation/iterating-families-of-maps.lagda.md +++ b/src/foundation/iterating-families-of-maps.lagda.md @@ -19,7 +19,6 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-homotopies open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.iterating-functions open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/lawveres-fixed-point-theorem.lagda.md b/src/foundation/lawveres-fixed-point-theorem.lagda.md index ab2527c307..603c14897d 100644 --- a/src/foundation/lawveres-fixed-point-theorem.lagda.md +++ b/src/foundation/lawveres-fixed-point-theorem.lagda.md @@ -9,7 +9,6 @@ module foundation.lawveres-fixed-point-theorem where ```agda open import foundation.dependent-pair-types open import foundation.existential-quantification -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.propositional-truncations open import foundation.surjective-maps diff --git a/src/foundation/negated-equality.lagda.md b/src/foundation/negated-equality.lagda.md index da22f198a4..6978557244 100644 --- a/src/foundation/negated-equality.lagda.md +++ b/src/foundation/negated-equality.lagda.md @@ -10,7 +10,6 @@ module foundation.negated-equality where open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.negation open import foundation.universe-levels diff --git a/src/foundation/precomposition-functions-into-subuniverses.lagda.md b/src/foundation/precomposition-functions-into-subuniverses.lagda.md index 0e0779dbba..73604dff9d 100644 --- a/src/foundation/precomposition-functions-into-subuniverses.lagda.md +++ b/src/foundation/precomposition-functions-into-subuniverses.lagda.md @@ -9,7 +9,6 @@ module foundation.precomposition-functions-into-subuniverses where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.precomposition-functions open import foundation.universe-levels diff --git a/src/foundation/pullback-cones.lagda.md b/src/foundation/pullback-cones.lagda.md index f35b29848d..8c6d7ad7d3 100644 --- a/src/foundation/pullback-cones.lagda.md +++ b/src/foundation/pullback-cones.lagda.md @@ -13,7 +13,6 @@ open import foundation.cones-over-cospan-diagrams open import foundation.cospan-diagrams open import foundation.dependent-pair-types open import foundation.dependent-universal-property-equivalences -open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies open import foundation.homotopy-induction diff --git a/src/foundation/set-quotients.lagda.md b/src/foundation/set-quotients.lagda.md index 903b9099cb..0c6fc3765f 100644 --- a/src/foundation/set-quotients.lagda.md +++ b/src/foundation/set-quotients.lagda.md @@ -13,7 +13,6 @@ open import foundation.effective-maps-equivalence-relations open import foundation.embeddings open import foundation.equivalence-classes open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.inhabited-subtypes diff --git a/src/foundation/symmetric-binary-relations.lagda.md b/src/foundation/symmetric-binary-relations.lagda.md index 9ec5848378..19d488fdc8 100644 --- a/src/foundation/symmetric-binary-relations.lagda.md +++ b/src/foundation/symmetric-binary-relations.lagda.md @@ -11,7 +11,6 @@ open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.equivalence-extensionality -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.morphisms-binary-relations open import foundation.symmetric-operations diff --git a/src/foundation/transport-split-type-families.lagda.md b/src/foundation/transport-split-type-families.lagda.md index f4fc0dad2f..39cc5cf77f 100644 --- a/src/foundation/transport-split-type-families.lagda.md +++ b/src/foundation/transport-split-type-families.lagda.md @@ -16,7 +16,6 @@ open import foundation.dependent-pair-types open import foundation.equivalence-extensionality open import foundation.equivalence-injective-type-families open import foundation.equivalences -open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.iterated-dependent-product-types open import foundation.transport-along-identifications diff --git a/src/foundation/type-arithmetic-unit-type.lagda.md b/src/foundation/type-arithmetic-unit-type.lagda.md index 7f3e6fc73e..b7be04701d 100644 --- a/src/foundation/type-arithmetic-unit-type.lagda.md +++ b/src/foundation/type-arithmetic-unit-type.lagda.md @@ -8,7 +8,6 @@ module foundation.type-arithmetic-unit-type where ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.unit-type open import foundation.universe-levels diff --git a/src/group-theory/group-actions.lagda.md b/src/group-theory/group-actions.lagda.md index 4741ac11e3..70d3c5ce40 100644 --- a/src/group-theory/group-actions.lagda.md +++ b/src/group-theory/group-actions.lagda.md @@ -10,7 +10,6 @@ module group-theory.group-actions where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies diff --git a/src/group-theory/monoid-actions.lagda.md b/src/group-theory/monoid-actions.lagda.md index 0a737b826e..e195c009af 100644 --- a/src/group-theory/monoid-actions.lagda.md +++ b/src/group-theory/monoid-actions.lagda.md @@ -10,7 +10,6 @@ module group-theory.monoid-actions where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.endomorphisms -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.sets diff --git a/src/linear-algebra/functoriality-vectors.lagda.md b/src/linear-algebra/functoriality-vectors.lagda.md index 61c74c2380..32c5958519 100644 --- a/src/linear-algebra/functoriality-vectors.lagda.md +++ b/src/linear-algebra/functoriality-vectors.lagda.md @@ -11,7 +11,6 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md index c33d16562a..b3d50a0edf 100644 --- a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md @@ -11,7 +11,6 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/metric-spaces/discrete-premetric-structures.lagda.md b/src/metric-spaces/discrete-premetric-structures.lagda.md index e7611f1876..3f8380308f 100644 --- a/src/metric-spaces/discrete-premetric-structures.lagda.md +++ b/src/metric-spaces/discrete-premetric-structures.lagda.md @@ -14,7 +14,6 @@ open import foundation.binary-relations open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md index deb9612d34..35ddad8925 100644 --- a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md @@ -17,7 +17,6 @@ open import category-theory.precategories open import foundation.category-of-sets open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies diff --git a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md index efc5aa2595..6726a6df32 100644 --- a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md @@ -17,7 +17,6 @@ open import category-theory.split-essentially-surjective-functors-precategories open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md index a3a62b7f90..f7304f2202 100644 --- a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md +++ b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md @@ -11,7 +11,6 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md index ebb8a53618..c879431681 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md @@ -14,7 +14,6 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/modal-type-theory/sharp-codiscrete-types.lagda.md b/src/modal-type-theory/sharp-codiscrete-types.lagda.md index 82641c2cc8..7b570a8aa2 100644 --- a/src/modal-type-theory/sharp-codiscrete-types.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-types.lagda.md @@ -13,7 +13,6 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.embeddings open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.identity-types diff --git a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md index 0ed70bca76..de81adfbd4 100644 --- a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md @@ -14,7 +14,6 @@ open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types open import foundation.equivalences open import foundation.evaluation-functions -open import foundation.function-extensionality open import foundation.function-types open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md index 2cc4966422..f38cbaa29d 100644 --- a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md @@ -20,7 +20,6 @@ open import foundation.dependent-sums-pullbacks open import foundation.equivalences open import foundation.fibered-maps open import foundation.fibers-of-maps -open import foundation.function-extensionality open import foundation.function-types open import foundation.functoriality-cartesian-product-types open import foundation.functoriality-coproduct-types diff --git a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md index 09700257be..b52a86162b 100644 --- a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md @@ -15,7 +15,6 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.extensions-types-global-subuniverses open import foundation.extensions-types-subuniverses -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.global-subuniverses diff --git a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md index 7d7e25d9c1..65092e62f1 100644 --- a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md @@ -13,7 +13,6 @@ open import foundation.bicomposition-functions open import foundation.composition-algebra open import foundation.dependent-pair-types open import foundation.equality-dependent-pair-types -open import foundation.function-extensionality open import foundation.function-types open import foundation.functoriality-morphisms-arrows open import foundation.functoriality-pullbacks diff --git a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md index 495d59bdb1..5368be41af 100644 --- a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md @@ -15,7 +15,6 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.extensions-types-global-subuniverses open import foundation.extensions-types-subuniverses -open import foundation.function-extensionality open import foundation.function-types open import foundation.global-subuniverses open import foundation.homotopies diff --git a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md index ac69503101..0776c8a973 100644 --- a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md @@ -14,7 +14,6 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.equivalences-arrows open import foundation.fibers-of-maps -open import foundation.function-extensionality open import foundation.function-types open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md index 787a963051..4287ccebae 100644 --- a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md @@ -17,7 +17,6 @@ open import foundation.equivalences open import foundation.equivalences-arrows open import foundation.extensions-types-global-subuniverses open import foundation.extensions-types-subuniverses -open import foundation.function-extensionality open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.global-subuniverses diff --git a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md index 41a30148b0..8c0864b033 100644 --- a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md @@ -11,7 +11,6 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md index f6f694955a..b5fba65323 100644 --- a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md @@ -14,7 +14,6 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.extensions-types open import foundation.extensions-types-global-subuniverses -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.global-subuniverses diff --git a/src/set-theory/baire-space.lagda.md b/src/set-theory/baire-space.lagda.md index 6e7075dc17..54eed47ea2 100644 --- a/src/set-theory/baire-space.lagda.md +++ b/src/set-theory/baire-space.lagda.md @@ -12,7 +12,6 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-types open import foundation.lawveres-fixed-point-theorem open import foundation.negation diff --git a/src/set-theory/cantors-diagonal-argument.lagda.md b/src/set-theory/cantors-diagonal-argument.lagda.md index 61626fbf9b..a8ca2a8d49 100644 --- a/src/set-theory/cantors-diagonal-argument.lagda.md +++ b/src/set-theory/cantors-diagonal-argument.lagda.md @@ -17,7 +17,6 @@ open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.discrete-types open import foundation.double-negation -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.isolated-elements diff --git a/src/set-theory/cardinalities.lagda.md b/src/set-theory/cardinalities.lagda.md index 70b7ccbab9..425ce33b32 100644 --- a/src/set-theory/cardinalities.lagda.md +++ b/src/set-theory/cardinalities.lagda.md @@ -10,7 +10,6 @@ module set-theory.cardinalities where open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.functoriality-propositional-truncation open import foundation.identity-types diff --git a/src/structured-types/pointed-equivalences.lagda.md b/src/structured-types/pointed-equivalences.lagda.md index 0a852924d2..5a20fab3e9 100644 --- a/src/structured-types/pointed-equivalences.lagda.md +++ b/src/structured-types/pointed-equivalences.lagda.md @@ -17,7 +17,6 @@ open import foundation.dependent-pair-types open import foundation.embeddings open import foundation.equivalences open import foundation.fibers-of-maps -open import foundation.function-extensionality open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/structured-types/pointed-homotopies.lagda.md b/src/structured-types/pointed-homotopies.lagda.md index ad8f346c7d..234c060172 100644 --- a/src/structured-types/pointed-homotopies.lagda.md +++ b/src/structured-types/pointed-homotopies.lagda.md @@ -15,7 +15,6 @@ open import foundation.commuting-triangles-of-identifications open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md index 9be4b27b1f..04da219539 100644 --- a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md @@ -14,7 +14,6 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.diagonal-maps-of-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.identity-types open import foundation.inhabited-types diff --git a/src/synthetic-homotopy-theory/descent-circle.lagda.md b/src/synthetic-homotopy-theory/descent-circle.lagda.md index bd3ccfe178..26cb9592d3 100644 --- a/src/synthetic-homotopy-theory/descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle.lagda.md @@ -15,7 +15,6 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md index 06ddbb6917..0714fee4d0 100644 --- a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md @@ -16,7 +16,6 @@ open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-function-types diff --git a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md index 492b1150f2..e4f7cfbde5 100644 --- a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md +++ b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md @@ -9,7 +9,6 @@ module synthetic-homotopy-theory.loop-homotopy-circle where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md index e9d9b0982c..34afc02b5e 100644 --- a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md +++ b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md @@ -9,7 +9,6 @@ module synthetic-homotopy-theory.multiplication-circle where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies diff --git a/src/type-theories/precategories-with-attributes.lagda.md b/src/type-theories/precategories-with-attributes.lagda.md index 2531279eac..d3f6859646 100644 --- a/src/type-theories/precategories-with-attributes.lagda.md +++ b/src/type-theories/precategories-with-attributes.lagda.md @@ -21,7 +21,6 @@ open import foundation.cartesian-product-types open import foundation.category-of-sets open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.identity-types open import foundation.sections open import foundation.sets diff --git a/src/type-theories/precategories-with-families.lagda.md b/src/type-theories/precategories-with-families.lagda.md index 386c313d65..7e2486e370 100644 --- a/src/type-theories/precategories-with-families.lagda.md +++ b/src/type-theories/precategories-with-families.lagda.md @@ -19,7 +19,6 @@ open import foundation.cartesian-product-types open import foundation.category-of-sets open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.identity-types open import foundation.sections open import foundation.sets diff --git a/src/univalent-combinatorics/coproduct-types.lagda.md b/src/univalent-combinatorics/coproduct-types.lagda.md index 4c7fb0ae57..fa7c12c72b 100644 --- a/src/univalent-combinatorics/coproduct-types.lagda.md +++ b/src/univalent-combinatorics/coproduct-types.lagda.md @@ -15,7 +15,6 @@ open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.equivalence-extensionality open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-coproduct-types diff --git a/src/univalent-combinatorics/locally-finite-types.lagda.md b/src/univalent-combinatorics/locally-finite-types.lagda.md index 04f398816f..2caa3d98a1 100644 --- a/src/univalent-combinatorics/locally-finite-types.lagda.md +++ b/src/univalent-combinatorics/locally-finite-types.lagda.md @@ -28,7 +28,6 @@ open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.fiber-inclusions open import foundation.fibers-of-maps -open import foundation.function-extensionality open import foundation.function-types open import foundation.functoriality-coproduct-types open import foundation.functoriality-dependent-pair-types From 19929d083d6f9f0b78d12a4d7effbb6525bc273e Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Wed, 19 Mar 2025 23:40:09 +0000 Subject: [PATCH 04/39] scripts --- scripts/add_funext_parameter.py | 199 +++++++++++++++++ scripts/build_dependency_graph.py | 281 +++++++++++++++++++++++++ scripts/remove_unused_funext_import.py | 85 ++++++++ 3 files changed, 565 insertions(+) create mode 100644 scripts/add_funext_parameter.py create mode 100644 scripts/build_dependency_graph.py create mode 100644 scripts/remove_unused_funext_import.py diff --git a/scripts/add_funext_parameter.py b/scripts/add_funext_parameter.py new file mode 100644 index 0000000000..078f9f42f3 --- /dev/null +++ b/scripts/add_funext_parameter.py @@ -0,0 +1,199 @@ +#!/usr/bin/env python3 + +import os +import re +import argparse +from pathlib import Path +import shutil +import sys + +# Import the dependency graph functionality +from build_dependency_graph import compute_transitive_closure, build_dependency_graph + +FUNEXT_MODULE = "foundation.function-extensionality" +FUNEXT_IMPORT = "open import foundation.function-extensionality-axiom" +FUNEXT_PARAM = "(funext : function-extensionality)" + +def find_module_declaration(content): + """Find the main module declaration in a file.""" + # Match 'module name.of.module' potentially with parameters + module_pattern = r'^module\s+([^\s\(]+)(?:\s+[^\n]*)?(?:\n|$)' + match = re.search(module_pattern, content, re.MULTILINE) + if match: + return match.group(0), match.group(1) + return None, None + +def modify_file_content(file_path, module_name, dependent_modules): + """ + Modify the content of an Agda file to: + 1. Remove any existing function extensionality imports + 2. Add function extensionality import right before module declaration + 3. Add funext parameter to module declaration + 4. Add funext parameter to dependent imports + """ + with open(file_path, 'r', encoding='utf-8') as f: + content = f.read() + + # Find module declaration + module_decl, module_id = find_module_declaration(content) + if not module_decl: + print(f"Warning: Could not find module declaration in {file_path}") + return None + + # Remove any existing function extensionality imports + modified_content = content + existing_import_pattern = rf'{re.escape(FUNEXT_IMPORT)}(?:\s*\n|\n)' + modified_content = re.sub(existing_import_pattern, '', modified_content) + + # If content changed, get updated module declaration + if modified_content != content: + print(f"Note: Removed existing function extensionality import in {file_path}") + module_decl, module_id = find_module_declaration(modified_content) + content = modified_content + + # Check if the module declaration already has funext parameter + has_funext_param = "funext" in module_decl + + # Add function extensionality import and update module declaration + lines = content.split('\n') + updated_lines = [] + module_line_found = False + + for line in lines: + # When we find the module declaration line + if not module_line_found and line.startswith('module '): + # Add the import before the module declaration + updated_lines.append(FUNEXT_IMPORT + '\n') + module_line_found = True + + # Add funext parameter to module declaration if needed + if not has_funext_param: + if "where" in line: + # If there's a 'where' clause, put parameters before it + updated_line = re.sub(r'(\s+where)', f" {FUNEXT_PARAM}\\1", line) + else: + # Otherwise, add at the end + updated_line = line.rstrip() + f" {FUNEXT_PARAM} where" + updated_lines.append(updated_line) + else: + updated_lines.append(line) + else: + updated_lines.append(line) + + modified_content = '\n'.join(updated_lines) + + # Modify imports of modules that depend on funext + for dep_module in dependent_modules: + # Find imports of this module + import_pattern = rf'open\s+import\s+{re.escape(dep_module)}(?:\s+[^\n]*)?(?:\n|$)' + for match in re.finditer(import_pattern, modified_content): + import_stmt = match.group(0) + # Skip if already has funext + if "funext" in import_stmt: + continue + + # Add funext parameter to the import + if import_stmt.strip().endswith(dep_module): + # No existing parameters + new_import = import_stmt.rstrip() + " funext\n" + else: + # Has other parameters, add funext + new_import = import_stmt.replace(dep_module, f"{dep_module} funext") + + modified_content = modified_content[:match.start()] + new_import + modified_content[match.end():] + + # Additionally, handle direct imports of foundation.function-extensionality + # Make sure we only match the exact module name, not ones that start with it + funext_direct_import_pattern = r'open\s+import\s+foundation\.function-extensionality\b(?!-axiom)' + + # Use finditer with the MULTILINE flag to ensure we catch all instances + for match in re.finditer(funext_direct_import_pattern, modified_content, re.MULTILINE): + import_stmt = match.group(0) + # Skip if already has funext + if "funext" in import_stmt: + continue + + # Add funext parameter to the import + if import_stmt.strip().endswith("foundation.function-extensionality"): + # No existing parameters + new_import = import_stmt.rstrip() + " funext\n" + else: + # Has other parameters, add funext appropriately + # Use a more specific pattern to ensure we only replace the exact module name + new_import = re.sub(r'(foundation\.function-extensionality)\b(?!-axiom)', r'\1 funext', import_stmt) + + modified_content = modified_content[:match.start()] + new_import + modified_content[match.end():] + + # Only return modified content if changes were made + if modified_content != content: + return modified_content + else: + print(f"No changes needed for {file_path}") + return None + +def main(): + parser = argparse.ArgumentParser(description='Add function extensionality parameter to Agda modules') + parser.add_argument('root_dir', help='Root directory of the Agda library') + parser.add_argument('--dry-run', action='store_true', + help='Show what would be changed without making actual changes') + parser.add_argument('--backup', action='store_true', + help='Create backup files before modifying') + args = parser.parse_args() + + root_dir = args.root_dir + + print(f"Building dependency graph for {root_dir}...") + graph, module_to_file = build_dependency_graph(root_dir) + + print("Computing transitive closure of dependencies...") + transitive_graph = compute_transitive_closure(graph) + + # Find all modules that depend on foundation.function-extensionality + funext_dependent_modules = [] + for module, deps in transitive_graph.items(): + if FUNEXT_MODULE in deps: + funext_dependent_modules.append(module) + + print(f"Found {len(funext_dependent_modules)} modules that depend on {FUNEXT_MODULE}") + + # Create a mapping of each file to its dependent modules + file_dependent_modules = {} + for module in funext_dependent_modules: + if module in module_to_file: + file_path = module_to_file[module] + file_dependent_modules[file_path] = [ + dep for dep in graph.get(module, []) + if dep in funext_dependent_modules + ] + + # Process each file + modified_count = 0 + for file_path, dependent_modules in file_dependent_modules.items(): + module_name = next((m for m, f in module_to_file.items() if f == file_path), None) + if not module_name: + continue + + print(f"Processing {module_name} ({file_path})...") + modified_content = modify_file_content(file_path, module_name, dependent_modules) + + if modified_content: + if args.dry_run: + print(f"Would modify: {file_path}") + else: + if args.backup: + backup_path = f"{file_path}.bak" + shutil.copy2(file_path, backup_path) + print(f"Created backup: {backup_path}") + + with open(file_path, 'w', encoding='utf-8') as f: + f.write(modified_content) + print(f"Modified: {file_path}") + modified_count += 1 + + if args.dry_run: + print(f"\nDry run completed. {modified_count} files would be modified.") + else: + print(f"\nCompleted. Modified {modified_count} files.") + +if __name__ == "__main__": + main() diff --git a/scripts/build_dependency_graph.py b/scripts/build_dependency_graph.py new file mode 100644 index 0000000000..6c6271c6d8 --- /dev/null +++ b/scripts/build_dependency_graph.py @@ -0,0 +1,281 @@ +#!/usr/bin/env python3 + +import os +import re +import argparse +import json +from collections import defaultdict, deque +from pathlib import Path + +# Import utils for Git-related functionality +import sys +import os.path +sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) +from scripts.utils import get_git_tracked_files + +def find_agda_files(root_dir): + """Find all Git-tracked Agda source files in the given directory tree.""" + # Get all Git-tracked files + git_tracked_files = get_git_tracked_files() + + # Filter to keep only Agda files that are tracked by Git + agda_files = [] + root_path = Path(root_dir).resolve() + + for file_path in git_tracked_files: + full_path = Path(file_path) + # Check if the file is in the specified root directory + if root_path in full_path.resolve().parents or root_path == full_path.resolve().parent: + if file_path.suffix == '.agda' or (file_path.suffix == '.md' and file_path.stem.endswith('.lagda')): + agda_files.append(str(file_path)) + + return agda_files + +def extract_imports(file_path): + """Extract all module imports from a file.""" + with open(file_path, 'r', encoding='utf-8') as f: + content = f.read() + + # Pattern to match "open import module.name" + import_pattern = r'open\s+import\s+(\S+)' + + # Find all matches + imports = re.findall(import_pattern, content) + return imports + +def build_dependency_graph(root_dir): + """Build a dependency graph from all Git-tracked Agda files in the directory.""" + agda_files = find_agda_files(root_dir) + + # Map each file to its module name (derived from path) + file_to_module = {} + for file_path in agda_files: + # Convert file path to module name + rel_path = os.path.relpath(file_path, root_dir) + # Remove extension and replace / with . + if rel_path.endswith('.lagda.md'): + module_name = rel_path[:-9] + else: # .agda + module_name = rel_path[:-5] + module_name = module_name.replace('/', '.') + file_to_module[file_path] = module_name + + # Invert the mapping for lookup + module_to_file = {v: k for k, v in file_to_module.items()} + + # Build the dependency graph + graph = defaultdict(list) + for file_path in agda_files: + module_name = file_to_module[file_path] + imports = extract_imports(file_path) + for imported_module in imports: + graph[module_name].append(imported_module) + + return graph, module_to_file + +def compute_transitive_closure(graph): + """ + Compute the transitive closure of the dependency graph. + Returns a new graph where each module has a list of all its + direct and indirect dependencies. + """ + transitive_closure = defaultdict(set) + + # For each module, perform BFS to find all dependencies + for module in graph: + queue = deque(graph[module]) + visited = set(graph[module]) + + while queue: + dep = queue.popleft() + transitive_closure[module].add(dep) + + # Add any dependencies of this dependency that we haven't seen yet + for next_dep in graph.get(dep, []): + if next_dep not in visited: + visited.add(next_dep) + queue.append(next_dep) + + # Convert sets back to lists for consistent output + return {module: list(deps) for module, deps in transitive_closure.items()} + +def export_to_dot(graph, output_file): + """Export the graph to DOT format for visualization with Graphviz.""" + with open(output_file, 'w') as f: + f.write('digraph Dependencies {\n') + f.write(' node [shape=box];\n') + + for module, deps in graph.items(): + for dep in deps: + f.write(f' "{module}" -> "{dep}";\n') + + f.write('}\n') + +def export_to_json(graph, output_file): + """Export the graph to JSON format.""" + with open(output_file, 'w') as f: + json.dump(graph, f, indent=2) + +def find_dependent_modules(graph, target_module): + """ + Find all modules that depend on the target module. + Uses the transitive closure of the dependency graph. + + Args: + graph: The transitive closure of the dependency graph + target_module: The module to check dependencies for + + Returns: + A list of modules that depend on the target module + """ + dependent_modules = [] + for module, dependencies in graph.items(): + if target_module in dependencies: + dependent_modules.append(module) + return dependent_modules + +def main(): + parser = argparse.ArgumentParser(description='Build dependency graph of Agda modules') + parser.add_argument('root_dir', help='Root directory of the Agda library') + parser.add_argument('--dot', help='Output file for DOT graph') + parser.add_argument('--json', help='Output file for JSON representation') + parser.add_argument('--transitive', action='store_true', + help='Compute transitive closure of dependencies') + parser.add_argument('--transitive-dot', help='Output file for transitive closure DOT graph') + parser.add_argument('--transitive-json', help='Output file for transitive closure JSON') + parser.add_argument('--top-dependent', type=int, default=10, + help='Print top N modules with most dependencies (default: 10)') + parser.add_argument('--find-dependents', metavar='MODULE', + help='Find all modules that depend on the specified module') + parser.add_argument('--quiet', action='store_true', + help='Suppress informational output, only show requested results') + # Remove the --omit-top-level argument as we'll always do this + args = parser.parse_args() + + # If find_dependents is used, enable quiet mode by default unless explicitly overridden + quiet_mode = args.quiet or (args.find_dependents and not any([args.transitive, args.dot, args.json, args.transitive_dot, args.transitive_json])) + + if not quiet_mode: + print(f"Analyzing Git-tracked Agda files in {args.root_dir}...") + graph, module_to_file = build_dependency_graph(args.root_dir) + + if not quiet_mode: + print(f"Found {len(graph)} tracked modules with dependencies.") + + if args.dot: + export_to_dot(graph, args.dot) + if not quiet_mode: + print(f"DOT graph exported to {args.dot}") + + if args.json: + export_to_json(graph, args.json) + if not quiet_mode: + print(f"JSON data exported to {args.json}") + + # Compute transitive closure if needed + transitive_graph = None + if args.transitive or args.transitive_dot or args.transitive_json or args.find_dependents: + if not quiet_mode: + print("Computing transitive closure of dependencies...") + transitive_graph = compute_transitive_closure(graph) + + if args.transitive_dot: + export_to_dot(transitive_graph, args.transitive_dot) + if not quiet_mode: + print(f"Transitive closure DOT graph exported to {args.transitive_dot}") + + if args.transitive_json: + export_to_json(transitive_graph, args.transitive_json) + if not quiet_mode: + print(f"Transitive closure JSON exported to {args.transitive_json}") + + if args.transitive and not (args.transitive_dot or args.transitive_json) and not quiet_mode: + # Print some statistics about the transitive closure + avg_deps = sum(len(deps) for deps in transitive_graph.values()) / len(transitive_graph) if transitive_graph else 0 + max_deps = max(len(deps) for deps in transitive_graph.values()) if transitive_graph else 0 + + print(f"\nTransitive closure statistics:") + print(f" Average dependencies per module: {avg_deps:.2f}") + print(f" Maximum dependencies for a module: {max_deps}") + + # Find module with most dependencies (among non-top-level modules) + non_top_level_modules = {module: deps for module, deps in transitive_graph.items() if '.' in module} + if non_top_level_modules: + most_deps_module = max(non_top_level_modules.items(), key=lambda x: len(x[1])) + print(f" Module with most dependencies: {most_deps_module[0]} ({len(most_deps_module[1])} deps)") + + # Only print transitive dependency top lists if not in quiet mode + if not quiet_mode: + # Always filter out top-level modules + filtered_transitive_graph = {module: deps for module, deps in transitive_graph.items() + if '.' in module} + if filtered_transitive_graph: + # Only print this if we've actually filtered out modules + if len(transitive_graph) != len(filtered_transitive_graph): + print(f"Filtered out {len(transitive_graph) - len(filtered_transitive_graph)} top-level modules.") + + # Print top modules with most dependencies (transitive) + print(f"\nTop {args.top_dependent} modules with most dependencies (including transitive):") + sorted_modules = sorted(filtered_transitive_graph.items(), key=lambda x: len(x[1]), reverse=True) + for i, (module, deps) in enumerate(sorted_modules[:args.top_dependent], 1): + print(f" {i}. `{module}` {len(deps)} dependencies") + else: + print("\nNo non-top-level modules found for transitive analysis.") + + # Check for modules that depend on a specific module + if args.find_dependents: + if not transitive_graph: + if not quiet_mode: + print("Computing transitive closure of dependencies...") + transitive_graph = compute_transitive_closure(graph) + + dependent_modules = find_dependent_modules(transitive_graph, args.find_dependents) + + print(f"\nModules that depend on '{args.find_dependents}':") + print(f"Found {len(dependent_modules)} dependent modules") + + if dependent_modules: + # Sort alphabetically for easier reading + for module in sorted(dependent_modules): + print(f" {module}") + + # Optionally export to a file if requested + if args.json: + dependents_json = os.path.splitext(args.json)[0] + f"-dependents-of-{args.find_dependents.replace('.', '-')}.json" + with open(dependents_json, 'w') as f: + json.dump(dependent_modules, f, indent=2) + print(f"Dependent modules exported to {dependents_json}") + else: + print(" No modules depend on this module") + + # Only print remaining statistics if not in quiet mode + if not quiet_mode: + # Always filter out top-level modules for direct dependencies + filtered_graph = {module: deps for module, deps in graph.items() if '.' in module} + + if filtered_graph: + # Print modules with most direct dependencies + direct_dep_count = {module: len(deps) for module, deps in filtered_graph.items()} + print(f"\nTop {args.top_dependent} modules with most direct dependencies:") + for i, (module, count) in enumerate(sorted(direct_dep_count.items(), key=lambda x: x[1], reverse=True)[:args.top_dependent], 1): + print(f" {i}. {module}: {count} direct dependencies") + else: + print("\nNo non-top-level modules found for direct dependency analysis.") + + if not any([args.dot, args.json, args.transitive, args.transitive_dot, args.transitive_json, args.find_dependents]): + # Filter the imported modules count to only include non-top-level modules + most_imported = defaultdict(int) + for _, deps in graph.items(): + for dep in deps: + if '.' in dep: # Only count imports of non-top-level modules + most_imported[dep] += 1 + + if most_imported: + print("\nTop 10 most imported non-top-level modules:") + for module, count in sorted(most_imported.items(), key=lambda x: x[1], reverse=True)[:10]: + print(f" `{module}` {count} imports") + else: + print("\nNo non-top-level modules found for import analysis.") + +if __name__ == "__main__": + main() diff --git a/scripts/remove_unused_funext_import.py b/scripts/remove_unused_funext_import.py new file mode 100644 index 0000000000..ff05d8ab84 --- /dev/null +++ b/scripts/remove_unused_funext_import.py @@ -0,0 +1,85 @@ +#!/usr/bin/env python3 + +import os +import re +import argparse +from pathlib import Path + +# Import utils for Git-related functionality +import sys +import os.path +sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) +from scripts.utils import get_git_tracked_files + +def find_agda_files(root_dir): + """Find all Git-tracked Agda source files in the given directory tree.""" + # Get all Git-tracked files + git_tracked_files = get_git_tracked_files() + + # Filter to keep only Agda files that are tracked by Git + agda_files = [] + root_path = Path(root_dir).resolve() + + for file_path in git_tracked_files: + full_path = Path(file_path) + # Check if the file is in the specified root directory + if root_path in full_path.resolve().parents or root_path == full_path.resolve().parent: + if file_path.suffix == '.agda' or (file_path.suffix == '.md' and file_path.stem.endswith('.lagda')): + agda_files.append(str(file_path)) + + return agda_files + +def process_file(file_path, dry_run=False): + """ + Check if the file contains the import line but doesn't use function extensionality. + Return True if the file was modified or would be modified. + """ + with open(file_path, 'r', encoding='utf-8') as f: + content = f.read() + + # Check if the file imports function-extensionality + target_import = "open import foundation.function-extensionality\n" + if target_import not in content: + return False + + # Check if the file uses either 'eq-htpy' or 'funext' + if 'eq-htpy' in content or 'funext' in content: + return False + + # The file has the import but doesn't appear to use it + if not dry_run: + # Remove the import line and write the file back + new_content = re.sub(f'^{re.escape(target_import)}', '', content, flags=re.MULTILINE) + with open(file_path, 'w', encoding='utf-8') as f: + f.write(new_content) + + return True + +def main(): + parser = argparse.ArgumentParser(description='Remove unused function-extensionality imports') + parser.add_argument('root_dir', help='Root directory of the Agda library') + parser.add_argument('--dry-run', action='store_true', + help='Only report files that would be modified without changing them') + args = parser.parse_args() + + print(f"Analyzing Git-tracked Agda files in {args.root_dir}...") + agda_files = find_agda_files(args.root_dir) + print(f"Found {len(agda_files)} tracked Agda files to check.") + + modified_files = [] + for file_path in agda_files: + if process_file(file_path, args.dry_run): + modified_files.append(file_path) + + if args.dry_run: + print(f"\nDry run: {len(modified_files)} files would be modified to remove unused imports.") + else: + print(f"\nModified {len(modified_files)} files to remove unused function-extensionality imports.") + + if modified_files: + print("\nModified files:") + for file_path in modified_files: + print(f" - {file_path}") + +if __name__ == "__main__": + main() From 5cafc70a5289a28e60755fedb3dc99f3654ec955 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 11:36:34 +0000 Subject: [PATCH 05/39] Revert "depostulate funext in `foundation.function-extensionality`" This reverts commit 406d2088bf0103d229e1bed8b20aa1392246f9a0. --- src/foundation.lagda.md | 1 - .../function-extensionality-axiom.lagda.md | 172 ------------------ .../function-extensionality.lagda.md | 124 +++++++++++-- 3 files changed, 109 insertions(+), 188 deletions(-) delete mode 100644 src/foundation/function-extensionality-axiom.lagda.md diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index 9979470954..fa5ed4f5b6 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -198,7 +198,6 @@ open import foundation.finitely-coherently-invertible-maps public open import foundation.fixed-points-endofunctions public open import foundation.full-subtypes public open import foundation.function-extensionality public -open import foundation.function-extensionality-axiom public open import foundation.function-types public open import foundation.functional-correspondences public open import foundation.functoriality-action-on-identifications-functions public diff --git a/src/foundation/function-extensionality-axiom.lagda.md b/src/foundation/function-extensionality-axiom.lagda.md deleted file mode 100644 index 3335f2bf9d..0000000000 --- a/src/foundation/function-extensionality-axiom.lagda.md +++ /dev/null @@ -1,172 +0,0 @@ -# The function extensionality axiom - -```agda -module foundation.function-extensionality-axiom where -``` - -
Imports - -```agda -open import foundation.action-on-identifications-binary-functions -open import foundation.action-on-identifications-functions -open import foundation.dependent-pair-types -open import foundation.evaluation-functions -open import foundation.implicit-function-types -open import foundation.universe-levels - -open import foundation-core.coherently-invertible-maps -open import foundation-core.equivalences -open import foundation-core.function-types -open import foundation-core.homotopies -open import foundation-core.identity-types -open import foundation-core.retractions -open import foundation-core.sections -``` - -
- -## Idea - -The -{{#concept "function extensionality axiom" Agda=function-extensionality Agda=funext}} -asserts that [identifications](foundation-core.identity-types.md) of (dependent) -functions are [equivalently](foundation-core.equivalences.md) described as -[homotopies](foundation-core.homotopies.md) between them. In other words, a -function is completely determined by its values. - -Function extensionality is postulated by stating that the canonical map - -```text - htpy-eq : f ＝ g → f ~ g -``` - -from identifications between two functions to homotopies between them is an -equivalence. The map `htpy-eq` is the unique map that fits in a -[commuting triangle](foundation-core.commuting-triangles-of-maps.md) - -```text - htpy-eq - (f ＝ g) ----------> (f ~ g) - \ / - ap (ev x) \ / ev x - ∨ ∨ - (f x ＝ g x) -``` - -In other words, we define - -```text - htpy-eq p x := ap (ev x) p. -``` - -It follows from this definition that `htpy-eq refl ≐ refl-htpy`, as expected. - -## Definitions - -### Equalities induce homotopies - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - htpy-eq : {f g : (x : A) → B x} → f ＝ g → f ~ g - htpy-eq p a = ap (ev a) p - - compute-htpy-eq-refl : {f : (x : A) → B x} → htpy-eq refl ＝ refl-htpy' f - compute-htpy-eq-refl = refl -``` - -### An instance of function extensionality - -This property asserts that, _given_ two functions `f` and `g`, the map - -```text - htpy-eq : f ＝ g → f ~ g -``` - -is an equivalence. - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - instance-function-extensionality : (f g : (x : A) → B x) → UU (l1 ⊔ l2) - instance-function-extensionality f g = is-equiv (htpy-eq {f = f} {g}) -``` - -### Based function extensionality - -This property asserts that, _given_ a function `f`, the map - -```text - htpy-eq : f ＝ g → f ~ g -``` - -is an equivalence for any function `g` of the same type. - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - based-function-extensionality : (f : (x : A) → B x) → UU (l1 ⊔ l2) - based-function-extensionality f = - (g : (x : A) → B x) → instance-function-extensionality f g -``` - -### The function extensionality principle with respect to a universe level - -```agda -function-extensionality-Level : (l1 l2 : Level) → UU (lsuc l1 ⊔ lsuc l2) -function-extensionality-Level l1 l2 = - {A : UU l1} {B : A → UU l2} - (f : (x : A) → B x) → based-function-extensionality f -``` - -### The function extensionality axiom - -```agda -function-extensionality : UUω -function-extensionality = {l1 l2 : Level} → function-extensionality-Level l1 l2 -``` - -## Properties - -### `htpy-eq` preserves inverses - -For any two functions `f g : (x : A) → B x` we have a -[commuting square](foundation-core.commuting-squares-of-maps.md) - -```text - inv - (f = g) ---------> (g = f) - | | - htpy-eq | | htpy-eq - ∨ ∨ - (f ~ g) ---------> (g ~ f). - inv-htpy -``` - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} - where - - compute-htpy-eq-inv : inv-htpy {f = f} {g} ∘ htpy-eq ~ htpy-eq ∘ inv - compute-htpy-eq-inv refl = refl - - compute-inv-htpy-htpy-eq : htpy-eq ∘ inv ~ inv-htpy {f = f} {g} ∘ htpy-eq - compute-inv-htpy-htpy-eq = inv-htpy compute-htpy-eq-inv -``` - -## See also - -- The fact that the univalence axiom implies function extensionality is proven - in - [`foundation.univalence-implies-function-extensionality`](foundation.univalence-implies-function-extensionality.md). -- Weak function extensionality is defined in - [`foundation.weak-function-extensionality`](foundation.weak-function-extensionality.md). -- Transporting along homotopies is defined in - [`foundation.transport-along-homotopies`](foundation.transport-along-homotopies.md). diff --git a/src/foundation/function-extensionality.lagda.md b/src/foundation/function-extensionality.lagda.md index 7dc5040a43..5633842ad1 100644 --- a/src/foundation/function-extensionality.lagda.md +++ b/src/foundation/function-extensionality.lagda.md @@ -1,12 +1,7 @@ # Function extensionality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.function-extensionality - (funext : function-extensionality) - where +module foundation.function-extensionality where ```
Imports @@ -68,8 +63,75 @@ It follows from this definition that `htpy-eq refl ≐ refl-htpy`, as expected. ## Definitions +### Equalities induce homotopies + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + htpy-eq : {f g : (x : A) → B x} → f ＝ g → f ~ g + htpy-eq p a = ap (ev a) p + + compute-htpy-eq-refl : {f : (x : A) → B x} → htpy-eq refl ＝ refl-htpy' f + compute-htpy-eq-refl = refl +``` + +### An instance of function extensionality + +This property asserts that, _given_ two functions `f` and `g`, the map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +is an equivalence. + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + instance-function-extensionality : (f g : (x : A) → B x) → UU (l1 ⊔ l2) + instance-function-extensionality f g = is-equiv (htpy-eq {f = f} {g}) +``` + +### Based function extensionality + +This property asserts that, _given_ a function `f`, the map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +is an equivalence for any function `g` of the same type. + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + based-function-extensionality : (f : (x : A) → B x) → UU (l1 ⊔ l2) + based-function-extensionality f = + (g : (x : A) → B x) → instance-function-extensionality f g +``` + +### The function extensionality principle with respect to a universe level + +```agda +function-extensionality-Level : (l1 l2 : Level) → UU (lsuc l1 ⊔ lsuc l2) +function-extensionality-Level l1 l2 = + {A : UU l1} {B : A → UU l2} + (f : (x : A) → B x) → based-function-extensionality f +``` + ### The function extensionality axiom +```agda +function-extensionality : UUω +function-extensionality = {l1 l2 : Level} → function-extensionality-Level l1 l2 +``` + Rather than postulating a witness of `function-extensionality` directly, we postulate the constituents of a coherent two-sided inverse to `htpy-eq`. The benefits are that we end up with a single converse map to `htpy-eq`, rather than @@ -82,23 +144,23 @@ module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} where - opaque + postulate eq-htpy : f ~ g → f ＝ g - eq-htpy = map-inv-is-equiv (funext f g) is-section-eq-htpy : is-section htpy-eq eq-htpy - is-section-eq-htpy = is-section-map-inv-is-equiv (funext f g) - is-retraction-eq-htpy : is-retraction htpy-eq eq-htpy - is-retraction-eq-htpy = is-retraction-map-inv-is-equiv (funext f g) + is-retraction-eq-htpy' : is-retraction htpy-eq eq-htpy - coh-eq-htpy : + coh-eq-htpy' : coherence-is-coherently-invertible ( htpy-eq) ( eq-htpy) ( is-section-eq-htpy) - ( is-retraction-eq-htpy) - coh-eq-htpy = coherence-map-inv-is-equiv (funext f g) + ( is-retraction-eq-htpy') + +funext : function-extensionality +funext f g = + is-equiv-is-invertible eq-htpy is-section-eq-htpy is-retraction-eq-htpy' module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} @@ -111,7 +173,12 @@ module _ is-equiv-eq-htpy : (f g : (x : A) → B x) → is-equiv (eq-htpy {f = f} {g}) is-equiv-eq-htpy f g = - is-equiv-is-invertible htpy-eq is-retraction-eq-htpy is-section-eq-htpy + is-equiv-is-invertible htpy-eq is-retraction-eq-htpy' is-section-eq-htpy + + abstract + is-retraction-eq-htpy : + {f g : (x : A) → B x} → is-retraction (htpy-eq {f = f} {g}) eq-htpy + is-retraction-eq-htpy {f} {g} = is-retraction-map-inv-is-equiv (funext f g) eq-htpy-refl-htpy : (f : (x : A) → B x) → eq-htpy (refl-htpy {f = f}) ＝ refl @@ -177,6 +244,33 @@ module _ ( is-retraction-eq-htpy (eq-htpy H ∙ eq-htpy K)) ``` +### `htpy-eq` preserves inverses + +For any two functions `f g : (x : A) → B x` we have a +[commuting square](foundation-core.commuting-squares-of-maps.md) + +```text + inv + (f = g) ---------> (g = f) + | | + htpy-eq | | htpy-eq + ∨ ∨ + (f ~ g) ---------> (g ~ f). + inv-htpy +``` + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} + where + + compute-htpy-eq-inv : inv-htpy {f = f} {g} ∘ htpy-eq ~ htpy-eq ∘ inv + compute-htpy-eq-inv refl = refl + + compute-inv-htpy-htpy-eq : htpy-eq ∘ inv ~ inv-htpy {f = f} {g} ∘ htpy-eq + compute-inv-htpy-htpy-eq = inv-htpy compute-htpy-eq-inv +``` + ### `eq-htpy` preserves inverses For any two functions `f g : (x : A) → B x` we have a commuting square From ff7f4370135cbb3897062b3634232a9193c7f292 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 11:38:04 +0000 Subject: [PATCH 06/39] Reapply "depostulate funext in `foundation.function-extensionality`" This reverts commit 5cafc70a5289a28e60755fedb3dc99f3654ec955. --- src/foundation.lagda.md | 1 + .../function-extensionality-axiom.lagda.md | 172 ++++++++++++++++++ .../function-extensionality.lagda.md | 96 +--------- 3 files changed, 175 insertions(+), 94 deletions(-) create mode 100644 src/foundation/function-extensionality-axiom.lagda.md diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index fa5ed4f5b6..9979470954 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -198,6 +198,7 @@ open import foundation.finitely-coherently-invertible-maps public open import foundation.fixed-points-endofunctions public open import foundation.full-subtypes public open import foundation.function-extensionality public +open import foundation.function-extensionality-axiom public open import foundation.function-types public open import foundation.functional-correspondences public open import foundation.functoriality-action-on-identifications-functions public diff --git a/src/foundation/function-extensionality-axiom.lagda.md b/src/foundation/function-extensionality-axiom.lagda.md new file mode 100644 index 0000000000..3335f2bf9d --- /dev/null +++ b/src/foundation/function-extensionality-axiom.lagda.md @@ -0,0 +1,172 @@ +# The function extensionality axiom + +```agda +module foundation.function-extensionality-axiom where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-binary-functions +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.evaluation-functions +open import foundation.implicit-function-types +open import foundation.universe-levels + +open import foundation-core.coherently-invertible-maps +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.retractions +open import foundation-core.sections +``` + +
+ +## Idea + +The +{{#concept "function extensionality axiom" Agda=function-extensionality Agda=funext}} +asserts that [identifications](foundation-core.identity-types.md) of (dependent) +functions are [equivalently](foundation-core.equivalences.md) described as +[homotopies](foundation-core.homotopies.md) between them. In other words, a +function is completely determined by its values. + +Function extensionality is postulated by stating that the canonical map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +from identifications between two functions to homotopies between them is an +equivalence. The map `htpy-eq` is the unique map that fits in a +[commuting triangle](foundation-core.commuting-triangles-of-maps.md) + +```text + htpy-eq + (f ＝ g) ----------> (f ~ g) + \ / + ap (ev x) \ / ev x + ∨ ∨ + (f x ＝ g x) +``` + +In other words, we define + +```text + htpy-eq p x := ap (ev x) p. +``` + +It follows from this definition that `htpy-eq refl ≐ refl-htpy`, as expected. + +## Definitions + +### Equalities induce homotopies + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + htpy-eq : {f g : (x : A) → B x} → f ＝ g → f ~ g + htpy-eq p a = ap (ev a) p + + compute-htpy-eq-refl : {f : (x : A) → B x} → htpy-eq refl ＝ refl-htpy' f + compute-htpy-eq-refl = refl +``` + +### An instance of function extensionality + +This property asserts that, _given_ two functions `f` and `g`, the map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +is an equivalence. + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + instance-function-extensionality : (f g : (x : A) → B x) → UU (l1 ⊔ l2) + instance-function-extensionality f g = is-equiv (htpy-eq {f = f} {g}) +``` + +### Based function extensionality + +This property asserts that, _given_ a function `f`, the map + +```text + htpy-eq : f ＝ g → f ~ g +``` + +is an equivalence for any function `g` of the same type. + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} + where + + based-function-extensionality : (f : (x : A) → B x) → UU (l1 ⊔ l2) + based-function-extensionality f = + (g : (x : A) → B x) → instance-function-extensionality f g +``` + +### The function extensionality principle with respect to a universe level + +```agda +function-extensionality-Level : (l1 l2 : Level) → UU (lsuc l1 ⊔ lsuc l2) +function-extensionality-Level l1 l2 = + {A : UU l1} {B : A → UU l2} + (f : (x : A) → B x) → based-function-extensionality f +``` + +### The function extensionality axiom + +```agda +function-extensionality : UUω +function-extensionality = {l1 l2 : Level} → function-extensionality-Level l1 l2 +``` + +## Properties + +### `htpy-eq` preserves inverses + +For any two functions `f g : (x : A) → B x` we have a +[commuting square](foundation-core.commuting-squares-of-maps.md) + +```text + inv + (f = g) ---------> (g = f) + | | + htpy-eq | | htpy-eq + ∨ ∨ + (f ~ g) ---------> (g ~ f). + inv-htpy +``` + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} + where + + compute-htpy-eq-inv : inv-htpy {f = f} {g} ∘ htpy-eq ~ htpy-eq ∘ inv + compute-htpy-eq-inv refl = refl + + compute-inv-htpy-htpy-eq : htpy-eq ∘ inv ~ inv-htpy {f = f} {g} ∘ htpy-eq + compute-inv-htpy-htpy-eq = inv-htpy compute-htpy-eq-inv +``` + +## See also + +- The fact that the univalence axiom implies function extensionality is proven + in + [`foundation.univalence-implies-function-extensionality`](foundation.univalence-implies-function-extensionality.md). +- Weak function extensionality is defined in + [`foundation.weak-function-extensionality`](foundation.weak-function-extensionality.md). +- Transporting along homotopies is defined in + [`foundation.transport-along-homotopies`](foundation.transport-along-homotopies.md). diff --git a/src/foundation/function-extensionality.lagda.md b/src/foundation/function-extensionality.lagda.md index 5633842ad1..a3fcfb1a31 100644 --- a/src/foundation/function-extensionality.lagda.md +++ b/src/foundation/function-extensionality.lagda.md @@ -1,6 +1,8 @@ # Function extensionality ```agda +open import foundation.function-extensionality-axiom + module foundation.function-extensionality where ``` @@ -63,75 +65,8 @@ It follows from this definition that `htpy-eq refl ≐ refl-htpy`, as expected. ## Definitions -### Equalities induce homotopies - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - htpy-eq : {f g : (x : A) → B x} → f ＝ g → f ~ g - htpy-eq p a = ap (ev a) p - - compute-htpy-eq-refl : {f : (x : A) → B x} → htpy-eq refl ＝ refl-htpy' f - compute-htpy-eq-refl = refl -``` - -### An instance of function extensionality - -This property asserts that, _given_ two functions `f` and `g`, the map - -```text - htpy-eq : f ＝ g → f ~ g -``` - -is an equivalence. - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - instance-function-extensionality : (f g : (x : A) → B x) → UU (l1 ⊔ l2) - instance-function-extensionality f g = is-equiv (htpy-eq {f = f} {g}) -``` - -### Based function extensionality - -This property asserts that, _given_ a function `f`, the map - -```text - htpy-eq : f ＝ g → f ~ g -``` - -is an equivalence for any function `g` of the same type. - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} - where - - based-function-extensionality : (f : (x : A) → B x) → UU (l1 ⊔ l2) - based-function-extensionality f = - (g : (x : A) → B x) → instance-function-extensionality f g -``` - -### The function extensionality principle with respect to a universe level - -```agda -function-extensionality-Level : (l1 l2 : Level) → UU (lsuc l1 ⊔ lsuc l2) -function-extensionality-Level l1 l2 = - {A : UU l1} {B : A → UU l2} - (f : (x : A) → B x) → based-function-extensionality f -``` - ### The function extensionality axiom -```agda -function-extensionality : UUω -function-extensionality = {l1 l2 : Level} → function-extensionality-Level l1 l2 -``` - Rather than postulating a witness of `function-extensionality` directly, we postulate the constituents of a coherent two-sided inverse to `htpy-eq`. The benefits are that we end up with a single converse map to `htpy-eq`, rather than @@ -244,33 +179,6 @@ module _ ( is-retraction-eq-htpy (eq-htpy H ∙ eq-htpy K)) ``` -### `htpy-eq` preserves inverses - -For any two functions `f g : (x : A) → B x` we have a -[commuting square](foundation-core.commuting-squares-of-maps.md) - -```text - inv - (f = g) ---------> (g = f) - | | - htpy-eq | | htpy-eq - ∨ ∨ - (f ~ g) ---------> (g ~ f). - inv-htpy -``` - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} - where - - compute-htpy-eq-inv : inv-htpy {f = f} {g} ∘ htpy-eq ~ htpy-eq ∘ inv - compute-htpy-eq-inv refl = refl - - compute-inv-htpy-htpy-eq : htpy-eq ∘ inv ~ inv-htpy {f = f} {g} ∘ htpy-eq - compute-inv-htpy-htpy-eq = inv-htpy compute-htpy-eq-inv -``` - ### `eq-htpy` preserves inverses For any two functions `f g : (x : A) → B x` we have a commuting square From 9cbef821443dda24c995d4a57169544bbb10ba55 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 14:41:16 +0000 Subject: [PATCH 07/39] remove unused imports --- .../precategory-of-functors.lagda.md | 1 - ...precategory-of-maps-precategories.lagda.md | 1 - .../archimedean-property-integers.lagda.md | 1 - ...himedean-property-natural-numbers.lagda.md | 1 - ...roperty-positive-rational-numbers.lagda.md | 2 -- .../equality-rational-numbers.lagda.md | 2 -- .../inequality-rational-numbers.lagda.md | 5 --- .../integer-fractions.lagda.md | 1 - ...-arithmetic-standard-finite-types.lagda.md | 1 - .../multiplication-integers.lagda.md | 7 ---- .../multiplication-natural-numbers.lagda.md | 1 - .../positive-integers.lagda.md | 2 -- .../positive-rational-numbers.lagda.md | 2 -- .../rational-numbers.lagda.md | 3 -- ...rtier-delooping-sign-homomorphism.lagda.md | 1 - .../delooping-sign-homomorphism.lagda.md | 1 - .../finite-semigroups.lagda.md | 1 - .../finite-type-groups.lagda.md | 1 - ...mpson-delooping-sign-homomorphism.lagda.md | 1 - .../commuting-prisms-of-maps.lagda.md | 4 +-- .../contractible-maps.lagda.md | 1 - ...-maps-cartesian-products-of-types.lagda.md | 2 -- src/foundation-core/fibers-of-maps.lagda.md | 1 - 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.../functoriality-morphisms-arrows.lagda.md | 1 - src/foundation/homotopy-induction.lagda.md | 1 - src/foundation/identity-systems.lagda.md | 4 --- src/foundation/inhabited-types.lagda.md | 2 -- src/foundation/injective-maps.lagda.md | 1 - .../iterating-families-of-maps.lagda.md | 14 -------- .../large-apartness-relations.lagda.md | 2 -- .../large-binary-relations.lagda.md | 1 - src/foundation/morphisms-cospans.lagda.md | 2 +- src/foundation/morphisms-spans.lagda.md | 2 -- ...stcomposition-dependent-functions.lagda.md | 1 - .../postcomposition-pullbacks.lagda.md | 1 - src/foundation/powersets.lagda.md | 4 --- ...ition-functions-into-subuniverses.lagda.md | 1 - src/foundation/pullback-cones.lagda.md | 13 ------- src/foundation/pullbacks.lagda.md | 10 ------ .../spans-families-of-types.lagda.md | 3 -- .../terminal-spans-families-of-types.lagda.md | 3 +- .../transport-split-type-families.lagda.md | 8 ----- ...dentifications-along-equivalences.lagda.md | 4 +-- .../type-arithmetic-unit-type.lagda.md | 1 - .../uniqueness-set-quotients.lagda.md | 1 - src/foundation/uniqueness-truncation.lagda.md | 1 - .../unital-binary-operations.lagda.md | 2 +- ...e-implies-function-extensionality.lagda.md | 1 - ...sal-property-dependent-pair-types.lagda.md | 2 -- ...property-family-of-fibers-of-maps.lagda.md | 1 - ...iversal-property-identity-systems.lagda.md | 1 - .../weak-function-extensionality.lagda.md | 1 - ...ing-identifications-concatenation.lagda.md | 4 --- .../binary-globular-maps.lagda.md | 1 - src/globular-types/globular-types.lagda.md | 1 - ...pendent-products-reflexive-graphs.lagda.md | 5 --- .../large-reflexive-graphs.lagda.md | 1 - src/group-theory/automorphism-groups.lagda.md | 3 -- src/group-theory/cayleys-theorem.lagda.md | 1 - src/group-theory/group-actions.lagda.md | 1 - .../homotopy-automorphism-groups.lagda.md | 13 ------- .../isomorphisms-semigroups.lagda.md | 1 - ...ultiplication-commutative-monoids.lagda.md | 4 --- .../minkowski-multiplication-monoids.lagda.md | 1 - ...nkowski-multiplication-semigroups.lagda.md | 1 - .../automorphism-groups.lagda.md | 4 --- .../functoriality-vectors.lagda.md | 1 - ...y-approximations-premetric-spaces.lagda.md | 3 -- .../discrete-premetric-structures.lagda.md | 10 ------ ...-functions-isometry-metric-spaces.lagda.md | 7 ---- ...gory-short-isometry-metric-spaces.lagda.md | 7 ---- ...pproximations-in-premetric-spaces.lagda.md | 7 ---- ...y-of-metric-spaces-and-isometries.lagda.md | 6 ---- ...metric-spaces-and-short-functions.lagda.md | 6 ---- .../decidable-total-orders.lagda.md | 1 - src/order-theory/large-inflattices.lagda.md | 3 -- .../least-upper-bounds-posets.lagda.md | 2 -- .../lower-bounds-large-posets.lagda.md | 1 - src/organic-chemistry/ethane.lagda.md | 1 - .../continuation-modalities.lagda.md | 9 ----- .../fiberwise-orthogonal-maps.lagda.md | 26 -------------- ...alizations-at-global-subuniverses.lagda.md | 11 ------ .../functoriality-pullback-hom.lagda.md | 16 --------- ...ty-reflective-global-subuniverses.lagda.md | 19 ----------- .../maps-local-at-maps.lagda.md | 17 ---------- .../pullback-hom.lagda.md | 4 --- .../reflective-global-subuniverses.lagda.md | 13 ------- .../reflective-subuniverses.lagda.md | 5 --- .../types-local-at-maps.lagda.md | 1 - ...alizations-at-global-subuniverses.lagda.md | 4 --- .../apartness-real-numbers.lagda.md | 3 -- ...thmetically-located-dedekind-cuts.lagda.md | 5 --- .../dedekind-real-numbers.lagda.md | 7 ---- ...ality-lower-dedekind-real-numbers.lagda.md | 2 -- .../inequality-real-numbers.lagda.md | 7 ---- ...ality-upper-dedekind-real-numbers.lagda.md | 1 - .../metric-space-of-real-numbers.lagda.md | 6 ---- ...lower-upper-dedekind-real-numbers.lagda.md | 2 -- .../negation-real-numbers.lagda.md | 14 -------- .../rational-real-numbers.lagda.md | 11 ------ .../similarity-real-numbers.lagda.md | 8 ----- .../strict-inequality-real-numbers.lagda.md | 2 -- src/set-theory/baire-space.lagda.md | 2 -- .../cantors-diagonal-argument.lagda.md | 7 ---- src/set-theory/cardinalities.lagda.md | 1 - .../pointed-equivalences.lagda.md | 7 ---- .../pointed-homotopies.lagda.md | 5 --- .../retractions-synthetic-categories.lagda.md | 3 -- .../sections-synthetic-categories.lagda.md | 3 -- .../synthetic-categories.lagda.md | 1 - .../1-acyclic-types.lagda.md | 1 - .../cofibers-of-maps.lagda.md | 1 - .../cofibers-of-pointed-maps.lagda.md | 11 ------ ...functoriality-sequential-colimits.lagda.md | 2 -- .../homotopy-groups.lagda.md | 3 -- .../loop-homotopy-circle.lagda.md | 7 ---- .../multiplication-circle.lagda.md | 3 -- .../smash-products-of-pointed-types.lagda.md | 2 -- .../truncated-acyclic-maps.lagda.md | 2 -- ...rsal-property-sequential-colimits.lagda.md | 1 - .../precategories-with-attributes.lagda.md | 5 --- .../precategories-with-families.lagda.md | 8 ----- .../2-element-decidable-subtypes.lagda.md | 2 -- .../binomial-types.lagda.md | 1 - .../coproduct-types.lagda.md | 1 - .../dependent-pair-types.lagda.md | 1 - .../fibers-of-maps.lagda.md | 1 - .../finite-types.lagda.md | 1 - .../function-types.lagda.md | 1 - .../locally-finite-types.lagda.md | 34 ------------------- .../repetitions-of-values.lagda.md | 1 - .../sigma-decompositions.lagda.md | 1 - .../type-duality.lagda.md | 1 - 155 files changed, 13 insertions(+), 595 deletions(-) diff --git a/src/category-theory/precategory-of-functors.lagda.md b/src/category-theory/precategory-of-functors.lagda.md index a77bc75a50..17626c170b 100644 --- a/src/category-theory/precategory-of-functors.lagda.md +++ b/src/category-theory/precategory-of-functors.lagda.md @@ -21,7 +21,6 @@ open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-pair-types open import foundation.identity-types open import foundation.logical-equivalences -open import foundation.propositions open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-maps-precategories.lagda.md b/src/category-theory/precategory-of-maps-precategories.lagda.md index 9967524c0f..cc303bf840 100644 --- a/src/category-theory/precategory-of-maps-precategories.lagda.md +++ b/src/category-theory/precategory-of-maps-precategories.lagda.md @@ -21,7 +21,6 @@ open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-pair-types open import foundation.identity-types open import foundation.logical-equivalences -open import foundation.propositions open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/archimedean-property-integers.lagda.md b/src/elementary-number-theory/archimedean-property-integers.lagda.md index c96fb799cf..21e49492ed 100644 --- a/src/elementary-number-theory/archimedean-property-integers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-integers.lagda.md @@ -25,7 +25,6 @@ open import foundation.dependent-pair-types open import foundation.existential-quantification open import foundation.identity-types open import foundation.propositional-truncations -open import foundation.transport-along-identifications ```
diff --git a/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md index d9f0edd2bd..a24fbc0a07 100644 --- a/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md @@ -10,7 +10,6 @@ module elementary-number-theory.archimedean-property-natural-numbers where open import elementary-number-theory.euclidean-division-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.dependent-pair-types diff --git a/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md index 532e026317..0a61a1bf8e 100644 --- a/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md @@ -12,7 +12,6 @@ module elementary-number-theory.archimedean-property-positive-rational-numbers w open import elementary-number-theory.archimedean-property-rational-numbers open import elementary-number-theory.integers open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers open import elementary-number-theory.natural-numbers open import elementary-number-theory.nonzero-natural-numbers open import elementary-number-theory.positive-rational-numbers @@ -20,7 +19,6 @@ open import elementary-number-theory.rational-numbers open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-transport open import foundation.dependent-pair-types open import foundation.existential-quantification open import foundation.identity-types diff --git a/src/elementary-number-theory/equality-rational-numbers.lagda.md b/src/elementary-number-theory/equality-rational-numbers.lagda.md index 6aa0e27499..aaf8ae64f0 100644 --- a/src/elementary-number-theory/equality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/equality-rational-numbers.lagda.md @@ -7,9 +7,7 @@ module elementary-number-theory.equality-rational-numbers where
Imports ```agda -open import elementary-number-theory.equality-integers open import elementary-number-theory.integer-fractions -open import elementary-number-theory.positive-integers open import elementary-number-theory.rational-numbers open import elementary-number-theory.reduced-integer-fractions diff --git a/src/elementary-number-theory/inequality-rational-numbers.lagda.md b/src/elementary-number-theory/inequality-rational-numbers.lagda.md index 12ddd6f34a..c8956f0ff1 100644 --- a/src/elementary-number-theory/inequality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-rational-numbers.lagda.md @@ -15,18 +15,13 @@ open import elementary-number-theory.difference-rational-numbers open import elementary-number-theory.inequality-integer-fractions open import elementary-number-theory.inequality-integers open import elementary-number-theory.integer-fractions -open import elementary-number-theory.integers open import elementary-number-theory.multiplication-integers open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers open import elementary-number-theory.rational-numbers open import elementary-number-theory.reduced-integer-fractions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.conjunction open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types diff --git a/src/elementary-number-theory/integer-fractions.lagda.md b/src/elementary-number-theory/integer-fractions.lagda.md index 246ccf0e7c..c2bc0db1a8 100644 --- a/src/elementary-number-theory/integer-fractions.lagda.md +++ b/src/elementary-number-theory/integer-fractions.lagda.md @@ -12,7 +12,6 @@ open import elementary-number-theory.greatest-common-divisor-integers open import elementary-number-theory.integers open import elementary-number-theory.multiplication-integers open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.positive-and-negative-integers open import elementary-number-theory.positive-integers open import foundation.action-on-identifications-functions diff --git a/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md b/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md index e7205258f8..302d0c9537 100644 --- a/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md @@ -26,7 +26,6 @@ open import foundation.equivalences open import foundation.function-types open import foundation.identity-types open import foundation.injective-maps -open import foundation.sets open import foundation.split-surjective-maps open import foundation.surjective-maps open import foundation.universe-levels diff --git a/src/elementary-number-theory/multiplication-integers.lagda.md b/src/elementary-number-theory/multiplication-integers.lagda.md index d8c89edf3b..9854c6cf70 100644 --- a/src/elementary-number-theory/multiplication-integers.lagda.md +++ b/src/elementary-number-theory/multiplication-integers.lagda.md @@ -9,16 +9,12 @@ module elementary-number-theory.multiplication-integers where ```agda open import elementary-number-theory.addition-integers open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.addition-positive-and-negative-integers open import elementary-number-theory.difference-integers open import elementary-number-theory.equality-integers -open import elementary-number-theory.inequality-integers open import elementary-number-theory.integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.positive-integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions @@ -29,10 +25,7 @@ open import foundation.function-types open import foundation.identity-types open import foundation.injective-maps open import foundation.interchange-law -open import foundation.sets -open import foundation.transport-along-identifications open import foundation.type-arithmetic-empty-type -open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/multiplication-natural-numbers.lagda.md b/src/elementary-number-theory/multiplication-natural-numbers.lagda.md index c4d6dd3e5f..b725a1a851 100644 --- a/src/elementary-number-theory/multiplication-natural-numbers.lagda.md +++ b/src/elementary-number-theory/multiplication-natural-numbers.lagda.md @@ -20,7 +20,6 @@ open import foundation.identity-types open import foundation.injective-maps open import foundation.interchange-law open import foundation.negated-equality -open import foundation.sets ```
diff --git a/src/elementary-number-theory/positive-integers.lagda.md b/src/elementary-number-theory/positive-integers.lagda.md index bc942b406f..d122134e21 100644 --- a/src/elementary-number-theory/positive-integers.lagda.md +++ b/src/elementary-number-theory/positive-integers.lagda.md @@ -23,8 +23,6 @@ open import foundation.existential-quantification open import foundation.function-types open import foundation.identity-types open import foundation.propositions -open import foundation.retractions -open import foundation.sections open import foundation.sets open import foundation.subtypes open import foundation.surjective-maps diff --git a/src/elementary-number-theory/positive-rational-numbers.lagda.md b/src/elementary-number-theory/positive-rational-numbers.lagda.md index 78ae9a569d..439940ac49 100644 --- a/src/elementary-number-theory/positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/positive-rational-numbers.lagda.md @@ -9,7 +9,6 @@ module elementary-number-theory.positive-rational-numbers where
Imports ```agda -open import elementary-number-theory.addition-integer-fractions open import elementary-number-theory.addition-rational-numbers open import elementary-number-theory.additive-group-of-rational-numbers open import elementary-number-theory.cross-multiplication-difference-integer-fractions @@ -30,7 +29,6 @@ open import elementary-number-theory.positive-and-negative-integers open import elementary-number-theory.positive-integer-fractions open import elementary-number-theory.positive-integers open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions open import elementary-number-theory.strict-inequality-integers open import elementary-number-theory.strict-inequality-rational-numbers diff --git a/src/elementary-number-theory/rational-numbers.lagda.md b/src/elementary-number-theory/rational-numbers.lagda.md index 001db38b16..732f9bb66f 100644 --- a/src/elementary-number-theory/rational-numbers.lagda.md +++ b/src/elementary-number-theory/rational-numbers.lagda.md @@ -13,7 +13,6 @@ open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers open import elementary-number-theory.mediant-integer-fractions open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.positive-and-negative-integers open import elementary-number-theory.positive-integers open import elementary-number-theory.reduced-integer-fractions @@ -28,8 +27,6 @@ open import foundation.reflecting-maps-equivalence-relations open import foundation.retracts-of-types open import foundation.sections open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps open import foundation.universe-levels open import set-theory.countable-sets diff --git a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md index ecac11c0d1..bf4f606cc2 100644 --- a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md @@ -33,7 +33,6 @@ open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type open import foundation.universe-levels -open import group-theory.concrete-groups open import group-theory.homomorphisms-concrete-groups open import group-theory.homomorphisms-groups open import group-theory.isomorphisms-groups diff --git a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md index cdb615bc50..4cc333bf45 100644 --- a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md @@ -60,7 +60,6 @@ open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation.whiskering-identifications-concatenation -open import group-theory.concrete-groups open import group-theory.generating-sets-groups open import group-theory.groups open import group-theory.homomorphisms-concrete-groups diff --git a/src/finite-group-theory/finite-semigroups.lagda.md b/src/finite-group-theory/finite-semigroups.lagda.md index 80e46d4e23..40f90172d9 100644 --- a/src/finite-group-theory/finite-semigroups.lagda.md +++ b/src/finite-group-theory/finite-semigroups.lagda.md @@ -19,7 +19,6 @@ open import foundation.mere-equivalences open import foundation.propositions open import foundation.set-truncations open import foundation.sets -open import foundation.subtypes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/finite-group-theory/finite-type-groups.lagda.md b/src/finite-group-theory/finite-type-groups.lagda.md index 4a1905d8df..4b7783f027 100644 --- a/src/finite-group-theory/finite-type-groups.lagda.md +++ b/src/finite-group-theory/finite-type-groups.lagda.md @@ -12,7 +12,6 @@ module finite-group-theory.finite-type-groups where open import elementary-number-theory.natural-numbers open import foundation.0-connected-types -open import foundation.1-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-dependent-pair-types diff --git a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md index 5e6d56f993..b416cd96b6 100644 --- a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md @@ -47,7 +47,6 @@ open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type open import foundation.universe-levels -open import group-theory.concrete-groups open import group-theory.groups open import group-theory.homomorphisms-concrete-groups open import group-theory.homomorphisms-groups diff --git a/src/foundation-core/commuting-prisms-of-maps.lagda.md b/src/foundation-core/commuting-prisms-of-maps.lagda.md index 68a2637fd1..40f37dea92 100644 --- a/src/foundation-core/commuting-prisms-of-maps.lagda.md +++ b/src/foundation-core/commuting-prisms-of-maps.lagda.md @@ -9,14 +9,14 @@ module foundation-core.commuting-prisms-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.commuting-pentagons-of-identifications -open import foundation.identity-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation open import foundation-core.commuting-squares-of-maps open import foundation-core.commuting-triangles-of-maps open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.whiskering-identifications-concatenation ```
diff --git a/src/foundation-core/contractible-maps.lagda.md b/src/foundation-core/contractible-maps.lagda.md index 2c2d1e9c41..12610e8c3d 100644 --- a/src/foundation-core/contractible-maps.lagda.md +++ b/src/foundation-core/contractible-maps.lagda.md @@ -16,7 +16,6 @@ open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.retractions open import foundation-core.sections diff --git a/src/foundation-core/diagonal-maps-cartesian-products-of-types.lagda.md b/src/foundation-core/diagonal-maps-cartesian-products-of-types.lagda.md index afab6f6e6a..7674be4787 100644 --- a/src/foundation-core/diagonal-maps-cartesian-products-of-types.lagda.md +++ b/src/foundation-core/diagonal-maps-cartesian-products-of-types.lagda.md @@ -15,8 +15,6 @@ open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps -open import foundation-core.function-types -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.retractions diff --git a/src/foundation-core/fibers-of-maps.lagda.md b/src/foundation-core/fibers-of-maps.lagda.md index 12a441cd2d..4728163858 100644 --- a/src/foundation-core/fibers-of-maps.lagda.md +++ b/src/foundation-core/fibers-of-maps.lagda.md @@ -16,7 +16,6 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.postcomposition-functions open import foundation-core.retractions open import foundation-core.sections open import foundation-core.transport-along-identifications diff --git a/src/foundation-core/functoriality-dependent-pair-types.lagda.md b/src/foundation-core/functoriality-dependent-pair-types.lagda.md index f3d941d326..9e6ceb2fb5 100644 --- a/src/foundation-core/functoriality-dependent-pair-types.lagda.md +++ b/src/foundation-core/functoriality-dependent-pair-types.lagda.md @@ -7,7 +7,6 @@ module foundation-core.functoriality-dependent-pair-types where
Imports ```agda -open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.transport-along-identifications diff --git a/src/foundation-core/invertible-maps.lagda.md b/src/foundation-core/invertible-maps.lagda.md index c4af35f5a7..b958fa00ab 100644 --- a/src/foundation-core/invertible-maps.lagda.md +++ b/src/foundation-core/invertible-maps.lagda.md @@ -7,7 +7,6 @@ module foundation-core.invertible-maps where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/action-on-homotopies-functions.lagda.md b/src/foundation/action-on-homotopies-functions.lagda.md index 0bb5100c4c..e8dbeeaaba 100644 --- a/src/foundation/action-on-homotopies-functions.lagda.md +++ b/src/foundation/action-on-homotopies-functions.lagda.md @@ -14,9 +14,7 @@ open import foundation.function-extensionality open import foundation.homotopy-induction open import foundation.universe-levels -open import foundation-core.constant-maps open import foundation-core.contractible-types -open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types ``` diff --git a/src/foundation/axiom-of-choice.lagda.md b/src/foundation/axiom-of-choice.lagda.md index 338419569b..aa6b055a68 100644 --- a/src/foundation/axiom-of-choice.lagda.md +++ b/src/foundation/axiom-of-choice.lagda.md @@ -13,7 +13,6 @@ open import foundation.functoriality-propositional-truncation open import foundation.inhabited-types open import foundation.postcomposition-functions open import foundation.projective-types -open import foundation.propositional-truncations open import foundation.sections open import foundation.split-surjective-maps open import foundation.surjective-maps diff --git a/src/foundation/binary-dependent-identifications.lagda.md b/src/foundation/binary-dependent-identifications.lagda.md index 28877b6bcd..325d574d1e 100644 --- a/src/foundation/binary-dependent-identifications.lagda.md +++ b/src/foundation/binary-dependent-identifications.lagda.md @@ -8,8 +8,9 @@ module foundation.binary-dependent-identifications where ```agda open import foundation.binary-transport -open import foundation.identity-types open import foundation.universe-levels + +open import foundation-core.identity-types ```
diff --git a/src/foundation/booleans.lagda.md b/src/foundation/booleans.lagda.md index 712d69cc6b..eedc11aacd 100644 --- a/src/foundation/booleans.lagda.md +++ b/src/foundation/booleans.lagda.md @@ -8,7 +8,6 @@ module foundation.booleans where ```agda open import foundation.decidable-equality -open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.discrete-types open import foundation.involutions @@ -24,7 +23,6 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.injective-maps open import foundation-core.negation open import foundation-core.propositions open import foundation-core.sections diff --git a/src/foundation/cantors-theorem.lagda.md b/src/foundation/cantors-theorem.lagda.md index a69aefcb83..f44e28067a 100644 --- a/src/foundation/cantors-theorem.lagda.md +++ b/src/foundation/cantors-theorem.lagda.md @@ -22,7 +22,6 @@ open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.fibers-of-maps -open import foundation-core.propositions open import logic.de-morgan-propositions open import logic.de-morgan-subtypes diff --git a/src/foundation/category-of-sets.lagda.md b/src/foundation/category-of-sets.lagda.md index 7587216503..05ad4d10cd 100644 --- a/src/foundation/category-of-sets.lagda.md +++ b/src/foundation/category-of-sets.lagda.md @@ -18,13 +18,8 @@ open import category-theory.large-precategories open import category-theory.limits-precategories open import category-theory.natural-transformations-functors-precategories open import category-theory.precategories -open import category-theory.right-extensions-precategories -open import category-theory.right-kan-extensions-precategories -open import category-theory.terminal-category -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-extensionality-axiom @@ -32,7 +27,6 @@ open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types open import foundation.isomorphisms-of-sets -open import foundation.multivariable-homotopies open import foundation.raising-universe-levels open import foundation.retractions open import foundation.sections diff --git a/src/foundation/connected-maps.lagda.md b/src/foundation/connected-maps.lagda.md index 850da31ae8..8dcb862a92 100644 --- a/src/foundation/connected-maps.lagda.md +++ b/src/foundation/connected-maps.lagda.md @@ -9,7 +9,6 @@ module foundation.connected-maps where ```agda open import foundation.connected-types open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction diff --git a/src/foundation/connected-types.lagda.md b/src/foundation/connected-types.lagda.md index 7b8af429f7..cc22ef2f73 100644 --- a/src/foundation/connected-types.lagda.md +++ b/src/foundation/connected-types.lagda.md @@ -19,7 +19,6 @@ open import foundation.truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import foundation-core.constant-maps open import foundation-core.contractible-maps open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types diff --git a/src/foundation/constant-type-families.lagda.md b/src/foundation/constant-type-families.lagda.md index 15db228460..80e1f984df 100644 --- a/src/foundation/constant-type-families.lagda.md +++ b/src/foundation/constant-type-families.lagda.md @@ -11,12 +11,12 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.identity-types -open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications open import foundation-core.dependent-identifications open import foundation-core.equivalences +open import foundation-core.transport-along-identifications ```
diff --git a/src/foundation/continuations.lagda.md b/src/foundation/continuations.lagda.md index 9ccca39732..f959426927 100644 --- a/src/foundation/continuations.lagda.md +++ b/src/foundation/continuations.lagda.md @@ -7,36 +7,22 @@ module foundation.continuations where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.empty-types -open import foundation.equality-cartesian-product-types open import foundation.evaluation-functions -open import foundation.logical-equivalences -open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-function-types -open import foundation.type-arithmetic-empty-type open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types open import foundation.universal-property-empty-type open import foundation.universal-property-equivalences open import foundation.universe-levels -open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.retractions -open import foundation-core.sections -open import foundation-core.transport-along-identifications open import orthogonal-factorization-systems.extensions-maps -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities ```
diff --git a/src/foundation/cospans.lagda.md b/src/foundation/cospans.lagda.md index 41f0b583d6..ac8a374d21 100644 --- a/src/foundation/cospans.lagda.md +++ b/src/foundation/cospans.lagda.md @@ -8,10 +8,7 @@ module foundation.cospans where ```agda open import foundation.dependent-pair-types -open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction open import foundation.structure-identity-principle -open import foundation.univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/diagonal-maps-of-types.lagda.md b/src/foundation/diagonal-maps-of-types.lagda.md index 9983e97332..8876d05884 100644 --- a/src/foundation/diagonal-maps-of-types.lagda.md +++ b/src/foundation/diagonal-maps-of-types.lagda.md @@ -9,27 +9,19 @@ module foundation.diagonal-maps-of-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-cartesian-product-types open import foundation.function-extensionality open import foundation.function-extensionality-axiom -open import foundation.functoriality-dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.retracts-of-types open import foundation.transposition-identifications-along-equivalences open import foundation.universe-levels -open import foundation-core.cartesian-product-types open import foundation-core.constant-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types +open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.injective-maps -open import foundation-core.propositions -open import foundation-core.retractions -open import foundation-core.sections ```
diff --git a/src/foundation/disjoint-subtypes.lagda.md b/src/foundation/disjoint-subtypes.lagda.md index e21739bbd5..1c8072a0ed 100644 --- a/src/foundation/disjoint-subtypes.lagda.md +++ b/src/foundation/disjoint-subtypes.lagda.md @@ -10,7 +10,6 @@ module foundation.disjoint-subtypes where open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.empty-types -open import foundation.intersections-subtypes open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/foundation/double-arrows.lagda.md b/src/foundation/double-arrows.lagda.md index aac5db2de6..a6c2d5afe3 100644 --- a/src/foundation/double-arrows.lagda.md +++ b/src/foundation/double-arrows.lagda.md @@ -7,9 +7,10 @@ module foundation.double-arrows where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels + +open import foundation-core.cartesian-product-types ```
diff --git a/src/foundation/equality-cartesian-product-types.lagda.md b/src/foundation/equality-cartesian-product-types.lagda.md index b500eb9d43..068c6de89a 100644 --- a/src/foundation/equality-cartesian-product-types.lagda.md +++ b/src/foundation/equality-cartesian-product-types.lagda.md @@ -13,7 +13,6 @@ open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies diff --git a/src/foundation/evaluation-functions.lagda.md b/src/foundation/evaluation-functions.lagda.md index 45faaf7850..9503610877 100644 --- a/src/foundation/evaluation-functions.lagda.md +++ b/src/foundation/evaluation-functions.lagda.md @@ -7,10 +7,7 @@ module foundation.evaluation-functions where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.universe-levels - -open import foundation-core.identity-types ```
diff --git a/src/foundation/exclusive-sum.lagda.md b/src/foundation/exclusive-sum.lagda.md index 7282c9e05d..e47925ccc5 100644 --- a/src/foundation/exclusive-sum.lagda.md +++ b/src/foundation/exclusive-sum.lagda.md @@ -14,13 +14,11 @@ open import foundation.dependent-pair-types open import foundation.negation open import foundation.propositional-extensionality open import foundation.symmetric-operations -open import foundation.universal-quantification open import foundation.universe-levels open import foundation.unordered-pairs open import foundation-core.cartesian-product-types open import foundation-core.decidable-propositions -open import foundation-core.embeddings open import foundation-core.empty-types open import foundation-core.equality-dependent-pair-types open import foundation-core.identity-types diff --git a/src/foundation/existential-quantification.lagda.md b/src/foundation/existential-quantification.lagda.md index 13a376ea80..370906429c 100644 --- a/src/foundation/existential-quantification.lagda.md +++ b/src/foundation/existential-quantification.lagda.md @@ -9,7 +9,6 @@ module foundation.existential-quantification where ```agda open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation open import foundation.logical-equivalences open import foundation.propositional-extensionality open import foundation.propositional-truncations @@ -18,7 +17,6 @@ open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions ``` diff --git a/src/foundation/function-extensionality-axiom.lagda.md b/src/foundation/function-extensionality-axiom.lagda.md index 3335f2bf9d..064197ecd1 100644 --- a/src/foundation/function-extensionality-axiom.lagda.md +++ b/src/foundation/function-extensionality-axiom.lagda.md @@ -7,20 +7,14 @@ module foundation.function-extensionality-axiom where
Imports ```agda -open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.dependent-pair-types open import foundation.evaluation-functions -open import foundation.implicit-function-types open import foundation.universe-levels -open import foundation-core.coherently-invertible-maps open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.retractions -open import foundation-core.sections ```
diff --git a/src/foundation/function-extensionality.lagda.md b/src/foundation/function-extensionality.lagda.md index a3fcfb1a31..d26c3c48c8 100644 --- a/src/foundation/function-extensionality.lagda.md +++ b/src/foundation/function-extensionality.lagda.md @@ -12,7 +12,6 @@ module foundation.function-extensionality where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.evaluation-functions open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation/functoriality-morphisms-arrows.lagda.md b/src/foundation/functoriality-morphisms-arrows.lagda.md index 8d9b3b82f2..aee689e627 100644 --- a/src/foundation/functoriality-morphisms-arrows.lagda.md +++ b/src/foundation/functoriality-morphisms-arrows.lagda.md @@ -32,7 +32,6 @@ open import foundation.precomposition-functions open import foundation.pullback-cones open import foundation.pullbacks open import foundation.retractions -open import foundation.retracts-of-maps open import foundation.sections open import foundation.standard-pullbacks open import foundation.universe-levels diff --git a/src/foundation/homotopy-induction.lagda.md b/src/foundation/homotopy-induction.lagda.md index f2d5add7c9..0e79b789dd 100644 --- a/src/foundation/homotopy-induction.lagda.md +++ b/src/foundation/homotopy-induction.lagda.md @@ -11,7 +11,6 @@ open import foundation.dependent-pair-types open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.identity-systems -open import foundation.universal-property-dependent-pair-types open import foundation.universal-property-identity-systems open import foundation.universe-levels diff --git a/src/foundation/identity-systems.lagda.md b/src/foundation/identity-systems.lagda.md index 76c39abcc7..f36c1352dd 100644 --- a/src/foundation/identity-systems.lagda.md +++ b/src/foundation/identity-systems.lagda.md @@ -14,11 +14,7 @@ open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.families-of-equivalences -open import foundation-core.function-types -open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types -open import foundation-core.propositions -open import foundation-core.retractions open import foundation-core.sections open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications diff --git a/src/foundation/inhabited-types.lagda.md b/src/foundation/inhabited-types.lagda.md index d53273c06a..ff290bc467 100644 --- a/src/foundation/inhabited-types.lagda.md +++ b/src/foundation/inhabited-types.lagda.md @@ -7,7 +7,6 @@ module foundation.inhabited-types where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equality-dependent-function-types @@ -19,7 +18,6 @@ open import foundation.univalence open import foundation.universe-levels open import foundation-core.equivalences -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.torsorial-type-families diff --git a/src/foundation/injective-maps.lagda.md b/src/foundation/injective-maps.lagda.md index 521e90d66d..3026f03a10 100644 --- a/src/foundation/injective-maps.lagda.md +++ b/src/foundation/injective-maps.lagda.md @@ -9,7 +9,6 @@ open import foundation-core.injective-maps public
Imports ```agda -open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality diff --git a/src/foundation/iterating-families-of-maps.lagda.md b/src/foundation/iterating-families-of-maps.lagda.md index d0f5296399..968976eaf1 100644 --- a/src/foundation/iterating-families-of-maps.lagda.md +++ b/src/foundation/iterating-families-of-maps.lagda.md @@ -7,29 +7,15 @@ module foundation.iterating-families-of-maps where
Imports ```agda -open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers -open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplicative-monoid-of-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions -open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.dependent-homotopies open import foundation.dependent-identifications -open import foundation.dependent-pair-types open import foundation.iterating-functions open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps -open import foundation-core.endomorphisms -open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.sets - -open import group-theory.monoid-actions ```
diff --git a/src/foundation/large-apartness-relations.lagda.md b/src/foundation/large-apartness-relations.lagda.md index 49844edacb..b87c9a5b09 100644 --- a/src/foundation/large-apartness-relations.lagda.md +++ b/src/foundation/large-apartness-relations.lagda.md @@ -7,8 +7,6 @@ module foundation.large-apartness-relations where
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.disjunction open import foundation.identity-types open import foundation.large-binary-relations open import foundation.negated-equality diff --git a/src/foundation/large-binary-relations.lagda.md b/src/foundation/large-binary-relations.lagda.md index 9077016804..2a4b155124 100644 --- a/src/foundation/large-binary-relations.lagda.md +++ b/src/foundation/large-binary-relations.lagda.md @@ -8,7 +8,6 @@ module foundation.large-binary-relations where ```agda open import foundation.binary-relations -open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.disjunction open import foundation.universe-levels diff --git a/src/foundation/morphisms-cospans.lagda.md b/src/foundation/morphisms-cospans.lagda.md index b3cdf33eb6..4eade956fa 100644 --- a/src/foundation/morphisms-cospans.lagda.md +++ b/src/foundation/morphisms-cospans.lagda.md @@ -7,11 +7,11 @@ module foundation.morphisms-cospans where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.cospans open import foundation.dependent-pair-types open import foundation.universe-levels +open import foundation-core.cartesian-product-types open import foundation-core.commuting-triangles-of-maps ``` diff --git a/src/foundation/morphisms-spans.lagda.md b/src/foundation/morphisms-spans.lagda.md index 0632d4ed00..10cddfab98 100644 --- a/src/foundation/morphisms-spans.lagda.md +++ b/src/foundation/morphisms-spans.lagda.md @@ -12,9 +12,7 @@ open import foundation.spans open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps open import foundation-core.commuting-triangles-of-maps -open import foundation-core.operations-spans ```
diff --git a/src/foundation/postcomposition-dependent-functions.lagda.md b/src/foundation/postcomposition-dependent-functions.lagda.md index d560165ad9..f01cde3833 100644 --- a/src/foundation/postcomposition-dependent-functions.lagda.md +++ b/src/foundation/postcomposition-dependent-functions.lagda.md @@ -16,7 +16,6 @@ open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-maps -open import foundation-core.function-types open import foundation-core.identity-types ``` diff --git a/src/foundation/postcomposition-pullbacks.lagda.md b/src/foundation/postcomposition-pullbacks.lagda.md index 255b8b04fd..7b3dc4fee2 100644 --- a/src/foundation/postcomposition-pullbacks.lagda.md +++ b/src/foundation/postcomposition-pullbacks.lagda.md @@ -21,7 +21,6 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types -open import foundation-core.homotopies open import foundation-core.postcomposition-functions open import foundation-core.pullbacks open import foundation-core.universal-property-pullbacks diff --git a/src/foundation/powersets.lagda.md b/src/foundation/powersets.lagda.md index b375489232..e40e0a8090 100644 --- a/src/foundation/powersets.lagda.md +++ b/src/foundation/powersets.lagda.md @@ -8,7 +8,6 @@ module foundation.powersets where ```agda open import foundation.dependent-pair-types -open import foundation.embeddings open import foundation.empty-types open import foundation.identity-types open import foundation.large-locale-of-propositions @@ -30,9 +29,6 @@ open import order-theory.large-meet-semilattices open import order-theory.large-posets open import order-theory.large-preorders open import order-theory.large-suplattices -open import order-theory.meet-semilattices -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders open import order-theory.posets open import order-theory.preorders open import order-theory.similarity-of-elements-large-posets diff --git a/src/foundation/precomposition-functions-into-subuniverses.lagda.md b/src/foundation/precomposition-functions-into-subuniverses.lagda.md index 73604dff9d..c6dcd9527c 100644 --- a/src/foundation/precomposition-functions-into-subuniverses.lagda.md +++ b/src/foundation/precomposition-functions-into-subuniverses.lagda.md @@ -17,7 +17,6 @@ open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.retractions diff --git a/src/foundation/pullback-cones.lagda.md b/src/foundation/pullback-cones.lagda.md index 8c6d7ad7d3..5a098e4403 100644 --- a/src/foundation/pullback-cones.lagda.md +++ b/src/foundation/pullback-cones.lagda.md @@ -7,36 +7,23 @@ module foundation.pullback-cones where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.cones-over-cospan-diagrams open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction open import foundation.identity-types -open import foundation.multivariable-homotopies open import foundation.pullbacks open import foundation.standard-pullbacks -open import foundation.structure-identity-principle open import foundation.unit-type open import foundation.universal-property-cartesian-product-types open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-maps -open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-pair-types open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.torsorial-type-families -open import foundation-core.transport-along-identifications open import foundation-core.universal-property-pullbacks -open import foundation-core.whiskering-identifications-concatenation ```
diff --git a/src/foundation/pullbacks.lagda.md b/src/foundation/pullbacks.lagda.md index 790d188583..db2de5b6a1 100644 --- a/src/foundation/pullbacks.lagda.md +++ b/src/foundation/pullbacks.lagda.md @@ -17,32 +17,22 @@ open import foundation.dependent-pair-types open import foundation.dependent-sums-pullbacks open import foundation.descent-equivalences open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-extensionality-axiom -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-function-types open import foundation.standard-pullbacks open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.cartesian-product-types -open import foundation-core.constant-maps open import foundation-core.contractible-types -open import foundation-core.diagonal-maps-cartesian-products-of-types open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.postcomposition-functions open import foundation-core.propositions -open import foundation-core.retractions -open import foundation-core.sections open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications open import foundation-core.whiskering-identifications-concatenation diff --git a/src/foundation/spans-families-of-types.lagda.md b/src/foundation/spans-families-of-types.lagda.md index 9a6b00a030..5ee8aecb7e 100644 --- a/src/foundation/spans-families-of-types.lagda.md +++ b/src/foundation/spans-families-of-types.lagda.md @@ -9,9 +9,6 @@ module foundation.spans-families-of-types where ```agda open import foundation.dependent-pair-types open import foundation.universe-levels - -open import foundation-core.equivalences -open import foundation-core.function-types ```
diff --git a/src/foundation/terminal-spans-families-of-types.lagda.md b/src/foundation/terminal-spans-families-of-types.lagda.md index 6b08b3e90f..697d998b8e 100644 --- a/src/foundation/terminal-spans-families-of-types.lagda.md +++ b/src/foundation/terminal-spans-families-of-types.lagda.md @@ -7,10 +7,11 @@ module foundation.terminal-spans-families-of-types where
Imports ```agda -open import foundation.contractible-types open import foundation.morphisms-spans-families-of-types open import foundation.spans-families-of-types open import foundation.universe-levels + +open import foundation-core.contractible-types ```
diff --git a/src/foundation/transport-split-type-families.lagda.md b/src/foundation/transport-split-type-families.lagda.md index 39cc5cf77f..0b2e91bc07 100644 --- a/src/foundation/transport-split-type-families.lagda.md +++ b/src/foundation/transport-split-type-families.lagda.md @@ -7,19 +7,11 @@ module foundation.transport-split-type-families where
Imports ```agda -open import elementary-number-theory.natural-numbers - -open import foundation.action-on-equivalences-functions -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality open import foundation.equivalence-injective-type-families open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.iterated-dependent-product-types open import foundation.transport-along-identifications -open import foundation.unit-type open import foundation.univalent-type-families open import foundation.universal-property-identity-systems open import foundation.universe-levels diff --git a/src/foundation/transposition-identifications-along-equivalences.lagda.md b/src/foundation/transposition-identifications-along-equivalences.lagda.md index ef7e0b1cc7..9870736681 100644 --- a/src/foundation/transposition-identifications-along-equivalences.lagda.md +++ b/src/foundation/transposition-identifications-along-equivalences.lagda.md @@ -9,14 +9,12 @@ module foundation.transposition-identifications-along-equivalences where ```agda open import foundation.action-on-identifications-functions open import foundation.commuting-triangles-of-identifications -open import foundation.dependent-pair-types open import foundation.identity-types open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation open import foundation-core.equivalences open import foundation-core.homotopies +open import foundation-core.whiskering-identifications-concatenation ```
diff --git a/src/foundation/type-arithmetic-unit-type.lagda.md b/src/foundation/type-arithmetic-unit-type.lagda.md index b7be04701d..92febc1ec5 100644 --- a/src/foundation/type-arithmetic-unit-type.lagda.md +++ b/src/foundation/type-arithmetic-unit-type.lagda.md @@ -15,7 +15,6 @@ open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.identity-types open import foundation-core.retractions open import foundation-core.sections ``` diff --git a/src/foundation/uniqueness-set-quotients.lagda.md b/src/foundation/uniqueness-set-quotients.lagda.md index f2afbd97e3..386076acce 100644 --- a/src/foundation/uniqueness-set-quotients.lagda.md +++ b/src/foundation/uniqueness-set-quotients.lagda.md @@ -10,7 +10,6 @@ module foundation.uniqueness-set-quotients where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.reflecting-maps-equivalence-relations open import foundation.sets diff --git a/src/foundation/uniqueness-truncation.lagda.md b/src/foundation/uniqueness-truncation.lagda.md index d8b7fadaa0..25971b85f3 100644 --- a/src/foundation/uniqueness-truncation.lagda.md +++ b/src/foundation/uniqueness-truncation.lagda.md @@ -7,7 +7,6 @@ module foundation.uniqueness-truncation where
Imports ```agda -open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/unital-binary-operations.lagda.md b/src/foundation/unital-binary-operations.lagda.md index 5c343797cf..ae3ffd6106 100644 --- a/src/foundation/unital-binary-operations.lagda.md +++ b/src/foundation/unital-binary-operations.lagda.md @@ -11,11 +11,11 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation open import foundation-core.cartesian-product-types open import foundation-core.homotopies open import foundation-core.identity-types +open import foundation-core.whiskering-identifications-concatenation ```
diff --git a/src/foundation/univalence-implies-function-extensionality.lagda.md b/src/foundation/univalence-implies-function-extensionality.lagda.md index a082f8d56b..a0d8b50ddc 100644 --- a/src/foundation/univalence-implies-function-extensionality.lagda.md +++ b/src/foundation/univalence-implies-function-extensionality.lagda.md @@ -9,7 +9,6 @@ module foundation.univalence-implies-function-extensionality where ```agda open import foundation.dependent-pair-types open import foundation.equivalence-induction -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.postcomposition-functions open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/universal-property-dependent-pair-types.lagda.md b/src/foundation/universal-property-dependent-pair-types.lagda.md index 54b12615b2..dcd8364df1 100644 --- a/src/foundation/universal-property-dependent-pair-types.lagda.md +++ b/src/foundation/universal-property-dependent-pair-types.lagda.md @@ -15,8 +15,6 @@ open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.retractions -open import foundation-core.sections ```
diff --git a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md index 4a72519240..b67eb5fad9 100644 --- a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md +++ b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md @@ -16,7 +16,6 @@ open import foundation.function-extensionality-axiom open import foundation.subtype-identity-principle open import foundation.universe-levels -open import foundation-core.constant-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/universal-property-identity-systems.lagda.md b/src/foundation/universal-property-identity-systems.lagda.md index a29595fa9d..b0e32181a0 100644 --- a/src/foundation/universal-property-identity-systems.lagda.md +++ b/src/foundation/universal-property-identity-systems.lagda.md @@ -13,7 +13,6 @@ open import foundation.universal-property-contractible-types open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels -open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.torsorial-type-families diff --git a/src/foundation/weak-function-extensionality.lagda.md b/src/foundation/weak-function-extensionality.lagda.md index be33e1492c..39801af669 100644 --- a/src/foundation/weak-function-extensionality.lagda.md +++ b/src/foundation/weak-function-extensionality.lagda.md @@ -11,7 +11,6 @@ open import foundation.action-on-identifications-functions open import foundation.decidable-equality open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation/whiskering-identifications-concatenation.lagda.md b/src/foundation/whiskering-identifications-concatenation.lagda.md index c2e632249a..c37fbc64cc 100644 --- a/src/foundation/whiskering-identifications-concatenation.lagda.md +++ b/src/foundation/whiskering-identifications-concatenation.lagda.md @@ -9,15 +9,11 @@ open import foundation-core.whiskering-identifications-concatenation public
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.identity-types open import foundation.universe-levels -open import foundation.whiskering-operations open import foundation-core.equivalences -open import foundation-core.function-types -open import foundation-core.homotopies ```
diff --git a/src/globular-types/binary-globular-maps.lagda.md b/src/globular-types/binary-globular-maps.lagda.md index aa89346264..cc3ec422c4 100644 --- a/src/globular-types/binary-globular-maps.lagda.md +++ b/src/globular-types/binary-globular-maps.lagda.md @@ -11,7 +11,6 @@ module globular-types.binary-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/globular-types.lagda.md b/src/globular-types/globular-types.lagda.md index 11ecfe44fa..84c0ef6e25 100644 --- a/src/globular-types/globular-types.lagda.md +++ b/src/globular-types/globular-types.lagda.md @@ -10,7 +10,6 @@ module globular-types.globular-types where ```agda open import foundation.dependent-pair-types -open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md index f0cee7443a..562665d1c4 100644 --- a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md @@ -8,7 +8,6 @@ module graph-theory.dependent-products-reflexive-graphs where ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-dependent-identifications open import foundation.binary-transport open import foundation.commuting-squares-of-identifications open import foundation.contractible-types @@ -22,19 +21,15 @@ open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies -open import foundation.homotopy-induction open import foundation.identity-types -open import foundation.reflexive-relations open import foundation.retractions open import foundation.sections open import foundation.structure-identity-principle open import foundation.torsorial-type-families -open import foundation.transport-along-identifications open import foundation.universe-levels open import graph-theory.base-change-dependent-reflexive-graphs open import graph-theory.cartesian-products-reflexive-graphs -open import graph-theory.dependent-products-directed-graphs open import graph-theory.dependent-reflexive-graphs open import graph-theory.directed-graphs open import graph-theory.morphisms-directed-graphs diff --git a/src/graph-theory/large-reflexive-graphs.lagda.md b/src/graph-theory/large-reflexive-graphs.lagda.md index 0885e859a1..e752ceaf5e 100644 --- a/src/graph-theory/large-reflexive-graphs.lagda.md +++ b/src/graph-theory/large-reflexive-graphs.lagda.md @@ -7,7 +7,6 @@ module graph-theory.large-reflexive-graphs where
Imports ```agda -open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/group-theory/automorphism-groups.lagda.md b/src/group-theory/automorphism-groups.lagda.md index 2214cbb69c..668dde054a 100644 --- a/src/group-theory/automorphism-groups.lagda.md +++ b/src/group-theory/automorphism-groups.lagda.md @@ -9,14 +9,11 @@ module group-theory.automorphism-groups where ```agda open import foundation.1-types open import foundation.connected-components -open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.subtype-identity-principle open import foundation.torsorial-type-families open import foundation.universe-levels diff --git a/src/group-theory/cayleys-theorem.lagda.md b/src/group-theory/cayleys-theorem.lagda.md index 7df1fa969a..b770b023ac 100644 --- a/src/group-theory/cayleys-theorem.lagda.md +++ b/src/group-theory/cayleys-theorem.lagda.md @@ -12,7 +12,6 @@ open import foundation.embeddings open import foundation.equivalence-extensionality open import foundation.identity-types open import foundation.injective-maps -open import foundation.sets open import foundation.universe-levels open import group-theory.embeddings-groups diff --git a/src/group-theory/group-actions.lagda.md b/src/group-theory/group-actions.lagda.md index 70d3c5ce40..ae7b61578f 100644 --- a/src/group-theory/group-actions.lagda.md +++ b/src/group-theory/group-actions.lagda.md @@ -19,7 +19,6 @@ open import foundation.universe-levels open import group-theory.groups open import group-theory.homomorphisms-groups -open import group-theory.subgroups open import group-theory.symmetric-groups open import group-theory.trivial-group-homomorphisms ``` diff --git a/src/group-theory/homotopy-automorphism-groups.lagda.md b/src/group-theory/homotopy-automorphism-groups.lagda.md index f9cd8b06dc..0e344923e4 100644 --- a/src/group-theory/homotopy-automorphism-groups.lagda.md +++ b/src/group-theory/homotopy-automorphism-groups.lagda.md @@ -7,26 +7,13 @@ module group-theory.homotopy-automorphism-groups where
Imports ```agda -open import foundation.1-types -open import foundation.connected-components -open import foundation.contractible-types -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families open import foundation.truncation-levels open import foundation.truncations open import foundation.universe-levels open import group-theory.automorphism-groups open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-groups -open import higher-group-theory.automorphism-groups open import higher-group-theory.higher-groups open import structured-types.pointed-types diff --git a/src/group-theory/isomorphisms-semigroups.lagda.md b/src/group-theory/isomorphisms-semigroups.lagda.md index bf3a93267a..c6f29143b3 100644 --- a/src/group-theory/isomorphisms-semigroups.lagda.md +++ b/src/group-theory/isomorphisms-semigroups.lagda.md @@ -13,7 +13,6 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md b/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md index e86970fa14..6433e5bbad 100644 --- a/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md +++ b/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md @@ -7,7 +7,6 @@ module group-theory.minkowski-multiplication-commutative-monoids where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.existential-quantification open import foundation.identity-types @@ -19,10 +18,7 @@ open import foundation.universe-levels open import group-theory.commutative-monoids open import group-theory.minkowski-multiplication-monoids -open import group-theory.monoids open import group-theory.subsets-commutative-monoids - -open import logic.functoriality-existential-quantification ```
diff --git a/src/group-theory/minkowski-multiplication-monoids.lagda.md b/src/group-theory/minkowski-multiplication-monoids.lagda.md index 1739e3919e..8ce30adb8f 100644 --- a/src/group-theory/minkowski-multiplication-monoids.lagda.md +++ b/src/group-theory/minkowski-multiplication-monoids.lagda.md @@ -20,7 +20,6 @@ open import foundation.universe-levels open import group-theory.minkowski-multiplication-semigroups open import group-theory.monoids -open import group-theory.semigroups open import group-theory.subsets-monoids ``` diff --git a/src/group-theory/minkowski-multiplication-semigroups.lagda.md b/src/group-theory/minkowski-multiplication-semigroups.lagda.md index a7215e29fe..0fea876135 100644 --- a/src/group-theory/minkowski-multiplication-semigroups.lagda.md +++ b/src/group-theory/minkowski-multiplication-semigroups.lagda.md @@ -17,7 +17,6 @@ open import foundation.functoriality-cartesian-product-types open import foundation.identity-types open import foundation.inhabited-subtypes open import foundation.powersets -open import foundation.propositions open import foundation.sets open import foundation.subtypes open import foundation.universe-levels diff --git a/src/higher-group-theory/automorphism-groups.lagda.md b/src/higher-group-theory/automorphism-groups.lagda.md index eabdf5bf0f..3c2e64a205 100644 --- a/src/higher-group-theory/automorphism-groups.lagda.md +++ b/src/higher-group-theory/automorphism-groups.lagda.md @@ -8,7 +8,6 @@ module higher-group-theory.automorphism-groups where ```agda open import foundation.0-connected-types -open import foundation.1-types open import foundation.connected-components open import foundation.contractible-types open import foundation.dependent-pair-types @@ -20,9 +19,6 @@ open import foundation.subtype-identity-principle open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-groups - open import higher-group-theory.equivalences-higher-groups open import higher-group-theory.higher-groups diff --git a/src/linear-algebra/functoriality-vectors.lagda.md b/src/linear-algebra/functoriality-vectors.lagda.md index 32c5958519..021cff9837 100644 --- a/src/linear-algebra/functoriality-vectors.lagda.md +++ b/src/linear-algebra/functoriality-vectors.lagda.md @@ -16,7 +16,6 @@ open import foundation.homotopies open import foundation.identity-types open import foundation.postcomposition-functions open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition open import linear-algebra.vectors diff --git a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md index b3d50a0edf..55627ce6e3 100644 --- a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md @@ -10,11 +10,8 @@ module metric-spaces.cauchy-approximations-premetric-spaces where open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types -open import foundation.equivalences open import foundation.function-types -open import foundation.homotopies open import foundation.identity-types -open import foundation.logical-equivalences open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/metric-spaces/discrete-premetric-structures.lagda.md b/src/metric-spaces/discrete-premetric-structures.lagda.md index 3f8380308f..7dfae22799 100644 --- a/src/metric-spaces/discrete-premetric-structures.lagda.md +++ b/src/metric-spaces/discrete-premetric-structures.lagda.md @@ -9,27 +9,17 @@ module metric-spaces.discrete-premetric-structures where ```agda open import elementary-number-theory.positive-rational-numbers -open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences open import foundation.function-types -open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types open import foundation.logical-equivalences -open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions open import foundation.sets open import foundation.subtypes -open import foundation.torsorial-type-families -open import foundation.transport-along-identifications -open import foundation.univalence open import foundation.universe-levels open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures open import metric-spaces.premetric-structures open import metric-spaces.reflexive-premetric-structures open import metric-spaces.symmetric-premetric-structures diff --git a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md index 35ddad8925..e825f25eff 100644 --- a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md @@ -10,22 +10,15 @@ module metric-spaces.functor-category-set-functions-isometry-metric-spaces where open import category-theory.conservative-functors-precategories open import category-theory.faithful-functors-precategories open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories open import foundation.category-of-sets open import foundation.dependent-pair-types -open import foundation.equivalences open import foundation.function-types -open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies open import foundation.identity-types open import foundation.isomorphisms-of-sets open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.category-of-metric-spaces-and-isometries open import metric-spaces.isometries-metric-spaces open import metric-spaces.metric-spaces open import metric-spaces.precategory-of-metric-spaces-and-isometries diff --git a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md index 6726a6df32..9e55f22584 100644 --- a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md @@ -10,19 +10,12 @@ module metric-spaces.functor-category-short-isometry-metric-spaces where open import category-theory.conservative-functors-precategories open import category-theory.faithful-functors-precategories open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories -open import category-theory.split-essentially-surjective-functors-precategories open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies open import foundation.identity-types open import foundation.universe-levels -open import metric-spaces.isometries-metric-spaces open import metric-spaces.precategory-of-metric-spaces-and-isometries open import metric-spaces.precategory-of-metric-spaces-and-short-functions open import metric-spaces.short-functions-metric-spaces diff --git a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md index f7304f2202..a3390d3a52 100644 --- a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md +++ b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md @@ -9,21 +9,14 @@ module metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces where ```agda open import elementary-number-theory.positive-rational-numbers -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies open import foundation.identity-types -open import foundation.logical-equivalences open import foundation.propositions -open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels open import metric-spaces.cauchy-approximations-premetric-spaces open import metric-spaces.extensional-premetric-structures open import metric-spaces.premetric-spaces -open import metric-spaces.short-functions-premetric-spaces open import metric-spaces.symmetric-premetric-structures open import metric-spaces.triangular-premetric-structures ``` diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md index c879431681..aceb047872 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md @@ -11,18 +11,12 @@ open import category-theory.isomorphisms-in-precategories open import category-theory.precategories open import foundation.action-on-identifications-functions -open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families -open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md index 886c4037e5..bc3ca88ffe 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md @@ -12,17 +12,12 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom -open import foundation.function-types open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions -open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -31,7 +26,6 @@ open import metric-spaces.functions-metric-spaces open import metric-spaces.isometric-equivalences-premetric-spaces open import metric-spaces.isometries-metric-spaces open import metric-spaces.metric-spaces -open import metric-spaces.precategory-of-metric-spaces-and-isometries open import metric-spaces.short-functions-metric-spaces ``` diff --git a/src/order-theory/decidable-total-orders.lagda.md b/src/order-theory/decidable-total-orders.lagda.md index b0cdb583ea..1b3086e12d 100644 --- a/src/order-theory/decidable-total-orders.lagda.md +++ b/src/order-theory/decidable-total-orders.lagda.md @@ -7,7 +7,6 @@ module order-theory.decidable-total-orders where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.coproduct-types open import foundation.decidable-propositions diff --git a/src/order-theory/large-inflattices.lagda.md b/src/order-theory/large-inflattices.lagda.md index cd6d850a4e..74860bf69e 100644 --- a/src/order-theory/large-inflattices.lagda.md +++ b/src/order-theory/large-inflattices.lagda.md @@ -7,12 +7,9 @@ module order-theory.large-inflattices where
Imports ```agda -open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types open import foundation.large-binary-relations open import foundation.logical-equivalences -open import foundation.propositions open import foundation.sets open import foundation.universe-levels diff --git a/src/order-theory/least-upper-bounds-posets.lagda.md b/src/order-theory/least-upper-bounds-posets.lagda.md index 2b428ad028..d0a5e74b02 100644 --- a/src/order-theory/least-upper-bounds-posets.lagda.md +++ b/src/order-theory/least-upper-bounds-posets.lagda.md @@ -10,11 +10,9 @@ module order-theory.least-upper-bounds-posets where open import foundation.action-on-identifications-functions open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.function-types open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/lower-bounds-large-posets.lagda.md b/src/order-theory/lower-bounds-large-posets.lagda.md index 99a8b2cb5d..3f527ccddc 100644 --- a/src/order-theory/lower-bounds-large-posets.lagda.md +++ b/src/order-theory/lower-bounds-large-posets.lagda.md @@ -7,7 +7,6 @@ module order-theory.lower-bounds-large-posets where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.conjunction open import foundation.dependent-pair-types open import foundation.logical-equivalences diff --git a/src/organic-chemistry/ethane.lagda.md b/src/organic-chemistry/ethane.lagda.md index 13bda1ab23..b20b3fe687 100644 --- a/src/organic-chemistry/ethane.lagda.md +++ b/src/organic-chemistry/ethane.lagda.md @@ -22,7 +22,6 @@ open import foundation.identity-types open import foundation.injective-maps open import foundation.propositional-truncations open import foundation.propositions -open import foundation.sets open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.unit-type diff --git a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md index de81adfbd4..37b7855617 100644 --- a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md @@ -7,24 +7,15 @@ module orthogonal-factorization-systems.continuation-modalities where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.continuations open import foundation.dependent-pair-types -open import foundation.equality-cartesian-product-types open import foundation.equivalences -open import foundation.evaluation-functions open import foundation.function-types -open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions -open import foundation.retractions -open import foundation.sections open import foundation.transport-along-identifications -open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-equivalences open import foundation.universe-levels open import orthogonal-factorization-systems.large-lawvere-tierney-topologies diff --git a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md index f38cbaa29d..544627106f 100644 --- a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md @@ -7,47 +7,21 @@ module orthogonal-factorization-systems.fiberwise-orthogonal-maps where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.cartesian-morphisms-arrows -open import foundation.cartesian-product-types -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.coproducts-pullbacks -open import foundation.dependent-pair-types -open import foundation.dependent-products-pullbacks -open import foundation.dependent-sums-pullbacks open import foundation.equivalences -open import foundation.fibered-maps open import foundation.fibers-of-maps open import foundation.function-types open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types open import foundation.homotopies -open import foundation.morphisms-arrows open import foundation.postcomposition-functions -open import foundation.postcomposition-pullbacks open import foundation.precomposition-functions -open import foundation.products-pullbacks -open import foundation.propositions open import foundation.pullbacks -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-dependent-function-types open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-equivalences -open import foundation.universal-property-pullbacks open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.lifting-structures-on-squares open import orthogonal-factorization-systems.null-maps open import orthogonal-factorization-systems.orthogonal-maps open import orthogonal-factorization-systems.pullback-hom -open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md index b52a86162b..2ba05b568a 100644 --- a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md @@ -8,33 +8,22 @@ module orthogonal-factorization-systems.functoriality-localizations-at-global-su ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types open import foundation.commuting-squares-of-maps -open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.extensions-types-global-subuniverses -open import foundation.extensions-types-subuniverses open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.global-subuniverses open import foundation.homotopies open import foundation.homotopy-induction open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.propositions open import foundation.retractions open import foundation.retracts-of-maps open import foundation.retracts-of-types -open import foundation.subuniverses -open import foundation.unit-type open import foundation.universe-levels open import orthogonal-factorization-systems.localizations-at-global-subuniverses -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction -open import orthogonal-factorization-systems.types-local-at-maps open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses ``` diff --git a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md index 65092e62f1..ba3af5d73b 100644 --- a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md @@ -7,27 +7,11 @@ module orthogonal-factorization-systems.functoriality-pullback-hom where
Imports ```agda -open import foundation.action-on-identifications-binary-functions -open import foundation.action-on-identifications-functions -open import foundation.bicomposition-functions -open import foundation.composition-algebra -open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-types open import foundation.functoriality-morphisms-arrows open import foundation.functoriality-pullbacks -open import foundation.homotopies -open import foundation.homotopies-morphisms-arrows -open import foundation.homotopies-morphisms-cospan-diagrams -open import foundation.identity-types open import foundation.morphisms-arrows open import foundation.morphisms-cospan-diagrams -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.retracts-of-maps open import foundation.universe-levels -open import foundation.whiskering-higher-homotopies-composition -open import foundation.whiskering-homotopies-composition open import orthogonal-factorization-systems.pullback-hom ``` diff --git a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md index 5368be41af..e3b1f8e7b4 100644 --- a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md @@ -7,35 +7,16 @@ module orthogonal-factorization-systems.functoriality-reflective-global-subunive
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.extensions-types-global-subuniverses -open import foundation.extensions-types-subuniverses open import foundation.function-types -open import foundation.global-subuniverses open import foundation.homotopies open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.propositions open import foundation.retractions -open import foundation.retracts-of-maps open import foundation.retracts-of-types -open import foundation.subuniverses -open import foundation.unit-type open import foundation.universe-levels open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses -open import orthogonal-factorization-systems.localizations-at-global-subuniverses -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction open import orthogonal-factorization-systems.reflective-global-subuniverses -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses ```
diff --git a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md index 0776c8a973..dd2128327c 100644 --- a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md @@ -7,32 +7,15 @@ module orthogonal-factorization-systems.maps-local-at-maps where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.cartesian-morphisms-arrows -open import foundation.cones-over-cospan-diagrams -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-functions open import foundation.propositions -open import foundation.pullbacks open import foundation.retracts-of-maps open import foundation.unit-type -open import foundation.universal-property-family-of-fibers-of-maps open import foundation.universe-levels open import orthogonal-factorization-systems.families-of-types-local-at-maps open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.pullback-hom open import orthogonal-factorization-systems.types-local-at-maps ``` diff --git a/src/orthogonal-factorization-systems/pullback-hom.lagda.md b/src/orthogonal-factorization-systems/pullback-hom.lagda.md index 4b50212f0f..6cd1e6d736 100644 --- a/src/orthogonal-factorization-systems/pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/pullback-hom.lagda.md @@ -10,7 +10,6 @@ module orthogonal-factorization-systems.pullback-hom where open import foundation.commuting-squares-of-maps open import foundation.commuting-triangles-of-maps open import foundation.cones-over-cospan-diagrams -open import foundation.cospan-diagrams open import foundation.dependent-pair-types open import foundation.equality-dependent-pair-types open import foundation.equivalences @@ -19,7 +18,6 @@ open import foundation.fibers-of-maps open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types -open import foundation.functoriality-dependent-pair-types open import foundation.functoriality-fibers-of-maps open import foundation.functoriality-morphisms-arrows open import foundation.higher-homotopies-morphisms-arrows @@ -35,8 +33,6 @@ open import foundation.pullbacks open import foundation.retractions open import foundation.sections open import foundation.standard-pullbacks -open import foundation.transport-along-identifications -open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-theoretic-principle-of-choice open import foundation.universal-property-pullbacks open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md index 4287ccebae..440719b15d 100644 --- a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md @@ -7,33 +7,20 @@ module orthogonal-factorization-systems.reflective-global-subuniverses where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams open import foundation.contractible-types open import foundation.cospan-diagrams -open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.equivalences-arrows open import foundation.extensions-types-global-subuniverses -open import foundation.extensions-types-subuniverses -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types open import foundation.global-subuniverses open import foundation.identity-types -open import foundation.precomposition-functions open import foundation.propositions open import foundation.pullback-cones -open import foundation.retractions open import foundation.subuniverses open import foundation.unit-type -open import foundation.universal-property-pullbacks open import foundation.universe-levels open import orthogonal-factorization-systems.localizations-at-global-subuniverses -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction open import orthogonal-factorization-systems.types-local-at-maps open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses ``` diff --git a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md index 8c0864b033..5c545e554c 100644 --- a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md @@ -7,14 +7,9 @@ module orthogonal-factorization-systems.reflective-subuniverses where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions open import foundation.subuniverses open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md index eaf92b9fa5..0e261e3ed9 100644 --- a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md @@ -34,7 +34,6 @@ open import foundation.retractions open import foundation.retracts-of-maps open import foundation.retracts-of-types open import foundation.sections -open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-function-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type diff --git a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md index b5fba65323..59815d7643 100644 --- a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md @@ -8,7 +8,6 @@ module orthogonal-factorization-systems.universal-property-localizations-at-glob ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences @@ -17,14 +16,11 @@ open import foundation.extensions-types-global-subuniverses open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.global-subuniverses -open import foundation.homotopies open import foundation.identity-types open import foundation.precomposition-functions open import foundation.propositions open import foundation.retractions open import foundation.sections -open import foundation.subuniverses -open import foundation.unit-type open import foundation.univalence open import foundation.universe-levels diff --git a/src/real-numbers/apartness-real-numbers.lagda.md b/src/real-numbers/apartness-real-numbers.lagda.md index da2485940d..610c8bcdbb 100644 --- a/src/real-numbers/apartness-real-numbers.lagda.md +++ b/src/real-numbers/apartness-real-numbers.lagda.md @@ -7,17 +7,14 @@ module real-numbers.apartness-real-numbers where
Imports ```agda -open import foundation.apartness-relations open import foundation.disjunction open import foundation.empty-types open import foundation.function-types -open import foundation.identity-types open import foundation.large-apartness-relations open import foundation.large-binary-relations open import foundation.negated-equality open import foundation.negation open import foundation.propositions -open import foundation.transport-along-identifications open import foundation.universe-levels open import real-numbers.dedekind-real-numbers diff --git a/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md b/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md index 82cf6a86a3..a378d58d72 100644 --- a/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md +++ b/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md @@ -17,17 +17,12 @@ open import elementary-number-theory.positive-rational-numbers open import elementary-number-theory.rational-numbers open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.binary-transport open import foundation.cartesian-product-types open import foundation.conjunction open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.disjunction open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.raising-universe-levels -open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/real-numbers/dedekind-real-numbers.lagda.md b/src/real-numbers/dedekind-real-numbers.lagda.md index 61408187db..36f5e8e621 100644 --- a/src/real-numbers/dedekind-real-numbers.lagda.md +++ b/src/real-numbers/dedekind-real-numbers.lagda.md @@ -13,8 +13,6 @@ open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.complements-subtypes open import foundation.conjunction open import foundation.coproduct-types open import foundation.dependent-pair-types @@ -22,7 +20,6 @@ open import foundation.disjoint-subtypes open import foundation.disjunction open import foundation.embeddings open import foundation.empty-types -open import foundation.equivalences open import foundation.existential-quantification open import foundation.function-types open import foundation.functoriality-cartesian-product-types @@ -31,17 +28,13 @@ open import foundation.identity-types open import foundation.logical-equivalences open import foundation.negation open import foundation.powersets -open import foundation.propositional-truncations open import foundation.propositions open import foundation.sets open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.truncated-types open import foundation.universal-quantification open import foundation.universe-levels -open import foundation-core.truncation-levels - open import logic.functoriality-existential-quantification open import real-numbers.lower-dedekind-real-numbers diff --git a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md index 26abd2fb42..87a1154a7f 100644 --- a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md @@ -16,8 +16,6 @@ open import foundation.dependent-pair-types open import foundation.empty-types open import foundation.existential-quantification open import foundation.logical-equivalences -open import foundation.negation -open import foundation.powersets open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/real-numbers/inequality-real-numbers.lagda.md b/src/real-numbers/inequality-real-numbers.lagda.md index 098feec9e9..06313f63bb 100644 --- a/src/real-numbers/inequality-real-numbers.lagda.md +++ b/src/real-numbers/inequality-real-numbers.lagda.md @@ -9,12 +9,9 @@ module real-numbers.inequality-real-numbers where ```agda open import elementary-number-theory.inequality-rational-numbers open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.complements-subtypes -open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types open import foundation.existential-quantification open import foundation.identity-types open import foundation.logical-equivalences @@ -30,11 +27,7 @@ open import order-theory.preorders open import real-numbers.dedekind-real-numbers open import real-numbers.inequality-lower-dedekind-real-numbers open import real-numbers.inequality-upper-dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.negation-lower-upper-dedekind-real-numbers -open import real-numbers.negation-real-numbers open import real-numbers.rational-real-numbers -open import real-numbers.upper-dedekind-real-numbers ```
diff --git a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md index 45cdddb26d..1c124e2f50 100644 --- a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md @@ -16,7 +16,6 @@ open import foundation.dependent-pair-types open import foundation.empty-types open import foundation.existential-quantification open import foundation.logical-equivalences -open import foundation.powersets open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/real-numbers/metric-space-of-real-numbers.lagda.md b/src/real-numbers/metric-space-of-real-numbers.lagda.md index 9db327d03c..7a4d12c506 100644 --- a/src/real-numbers/metric-space-of-real-numbers.lagda.md +++ b/src/real-numbers/metric-space-of-real-numbers.lagda.md @@ -11,17 +11,12 @@ module real-numbers.metric-space-of-real-numbers where ```agda open import elementary-number-theory.addition-rational-numbers open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers open import elementary-number-theory.positive-rational-numbers open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.diagonal-maps-cartesian-products-of-types -open import foundation.empty-types open import foundation.existential-quantification open import foundation.function-types open import foundation.functoriality-cartesian-product-types @@ -37,7 +32,6 @@ open import metric-spaces.isometries-metric-spaces open import metric-spaces.metric-space-of-rational-numbers open import metric-spaces.metric-spaces open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures open import metric-spaces.premetric-spaces open import metric-spaces.premetric-structures open import metric-spaces.pseudometric-structures diff --git a/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md index 5ee824c84c..0fe42bfd07 100644 --- a/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md @@ -28,8 +28,6 @@ open import foundation.universe-levels open import logic.functoriality-existential-quantification -open import real-numbers.inequality-lower-dedekind-real-numbers -open import real-numbers.inequality-upper-dedekind-real-numbers open import real-numbers.lower-dedekind-real-numbers open import real-numbers.rational-lower-dedekind-real-numbers open import real-numbers.rational-upper-dedekind-real-numbers diff --git a/src/real-numbers/negation-real-numbers.lagda.md b/src/real-numbers/negation-real-numbers.lagda.md index f86c08a666..54744b5d9d 100644 --- a/src/real-numbers/negation-real-numbers.lagda.md +++ b/src/real-numbers/negation-real-numbers.lagda.md @@ -9,36 +9,22 @@ module real-numbers.negation-real-numbers where
Imports ```agda -open import elementary-number-theory.positive-rational-numbers open import elementary-number-theory.rational-numbers open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.disjoint-subtypes open import foundation.disjunction -open import foundation.empty-types -open import foundation.existential-quantification open import foundation.function-types open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification - open import real-numbers.dedekind-real-numbers open import real-numbers.lower-dedekind-real-numbers open import real-numbers.negation-lower-upper-dedekind-real-numbers -open import real-numbers.rational-lower-dedekind-real-numbers open import real-numbers.rational-real-numbers -open import real-numbers.rational-upper-dedekind-real-numbers open import real-numbers.upper-dedekind-real-numbers ``` diff --git a/src/real-numbers/rational-real-numbers.lagda.md b/src/real-numbers/rational-real-numbers.lagda.md index 19ff6b404c..c5dfe24fcc 100644 --- a/src/real-numbers/rational-real-numbers.lagda.md +++ b/src/real-numbers/rational-real-numbers.lagda.md @@ -9,25 +9,18 @@ module real-numbers.rational-real-numbers where
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers open import elementary-number-theory.rational-numbers open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types open import foundation.conjunction open import foundation.dependent-pair-types open import foundation.disjunction -open import foundation.embeddings open import foundation.empty-types open import foundation.equivalences -open import foundation.existential-quantification open import foundation.function-types -open import foundation.homotopies open import foundation.identity-types -open import foundation.logical-equivalences open import foundation.negation -open import foundation.propositional-truncations open import foundation.propositions open import foundation.retractions open import foundation.sections @@ -35,14 +28,10 @@ open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification - open import real-numbers.dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers open import real-numbers.rational-lower-dedekind-real-numbers open import real-numbers.rational-upper-dedekind-real-numbers open import real-numbers.similarity-real-numbers -open import real-numbers.upper-dedekind-real-numbers ```
diff --git a/src/real-numbers/similarity-real-numbers.lagda.md b/src/real-numbers/similarity-real-numbers.lagda.md index 5691544027..d7b13097d2 100644 --- a/src/real-numbers/similarity-real-numbers.lagda.md +++ b/src/real-numbers/similarity-real-numbers.lagda.md @@ -7,12 +7,7 @@ module real-numbers.similarity-real-numbers where
Imports ```agda -open import elementary-number-theory.strict-inequality-rational-numbers - open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.function-types open import foundation.identity-types open import foundation.logical-equivalences open import foundation.powersets @@ -20,9 +15,6 @@ open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.similarity-of-elements-large-posets - open import real-numbers.dedekind-real-numbers ``` diff --git a/src/real-numbers/strict-inequality-real-numbers.lagda.md b/src/real-numbers/strict-inequality-real-numbers.lagda.md index 0deea45410..2b2ccc6a6b 100644 --- a/src/real-numbers/strict-inequality-real-numbers.lagda.md +++ b/src/real-numbers/strict-inequality-real-numbers.lagda.md @@ -12,7 +12,6 @@ module real-numbers.strict-inequality-real-numbers where open import elementary-number-theory.rational-numbers open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.cartesian-product-types open import foundation.conjunction open import foundation.coproduct-types open import foundation.dependent-pair-types @@ -27,7 +26,6 @@ open import foundation.logical-equivalences open import foundation.negation open import foundation.propositional-truncations open import foundation.propositions -open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/set-theory/baire-space.lagda.md b/src/set-theory/baire-space.lagda.md index 54eed47ea2..884e7587bd 100644 --- a/src/set-theory/baire-space.lagda.md +++ b/src/set-theory/baire-space.lagda.md @@ -10,7 +10,6 @@ module set-theory.baire-space where open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-types open import foundation.lawveres-fixed-point-theorem @@ -21,7 +20,6 @@ open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.identity-types -open import foundation-core.propositions open import set-theory.cantors-diagonal-argument open import set-theory.countable-sets diff --git a/src/set-theory/cantors-diagonal-argument.lagda.md b/src/set-theory/cantors-diagonal-argument.lagda.md index a8ca2a8d49..1ff1284a90 100644 --- a/src/set-theory/cantors-diagonal-argument.lagda.md +++ b/src/set-theory/cantors-diagonal-argument.lagda.md @@ -11,19 +11,13 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-subtypes open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.discrete-types -open import foundation.double-negation open import foundation.function-extensionality-axiom open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.logical-equivalences open import foundation.negated-equality open import foundation.negation -open import foundation.powersets open import foundation.propositional-truncations open import foundation.sets open import foundation.surjective-maps @@ -34,7 +28,6 @@ open import foundation-core.fibers-of-maps open import foundation-core.propositions open import set-theory.countable-sets -open import set-theory.infinite-sets open import set-theory.uncountable-sets ``` diff --git a/src/set-theory/cardinalities.lagda.md b/src/set-theory/cardinalities.lagda.md index 425ce33b32..27c781d4cc 100644 --- a/src/set-theory/cardinalities.lagda.md +++ b/src/set-theory/cardinalities.lagda.md @@ -7,7 +7,6 @@ module set-theory.cardinalities where
Imports ```agda -open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality-axiom diff --git a/src/structured-types/pointed-equivalences.lagda.md b/src/structured-types/pointed-equivalences.lagda.md index 5a20fab3e9..0305b2134d 100644 --- a/src/structured-types/pointed-equivalences.lagda.md +++ b/src/structured-types/pointed-equivalences.lagda.md @@ -9,14 +9,8 @@ module structured-types.pointed-equivalences where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-equivalences -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-maps -open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.embeddings open import foundation.equivalences -open import foundation.fibers-of-maps open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.homotopies @@ -28,7 +22,6 @@ open import foundation.retractions open import foundation.sections open import foundation.structure-identity-principle open import foundation.torsorial-type-families -open import foundation.transposition-identifications-along-equivalences open import foundation.type-arithmetic-dependent-pair-types open import foundation.univalence open import foundation.universe-levels diff --git a/src/structured-types/pointed-homotopies.lagda.md b/src/structured-types/pointed-homotopies.lagda.md index 234c060172..dabdeef3c9 100644 --- a/src/structured-types/pointed-homotopies.lagda.md +++ b/src/structured-types/pointed-homotopies.lagda.md @@ -7,12 +7,9 @@ module structured-types.pointed-homotopies where
Imports ```agda -open import foundation.action-on-higher-identifications-functions -open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.commuting-triangles-of-identifications -open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-types @@ -21,10 +18,8 @@ open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies open import foundation.homotopy-induction open import foundation.identity-types -open import foundation.path-algebra open import foundation.structure-identity-principle open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition open import foundation.whiskering-identifications-concatenation open import foundation-core.torsorial-type-families diff --git a/src/synthetic-category-theory/retractions-synthetic-categories.lagda.md b/src/synthetic-category-theory/retractions-synthetic-categories.lagda.md index 9eefe32176..9c81fdcf53 100644 --- a/src/synthetic-category-theory/retractions-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/retractions-synthetic-categories.lagda.md @@ -9,12 +9,9 @@ module synthetic-category-theory.retractions-synthetic-categories where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-types - open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/sections-synthetic-categories.lagda.md b/src/synthetic-category-theory/sections-synthetic-categories.lagda.md index e24866c194..12556a69e2 100644 --- a/src/synthetic-category-theory/sections-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/sections-synthetic-categories.lagda.md @@ -9,12 +9,9 @@ module synthetic-category-theory.sections-synthetic-categories where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-types - open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/synthetic-categories.lagda.md b/src/synthetic-category-theory/synthetic-categories.lagda.md index 5deaf488e8..cc5990a41f 100644 --- a/src/synthetic-category-theory/synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/synthetic-categories.lagda.md @@ -9,7 +9,6 @@ module synthetic-category-theory.synthetic-categories where
Imports ```agda -open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types diff --git a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md index 04da219539..c7e47d89d0 100644 --- a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md @@ -9,7 +9,6 @@ module synthetic-homotopy-theory.1-acyclic-types where ```agda open import foundation.0-connected-types open import foundation.binary-transport -open import foundation.constant-maps open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.diagonal-maps-of-types diff --git a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md index 09fde243e6..e14dce732d 100644 --- a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md @@ -7,7 +7,6 @@ module synthetic-homotopy-theory.cofibers-of-maps where
Imports ```agda -open import foundation.constant-maps open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences diff --git a/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md b/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md index 87be7c63e3..0da2de0601 100644 --- a/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md +++ b/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md @@ -7,11 +7,6 @@ module synthetic-homotopy-theory.cofibers-of-pointed-maps where
Imports ```agda -open import foundation.constant-maps -open import foundation.contractible-types -open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.unit-type open import foundation.universe-levels open import structured-types.pointed-maps @@ -19,13 +14,7 @@ open import structured-types.pointed-types open import structured-types.pointed-unit-type open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.cofibers-of-maps -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.pushouts open import synthetic-homotopy-theory.pushouts-of-pointed-types -open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md index 1381dac51b..52944f00cd 100644 --- a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md @@ -15,10 +15,8 @@ open import foundation.commuting-squares-of-homotopies open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types -open import foundation.functoriality-dependent-pair-types open import foundation.homotopies open import foundation.retractions open import foundation.retracts-of-types diff --git a/src/synthetic-homotopy-theory/homotopy-groups.lagda.md b/src/synthetic-homotopy-theory/homotopy-groups.lagda.md index 5d30f801f9..2576e23f3b 100644 --- a/src/synthetic-homotopy-theory/homotopy-groups.lagda.md +++ b/src/synthetic-homotopy-theory/homotopy-groups.lagda.md @@ -9,12 +9,9 @@ module synthetic-homotopy-theory.homotopy-groups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-components open import foundation.dependent-pair-types open import foundation.set-truncations open import foundation.sets -open import foundation.truncation-levels -open import foundation.truncations open import foundation.universe-levels open import group-theory.concrete-groups diff --git a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md index e4f7cfbde5..350415b83a 100644 --- a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md +++ b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md @@ -7,18 +7,11 @@ module synthetic-homotopy-theory.loop-homotopy-circle where
Imports ```agda -open import foundation.action-on-identifications-functions -open import foundation.dependent-pair-types open import foundation.function-types open import foundation.homotopies open import foundation.identity-types open import foundation.negated-equality open import foundation.negation -open import foundation.transport-along-identifications -open import foundation.universe-levels - -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps open import synthetic-homotopy-theory.circle ``` diff --git a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md index 34afc02b5e..7e6b3a6784 100644 --- a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md +++ b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md @@ -10,11 +10,8 @@ module synthetic-homotopy-theory.multiplication-circle where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-extensionality-axiom -open import foundation.function-types open import foundation.homotopies open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md index b23c3d17b8..92f38de1c4 100644 --- a/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md @@ -25,10 +25,8 @@ open import structured-types.pointed-types open import structured-types.pointed-unit-type open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.cofibers-of-maps open import synthetic-homotopy-theory.cofibers-of-pointed-maps open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.pushouts-of-pointed-types open import synthetic-homotopy-theory.wedges-of-pointed-types ``` diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md index 7363019965..95872ea9f7 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md @@ -13,7 +13,6 @@ open import foundation.cones-over-cospan-diagrams open import foundation.connected-maps open import foundation.connected-types open import foundation.constant-maps -open import foundation.contractible-types open import foundation.dependent-epimorphisms-with-respect-to-truncated-types open import foundation.dependent-pair-types open import foundation.dependent-universal-property-equivalences @@ -52,7 +51,6 @@ open import foundation.universe-levels open import synthetic-homotopy-theory.cocones-under-spans open import synthetic-homotopy-theory.codiagonals-of-maps open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.suspensions-of-types open import synthetic-homotopy-theory.truncated-acyclic-types open import synthetic-homotopy-theory.universal-property-pushouts ``` diff --git a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md index 4a4aced8a5..7969ee8012 100644 --- a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md @@ -17,7 +17,6 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps -open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/type-theories/precategories-with-attributes.lagda.md b/src/type-theories/precategories-with-attributes.lagda.md index d3f6859646..c092065934 100644 --- a/src/type-theories/precategories-with-attributes.lagda.md +++ b/src/type-theories/precategories-with-attributes.lagda.md @@ -10,7 +10,6 @@ module type-theories.precategories-with-attributes where open import category-theory.commuting-squares-of-morphisms-in-precategories open import category-theory.functors-precategories open import category-theory.natural-transformations-functors-precategories -open import category-theory.opposite-precategories open import category-theory.precategories open import category-theory.precategory-of-elements-of-a-presheaf open import category-theory.presheaf-categories @@ -18,14 +17,10 @@ open import category-theory.pullbacks-in-precategories open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types -open import foundation.category-of-sets open import foundation.dependent-pair-types -open import foundation.equivalences open import foundation.identity-types -open import foundation.sections open import foundation.sets open import foundation.subtypes -open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/type-theories/precategories-with-families.lagda.md b/src/type-theories/precategories-with-families.lagda.md index 7e2486e370..5a8bc8f46e 100644 --- a/src/type-theories/precategories-with-families.lagda.md +++ b/src/type-theories/precategories-with-families.lagda.md @@ -8,21 +8,13 @@ module type-theories.precategories-with-families where ```agda open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.opposite-precategories open import category-theory.precategories open import category-theory.precategory-of-elements-of-a-presheaf open import category-theory.presheaf-categories -open import category-theory.pullbacks-in-precategories -open import foundation.cartesian-product-types -open import foundation.category-of-sets open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.identity-types -open import foundation.sections -open import foundation.sets -open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md index f223fc9b23..eec01ce47a 100644 --- a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md @@ -13,7 +13,6 @@ open import elementary-number-theory.well-ordering-principle-standard-finite-typ open import foundation.automorphisms open import foundation.booleans -open import foundation.coproduct-types open import foundation.decidable-equality open import foundation.decidable-propositions open import foundation.decidable-types @@ -34,7 +33,6 @@ open import foundation.negated-equality open import foundation.negation open import foundation.propositional-truncations open import foundation.propositions -open import foundation.sets open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.type-arithmetic-coproduct-types diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index f815dbd237..30cfb287ac 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -27,7 +27,6 @@ open import foundation.fibers-of-maps open import foundation.function-types open import foundation.functoriality-coproduct-types open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-function-types open import foundation.functoriality-propositional-truncation open import foundation.logical-equivalences open import foundation.maybe diff --git a/src/univalent-combinatorics/coproduct-types.lagda.md b/src/univalent-combinatorics/coproduct-types.lagda.md index fa7c12c72b..03c7063c2b 100644 --- a/src/univalent-combinatorics/coproduct-types.lagda.md +++ b/src/univalent-combinatorics/coproduct-types.lagda.md @@ -21,7 +21,6 @@ open import foundation.functoriality-coproduct-types open import foundation.functoriality-propositional-truncation open import foundation.homotopies open import foundation.identity-types -open import foundation.injective-maps open import foundation.mere-equivalences open import foundation.propositional-truncations open import foundation.type-arithmetic-coproduct-types diff --git a/src/univalent-combinatorics/dependent-pair-types.lagda.md b/src/univalent-combinatorics/dependent-pair-types.lagda.md index 491d05e318..ce7fef9510 100644 --- a/src/univalent-combinatorics/dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/dependent-pair-types.lagda.md @@ -10,7 +10,6 @@ open import foundation.dependent-pair-types public ```agda open import foundation.complements -open import foundation.contractible-types open import foundation.decidable-types open import foundation.empty-types open import foundation.equality-dependent-pair-types diff --git a/src/univalent-combinatorics/fibers-of-maps.lagda.md b/src/univalent-combinatorics/fibers-of-maps.lagda.md index 2d9e458ea5..31ba87543e 100644 --- a/src/univalent-combinatorics/fibers-of-maps.lagda.md +++ b/src/univalent-combinatorics/fibers-of-maps.lagda.md @@ -12,7 +12,6 @@ open import foundation.fibers-of-maps public open import elementary-number-theory.natural-numbers open import elementary-number-theory.sums-of-natural-numbers -open import foundation.contractible-types open import foundation.decidable-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/univalent-combinatorics/finite-types.lagda.md b/src/univalent-combinatorics/finite-types.lagda.md index 0ddff4cb5a..747292e801 100644 --- a/src/univalent-combinatorics/finite-types.lagda.md +++ b/src/univalent-combinatorics/finite-types.lagda.md @@ -43,7 +43,6 @@ open import foundation.universe-levels open import foundation-core.torsorial-type-families open import univalent-combinatorics.counting -open import univalent-combinatorics.double-counting open import univalent-combinatorics.standard-finite-types ``` diff --git a/src/univalent-combinatorics/function-types.lagda.md b/src/univalent-combinatorics/function-types.lagda.md index 9929152a41..f461d7df2d 100644 --- a/src/univalent-combinatorics/function-types.lagda.md +++ b/src/univalent-combinatorics/function-types.lagda.md @@ -9,7 +9,6 @@ module univalent-combinatorics.function-types where ```agda open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.exponentiation-natural-numbers -open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.equivalences diff --git a/src/univalent-combinatorics/locally-finite-types.lagda.md b/src/univalent-combinatorics/locally-finite-types.lagda.md index 2caa3d98a1..273e1cd35b 100644 --- a/src/univalent-combinatorics/locally-finite-types.lagda.md +++ b/src/univalent-combinatorics/locally-finite-types.lagda.md @@ -9,66 +9,32 @@ module univalent-combinatorics.locally-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types open import foundation.1-types -open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types -open import foundation.constant-maps open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-types open import foundation.dependent-universal-property-equivalences -open import foundation.embeddings open import foundation.empty-types open import foundation.equality-cartesian-product-types -open import foundation.equality-coproduct-types open import foundation.equality-dependent-pair-types open import foundation.equivalences -open import foundation.fiber-inclusions -open import foundation.fibers-of-maps open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-set-truncation -open import foundation.homotopies open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.maybe -open import foundation.mere-equality -open import foundation.mere-equivalences -open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps open import foundation.transport-along-identifications -open import foundation.truncated-types -open import foundation.truncation-levels -open import foundation.type-arithmetic-coproduct-types open import foundation.unit-type -open import foundation.univalence open import foundation.universal-property-coproduct-types open import foundation.universal-property-empty-type open import foundation.universal-property-unit-type open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.coproduct-types open import univalent-combinatorics.counting -open import univalent-combinatorics.dependent-function-types open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products open import univalent-combinatorics.equality-finite-types open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-presented-types -open import univalent-combinatorics.function-types -open import univalent-combinatorics.image-of-maps open import univalent-combinatorics.standard-finite-types ``` diff --git a/src/univalent-combinatorics/repetitions-of-values.lagda.md b/src/univalent-combinatorics/repetitions-of-values.lagda.md index f051b846bd..49862e4292 100644 --- a/src/univalent-combinatorics/repetitions-of-values.lagda.md +++ b/src/univalent-combinatorics/repetitions-of-values.lagda.md @@ -18,7 +18,6 @@ open import foundation.identity-types open import foundation.injective-maps open import foundation.negated-equality open import foundation.negation -open import foundation.sets open import univalent-combinatorics.decidable-dependent-function-types open import univalent-combinatorics.decidable-propositions diff --git a/src/univalent-combinatorics/sigma-decompositions.lagda.md b/src/univalent-combinatorics/sigma-decompositions.lagda.md index 1a8c3c1436..3fe2f92b9c 100644 --- a/src/univalent-combinatorics/sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/sigma-decompositions.lagda.md @@ -19,7 +19,6 @@ open import foundation.homotopies open import foundation.identity-types open import foundation.inhabited-types open import foundation.logical-equivalences -open import foundation.precomposition-functions open import foundation.propositions open import foundation.relaxed-sigma-decompositions open import foundation.subtypes diff --git a/src/univalent-combinatorics/type-duality.lagda.md b/src/univalent-combinatorics/type-duality.lagda.md index bdfc816854..fc008806c9 100644 --- a/src/univalent-combinatorics/type-duality.lagda.md +++ b/src/univalent-combinatorics/type-duality.lagda.md @@ -15,7 +15,6 @@ open import foundation.equivalences open import foundation.full-subtypes open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-function-types open import foundation.inhabited-types open import foundation.postcomposition-functions open import foundation.propositions From 70bdce74a4aaf3d7541e331c7a41d3cfa0c18c7e Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 15:54:45 +0000 Subject: [PATCH 08/39] =?UTF-8?q?factor=20out=20`is-contr-=CE=A0`=20and=20?= =?UTF-8?q?`is-prop-=CE=A0`?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../contractible-types.lagda.md | 74 ------ .../decidable-propositions.lagda.md | 1 + ...oriality-dependent-function-types.lagda.md | 1 + src/foundation-core/propositions.lagda.md | 156 +---------- src/foundation-core/subtypes.lagda.md | 1 + src/foundation-core/truncated-types.lagda.md | 1 + src/foundation.lagda.md | 2 + src/foundation/apartness-relations.lagda.md | 1 + ...inary-functoriality-set-quotients.lagda.md | 1 + ...ecting-maps-equivalence-relations.lagda.md | 1 + src/foundation/binary-relations.lagda.md | 1 + .../coherently-invertible-maps.lagda.md | 1 + src/foundation/conjunction.lagda.md | 1 + src/foundation/connected-maps.lagda.md | 1 + src/foundation/continuations.lagda.md | 1 + src/foundation/contractible-types.lagda.md | 2 +- src/foundation/decidable-embeddings.lagda.md | 1 + src/foundation/decidable-equality.lagda.md | 1 + .../decidable-equivalence-relations.lagda.md | 1 + src/foundation/decidable-subtypes.lagda.md | 1 + ...ndent-products-contractible-types.lagda.md | 99 +++++++ .../dependent-products-propositions.lagda.md | 246 ++++++++++++++++++ .../discrete-binary-relations.lagda.md | 1 + .../discrete-reflexive-relations.lagda.md | 1 + ...rete-relaxed-sigma-decompositions.lagda.md | 1 + .../discrete-sigma-decompositions.lagda.md | 1 + src/foundation/disjoint-subtypes.lagda.md | 1 + .../double-negation-stable-equality.lagda.md | 1 + ...uble-negation-stable-propositions.lagda.md | 1 + src/foundation/double-powersets.lagda.md | 1 + .../dubuc-penon-compact-types.lagda.md | 1 + src/foundation/embeddings.lagda.md | 1 + src/foundation/empty-types.lagda.md | 1 + ...s-with-respect-to-truncated-types.lagda.md | 1 + ...equality-dependent-function-types.lagda.md | 1 + .../equivalence-extensionality.lagda.md | 1 + ...uivalence-injective-type-families.lagda.md | 1 + src/foundation/equivalences.lagda.md | 1 + src/foundation/exclusive-disjunction.lagda.md | 1 + src/foundation/exclusive-sum.lagda.md | 1 + .../existential-quantification.lagda.md | 1 + .../exponents-set-quotients.lagda.md | 1 + .../families-of-equivalences.lagda.md | 1 + src/foundation/families-of-maps.lagda.md | 1 + src/foundation/fibered-maps.lagda.md | 1 + src/foundation/full-subtypes.lagda.md | 1 + .../functional-correspondences.lagda.md | 1 + .../functoriality-morphisms-arrows.lagda.md | 1 + ...oriality-propositional-truncation.lagda.md | 1 + .../functoriality-set-quotients.lagda.md | 1 + .../functoriality-set-truncation.lagda.md | 1 + src/foundation/idempotent-maps.lagda.md | 1 + .../impredicative-encodings.lagda.md | 1 + src/foundation/injective-maps.lagda.md | 1 + .../intersections-subtypes.lagda.md | 1 + .../irrefutable-propositions.lagda.md | 1 + src/foundation/isolated-elements.lagda.md | 1 + .../iterated-dependent-product-types.lagda.md | 2 + .../large-locale-of-propositions.lagda.md | 1 + .../law-of-excluded-middle.lagda.md | 1 + ...-limited-principle-of-omniscience.lagda.md | 1 + .../limited-principle-of-omniscience.lagda.md | 1 + src/foundation/locally-small-types.lagda.md | 1 + src/foundation/logical-equivalences.lagda.md | 1 + .../maps-in-global-subuniverses.lagda.md | 1 + .../mere-path-cosplit-maps.lagda.md | 1 + src/foundation/monomorphisms.lagda.md | 1 + src/foundation/negation.lagda.md | 1 + src/foundation/partitions.lagda.md | 1 + src/foundation/path-cosplit-maps.lagda.md | 2 + .../path-split-type-families.lagda.md | 1 + src/foundation/pi-decompositions.lagda.md | 1 + .../pointed-torsorial-type-families.lagda.md | 1 + .../principle-of-omniscience.lagda.md | 1 + ...roduct-decompositions-subuniverse.lagda.md | 2 + .../propositional-extensionality.lagda.md | 2 + src/foundation/propositional-maps.lagda.md | 1 + .../propositional-resizing.lagda.md | 1 + .../propositional-truncations.lagda.md | 1 + src/foundation/propositions.lagda.md | 1 + .../quasicoherently-idempotent-maps.lagda.md | 1 + ...ecting-maps-equivalence-relations.lagda.md | 1 + .../relaxed-sigma-decompositions.lagda.md | 1 + src/foundation/sections.lagda.md | 1 + .../separated-types-subuniverses.lagda.md | 1 + src/foundation/set-presented-types.lagda.md | 1 + src/foundation/set-quotients.lagda.md | 1 + src/foundation/sigma-decompositions.lagda.md | 1 + src/foundation/slice.lagda.md | 1 + src/foundation/small-maps.lagda.md | 1 + src/foundation/subtypes.lagda.md | 1 + src/foundation/surjective-maps.lagda.md | 1 + src/foundation/symmetric-operations.lagda.md | 1 + .../total-partial-functions.lagda.md | 1 + src/foundation/truncated-maps.lagda.md | 1 + ...uniformly-decidable-type-families.lagda.md | 1 + ...universal-property-identity-types.lagda.md | 1 + ...property-propositional-truncation.lagda.md | 1 + .../universal-property-set-quotients.lagda.md | 1 + .../universal-property-truncation.lagda.md | 1 + .../universal-quantification.lagda.md | 1 + src/logic/de-morgan-subtypes.lagda.md | 1 + src/logic/de-morgan-types.lagda.md | 1 + src/logic/de-morgans-law.lagda.md | 1 + .../double-negation-elimination.lagda.md | 1 + .../double-negation-stable-subtypes.lagda.md | 1 + src/logic/markovian-types.lagda.md | 1 + src/order-theory/zorns-lemma.lagda.md | 1 + .../double-negation-sheaves.lagda.md | 1 + 109 files changed, 456 insertions(+), 230 deletions(-) create mode 100644 src/foundation/dependent-products-contractible-types.lagda.md create mode 100644 src/foundation/dependent-products-propositions.lagda.md diff --git a/src/foundation-core/contractible-types.lagda.md b/src/foundation-core/contractible-types.lagda.md index d86bdea803..f6b56e6169 100644 --- a/src/foundation-core/contractible-types.lagda.md +++ b/src/foundation-core/contractible-types.lagda.md @@ -10,8 +10,6 @@ module foundation-core.contractible-types where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.implicit-function-types open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -256,75 +254,3 @@ is-prop-is-contr : pr1 (is-prop-is-contr H x y) = eq-is-contr H pr2 (is-prop-is-contr H x .x) refl = left-inv (pr2 H x) ``` - -### Products of families of contractible types are contractible - -```agda -abstract - is-contr-Π : - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → - ((x : A) → is-contr (B x)) → is-contr ((x : A) → B x) - pr1 (is-contr-Π {A = A} {B = B} H) x = center (H x) - pr2 (is-contr-Π {A = A} {B = B} H) f = - eq-htpy (λ x → contraction (H x) (f x)) - -abstract - is-contr-implicit-Π : - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → - ((x : A) → is-contr (B x)) → is-contr ({x : A} → B x) - is-contr-implicit-Π H = - is-contr-equiv _ equiv-explicit-implicit-Π (is-contr-Π H) -``` - -### The type of functions into a contractible type is contractible - -```agda -is-contr-function-type : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → - is-contr B → is-contr (A → B) -is-contr-function-type is-contr-B = is-contr-Π (λ _ → is-contr-B) -``` - -### The type of equivalences between contractible types is contractible - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - is-contr-equiv-is-contr : - is-contr A → is-contr B → is-contr (A ≃ B) - is-contr-equiv-is-contr (pair a α) (pair b β) = - is-contr-Σ - ( is-contr-function-type (pair b β)) - ( λ x → b) - ( is-contr-product - ( is-contr-Σ - ( is-contr-function-type (pair a α)) - ( λ y → a) - ( is-contr-Π (is-prop-is-contr (pair b β) b))) - ( is-contr-Σ - ( is-contr-function-type (pair a α)) - ( λ y → a) - ( is-contr-Π (is-prop-is-contr (pair a α) a)))) -``` - -### Being contractible is a proposition - -```agda -module _ - {l : Level} {A : UU l} - where - - abstract - is-contr-is-contr : is-contr A → is-contr (is-contr A) - is-contr-is-contr (pair a α) = - is-contr-Σ - ( pair a α) - ( a) - ( is-contr-Π (is-prop-is-contr (pair a α) a)) - - abstract - is-property-is-contr : (H K : is-contr A) → is-contr (H ＝ K) - is-property-is-contr H = is-prop-is-contr (is-contr-is-contr H) H -``` diff --git a/src/foundation-core/decidable-propositions.lagda.md b/src/foundation-core/decidable-propositions.lagda.md index eb48a26b7d..8337ddd8fa 100644 --- a/src/foundation-core/decidable-propositions.lagda.md +++ b/src/foundation-core/decidable-propositions.lagda.md @@ -10,6 +10,7 @@ module foundation-core.decidable-propositions where open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.negation open import foundation.propositional-truncations diff --git a/src/foundation-core/functoriality-dependent-function-types.lagda.md b/src/foundation-core/functoriality-dependent-function-types.lagda.md index 1ed18e0b4c..6c17228aec 100644 --- a/src/foundation-core/functoriality-dependent-function-types.lagda.md +++ b/src/foundation-core/functoriality-dependent-function-types.lagda.md @@ -8,6 +8,7 @@ module foundation-core.functoriality-dependent-function-types where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-extensionality open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation-core/propositions.lagda.md b/src/foundation-core/propositions.lagda.md index 73341db418..c35bb3436e 100644 --- a/src/foundation-core/propositions.lagda.md +++ b/src/foundation-core/propositions.lagda.md @@ -16,7 +16,6 @@ open import foundation-core.contractible-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.transport-along-identifications ``` @@ -236,141 +235,7 @@ module _ product-Prop = (type-product-Prop , is-prop-product-Prop) ``` -### Products of families of propositions are propositions - -```agda -abstract - is-prop-Π : - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → - ((x : A) → is-prop (B x)) → is-prop ((x : A) → B x) - is-prop-Π H = - is-prop-is-proof-irrelevant - ( λ f → is-contr-Π (λ x → is-proof-irrelevant-is-prop (H x) (f x))) - -module _ - {l1 l2 : Level} (A : UU l1) (P : A → Prop l2) - where - - type-Π-Prop : UU (l1 ⊔ l2) - type-Π-Prop = (x : A) → type-Prop (P x) - - is-prop-Π-Prop : is-prop type-Π-Prop - is-prop-Π-Prop = is-prop-Π (λ x → is-prop-type-Prop (P x)) - - Π-Prop : Prop (l1 ⊔ l2) - pr1 Π-Prop = type-Π-Prop - pr2 Π-Prop = is-prop-Π-Prop -``` - -We now repeat the above for implicit Π-types. - -```agda -abstract - is-prop-implicit-Π : - {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → - ((x : A) → is-prop (B x)) → is-prop ({x : A} → B x) - is-prop-implicit-Π H = - is-prop-equiv - ( ( λ f x → f {x}) , - ( is-equiv-is-invertible (λ g {x} → g x) (refl-htpy) (refl-htpy))) - ( is-prop-Π H) - -module _ - {l1 l2 : Level} (A : UU l1) (P : A → Prop l2) - where - - type-implicit-Π-Prop : UU (l1 ⊔ l2) - type-implicit-Π-Prop = {x : A} → type-Prop (P x) - - is-prop-implicit-Π-Prop : is-prop type-implicit-Π-Prop - is-prop-implicit-Π-Prop = - is-prop-implicit-Π (λ x → is-prop-type-Prop (P x)) - - implicit-Π-Prop : Prop (l1 ⊔ l2) - pr1 implicit-Π-Prop = type-implicit-Π-Prop - pr2 implicit-Π-Prop = is-prop-implicit-Π-Prop -``` - -### The type of functions into a proposition is a proposition - -```agda -abstract - is-prop-function-type : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → - is-prop B → is-prop (A → B) - is-prop-function-type H = is-prop-Π (λ _ → H) - -type-function-Prop : - {l1 l2 : Level} → UU l1 → Prop l2 → UU (l1 ⊔ l2) -type-function-Prop A P = A → type-Prop P - -is-prop-function-Prop : - {l1 l2 : Level} {A : UU l1} (P : Prop l2) → - is-prop (type-function-Prop A P) -is-prop-function-Prop P = - is-prop-function-type (is-prop-type-Prop P) - -function-Prop : - {l1 l2 : Level} → UU l1 → Prop l2 → Prop (l1 ⊔ l2) -pr1 (function-Prop A P) = type-function-Prop A P -pr2 (function-Prop A P) = is-prop-function-Prop P - -type-hom-Prop : - {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → UU (l1 ⊔ l2) -type-hom-Prop P = type-function-Prop (type-Prop P) - -is-prop-hom-Prop : - {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → - is-prop (type-hom-Prop P Q) -is-prop-hom-Prop P = is-prop-function-Prop - -hom-Prop : - {l1 l2 : Level} → Prop l1 → Prop l2 → Prop (l1 ⊔ l2) -pr1 (hom-Prop P Q) = type-hom-Prop P Q -pr2 (hom-Prop P Q) = is-prop-hom-Prop P Q - -infixr 5 _⇒_ -_⇒_ = hom-Prop -``` - -### The type of equivalences between two propositions is a proposition - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - is-prop-equiv-is-prop : is-prop A → is-prop B → is-prop (A ≃ B) - is-prop-equiv-is-prop H K = - is-prop-Σ - ( is-prop-function-type K) - ( λ f → - is-prop-product - ( is-prop-Σ - ( is-prop-function-type H) - ( λ g → is-prop-is-contr (is-contr-Π (λ y → K (f (g y)) y)))) - ( is-prop-Σ - ( is-prop-function-type H) - ( λ h → is-prop-is-contr (is-contr-Π (λ x → H (h (f x)) x))))) - -type-equiv-Prop : - { l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → UU (l1 ⊔ l2) -type-equiv-Prop P Q = (type-Prop P) ≃ (type-Prop Q) - -abstract - is-prop-type-equiv-Prop : - {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → - is-prop (type-equiv-Prop P Q) - is-prop-type-equiv-Prop P Q = - is-prop-equiv-is-prop (is-prop-type-Prop P) (is-prop-type-Prop Q) - -equiv-Prop : - { l1 l2 : Level} → Prop l1 → Prop l2 → Prop (l1 ⊔ l2) -pr1 (equiv-Prop P Q) = type-equiv-Prop P Q -pr2 (equiv-Prop P Q) = is-prop-type-equiv-Prop P Q -``` - -### A type is a proposition if and only if the type of its endomaps is contractible +### A type is a proposition if the type of its endomaps is contractible ```agda abstract @@ -378,25 +243,6 @@ abstract {l : Level} (P : UU l) → is-contr (P → P) → is-prop P is-prop-is-contr-endomaps P H = is-prop-all-elements-equal (λ x → htpy-eq (eq-is-contr H)) - -abstract - is-contr-endomaps-is-prop : - {l : Level} (P : UU l) → is-prop P → is-contr (P → P) - is-contr-endomaps-is-prop P is-prop-P = - is-proof-irrelevant-is-prop (is-prop-function-type is-prop-P) id -``` - -### Being a proposition is a proposition - -```agda -abstract - is-prop-is-prop : - {l : Level} (A : UU l) → is-prop (is-prop A) - is-prop-is-prop A = is-prop-Π (λ x → is-prop-Π (λ y → is-property-is-contr)) - -is-prop-Prop : {l : Level} (A : UU l) → Prop l -pr1 (is-prop-Prop A) = is-prop A -pr2 (is-prop-Prop A) = is-prop-is-prop A ``` ## See also diff --git a/src/foundation-core/subtypes.lagda.md b/src/foundation-core/subtypes.lagda.md index 128f682668..c6a4afc4c4 100644 --- a/src/foundation-core/subtypes.lagda.md +++ b/src/foundation-core/subtypes.lagda.md @@ -9,6 +9,7 @@ module foundation-core.subtypes where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.logical-equivalences open import foundation.subtype-identity-principle open import foundation.universe-levels diff --git a/src/foundation-core/truncated-types.lagda.md b/src/foundation-core/truncated-types.lagda.md index 32a4282a70..aab89dd8cf 100644 --- a/src/foundation-core/truncated-types.lagda.md +++ b/src/foundation-core/truncated-types.lagda.md @@ -10,6 +10,7 @@ module foundation-core.truncated-types where open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality open import foundation.function-extensionality-axiom diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index 9979470954..0639393861 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -120,6 +120,8 @@ open import foundation.dependent-homotopies public open import foundation.dependent-identifications public open import foundation.dependent-inverse-sequential-diagrams public open import foundation.dependent-pair-types public +open import foundation.dependent-products-contractible-types public +open import foundation.dependent-products-propositions public open import foundation.dependent-products-pullbacks public open import foundation.dependent-sequences public open import foundation.dependent-sums-pullbacks public diff --git a/src/foundation/apartness-relations.lagda.md b/src/foundation/apartness-relations.lagda.md index ed13a9135d..605d8b5b43 100644 --- a/src/foundation/apartness-relations.lagda.md +++ b/src/foundation/apartness-relations.lagda.md @@ -9,6 +9,7 @@ module foundation.apartness-relations where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.existential-quantification open import foundation.propositional-truncations diff --git a/src/foundation/binary-functoriality-set-quotients.lagda.md b/src/foundation/binary-functoriality-set-quotients.lagda.md index 991ebbee26..767805918d 100644 --- a/src/foundation/binary-functoriality-set-quotients.lagda.md +++ b/src/foundation/binary-functoriality-set-quotients.lagda.md @@ -11,6 +11,7 @@ module foundation.binary-functoriality-set-quotients where ```agda open import foundation.binary-homotopies open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.exponents-set-quotients open import foundation.function-extensionality open import foundation.function-extensionality-axiom diff --git a/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md b/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md index eb1244a707..954e06617b 100644 --- a/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md +++ b/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md @@ -8,6 +8,7 @@ module foundation.binary-reflecting-maps-equivalence-relations where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction diff --git a/src/foundation/binary-relations.lagda.md b/src/foundation/binary-relations.lagda.md index b9ad577958..7c18b153ba 100644 --- a/src/foundation/binary-relations.lagda.md +++ b/src/foundation/binary-relations.lagda.md @@ -8,6 +8,7 @@ module foundation.binary-relations where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.iterated-dependent-product-types diff --git a/src/foundation/coherently-invertible-maps.lagda.md b/src/foundation/coherently-invertible-maps.lagda.md index 03f1ed4655..d811bbad78 100644 --- a/src/foundation/coherently-invertible-maps.lagda.md +++ b/src/foundation/coherently-invertible-maps.lagda.md @@ -10,6 +10,7 @@ open import foundation-core.coherently-invertible-maps public ```agda open import foundation.action-on-identifications-functions +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/foundation/conjunction.lagda.md b/src/foundation/conjunction.lagda.md index 54c4cc00c9..0ba08d98b8 100644 --- a/src/foundation/conjunction.lagda.md +++ b/src/foundation/conjunction.lagda.md @@ -9,6 +9,7 @@ module foundation.conjunction where ```agda open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.logical-equivalences open import foundation.propositional-truncations open import foundation.universal-property-cartesian-product-types diff --git a/src/foundation/connected-maps.lagda.md b/src/foundation/connected-maps.lagda.md index 8dcb862a92..74bc45c267 100644 --- a/src/foundation/connected-maps.lagda.md +++ b/src/foundation/connected-maps.lagda.md @@ -9,6 +9,7 @@ module foundation.connected-maps where ```agda open import foundation.connected-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction diff --git a/src/foundation/continuations.lagda.md b/src/foundation/continuations.lagda.md index f959426927..8792570be4 100644 --- a/src/foundation/continuations.lagda.md +++ b/src/foundation/continuations.lagda.md @@ -8,6 +8,7 @@ module foundation.continuations where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.evaluation-functions open import foundation.type-arithmetic-dependent-function-types diff --git a/src/foundation/contractible-types.lagda.md b/src/foundation/contractible-types.lagda.md index fb64cece68..6491e0a1ed 100644 --- a/src/foundation/contractible-types.lagda.md +++ b/src/foundation/contractible-types.lagda.md @@ -4,6 +4,7 @@ module foundation.contractible-types where open import foundation-core.contractible-types public +open import foundation.dependent-products-contractible-types public ```
Imports @@ -19,7 +20,6 @@ open import foundation.subuniverses open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.constant-maps open import foundation-core.contractible-maps open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/decidable-embeddings.lagda.md b/src/foundation/decidable-embeddings.lagda.md index f4780285bd..3b869167e1 100644 --- a/src/foundation/decidable-embeddings.lagda.md +++ b/src/foundation/decidable-embeddings.lagda.md @@ -13,6 +13,7 @@ open import foundation.decidable-maps open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.fibers-of-maps open import foundation.functoriality-cartesian-product-types diff --git a/src/foundation/decidable-equality.lagda.md b/src/foundation/decidable-equality.lagda.md index 05a5b5b201..dbd26b93ec 100644 --- a/src/foundation/decidable-equality.lagda.md +++ b/src/foundation/decidable-equality.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.injective-maps open import foundation.negation diff --git a/src/foundation/decidable-equivalence-relations.lagda.md b/src/foundation/decidable-equivalence-relations.lagda.md index 149af1b5ca..935c973f50 100644 --- a/src/foundation/decidable-equivalence-relations.lagda.md +++ b/src/foundation/decidable-equivalence-relations.lagda.md @@ -14,6 +14,7 @@ open import foundation.decidable-relations open import foundation.decidable-subtypes open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.effective-maps-equivalence-relations open import foundation.equivalence-classes open import foundation.equivalence-relations diff --git a/src/foundation/decidable-subtypes.lagda.md b/src/foundation/decidable-subtypes.lagda.md index 0bd5ecec7f..208d8f6862 100644 --- a/src/foundation/decidable-subtypes.lagda.md +++ b/src/foundation/decidable-subtypes.lagda.md @@ -14,6 +14,7 @@ open import foundation.decidable-maps open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.functoriality-cartesian-product-types open import foundation.functoriality-dependent-function-types diff --git a/src/foundation/dependent-products-contractible-types.lagda.md b/src/foundation/dependent-products-contractible-types.lagda.md new file mode 100644 index 0000000000..0cf967700c --- /dev/null +++ b/src/foundation/dependent-products-contractible-types.lagda.md @@ -0,0 +1,99 @@ +# Dependent products of contractible types + +```agda +module foundation.dependent-products-contractible-types where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.function-extensionality +open import foundation.implicit-function-types +open import foundation.universe-levels + +open import foundation-core.contractible-types +open import foundation-core.equivalences +open import foundation-core.identity-types +``` + +
+ +## Idea + +Contractible types are types that have, up to identification, exactly one +element. + +## Properties + +### Products of families of contractible types are contractible + +```agda +abstract + is-contr-Π : + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → + ((x : A) → is-contr (B x)) → is-contr ((x : A) → B x) + pr1 (is-contr-Π {A = A} {B = B} H) x = center (H x) + pr2 (is-contr-Π {A = A} {B = B} H) f = + eq-htpy (λ x → contraction (H x) (f x)) + +abstract + is-contr-implicit-Π : + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → + ((x : A) → is-contr (B x)) → is-contr ({x : A} → B x) + is-contr-implicit-Π H = + is-contr-equiv _ equiv-explicit-implicit-Π (is-contr-Π H) +``` + +### The type of functions into a contractible type is contractible + +```agda +is-contr-function-type : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → + is-contr B → is-contr (A → B) +is-contr-function-type is-contr-B = is-contr-Π (λ _ → is-contr-B) +``` + +### The type of equivalences between contractible types is contractible + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + is-contr-equiv-is-contr : + is-contr A → is-contr B → is-contr (A ≃ B) + is-contr-equiv-is-contr (pair a α) (pair b β) = + is-contr-Σ + ( is-contr-function-type (pair b β)) + ( λ x → b) + ( is-contr-product + ( is-contr-Σ + ( is-contr-function-type (pair a α)) + ( λ y → a) + ( is-contr-Π (is-prop-is-contr (pair b β) b))) + ( is-contr-Σ + ( is-contr-function-type (pair a α)) + ( λ y → a) + ( is-contr-Π (is-prop-is-contr (pair a α) a)))) +``` + +### Being contractible is a proposition + +```agda +module _ + {l : Level} {A : UU l} + where + + abstract + is-contr-is-contr : is-contr A → is-contr (is-contr A) + is-contr-is-contr (pair a α) = + is-contr-Σ + ( pair a α) + ( a) + ( is-contr-Π (is-prop-is-contr (pair a α) a)) + + abstract + is-property-is-contr : (H K : is-contr A) → is-contr (H ＝ K) + is-property-is-contr H = is-prop-is-contr (is-contr-is-contr H) H +``` diff --git a/src/foundation/dependent-products-propositions.lagda.md b/src/foundation/dependent-products-propositions.lagda.md new file mode 100644 index 0000000000..029f396e8a --- /dev/null +++ b/src/foundation/dependent-products-propositions.lagda.md @@ -0,0 +1,246 @@ +# Dependent products of propositions + +```agda +module foundation.dependent-products-propositions where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.universe-levels + +open import foundation-core.contractible-types +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.propositions +``` + +
+ +## Idea + +A type is a {{#concept "proposition" Agda=is-prop}} if its +[identity types](foundation-core.identity-types.md) are +[contractible](foundation-core.contractible-types.md). This condition is +[equivalent](foundation-core.equivalences.md) to the condition that it has up to +identification at most one element. + +## Definitions + +### Products of families of propositions are propositions + +```agda +abstract + is-prop-Π : + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → + ((x : A) → is-prop (B x)) → is-prop ((x : A) → B x) + is-prop-Π H = + is-prop-is-proof-irrelevant + ( λ f → is-contr-Π (λ x → is-proof-irrelevant-is-prop (H x) (f x))) + +module _ + {l1 l2 : Level} (A : UU l1) (P : A → Prop l2) + where + + type-Π-Prop : UU (l1 ⊔ l2) + type-Π-Prop = (x : A) → type-Prop (P x) + + is-prop-Π-Prop : is-prop type-Π-Prop + is-prop-Π-Prop = is-prop-Π (λ x → is-prop-type-Prop (P x)) + + Π-Prop : Prop (l1 ⊔ l2) + pr1 Π-Prop = type-Π-Prop + pr2 Π-Prop = is-prop-Π-Prop +``` + +We now repeat the above for implicit Π-types. + +```agda +abstract + is-prop-implicit-Π : + {l1 l2 : Level} {A : UU l1} {B : A → UU l2} → + ((x : A) → is-prop (B x)) → is-prop ({x : A} → B x) + is-prop-implicit-Π H = + is-prop-equiv + ( ( λ f x → f {x}) , + ( is-equiv-is-invertible (λ g {x} → g x) (refl-htpy) (refl-htpy))) + ( is-prop-Π H) + +module _ + {l1 l2 : Level} (A : UU l1) (P : A → Prop l2) + where + + type-implicit-Π-Prop : UU (l1 ⊔ l2) + type-implicit-Π-Prop = {x : A} → type-Prop (P x) + + is-prop-implicit-Π-Prop : is-prop type-implicit-Π-Prop + is-prop-implicit-Π-Prop = + is-prop-implicit-Π (λ x → is-prop-type-Prop (P x)) + + implicit-Π-Prop : Prop (l1 ⊔ l2) + pr1 implicit-Π-Prop = type-implicit-Π-Prop + pr2 implicit-Π-Prop = is-prop-implicit-Π-Prop +``` + +### The type of functions into a proposition is a proposition + +```agda +abstract + is-prop-function-type : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → + is-prop B → is-prop (A → B) + is-prop-function-type H = is-prop-Π (λ _ → H) + +type-function-Prop : + {l1 l2 : Level} → UU l1 → Prop l2 → UU (l1 ⊔ l2) +type-function-Prop A P = A → type-Prop P + +is-prop-function-Prop : + {l1 l2 : Level} {A : UU l1} (P : Prop l2) → + is-prop (type-function-Prop A P) +is-prop-function-Prop P = + is-prop-function-type (is-prop-type-Prop P) + +function-Prop : + {l1 l2 : Level} → UU l1 → Prop l2 → Prop (l1 ⊔ l2) +pr1 (function-Prop A P) = type-function-Prop A P +pr2 (function-Prop A P) = is-prop-function-Prop P + +type-hom-Prop : + {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → UU (l1 ⊔ l2) +type-hom-Prop P = type-function-Prop (type-Prop P) + +is-prop-hom-Prop : + {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → + is-prop (type-hom-Prop P Q) +is-prop-hom-Prop P = is-prop-function-Prop + +hom-Prop : + {l1 l2 : Level} → Prop l1 → Prop l2 → Prop (l1 ⊔ l2) +pr1 (hom-Prop P Q) = type-hom-Prop P Q +pr2 (hom-Prop P Q) = is-prop-hom-Prop P Q + +infixr 5 _⇒_ +_⇒_ = hom-Prop +``` + +### The type of equivalences between two propositions is a proposition + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + is-prop-equiv-is-prop : is-prop A → is-prop B → is-prop (A ≃ B) + is-prop-equiv-is-prop H K = + is-prop-Σ + ( is-prop-function-type K) + ( λ f → + is-prop-product + ( is-prop-Σ + ( is-prop-function-type H) + ( λ g → is-prop-is-contr (is-contr-Π (λ y → K (f (g y)) y)))) + ( is-prop-Σ + ( is-prop-function-type H) + ( λ h → is-prop-is-contr (is-contr-Π (λ x → H (h (f x)) x))))) + +type-equiv-Prop : + { l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → UU (l1 ⊔ l2) +type-equiv-Prop P Q = (type-Prop P) ≃ (type-Prop Q) + +abstract + is-prop-type-equiv-Prop : + {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) → + is-prop (type-equiv-Prop P Q) + is-prop-type-equiv-Prop P Q = + is-prop-equiv-is-prop (is-prop-type-Prop P) (is-prop-type-Prop Q) + +equiv-Prop : + { l1 l2 : Level} → Prop l1 → Prop l2 → Prop (l1 ⊔ l2) +pr1 (equiv-Prop P Q) = type-equiv-Prop P Q +pr2 (equiv-Prop P Q) = is-prop-type-equiv-Prop P Q +``` + +### A type is a proposition if and only if the type of its endomaps is contractible + +```agda +abstract + is-contr-endomaps-is-prop : + {l : Level} (P : UU l) → is-prop P → is-contr (P → P) + is-contr-endomaps-is-prop P is-prop-P = + is-proof-irrelevant-is-prop (is-prop-function-type is-prop-P) id +``` + +### Being a proposition is a proposition + +```agda +abstract + is-prop-is-prop : + {l : Level} (A : UU l) → is-prop (is-prop A) + is-prop-is-prop A = is-prop-Π (λ x → is-prop-Π (λ y → is-property-is-contr)) + +is-prop-Prop : {l : Level} (A : UU l) → Prop l +pr1 (is-prop-Prop A) = is-prop A +pr2 (is-prop-Prop A) = is-prop-is-prop A +``` + +## See also + +### Operations on propositions + +There is a wide range of operations on propositions due to the rich structure of +intuitionistic logic. Below we give a structured overview of a notable selection +of such operations and their notation in the library. + +The list is split into two sections, the first consists of operations that +generalize to arbitrary types and even sufficiently nice +[subuniverses](foundation.subuniverses.md), such as +$n$-[types](foundation-core.truncated-types.md). + +| Name | Operator on types | Operator on propositions/subtypes | +| ----------------------------------------------------------- | ----------------- | --------------------------------- | +| [Dependent sum](foundation.dependent-pair-types.md) | `Σ` | `Σ-Prop` | +| [Dependent product](foundation.dependent-function-types.md) | `Π` | `Π-Prop` | +| [Functions](foundation-core.function-types.md) | `→` | `⇒` | +| [Logical equivalence](foundation.logical-equivalences.md) | `↔` | `⇔` | +| [Product](foundation-core.cartesian-product-types.md) | `×` | `product-Prop` | +| [Join](synthetic-homotopy-theory.joins-of-types.md) | `*` | `join-Prop` | +| [Exclusive sum](foundation.exclusive-sum.md) | `exclusive-sum` | `exclusive-sum-Prop` | +| [Coproduct](foundation-core.coproduct-types.md) | `+` | _N/A_ | + +Note that for many operations in the second section, there is an equivalent +operation on propositions in the first. + +| Name | Operator on types | Operator on propositions/subtypes | +| ---------------------------------------------------------------------------- | --------------------------- | ---------------------------------------- | +| [Initial object](foundation-core.empty-types.md) | `empty` | `empty-Prop` | +| [Terminal object](foundation.unit-type.md) | `unit` | `unit-Prop` | +| [Existential quantification](foundation.existential-quantification.md) | `exists-structure` | `∃` | +| [Unique existential quantification](foundation.uniqueness-quantification.md) | `uniquely-exists-structure` | `∃!` | +| [Universal quantification](foundation.universal-quantification.md) | | `∀'` (equivalent to `Π-Prop`) | +| [Conjunction](foundation.conjunction.md) | | `∧` (equivalent to `product-Prop`) | +| [Disjunction](foundation.disjunction.md) | `disjunction-type` | `∨` (equivalent to `join-Prop`) | +| [Exclusive disjunction](foundation.exclusive-disjunction.md) | `xor-type` | `⊻` (equivalent to `exclusive-sum-Prop`) | +| [Negation](foundation.negation.md) | `¬` | `¬'` | +| [Double negation](foundation.double-negation.md) | `¬¬` | `¬¬'` | + +We can also organize these operations by indexed and binary variants, giving us +the following table: + +| Name | Binary | Indexed | +| ---------------------- | ------ | ------- | +| Product | `×` | `Π` | +| Conjunction | `∧` | `∀'` | +| Constructive existence | `+` | `Σ` | +| Existence | `∨` | `∃` | +| Unique existence | `⊻` | `∃!` | + +### Table of files about propositional logic + +The following table gives an overview of basic constructions in propositional +logic and related considerations. + +{{#include tables/propositional-logic.md}} diff --git a/src/foundation/discrete-binary-relations.lagda.md b/src/foundation/discrete-binary-relations.lagda.md index 9edf7ffd3f..ef556b6912 100644 --- a/src/foundation/discrete-binary-relations.lagda.md +++ b/src/foundation/discrete-binary-relations.lagda.md @@ -8,6 +8,7 @@ module foundation.discrete-binary-relations where ```agda open import foundation.binary-relations +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/foundation/discrete-reflexive-relations.lagda.md b/src/foundation/discrete-reflexive-relations.lagda.md index 236e380874..2bb6edc906 100644 --- a/src/foundation/discrete-reflexive-relations.lagda.md +++ b/src/foundation/discrete-reflexive-relations.lagda.md @@ -10,6 +10,7 @@ module foundation.discrete-reflexive-relations where open import foundation.binary-relations open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.reflexive-relations open import foundation.torsorial-type-families open import foundation.universe-levels diff --git a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md index 76cdac43a7..349b82ae5a 100644 --- a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md @@ -10,6 +10,7 @@ module foundation.discrete-relaxed-sigma-decompositions where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.relaxed-sigma-decompositions open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/discrete-sigma-decompositions.lagda.md b/src/foundation/discrete-sigma-decompositions.lagda.md index 3ed376b244..9b44f7a2e0 100644 --- a/src/foundation/discrete-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-sigma-decompositions.lagda.md @@ -10,6 +10,7 @@ module foundation.discrete-sigma-decompositions where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.propositional-truncations open import foundation.sigma-decompositions diff --git a/src/foundation/disjoint-subtypes.lagda.md b/src/foundation/disjoint-subtypes.lagda.md index 1c8072a0ed..f336231418 100644 --- a/src/foundation/disjoint-subtypes.lagda.md +++ b/src/foundation/disjoint-subtypes.lagda.md @@ -9,6 +9,7 @@ module foundation.disjoint-subtypes where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.propositions open import foundation.subtypes diff --git a/src/foundation/double-negation-stable-equality.lagda.md b/src/foundation/double-negation-stable-equality.lagda.md index 8917c7da41..9dced91af2 100644 --- a/src/foundation/double-negation-stable-equality.lagda.md +++ b/src/foundation/double-negation-stable-equality.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.equality-cartesian-product-types open import foundation.equality-dependent-pair-types diff --git a/src/foundation/double-negation-stable-propositions.lagda.md b/src/foundation/double-negation-stable-propositions.lagda.md index 0ba325bf24..8fb70bf27b 100644 --- a/src/foundation/double-negation-stable-propositions.lagda.md +++ b/src/foundation/double-negation-stable-propositions.lagda.md @@ -13,6 +13,7 @@ open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.double-negation open import foundation.embeddings diff --git a/src/foundation/double-powersets.lagda.md b/src/foundation/double-powersets.lagda.md index 45d84375c0..19aabecf18 100644 --- a/src/foundation/double-powersets.lagda.md +++ b/src/foundation/double-powersets.lagda.md @@ -8,6 +8,7 @@ module foundation.double-powersets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.powersets open import foundation.propositional-truncations diff --git a/src/foundation/dubuc-penon-compact-types.lagda.md b/src/foundation/dubuc-penon-compact-types.lagda.md index 7a80fcc588..6f726c9481 100644 --- a/src/foundation/dubuc-penon-compact-types.lagda.md +++ b/src/foundation/dubuc-penon-compact-types.lagda.md @@ -7,6 +7,7 @@ module foundation.dubuc-penon-compact-types where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.universal-quantification open import foundation.universe-levels diff --git a/src/foundation/embeddings.lagda.md b/src/foundation/embeddings.lagda.md index 6631d6bead..16bc0c8d80 100644 --- a/src/foundation/embeddings.lagda.md +++ b/src/foundation/embeddings.lagda.md @@ -12,6 +12,7 @@ open import foundation-core.embeddings public open import foundation.action-on-identifications-functions open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-cartesian-product-types open import foundation.functoriality-dependent-pair-types diff --git a/src/foundation/empty-types.lagda.md b/src/foundation/empty-types.lagda.md index 67cfc187b9..28925f767f 100644 --- a/src/foundation/empty-types.lagda.md +++ b/src/foundation/empty-types.lagda.md @@ -10,6 +10,7 @@ open import foundation-core.empty-types public ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.propositional-truncations diff --git a/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md b/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md index e5ff5b16a5..3a0d69c835 100644 --- a/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md +++ b/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-squares-of-maps open import foundation.connected-maps open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.function-extensionality open import foundation.functoriality-truncation diff --git a/src/foundation/equality-dependent-function-types.lagda.md b/src/foundation/equality-dependent-function-types.lagda.md index 04e62574f7..2512259ea6 100644 --- a/src/foundation/equality-dependent-function-types.lagda.md +++ b/src/foundation/equality-dependent-function-types.lagda.md @@ -8,6 +8,7 @@ module foundation.equality-dependent-function-types where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.fundamental-theorem-of-identity-types open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation/equivalence-extensionality.lagda.md b/src/foundation/equivalence-extensionality.lagda.md index 2666bf9f62..6facfb0297 100644 --- a/src/foundation/equivalence-extensionality.lagda.md +++ b/src/foundation/equivalence-extensionality.lagda.md @@ -8,6 +8,7 @@ module foundation.equivalence-extensionality where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-universal-property-equivalences open import foundation.function-extensionality open import foundation.function-extensionality-axiom diff --git a/src/foundation/equivalence-injective-type-families.lagda.md b/src/foundation/equivalence-injective-type-families.lagda.md index 5b1ea1cb5f..3fcc142fd6 100644 --- a/src/foundation/equivalence-injective-type-families.lagda.md +++ b/src/foundation/equivalence-injective-type-families.lagda.md @@ -8,6 +8,7 @@ module foundation.equivalence-injective-type-families where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.functoriality-dependent-function-types open import foundation.iterated-dependent-product-types open import foundation.univalence diff --git a/src/foundation/equivalences.lagda.md b/src/foundation/equivalences.lagda.md index 14919d3b92..c7c26fb5c4 100644 --- a/src/foundation/equivalences.lagda.md +++ b/src/foundation/equivalences.lagda.md @@ -12,6 +12,7 @@ open import foundation-core.equivalences public open import foundation.action-on-identifications-functions open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalence-extensionality open import foundation.function-extensionality open import foundation.functoriality-fibers-of-maps diff --git a/src/foundation/exclusive-disjunction.lagda.md b/src/foundation/exclusive-disjunction.lagda.md index 92407933be..5d95f4c232 100644 --- a/src/foundation/exclusive-disjunction.lagda.md +++ b/src/foundation/exclusive-disjunction.lagda.md @@ -10,6 +10,7 @@ module foundation.exclusive-disjunction where open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-coproduct-types open import foundation.exclusive-sum open import foundation.functoriality-coproduct-types diff --git a/src/foundation/exclusive-sum.lagda.md b/src/foundation/exclusive-sum.lagda.md index e47925ccc5..d18bfe341a 100644 --- a/src/foundation/exclusive-sum.lagda.md +++ b/src/foundation/exclusive-sum.lagda.md @@ -11,6 +11,7 @@ open import foundation.conjunction open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.negation open import foundation.propositional-extensionality open import foundation.symmetric-operations diff --git a/src/foundation/existential-quantification.lagda.md b/src/foundation/existential-quantification.lagda.md index 370906429c..1cb3523d44 100644 --- a/src/foundation/existential-quantification.lagda.md +++ b/src/foundation/existential-quantification.lagda.md @@ -9,6 +9,7 @@ module foundation.existential-quantification where ```agda open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.logical-equivalences open import foundation.propositional-extensionality open import foundation.propositional-truncations diff --git a/src/foundation/exponents-set-quotients.lagda.md b/src/foundation/exponents-set-quotients.lagda.md index 8290ecd3dd..7002792799 100644 --- a/src/foundation/exponents-set-quotients.lagda.md +++ b/src/foundation/exponents-set-quotients.lagda.md @@ -11,6 +11,7 @@ module foundation.exponents-set-quotients where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.functoriality-set-quotients diff --git a/src/foundation/families-of-equivalences.lagda.md b/src/foundation/families-of-equivalences.lagda.md index 3cfded46ff..172bf565b9 100644 --- a/src/foundation/families-of-equivalences.lagda.md +++ b/src/foundation/families-of-equivalences.lagda.md @@ -9,6 +9,7 @@ open import foundation-core.families-of-equivalences public
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.universe-levels diff --git a/src/foundation/families-of-maps.lagda.md b/src/foundation/families-of-maps.lagda.md index be752e98b8..ffcfb2087d 100644 --- a/src/foundation/families-of-maps.lagda.md +++ b/src/foundation/families-of-maps.lagda.md @@ -8,6 +8,7 @@ module foundation.families-of-maps where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.type-arithmetic-dependent-pair-types open import foundation.universal-property-dependent-pair-types diff --git a/src/foundation/fibered-maps.lagda.md b/src/foundation/fibered-maps.lagda.md index 686a7b601f..2e4565e278 100644 --- a/src/foundation/fibered-maps.lagda.md +++ b/src/foundation/fibered-maps.lagda.md @@ -9,6 +9,7 @@ module foundation.fibered-maps where ```agda open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction diff --git a/src/foundation/full-subtypes.lagda.md b/src/foundation/full-subtypes.lagda.md index 57a9714080..565bd3f72b 100644 --- a/src/foundation/full-subtypes.lagda.md +++ b/src/foundation/full-subtypes.lagda.md @@ -9,6 +9,7 @@ module foundation.full-subtypes where ```agda open import foundation.decidable-subtypes open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/functional-correspondences.lagda.md b/src/foundation/functional-correspondences.lagda.md index ed5998a661..d2a98ae2fe 100644 --- a/src/foundation/functional-correspondences.lagda.md +++ b/src/foundation/functional-correspondences.lagda.md @@ -10,6 +10,7 @@ module foundation.functional-correspondences where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types diff --git a/src/foundation/functoriality-morphisms-arrows.lagda.md b/src/foundation/functoriality-morphisms-arrows.lagda.md index aee689e627..8ad3592690 100644 --- a/src/foundation/functoriality-morphisms-arrows.lagda.md +++ b/src/foundation/functoriality-morphisms-arrows.lagda.md @@ -15,6 +15,7 @@ open import foundation.composition-algebra open import foundation.cones-over-cospan-diagrams open import foundation.cospan-diagrams open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/foundation/functoriality-propositional-truncation.lagda.md b/src/foundation/functoriality-propositional-truncation.lagda.md index 3166bf1b47..32fdfc1b87 100644 --- a/src/foundation/functoriality-propositional-truncation.lagda.md +++ b/src/foundation/functoriality-propositional-truncation.lagda.md @@ -9,6 +9,7 @@ module foundation.functoriality-propositional-truncation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-extensionality-axiom open import foundation.logical-equivalences open import foundation.propositional-truncations diff --git a/src/foundation/functoriality-set-quotients.lagda.md b/src/foundation/functoriality-set-quotients.lagda.md index 556c6b19c2..31b756d2f8 100644 --- a/src/foundation/functoriality-set-quotients.lagda.md +++ b/src/foundation/functoriality-set-quotients.lagda.md @@ -11,6 +11,7 @@ module foundation.functoriality-set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction diff --git a/src/foundation/functoriality-set-truncation.lagda.md b/src/foundation/functoriality-set-truncation.lagda.md index 6e1fb2db8d..e10e05a582 100644 --- a/src/foundation/functoriality-set-truncation.lagda.md +++ b/src/foundation/functoriality-set-truncation.lagda.md @@ -9,6 +9,7 @@ module foundation.functoriality-set-truncation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.functoriality-truncation open import foundation.images open import foundation.injective-maps diff --git a/src/foundation/idempotent-maps.lagda.md b/src/foundation/idempotent-maps.lagda.md index 791fca96fa..3e0e0adf77 100644 --- a/src/foundation/idempotent-maps.lagda.md +++ b/src/foundation/idempotent-maps.lagda.md @@ -8,6 +8,7 @@ module foundation.idempotent-maps where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.homotopy-algebra open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/impredicative-encodings.lagda.md b/src/foundation/impredicative-encodings.lagda.md index dbf1136729..fadc6aea05 100644 --- a/src/foundation/impredicative-encodings.lagda.md +++ b/src/foundation/impredicative-encodings.lagda.md @@ -9,6 +9,7 @@ module foundation.impredicative-encodings where ```agda open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.empty-types open import foundation.existential-quantification diff --git a/src/foundation/injective-maps.lagda.md b/src/foundation/injective-maps.lagda.md index 3026f03a10..09640c54b1 100644 --- a/src/foundation/injective-maps.lagda.md +++ b/src/foundation/injective-maps.lagda.md @@ -11,6 +11,7 @@ open import foundation-core.injective-maps public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.logical-equivalences diff --git a/src/foundation/intersections-subtypes.lagda.md b/src/foundation/intersections-subtypes.lagda.md index 3ff9cc3f3b..776056c8e1 100644 --- a/src/foundation/intersections-subtypes.lagda.md +++ b/src/foundation/intersections-subtypes.lagda.md @@ -10,6 +10,7 @@ module foundation.intersections-subtypes where open import foundation.conjunction open import foundation.decidable-subtypes open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.large-locale-of-subtypes open import foundation.powersets open import foundation.universe-levels diff --git a/src/foundation/irrefutable-propositions.lagda.md b/src/foundation/irrefutable-propositions.lagda.md index a6a0d7fcde..d89ec3fd7b 100644 --- a/src/foundation/irrefutable-propositions.lagda.md +++ b/src/foundation/irrefutable-propositions.lagda.md @@ -13,6 +13,7 @@ open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.empty-types open import foundation.function-types diff --git a/src/foundation/isolated-elements.lagda.md b/src/foundation/isolated-elements.lagda.md index ebf38b94f7..f4af701d09 100644 --- a/src/foundation/isolated-elements.lagda.md +++ b/src/foundation/isolated-elements.lagda.md @@ -14,6 +14,7 @@ open import foundation.decidable-equality open import foundation.decidable-maps open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/foundation/iterated-dependent-product-types.lagda.md b/src/foundation/iterated-dependent-product-types.lagda.md index eb1217e03e..80ace77d32 100644 --- a/src/foundation/iterated-dependent-product-types.lagda.md +++ b/src/foundation/iterated-dependent-product-types.lagda.md @@ -11,6 +11,8 @@ open import foundation.telescopes public ```agda open import elementary-number-theory.natural-numbers +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation/large-locale-of-propositions.lagda.md b/src/foundation/large-locale-of-propositions.lagda.md index d5ef3ea50a..671ef5ad4b 100644 --- a/src/foundation/large-locale-of-propositions.lagda.md +++ b/src/foundation/large-locale-of-propositions.lagda.md @@ -8,6 +8,7 @@ module foundation.large-locale-of-propositions where ```agda open import foundation.conjunction +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.existential-quantification open import foundation.logical-equivalences diff --git a/src/foundation/law-of-excluded-middle.lagda.md b/src/foundation/law-of-excluded-middle.lagda.md index a633ea32d6..2a3935ebdc 100644 --- a/src/foundation/law-of-excluded-middle.lagda.md +++ b/src/foundation/law-of-excluded-middle.lagda.md @@ -9,6 +9,7 @@ module foundation.law-of-excluded-middle where ```agda open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.universe-levels open import foundation-core.decidable-propositions diff --git a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md index 242c9b27b6..a91743a9f5 100644 --- a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md +++ b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.parity-natural-numbers open import foundation.booleans open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.universal-quantification open import foundation.universe-levels diff --git a/src/foundation/limited-principle-of-omniscience.lagda.md b/src/foundation/limited-principle-of-omniscience.lagda.md index e66cea9ad0..c9a3616681 100644 --- a/src/foundation/limited-principle-of-omniscience.lagda.md +++ b/src/foundation/limited-principle-of-omniscience.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.booleans open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.existential-quantification open import foundation.negation diff --git a/src/foundation/locally-small-types.lagda.md b/src/foundation/locally-small-types.lagda.md index d46bd2d4bb..3640cd7534 100644 --- a/src/foundation/locally-small-types.lagda.md +++ b/src/foundation/locally-small-types.lagda.md @@ -8,6 +8,7 @@ module foundation.locally-small-types where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.inhabited-subtypes diff --git a/src/foundation/logical-equivalences.lagda.md b/src/foundation/logical-equivalences.lagda.md index d806e1ca3d..2fc722214b 100644 --- a/src/foundation/logical-equivalences.lagda.md +++ b/src/foundation/logical-equivalences.lagda.md @@ -8,6 +8,7 @@ module foundation.logical-equivalences where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-cartesian-product-types open import foundation.equivalence-extensionality open import foundation.function-extensionality diff --git a/src/foundation/maps-in-global-subuniverses.lagda.md b/src/foundation/maps-in-global-subuniverses.lagda.md index c3f263ac66..93a167a49c 100644 --- a/src/foundation/maps-in-global-subuniverses.lagda.md +++ b/src/foundation/maps-in-global-subuniverses.lagda.md @@ -9,6 +9,7 @@ module foundation.maps-in-global-subuniverses where ```agda open import foundation.cartesian-morphisms-arrows open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.fibers-of-maps open import foundation.functoriality-fibers-of-maps open import foundation.global-subuniverses diff --git a/src/foundation/mere-path-cosplit-maps.lagda.md b/src/foundation/mere-path-cosplit-maps.lagda.md index dd39c03112..5cd5644ffe 100644 --- a/src/foundation/mere-path-cosplit-maps.lagda.md +++ b/src/foundation/mere-path-cosplit-maps.lagda.md @@ -9,6 +9,7 @@ module foundation.mere-path-cosplit-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences-arrows open import foundation.inhabited-types open import foundation.iterated-dependent-product-types diff --git a/src/foundation/monomorphisms.lagda.md b/src/foundation/monomorphisms.lagda.md index 1908560489..9fc0e6bd82 100644 --- a/src/foundation/monomorphisms.lagda.md +++ b/src/foundation/monomorphisms.lagda.md @@ -9,6 +9,7 @@ module foundation.monomorphisms where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.function-extensionality open import foundation.functoriality-function-types diff --git a/src/foundation/negation.lagda.md b/src/foundation/negation.lagda.md index 273c37d133..18aab537b4 100644 --- a/src/foundation/negation.lagda.md +++ b/src/foundation/negation.lagda.md @@ -10,6 +10,7 @@ open import foundation-core.negation public ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.logical-equivalences open import foundation.universe-levels diff --git a/src/foundation/partitions.lagda.md b/src/foundation/partitions.lagda.md index 11658b834b..b46f3f5c10 100644 --- a/src/foundation/partitions.lagda.md +++ b/src/foundation/partitions.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.conjunction open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.existential-quantification diff --git a/src/foundation/path-cosplit-maps.lagda.md b/src/foundation/path-cosplit-maps.lagda.md index 6a4f96e2e3..602902e4a9 100644 --- a/src/foundation/path-cosplit-maps.lagda.md +++ b/src/foundation/path-cosplit-maps.lagda.md @@ -13,6 +13,8 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-triangles-of-maps open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-cartesian-product-types open import foundation.equality-coproduct-types diff --git a/src/foundation/path-split-type-families.lagda.md b/src/foundation/path-split-type-families.lagda.md index 690d6d1a74..0aad6110c8 100644 --- a/src/foundation/path-split-type-families.lagda.md +++ b/src/foundation/path-split-type-families.lagda.md @@ -9,6 +9,7 @@ module foundation.path-split-type-families where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.embeddings open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/pi-decompositions.lagda.md b/src/foundation/pi-decompositions.lagda.md index 1d57a83088..dcbbb9f548 100644 --- a/src/foundation/pi-decompositions.lagda.md +++ b/src/foundation/pi-decompositions.lagda.md @@ -10,6 +10,7 @@ module foundation.pi-decompositions where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.functoriality-dependent-function-types diff --git a/src/foundation/pointed-torsorial-type-families.lagda.md b/src/foundation/pointed-torsorial-type-families.lagda.md index 247b60ec3a..ac06797f4c 100644 --- a/src/foundation/pointed-torsorial-type-families.lagda.md +++ b/src/foundation/pointed-torsorial-type-families.lagda.md @@ -9,6 +9,7 @@ module foundation.pointed-torsorial-type-families where ```agda open import foundation.0-connected-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.locally-small-types diff --git a/src/foundation/principle-of-omniscience.lagda.md b/src/foundation/principle-of-omniscience.lagda.md index cf03f741b2..6b5ce7a3d1 100644 --- a/src/foundation/principle-of-omniscience.lagda.md +++ b/src/foundation/principle-of-omniscience.lagda.md @@ -8,6 +8,7 @@ module foundation.principle-of-omniscience where ```agda open import foundation.decidable-subtypes +open import foundation.dependent-products-propositions open import foundation.propositional-truncations open import foundation.universe-levels diff --git a/src/foundation/product-decompositions-subuniverse.lagda.md b/src/foundation/product-decompositions-subuniverse.lagda.md index 8b340ce9dd..beb392b79c 100644 --- a/src/foundation/product-decompositions-subuniverse.lagda.md +++ b/src/foundation/product-decompositions-subuniverse.lagda.md @@ -9,6 +9,8 @@ module foundation.product-decompositions-subuniverse where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.subuniverses open import foundation.type-arithmetic-cartesian-product-types diff --git a/src/foundation/propositional-extensionality.lagda.md b/src/foundation/propositional-extensionality.lagda.md index a92f6d6176..495e07ec8a 100644 --- a/src/foundation/propositional-extensionality.lagda.md +++ b/src/foundation/propositional-extensionality.lagda.md @@ -8,6 +8,8 @@ module foundation.propositional-extensionality where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.fundamental-theorem-of-identity-types open import foundation.logical-equivalences diff --git a/src/foundation/propositional-maps.lagda.md b/src/foundation/propositional-maps.lagda.md index 39115738b7..00de80bd25 100644 --- a/src/foundation/propositional-maps.lagda.md +++ b/src/foundation/propositional-maps.lagda.md @@ -10,6 +10,7 @@ open import foundation-core.propositional-maps public ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.logical-equivalences open import foundation.truncated-maps diff --git a/src/foundation/propositional-resizing.lagda.md b/src/foundation/propositional-resizing.lagda.md index 4abe732a36..22cb73035d 100644 --- a/src/foundation/propositional-resizing.lagda.md +++ b/src/foundation/propositional-resizing.lagda.md @@ -8,6 +8,7 @@ module foundation.propositional-resizing where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/propositional-truncations.lagda.md b/src/foundation/propositional-truncations.lagda.md index 2ae3713137..c9ae9be7fc 100644 --- a/src/foundation/propositional-truncations.lagda.md +++ b/src/foundation/propositional-truncations.lagda.md @@ -9,6 +9,7 @@ module foundation.propositional-truncations where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.functoriality-cartesian-product-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/foundation/propositions.lagda.md b/src/foundation/propositions.lagda.md index e4bf1eb773..75b2a12684 100644 --- a/src/foundation/propositions.lagda.md +++ b/src/foundation/propositions.lagda.md @@ -4,6 +4,7 @@ module foundation.propositions where open import foundation-core.propositions public +open import foundation.dependent-products-propositions public ```
Imports diff --git a/src/foundation/quasicoherently-idempotent-maps.lagda.md b/src/foundation/quasicoherently-idempotent-maps.lagda.md index bec945c76a..0cda3d0440 100644 --- a/src/foundation/quasicoherently-idempotent-maps.lagda.md +++ b/src/foundation/quasicoherently-idempotent-maps.lagda.md @@ -11,6 +11,7 @@ open import foundation.1-types open import foundation.action-on-identifications-functions open import foundation.commuting-squares-of-homotopies open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-algebra diff --git a/src/foundation/reflecting-maps-equivalence-relations.lagda.md b/src/foundation/reflecting-maps-equivalence-relations.lagda.md index e3ff095700..dda9020f8c 100644 --- a/src/foundation/reflecting-maps-equivalence-relations.lagda.md +++ b/src/foundation/reflecting-maps-equivalence-relations.lagda.md @@ -8,6 +8,7 @@ module foundation.reflecting-maps-equivalence-relations where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.effective-maps-equivalence-relations open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction diff --git a/src/foundation/relaxed-sigma-decompositions.lagda.md b/src/foundation/relaxed-sigma-decompositions.lagda.md index 521c531132..9280f10597 100644 --- a/src/foundation/relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/relaxed-sigma-decompositions.lagda.md @@ -11,6 +11,7 @@ module foundation.relaxed-sigma-decompositions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types diff --git a/src/foundation/sections.lagda.md b/src/foundation/sections.lagda.md index 0c9cd52162..0ec87899b6 100644 --- a/src/foundation/sections.lagda.md +++ b/src/foundation/sections.lagda.md @@ -12,6 +12,7 @@ open import foundation-core.sections public open import foundation.action-on-identifications-functions open import foundation.commuting-triangles-of-homotopies open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-extensionality open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/separated-types-subuniverses.lagda.md b/src/foundation/separated-types-subuniverses.lagda.md index cc812fa34d..cb0571d472 100644 --- a/src/foundation/separated-types-subuniverses.lagda.md +++ b/src/foundation/separated-types-subuniverses.lagda.md @@ -7,6 +7,7 @@ module foundation.separated-types-subuniverses where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.subuniverses open import foundation.universe-levels diff --git a/src/foundation/set-presented-types.lagda.md b/src/foundation/set-presented-types.lagda.md index 658f0388f7..ae88a8fae8 100644 --- a/src/foundation/set-presented-types.lagda.md +++ b/src/foundation/set-presented-types.lagda.md @@ -10,6 +10,7 @@ module foundation.set-presented-types where open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.empty-types open import foundation.equality-coproduct-types diff --git a/src/foundation/set-quotients.lagda.md b/src/foundation/set-quotients.lagda.md index 0c6fc3765f..883cf8111f 100644 --- a/src/foundation/set-quotients.lagda.md +++ b/src/foundation/set-quotients.lagda.md @@ -9,6 +9,7 @@ module foundation.set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.effective-maps-equivalence-relations open import foundation.embeddings open import foundation.equivalence-classes diff --git a/src/foundation/sigma-decompositions.lagda.md b/src/foundation/sigma-decompositions.lagda.md index 720de58abb..b3c759f936 100644 --- a/src/foundation/sigma-decompositions.lagda.md +++ b/src/foundation/sigma-decompositions.lagda.md @@ -11,6 +11,7 @@ module foundation.sigma-decompositions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types diff --git a/src/foundation/slice.lagda.md b/src/foundation/slice.lagda.md index 0a41b6dd82..621d6af8f9 100644 --- a/src/foundation/slice.lagda.md +++ b/src/foundation/slice.lagda.md @@ -9,6 +9,7 @@ module foundation.slice where ```agda open import foundation.commuting-triangles-of-homotopies open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types diff --git a/src/foundation/small-maps.lagda.md b/src/foundation/small-maps.lagda.md index 59c0c702b7..4084071783 100644 --- a/src/foundation/small-maps.lagda.md +++ b/src/foundation/small-maps.lagda.md @@ -8,6 +8,7 @@ module foundation.small-maps where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.locally-small-types open import foundation.retracts-of-maps open import foundation.split-idempotent-maps diff --git a/src/foundation/subtypes.lagda.md b/src/foundation/subtypes.lagda.md index 291b0c918d..20def667fe 100644 --- a/src/foundation/subtypes.lagda.md +++ b/src/foundation/subtypes.lagda.md @@ -10,6 +10,7 @@ open import foundation-core.subtypes public ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/foundation/surjective-maps.lagda.md b/src/foundation/surjective-maps.lagda.md index f6fc1ffb05..57a649a995 100644 --- a/src/foundation/surjective-maps.lagda.md +++ b/src/foundation/surjective-maps.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.connected-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.diagonal-maps-of-types open import foundation.embeddings open import foundation.equality-cartesian-product-types diff --git a/src/foundation/symmetric-operations.lagda.md b/src/foundation/symmetric-operations.lagda.md index f5ab5c00de..317c977990 100644 --- a/src/foundation/symmetric-operations.lagda.md +++ b/src/foundation/symmetric-operations.lagda.md @@ -10,6 +10,7 @@ module foundation.symmetric-operations where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-extensionality open import foundation.function-extensionality open import foundation.functoriality-coproduct-types diff --git a/src/foundation/total-partial-functions.lagda.md b/src/foundation/total-partial-functions.lagda.md index c8510fac75..7b1083887d 100644 --- a/src/foundation/total-partial-functions.lagda.md +++ b/src/foundation/total-partial-functions.lagda.md @@ -8,6 +8,7 @@ module foundation.total-partial-functions where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.partial-functions open import foundation.universe-levels diff --git a/src/foundation/truncated-maps.lagda.md b/src/foundation/truncated-maps.lagda.md index 5107b35a68..5d640a4f3c 100644 --- a/src/foundation/truncated-maps.lagda.md +++ b/src/foundation/truncated-maps.lagda.md @@ -11,6 +11,7 @@ open import foundation-core.truncated-maps public ```agda open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.functoriality-fibers-of-maps open import foundation.universe-levels diff --git a/src/foundation/uniformly-decidable-type-families.lagda.md b/src/foundation/uniformly-decidable-type-families.lagda.md index 01904ea182..0d848563b6 100644 --- a/src/foundation/uniformly-decidable-type-families.lagda.md +++ b/src/foundation/uniformly-decidable-type-families.lagda.md @@ -11,6 +11,7 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-coproduct-types open import foundation.inhabited-types open import foundation.negation diff --git a/src/foundation/universal-property-identity-types.lagda.md b/src/foundation/universal-property-identity-types.lagda.md index 1412af1bae..1e4268ca8f 100644 --- a/src/foundation/universal-property-identity-types.lagda.md +++ b/src/foundation/universal-property-identity-types.lagda.md @@ -9,6 +9,7 @@ module foundation.universal-property-identity-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.dependent-universal-property-equivalences open import foundation.embeddings open import foundation.equivalences diff --git a/src/foundation/universal-property-propositional-truncation.lagda.md b/src/foundation/universal-property-propositional-truncation.lagda.md index 61fbe14f5b..1cadb2f5f2 100644 --- a/src/foundation/universal-property-propositional-truncation.lagda.md +++ b/src/foundation/universal-property-propositional-truncation.lagda.md @@ -8,6 +8,7 @@ module foundation.universal-property-propositional-truncation where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.functoriality-cartesian-product-types diff --git a/src/foundation/universal-property-set-quotients.lagda.md b/src/foundation/universal-property-set-quotients.lagda.md index a4e565199c..8ff5cf6b79 100644 --- a/src/foundation/universal-property-set-quotients.lagda.md +++ b/src/foundation/universal-property-set-quotients.lagda.md @@ -11,6 +11,7 @@ module foundation.universal-property-set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.dependent-universal-property-equivalences open import foundation.effective-maps-equivalence-relations open import foundation.epimorphisms-with-respect-to-sets diff --git a/src/foundation/universal-property-truncation.lagda.md b/src/foundation/universal-property-truncation.lagda.md index 3d261465a4..3a47918c45 100644 --- a/src/foundation/universal-property-truncation.lagda.md +++ b/src/foundation/universal-property-truncation.lagda.md @@ -12,6 +12,7 @@ open import foundation-core.universal-property-truncation public open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-extensionality open import foundation.identity-types open import foundation.propositional-truncations diff --git a/src/foundation/universal-quantification.lagda.md b/src/foundation/universal-quantification.lagda.md index e4b0bd024f..63a9a9e0e7 100644 --- a/src/foundation/universal-quantification.lagda.md +++ b/src/foundation/universal-quantification.lagda.md @@ -8,6 +8,7 @@ module foundation.universal-quantification where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.evaluation-functions open import foundation.logical-equivalences open import foundation.propositional-truncations diff --git a/src/logic/de-morgan-subtypes.lagda.md b/src/logic/de-morgan-subtypes.lagda.md index 8981009f85..b01a79ab1f 100644 --- a/src/logic/de-morgan-subtypes.lagda.md +++ b/src/logic/de-morgan-subtypes.lagda.md @@ -10,6 +10,7 @@ module logic.de-morgan-subtypes where open import foundation.1-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.functoriality-cartesian-product-types open import foundation.functoriality-dependent-pair-types diff --git a/src/logic/de-morgan-types.lagda.md b/src/logic/de-morgan-types.lagda.md index a87cd18593..749e83645f 100644 --- a/src/logic/de-morgan-types.lagda.md +++ b/src/logic/de-morgan-types.lagda.md @@ -13,6 +13,7 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.double-negation open import foundation.empty-types diff --git a/src/logic/de-morgans-law.lagda.md b/src/logic/de-morgans-law.lagda.md index b680aef549..670b532a88 100644 --- a/src/logic/de-morgans-law.lagda.md +++ b/src/logic/de-morgans-law.lagda.md @@ -12,6 +12,7 @@ open import foundation.conjunction open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.double-negation open import foundation.empty-types diff --git a/src/logic/double-negation-elimination.lagda.md b/src/logic/double-negation-elimination.lagda.md index 1acfd21ebb..cdc299f056 100644 --- a/src/logic/double-negation-elimination.lagda.md +++ b/src/logic/double-negation-elimination.lagda.md @@ -11,6 +11,7 @@ open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.evaluation-functions open import foundation.hilberts-epsilon-operators diff --git a/src/logic/double-negation-stable-subtypes.lagda.md b/src/logic/double-negation-stable-subtypes.lagda.md index 6614510a1b..5780836046 100644 --- a/src/logic/double-negation-stable-subtypes.lagda.md +++ b/src/logic/double-negation-stable-subtypes.lagda.md @@ -10,6 +10,7 @@ module logic.double-negation-stable-subtypes where open import foundation.1-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation-stable-propositions open import foundation.equality-dependent-function-types open import foundation.functoriality-cartesian-product-types diff --git a/src/logic/markovian-types.lagda.md b/src/logic/markovian-types.lagda.md index 54b779cddd..cdf5521276 100644 --- a/src/logic/markovian-types.lagda.md +++ b/src/logic/markovian-types.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.booleans open import foundation.decidable-subtypes open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.existential-quantification open import foundation.function-types diff --git a/src/order-theory/zorns-lemma.lagda.md b/src/order-theory/zorns-lemma.lagda.md index a2e403817a..8d1381868b 100644 --- a/src/order-theory/zorns-lemma.lagda.md +++ b/src/order-theory/zorns-lemma.lagda.md @@ -8,6 +8,7 @@ module order-theory.zorns-lemma where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.existential-quantification open import foundation.inhabited-types diff --git a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md index eb2cbcdba9..d48dc64cdd 100644 --- a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md +++ b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md @@ -9,6 +9,7 @@ module orthogonal-factorization-systems.double-negation-sheaves where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation-stable-propositions open import foundation.empty-types open import foundation.irrefutable-propositions From 35ba0ff72c8c91eeb2708ab58ab48b7541f672e8 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 15:54:58 +0000 Subject: [PATCH 09/39] fix `multiplication-integers` --- scripts/remove_unused_imports.py | 2 +- .../multiplication-integers.lagda.md | 55 ++++++++++--------- 2 files changed, 29 insertions(+), 28 deletions(-) diff --git a/scripts/remove_unused_imports.py b/scripts/remove_unused_imports.py index c1c56aaa4c..14ad2f055f 100755 --- a/scripts/remove_unused_imports.py +++ b/scripts/remove_unused_imports.py @@ -115,7 +115,7 @@ def filter_agda_files(f): return utils.is_agda_file(pathlib.Path(f)) and os.path temp_dir = 'temp' status = 0 - agda_options = '--without-K --exact-split --no-import-sorts --auto-inline --no-caching' + agda_options = '--without-K --exact-split --no-import-sorts --auto-inline --no-caching -WnoPatternShadowsConstructor' temp_root = os.path.join(root, temp_dir) shutil.rmtree(temp_root, ignore_errors=True) diff --git a/src/elementary-number-theory/multiplication-integers.lagda.md b/src/elementary-number-theory/multiplication-integers.lagda.md index 9854c6cf70..41d4dfcc1b 100644 --- a/src/elementary-number-theory/multiplication-integers.lagda.md +++ b/src/elementary-number-theory/multiplication-integers.lagda.md @@ -26,6 +26,7 @@ open import foundation.identity-types open import foundation.injective-maps open import foundation.interchange-law open import foundation.type-arithmetic-empty-type +open import foundation.unit-type open import foundation.universe-levels ``` @@ -46,7 +47,7 @@ and derive its basic properties with respect to `succ-ℤ`, `pred-ℤ`, `neg-ℤ mul-ℤ : ℤ → ℤ → ℤ mul-ℤ (inl zero-ℕ) l = neg-ℤ l mul-ℤ (inl (succ-ℕ x)) l = (neg-ℤ l) +ℤ (mul-ℤ (inl x) l) -mul-ℤ (inr (inl star)) l = zero-ℤ +mul-ℤ (inr (inl _)) l = zero-ℤ mul-ℤ (inr (inr zero-ℕ)) l = l mul-ℤ (inr (inr (succ-ℕ x))) l = l +ℤ (mul-ℤ (inr (inr x)) l) @@ -66,13 +67,13 @@ ap-mul-ℤ p q = ap-binary mul-ℤ p q ```agda explicit-mul-ℤ : ℤ → ℤ → ℤ explicit-mul-ℤ (inl x) (inl y) = int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)) -explicit-mul-ℤ (inl x) (inr (inl star)) = zero-ℤ +explicit-mul-ℤ (inl x) (inr (inl _)) = zero-ℤ explicit-mul-ℤ (inl x) (inr (inr y)) = neg-ℤ (int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y))) -explicit-mul-ℤ (inr (inl star)) (inl y) = zero-ℤ +explicit-mul-ℤ (inr (inl _)) (inl y) = zero-ℤ explicit-mul-ℤ (inr (inr x)) (inl y) = neg-ℤ (int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y))) -explicit-mul-ℤ (inr (inl star)) (inr (inl star)) = zero-ℤ -explicit-mul-ℤ (inr (inl star)) (inr (inr y)) = zero-ℤ -explicit-mul-ℤ (inr (inr x)) (inr (inl star)) = zero-ℤ +explicit-mul-ℤ (inr (inl _)) (inr (inl _)) = zero-ℤ +explicit-mul-ℤ (inr (inl _)) (inr (inr y)) = zero-ℤ +explicit-mul-ℤ (inr (inr x)) (inr (inl _)) = zero-ℤ explicit-mul-ℤ (inr (inr x)) (inr (inr y)) = int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)) explicit-mul-ℤ' : ℤ → ℤ → ℤ @@ -98,7 +99,7 @@ right-zero-law-mul-ℤ : (k : ℤ) → k *ℤ zero-ℤ ＝ zero-ℤ right-zero-law-mul-ℤ (inl zero-ℕ) = refl right-zero-law-mul-ℤ (inl (succ-ℕ n)) = right-zero-law-mul-ℤ (inl n) -right-zero-law-mul-ℤ (inr (inl star)) = refl +right-zero-law-mul-ℤ (inr (inl _)) = refl right-zero-law-mul-ℤ (inr (inr zero-ℕ)) = refl right-zero-law-mul-ℤ (inr (inr (succ-ℕ n))) = right-zero-law-mul-ℤ (inr (inr n)) @@ -114,7 +115,7 @@ right-unit-law-mul-ℤ : (k : ℤ) → k *ℤ one-ℤ ＝ k right-unit-law-mul-ℤ (inl zero-ℕ) = refl right-unit-law-mul-ℤ (inl (succ-ℕ n)) = ap ((neg-one-ℤ) +ℤ_) (right-unit-law-mul-ℤ (inl n)) -right-unit-law-mul-ℤ (inr (inl star)) = refl +right-unit-law-mul-ℤ (inr (inl _)) = refl right-unit-law-mul-ℤ (inr (inr zero-ℕ)) = refl right-unit-law-mul-ℤ (inr (inr (succ-ℕ n))) = ap (one-ℤ +ℤ_) (right-unit-law-mul-ℤ (inr (inr n))) @@ -130,7 +131,7 @@ right-neg-unit-law-mul-ℤ : (k : ℤ) → k *ℤ neg-one-ℤ ＝ neg-ℤ k right-neg-unit-law-mul-ℤ (inl zero-ℕ) = refl right-neg-unit-law-mul-ℤ (inl (succ-ℕ n)) = ap (one-ℤ +ℤ_) (right-neg-unit-law-mul-ℤ (inl n)) -right-neg-unit-law-mul-ℤ (inr (inl star)) = refl +right-neg-unit-law-mul-ℤ (inr (inl _)) = refl right-neg-unit-law-mul-ℤ (inr (inr zero-ℕ)) = refl right-neg-unit-law-mul-ℤ (inr (inr (succ-ℕ n))) = ap (neg-one-ℤ +ℤ_) (right-neg-unit-law-mul-ℤ (inr (inr n))) @@ -149,7 +150,7 @@ left-successor-law-mul-ℤ (inl (succ-ℕ n)) l = ( _+ℤ ((inl n) *ℤ l)) ( inv (right-inverse-law-add-ℤ l)))) ∙ ( associative-add-ℤ l (neg-ℤ l) ((inl n) *ℤ l)) -left-successor-law-mul-ℤ (inr (inl star)) l = +left-successor-law-mul-ℤ (inr (inl _)) l = inv (right-unit-law-add-ℤ l) left-successor-law-mul-ℤ (inr (inr n)) l = refl @@ -162,7 +163,7 @@ left-successor-law-mul-ℤ' k l = left-predecessor-law-mul-ℤ : (k l : ℤ) → (pred-ℤ k) *ℤ l ＝ (neg-ℤ l) +ℤ (k *ℤ l) left-predecessor-law-mul-ℤ (inl n) l = refl -left-predecessor-law-mul-ℤ (inr (inl star)) l = +left-predecessor-law-mul-ℤ (inr (inl _)) l = ( left-neg-unit-law-mul-ℤ l) ∙ ( inv (right-unit-law-add-ℤ (neg-ℤ l))) left-predecessor-law-mul-ℤ (inr (inr zero-ℕ)) l = @@ -202,7 +203,7 @@ right-successor-law-mul-ℤ (inl (succ-ℕ n)) l = ( ( ap succ-ℤ (inv (pred-neg-ℤ l))) ∙ ( is-section-pred-ℤ (neg-ℤ l)))))))) ∙ ( associative-add-ℤ (inl (succ-ℕ n)) (neg-ℤ l) ((inl n) *ℤ l))))) -right-successor-law-mul-ℤ (inr (inl star)) l = refl +right-successor-law-mul-ℤ (inr (inl _)) l = refl right-successor-law-mul-ℤ (inr (inr zero-ℕ)) l = refl right-successor-law-mul-ℤ (inr (inr (succ-ℕ n))) l = ( left-successor-law-mul-ℤ (in-pos-ℤ n) (succ-ℤ l)) ∙ @@ -242,7 +243,7 @@ right-predecessor-law-mul-ℤ (inl (succ-ℕ n)) l = ( ( ap succ-ℤ (commutative-add-ℤ (neg-ℤ l) (in-pos-ℤ n))) ∙ ( inv (left-successor-law-add-ℤ (in-pos-ℤ n) (neg-ℤ l))))))) ∙ ( associative-add-ℤ (in-pos-ℤ (succ-ℕ n)) (neg-ℤ l) ((inl n) *ℤ l))))) -right-predecessor-law-mul-ℤ (inr (inl star)) l = refl +right-predecessor-law-mul-ℤ (inr (inl _)) l = refl right-predecessor-law-mul-ℤ (inr (inr zero-ℕ)) l = refl right-predecessor-law-mul-ℤ (inr (inr (succ-ℕ n))) l = ( left-successor-law-mul-ℤ (in-pos-ℤ n) (pred-ℤ l)) ∙ @@ -280,7 +281,7 @@ right-distributive-mul-add-ℤ (inl (succ-ℕ x)) l m = ( left-predecessor-law-mul-ℤ ((inl x) +ℤ l) m) ∙ ( ( ap ((neg-ℤ m) +ℤ_) (right-distributive-mul-add-ℤ (inl x) l m)) ∙ ( inv (associative-add-ℤ (neg-ℤ m) ((inl x) *ℤ m) (l *ℤ m)))) -right-distributive-mul-add-ℤ (inr (inl star)) l m = refl +right-distributive-mul-add-ℤ (inr (inl _)) l m = refl right-distributive-mul-add-ℤ (inr (inr zero-ℕ)) l m = left-successor-law-mul-ℤ l m right-distributive-mul-add-ℤ (inr (inr (succ-ℕ n))) l m = @@ -302,7 +303,7 @@ left-negative-law-mul-ℤ (inl (succ-ℕ n)) l = ( ( left-successor-law-mul-ℤ (neg-ℤ (inl n)) l) ∙ ( ( ap (l +ℤ_) (left-negative-law-mul-ℤ (inl n) l)) ∙ ( right-negative-law-add-ℤ l ((inl n) *ℤ l)))) -left-negative-law-mul-ℤ (inr (inl star)) l = refl +left-negative-law-mul-ℤ (inr (inl _)) l = refl left-negative-law-mul-ℤ (inr (inr zero-ℕ)) l = refl left-negative-law-mul-ℤ (inr (inr (succ-ℕ n))) l = ( left-predecessor-law-mul-ℤ (inl n) l) ∙ @@ -323,7 +324,7 @@ associative-mul-ℤ (inl (succ-ℕ n)) l m = ( ap ( _+ℤ ((inl n) *ℤ (l *ℤ m))) ( left-negative-law-mul-ℤ l m))) -associative-mul-ℤ (inr (inl star)) l m = refl +associative-mul-ℤ (inr (inl _)) l m = refl associative-mul-ℤ (inr (inr zero-ℕ)) l m = refl associative-mul-ℤ (inr (inr (succ-ℕ n))) l m = ( right-distributive-mul-add-ℤ l ((in-pos-ℤ n) *ℤ l) m) ∙ @@ -339,7 +340,7 @@ commutative-mul-ℤ (inl zero-ℕ) l = inv (right-neg-unit-law-mul-ℤ l) commutative-mul-ℤ (inl (succ-ℕ n)) l = ( ap ((neg-ℤ l) +ℤ_) (commutative-mul-ℤ (inl n) l)) ∙ ( inv (right-predecessor-law-mul-ℤ l (inl n))) -commutative-mul-ℤ (inr (inl star)) l = inv (right-zero-law-mul-ℤ l) +commutative-mul-ℤ (inr (inl _)) l = inv (right-zero-law-mul-ℤ l) commutative-mul-ℤ (inr (inr zero-ℕ)) l = inv (right-unit-law-mul-ℤ l) commutative-mul-ℤ (inr (inr (succ-ℕ n))) l = ( ap (l +ℤ_) (commutative-mul-ℤ (inr (inr n)) l)) ∙ @@ -416,9 +417,9 @@ compute-mul-ℤ (inl (succ-ℕ x)) (inl y) = ( int-ℕ (succ-ℕ y)) ( int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y))))) ∙ ( add-int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)) (succ-ℕ y)) -compute-mul-ℤ (inl zero-ℕ) (inr (inl star)) = refl +compute-mul-ℤ (inl zero-ℕ) (inr (inl _)) = refl compute-mul-ℤ (inl zero-ℕ) (inr (inr x)) = ap inl (inv (left-unit-law-add-ℕ x)) -compute-mul-ℤ (inl (succ-ℕ x)) (inr (inl star)) = right-zero-law-mul-ℤ (inl x) +compute-mul-ℤ (inl (succ-ℕ x)) (inr (inl _)) = right-zero-law-mul-ℤ (inl x) compute-mul-ℤ (inl (succ-ℕ x)) (inr (inr y)) = ( ( ( ap ((inl y) +ℤ_) (compute-mul-ℤ (inl x) (inr (inr y)))) ∙ ( inv @@ -431,7 +432,7 @@ compute-mul-ℤ (inl (succ-ℕ x)) (inr (inr y)) = ( int-ℕ (succ-ℕ y)) ( int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)))))) ∙ ( ap neg-ℤ (add-int-ℕ ((succ-ℕ x) *ℕ (succ-ℕ y)) (succ-ℕ y))) -compute-mul-ℤ (inr (inl star)) (inl y) = refl +compute-mul-ℤ (inr (inl _)) (inl y) = refl compute-mul-ℤ (inr (inr zero-ℕ)) (inl y) = ap inl (inv (left-unit-law-add-ℕ y)) compute-mul-ℤ (inr (inr (succ-ℕ x))) (inl y) = ( ap ((inl y) +ℤ_) (compute-mul-ℤ (inr (inr x)) (inl y))) ∙ @@ -446,10 +447,10 @@ compute-mul-ℤ (inr (inr (succ-ℕ x))) (inl y) = ( inr ∘ inr) ( left-successor-law-add-ℕ y ((x *ℕ (succ-ℕ y)) +ℕ y)))))) ∙ ( ap inl (commutative-add-ℕ y ((succ-ℕ x) *ℕ (succ-ℕ y))))) -compute-mul-ℤ (inr (inl star)) (inr (inl star)) = refl -compute-mul-ℤ (inr (inl star)) (inr (inr y)) = refl -compute-mul-ℤ (inr (inr zero-ℕ)) (inr (inl star)) = refl -compute-mul-ℤ (inr (inr (succ-ℕ x))) (inr (inl star)) = +compute-mul-ℤ (inr (inl _)) (inr (inl _)) = refl +compute-mul-ℤ (inr (inl _)) (inr (inr y)) = refl +compute-mul-ℤ (inr (inr zero-ℕ)) (inr (inl _)) = refl +compute-mul-ℤ (inr (inr (succ-ℕ x))) (inr (inl _)) = right-zero-law-mul-ℤ (inr (inr (succ-ℕ x))) compute-mul-ℤ (inr (inr zero-ℕ)) (inr (inr y)) = ap @@ -486,13 +487,13 @@ is-zero-is-zero-mul-ℤ : (x y : ℤ) → is-zero-ℤ (x *ℤ y) → (is-zero-ℤ x) + (is-zero-ℤ y) is-zero-is-zero-mul-ℤ (inl x) (inl y) H = ex-falso (Eq-eq-ℤ (inv (compute-mul-ℤ (inl x) (inl y)) ∙ H)) -is-zero-is-zero-mul-ℤ (inl x) (inr (inl star)) H = inr refl +is-zero-is-zero-mul-ℤ (inl x) (inr (inl _)) H = inr refl is-zero-is-zero-mul-ℤ (inl x) (inr (inr y)) H = ex-falso (Eq-eq-ℤ (inv (compute-mul-ℤ (inl x) (inr (inr y))) ∙ H)) -is-zero-is-zero-mul-ℤ (inr (inl star)) y H = inl refl +is-zero-is-zero-mul-ℤ (inr (inl _)) y H = inl refl is-zero-is-zero-mul-ℤ (inr (inr x)) (inl y) H = ex-falso (Eq-eq-ℤ (inv (compute-mul-ℤ (inr (inr x)) (inl y)) ∙ H)) -is-zero-is-zero-mul-ℤ (inr (inr x)) (inr (inl star)) H = inr refl +is-zero-is-zero-mul-ℤ (inr (inr x)) (inr (inl _)) H = inr refl is-zero-is-zero-mul-ℤ (inr (inr x)) (inr (inr y)) H = ex-falso (Eq-eq-ℤ (inv (compute-mul-ℤ (inr (inr x)) (inr (inr y))) ∙ H)) ``` From 80f80bbaaee854e271399aea24290725c315d3e8 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 16:11:11 +0000 Subject: [PATCH 10/39] move retract precomp/postcomp --- .../retracts-of-types.lagda.md | 38 ------------------- src/foundation/retracts-of-maps.lagda.md | 2 +- src/foundation/retracts-of-types.lagda.md | 37 ++++++++++++++++++ 3 files changed, 38 insertions(+), 39 deletions(-) diff --git a/src/foundation-core/retracts-of-types.lagda.md b/src/foundation-core/retracts-of-types.lagda.md index 43c71c5134..6aea379f91 100644 --- a/src/foundation-core/retracts-of-types.lagda.md +++ b/src/foundation-core/retracts-of-types.lagda.md @@ -9,15 +9,11 @@ module foundation-core.retracts-of-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality open import foundation.universe-levels -open import foundation.whiskering-homotopies-composition open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.postcomposition-functions -open import foundation-core.precomposition-functions open import foundation-core.retractions open import foundation-core.sections ``` @@ -140,40 +136,6 @@ module _ pr2 retract-eq = retraction-ap (inclusion-retract R) (retraction-retract R) ``` -### If `A` is a retract of `B` then `A → S` is a retract of `B → S` via precomposition - -```agda -module _ - {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} (R : A retract-of B) (S : UU l3) - where - - retract-precomp : - (A → S) retract-of (B → S) - pr1 retract-precomp = - precomp (map-retraction-retract R) S - pr1 (pr2 retract-precomp) = - precomp (inclusion-retract R) S - pr2 (pr2 retract-precomp) h = - eq-htpy (h ·l is-retraction-map-retraction-retract R) -``` - -### If `A` is a retract of `B` then `S → A` is a retract of `S → B` via postcomposition - -```agda -module _ - {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} (S : UU l3) (R : A retract-of B) - where - - retract-postcomp : - (S → A) retract-of (S → B) - pr1 retract-postcomp = - postcomp S (inclusion-retract R) - pr1 (pr2 retract-postcomp) = - postcomp S (map-retraction-retract R) - pr2 (pr2 retract-postcomp) h = - eq-htpy (is-retraction-map-retraction-retract R ·r h) -``` - ### Every type is a retract of itself ```agda diff --git a/src/foundation/retracts-of-maps.lagda.md b/src/foundation/retracts-of-maps.lagda.md index bf904c18bc..4a6ba64557 100644 --- a/src/foundation/retracts-of-maps.lagda.md +++ b/src/foundation/retracts-of-maps.lagda.md @@ -19,6 +19,7 @@ open import foundation.homotopy-algebra open import foundation.morphisms-arrows open import foundation.postcomposition-functions open import foundation.precomposition-functions +open import foundation.retracts-of-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -30,7 +31,6 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.retractions -open import foundation-core.retracts-of-types open import foundation-core.sections ``` diff --git a/src/foundation/retracts-of-types.lagda.md b/src/foundation/retracts-of-types.lagda.md index 56c7476a61..e180da55c5 100644 --- a/src/foundation/retracts-of-types.lagda.md +++ b/src/foundation/retracts-of-types.lagda.md @@ -11,6 +11,7 @@ open import foundation-core.retracts-of-types public ```agda open import foundation.dependent-pair-types open import foundation.equivalences +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies open import foundation.homotopy-algebra @@ -25,6 +26,8 @@ open import foundation-core.contractible-types open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types +open import foundation-core.postcomposition-functions +open import foundation-core.precomposition-functions open import foundation-core.torsorial-type-families ``` @@ -180,6 +183,40 @@ iff-retract' : iff-retract' = inv-iff ∘ iff-retract ``` +### If `A` is a retract of `B` then `A → S` is a retract of `B → S` via precomposition + +```agda +module _ + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} (R : A retract-of B) (S : UU l3) + where + + retract-precomp : + (A → S) retract-of (B → S) + pr1 retract-precomp = + precomp (map-retraction-retract R) S + pr1 (pr2 retract-precomp) = + precomp (inclusion-retract R) S + pr2 (pr2 retract-precomp) h = + eq-htpy (h ·l is-retraction-map-retraction-retract R) +``` + +### If `A` is a retract of `B` then `S → A` is a retract of `S → B` via postcomposition + +```agda +module _ + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} (S : UU l3) (R : A retract-of B) + where + + retract-postcomp : + (S → A) retract-of (S → B) + pr1 retract-postcomp = + postcomp S (inclusion-retract R) + pr1 (pr2 retract-postcomp) = + postcomp S (map-retraction-retract R) + pr2 (pr2 retract-postcomp) h = + eq-htpy (is-retraction-map-retraction-retract R ·r h) +``` + ## See also - [Retracts of maps](foundation.retracts-of-maps.md) From 217ed4cafbc11107ce3311685e219b563247a13b Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 16:42:04 +0000 Subject: [PATCH 11/39] `foundation-core.logical-equivalences` --- src/foundation-core.lagda.md | 1 + .../logical-equivalences.lagda.md | 227 ++++++++++++++++++ src/foundation-core/negation.lagda.md | 20 +- src/foundation/logical-equivalences.lagda.md | 197 +-------------- src/foundation/negation.lagda.md | 12 - 5 files changed, 259 insertions(+), 198 deletions(-) create mode 100644 src/foundation-core/logical-equivalences.lagda.md diff --git a/src/foundation-core.lagda.md b/src/foundation-core.lagda.md index 9b9dd2512c..833226f9fd 100644 --- a/src/foundation-core.lagda.md +++ b/src/foundation-core.lagda.md @@ -36,6 +36,7 @@ open import foundation-core.homotopies public open import foundation-core.identity-types public open import foundation-core.injective-maps public open import foundation-core.invertible-maps public +open import foundation-core.logical-equivalences public open import foundation-core.negation public open import foundation-core.operations-span-diagrams public open import foundation-core.operations-spans public diff --git a/src/foundation-core/logical-equivalences.lagda.md b/src/foundation-core/logical-equivalences.lagda.md new file mode 100644 index 0000000000..bbfe9f6441 --- /dev/null +++ b/src/foundation-core/logical-equivalences.lagda.md @@ -0,0 +1,227 @@ +# Logical equivalences + +```agda +module foundation-core.logical-equivalences where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.equality-cartesian-product-types +open import foundation.type-arithmetic-dependent-pair-types +open import foundation.universe-levels + +open import foundation-core.cartesian-product-types +open import foundation-core.equivalences +open import foundation-core.fibers-of-maps +open import foundation-core.function-types +open import foundation-core.functoriality-dependent-pair-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.propositions +open import foundation-core.torsorial-type-families +``` + +
+ +## Idea + +{{#concept "Logical equivalences" Disambiguation="of types" Agda=iff}} between +two types `A` and `B` consist of a map `A → B` and a map `B → A`. The type of +logical equivalences between types is the +[Curry–Howard interpretation](https://en.wikipedia.org/wiki/Curry–Howard_correspondence) +of logical equivalences between [propositions](foundation-core.propositions.md). + +## Definition + +### The structure on a map of being a logical equivalence + +```agda +has-converse : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A → B) → UU (l1 ⊔ l2) +has-converse {A = A} {B} f = (B → A) +``` + +### Logical equivalences between types + +```agda +iff : {l1 l2 : Level} → UU l1 → UU l2 → UU (l1 ⊔ l2) +iff A B = Σ (A → B) has-converse + +infix 6 _↔_ + +_↔_ : {l1 l2 : Level} → UU l1 → UU l2 → UU (l1 ⊔ l2) +_↔_ = iff + +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} (H : A ↔ B) + where + + forward-implication : A → B + forward-implication = pr1 H + + backward-implication : B → A + backward-implication = pr2 H +``` + +### The identity logical equivalence + +```agda +id-iff : {l1 : Level} {A : UU l1} → A ↔ A +id-iff = (id , id) +``` + +### Composition of logical equivalences + +```agda +infixr 15 _∘iff_ + +_∘iff_ : + {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} {C : UU l3} → + (B ↔ C) → (A ↔ B) → (A ↔ C) +pr1 ((g1 , g2) ∘iff (f1 , f2)) = g1 ∘ f1 +pr2 ((g1 , g2) ∘iff (f1 , f2)) = f2 ∘ g2 +``` + +### Inverting a logical equivalence + +```agda +inv-iff : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ↔ B) → (B ↔ A) +pr1 (inv-iff (f , g)) = g +pr2 (inv-iff (f , g)) = f +``` + +## Properties + +### Homotopies of logical equivalences + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + htpy-iff : (f g : A ↔ B) → UU (l1 ⊔ l2) + htpy-iff f g = + ( forward-implication f ~ forward-implication g) × + ( backward-implication f ~ backward-implication g) +``` + +### Logical equivalences between propositions induce equivalences + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + abstract + is-equiv-has-converse-is-prop : + is-prop A → is-prop B → {f : A → B} → (B → A) → is-equiv f + is-equiv-has-converse-is-prop is-prop-A is-prop-B {f} g = + is-equiv-is-invertible + ( g) + ( λ y → eq-is-prop is-prop-B) + ( λ x → eq-is-prop is-prop-A) + + abstract + equiv-iff-is-prop : is-prop A → is-prop B → (A → B) → (B → A) → A ≃ B + pr1 (equiv-iff-is-prop is-prop-A is-prop-B f g) = f + pr2 (equiv-iff-is-prop is-prop-A is-prop-B f g) = + is-equiv-has-converse-is-prop is-prop-A is-prop-B g + +module _ + {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) + where + + abstract + is-equiv-has-converse : + {f : type-Prop P → type-Prop Q} → (type-Prop Q → type-Prop P) → is-equiv f + is-equiv-has-converse = + is-equiv-has-converse-is-prop + ( is-prop-type-Prop P) + ( is-prop-type-Prop Q) + + equiv-iff' : (type-Prop P ↔ type-Prop Q) → (type-Prop P ≃ type-Prop Q) + pr1 (equiv-iff' t) = forward-implication t + pr2 (equiv-iff' t) = + is-equiv-has-converse-is-prop + ( is-prop-type-Prop P) + ( is-prop-type-Prop Q) + ( backward-implication t) + + equiv-iff : + (type-Prop P → type-Prop Q) → (type-Prop Q → type-Prop P) → + type-Prop P ≃ type-Prop Q + equiv-iff f g = equiv-iff' (f , g) +``` + +### Equivalences are logical equivalences + +```agda +iff-equiv : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ≃ B) → (A ↔ B) +pr1 (iff-equiv e) = map-equiv e +pr2 (iff-equiv e) = map-inv-equiv e + +iff-equiv' : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ≃ B) → (B ↔ A) +pr1 (iff-equiv' e) = map-inv-equiv e +pr2 (iff-equiv' e) = map-equiv e + +compute-fiber-iff-equiv' : + {l1 l2 : Level} {A : UU l1} {B : UU l2} ((f , g) : A ↔ B) → + fiber (iff-equiv) (f , g) ≃ Σ (is-equiv f) (λ f' → map-inv-is-equiv f' ＝ g) +compute-fiber-iff-equiv' {A = A} {B} (f , g) = + ( left-unit-law-Σ-is-contr (is-torsorial-Id' f) (f , refl)) ∘e + ( inv-associative-Σ (A → B) (_＝ f) _) ∘e + ( equiv-tot (λ _ → equiv-left-swap-Σ)) ∘e + ( associative-Σ (A → B) _ _) ∘e + ( equiv-tot (λ e → equiv-pair-eq (iff-equiv e) (f , g))) +``` + +### Two equal propositions are logically equivalent + +```agda +iff-eq : {l1 : Level} {P Q : Prop l1} → P ＝ Q → (type-Prop P ↔ type-Prop Q) +pr1 (iff-eq refl) = id +pr2 (iff-eq refl) = id +``` + +## Logical equivalences between dependent function types + +```agda +module _ + {l1 l2 l3 : Level} {I : UU l1} {A : I → UU l2} {B : I → UU l3} + where + + iff-Π-iff-family : ((i : I) → A i ↔ B i) → ((i : I) → A i) ↔ ((i : I) → B i) + pr1 (iff-Π-iff-family e) a i = forward-implication (e i) (a i) + pr2 (iff-Π-iff-family e) b i = backward-implication (e i) (b i) +``` + +## Reasoning with logical equivalences + +Logical equivalences can be constructed by equational reasoning in the following +way: + +```text +logical-equivalence-reasoning + X ↔ Y by equiv-1 + ↔ Z by equiv-2 + ↔ V by equiv-3 +``` + +```agda +infixl 1 logical-equivalence-reasoning_ +infixl 0 step-logical-equivalence-reasoning + +logical-equivalence-reasoning_ : + {l1 : Level} (X : UU l1) → X ↔ X +pr1 (logical-equivalence-reasoning X) = id +pr2 (logical-equivalence-reasoning X) = id + +step-logical-equivalence-reasoning : + {l1 l2 l3 : Level} {X : UU l1} {Y : UU l2} → + (X ↔ Y) → (Z : UU l3) → (Y ↔ Z) → (X ↔ Z) +step-logical-equivalence-reasoning e Z f = f ∘iff e + +syntax step-logical-equivalence-reasoning e Z f = e ↔ Z by f +``` diff --git a/src/foundation-core/negation.lagda.md b/src/foundation-core/negation.lagda.md index 620f220429..720d64e266 100644 --- a/src/foundation-core/negation.lagda.md +++ b/src/foundation-core/negation.lagda.md @@ -10,6 +10,7 @@ module foundation-core.negation where open import foundation.universe-levels open import foundation-core.empty-types +open import foundation-core.logical-equivalences ```
@@ -23,7 +24,7 @@ using propositions as types. Thus, the {{#concept "negation" Disambiguation="of a type" WDID=Q190558 WD="logical negation" Agda=¬_}} of a type `A` is the type `A → empty`. -## Definition +## Definitions ```agda infix 25 ¬_ @@ -37,6 +38,23 @@ map-neg : map-neg f nq p = nq (f p) ``` +### Reductio ad absurdum + +```agda +reductio-ad-absurdum : {l1 l2 : Level} {P : UU l1} {Q : UU l2} → P → ¬ P → Q +reductio-ad-absurdum p np = ex-falso (np p) +``` + +### Negation has no fixed points + +```agda +no-fixed-points-neg : + {l : Level} (A : UU l) → ¬ (A ↔ ¬ A) +no-fixed-points-neg A e = + ( λ (h : ¬ A) → h (backward-implication e h)) + ( λ (a : A) → forward-implication e a a) +``` + ## External links - [negation](https://ncatlab.org/nlab/show/negation) at $n$Lab diff --git a/src/foundation/logical-equivalences.lagda.md b/src/foundation/logical-equivalences.lagda.md index 2fc722214b..f95d0aacb7 100644 --- a/src/foundation/logical-equivalences.lagda.md +++ b/src/foundation/logical-equivalences.lagda.md @@ -2,6 +2,8 @@ ```agda module foundation.logical-equivalences where + +open import foundation-core.logical-equivalences public ```
Imports @@ -44,16 +46,10 @@ of logical equivalences between [propositions](foundation-core.propositions.md). ### The structure on a map of being a logical equivalence ```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - has-converse : (A → B) → UU (l1 ⊔ l2) - has-converse f = B → A - - is-prop-has-converse : - is-prop A → (f : A → B) → is-prop (has-converse f) - is-prop-has-converse is-prop-A f = is-prop-function-type is-prop-A +is-prop-has-converse : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → + is-prop A → (f : A → B) → is-prop (has-converse f) +is-prop-has-converse is-prop-A f = is-prop-function-type is-prop-A has-converse-Prop : {l1 l2 : Level} (A : Prop l1) {B : UU l2} → (type-Prop A → B) → Prop (l1 ⊔ l2) @@ -62,28 +58,6 @@ has-converse-Prop A f = is-prop-has-converse (is-prop-type-Prop A) f) ``` -### Logical equivalences between types - -```agda -iff : {l1 l2 : Level} → UU l1 → UU l2 → UU (l1 ⊔ l2) -iff A B = Σ (A → B) has-converse - -infix 6 _↔_ - -_↔_ : {l1 l2 : Level} → UU l1 → UU l2 → UU (l1 ⊔ l2) -_↔_ = iff - -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} (H : A ↔ B) - where - - forward-implication : A → B - forward-implication = pr1 H - - backward-implication : B → A - backward-implication = pr2 H -``` - ### Logical equivalences between propositions ```agda @@ -110,34 +84,6 @@ module _ _⇔_ = iff-Prop ``` -### The identity logical equivalence - -```agda -id-iff : {l1 : Level} {A : UU l1} → A ↔ A -id-iff = (id , id) -``` - -### Composition of logical equivalences - -```agda -infixr 15 _∘iff_ - -_∘iff_ : - {l1 l2 l3 : Level} {A : UU l1} {B : UU l2} {C : UU l3} → - (B ↔ C) → (A ↔ B) → (A ↔ C) -pr1 ((g1 , g2) ∘iff (f1 , f2)) = g1 ∘ f1 -pr2 ((g1 , g2) ∘iff (f1 , f2)) = f2 ∘ g2 -``` - -### Inverting a logical equivalence - -```agda -inv-iff : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ↔ B) → (B ↔ A) -pr1 (inv-iff (f , g)) = g -pr2 (inv-iff (f , g)) = f -``` - ## Properties ### Characterizing equality of logical equivalences @@ -147,11 +93,6 @@ module _ {l1 l2 : Level} {A : UU l1} {B : UU l2} where - htpy-iff : (f g : A ↔ B) → UU (l1 ⊔ l2) - htpy-iff f g = - ( forward-implication f ~ forward-implication g) × - ( backward-implication f ~ backward-implication g) - ext-iff : (f g : A ↔ B) → (f ＝ g) ≃ htpy-iff f g ext-iff f g = equiv-product equiv-funext equiv-funext ∘e equiv-pair-eq f g @@ -166,89 +107,6 @@ module _ eq-htpy-iff f g = map-inv-equiv (ext-iff f g) ``` -### Logical equivalences between propositions induce equivalences - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - abstract - is-equiv-has-converse-is-prop : - is-prop A → is-prop B → {f : A → B} → (B → A) → is-equiv f - is-equiv-has-converse-is-prop is-prop-A is-prop-B {f} g = - is-equiv-is-invertible - ( g) - ( λ y → eq-is-prop is-prop-B) - ( λ x → eq-is-prop is-prop-A) - - abstract - equiv-iff-is-prop : is-prop A → is-prop B → (A → B) → (B → A) → A ≃ B - pr1 (equiv-iff-is-prop is-prop-A is-prop-B f g) = f - pr2 (equiv-iff-is-prop is-prop-A is-prop-B f g) = - is-equiv-has-converse-is-prop is-prop-A is-prop-B g - -module _ - {l1 l2 : Level} (P : Prop l1) (Q : Prop l2) - where - - abstract - is-equiv-has-converse : - {f : type-Prop P → type-Prop Q} → (type-Prop Q → type-Prop P) → is-equiv f - is-equiv-has-converse = - is-equiv-has-converse-is-prop - ( is-prop-type-Prop P) - ( is-prop-type-Prop Q) - - equiv-iff' : type-Prop (P ⇔ Q) → (type-Prop P ≃ type-Prop Q) - pr1 (equiv-iff' t) = forward-implication t - pr2 (equiv-iff' t) = - is-equiv-has-converse-is-prop - ( is-prop-type-Prop P) - ( is-prop-type-Prop Q) - ( backward-implication t) - - equiv-iff : - (type-Prop P → type-Prop Q) → (type-Prop Q → type-Prop P) → - type-Prop P ≃ type-Prop Q - equiv-iff f g = equiv-iff' (f , g) -``` - -### Equivalences are logical equivalences - -```agda -iff-equiv : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ≃ B) → (A ↔ B) -pr1 (iff-equiv e) = map-equiv e -pr2 (iff-equiv e) = map-inv-equiv e - -iff-equiv' : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (A ≃ B) → (B ↔ A) -pr1 (iff-equiv' e) = map-inv-equiv e -pr2 (iff-equiv' e) = map-equiv e - -is-injective-iff-equiv : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → is-injective (iff-equiv {A = A} {B}) -is-injective-iff-equiv p = eq-htpy-equiv (pr1 (htpy-eq-iff p)) - -compute-fiber-iff-equiv : - {l1 l2 : Level} {A : UU l1} {B : UU l2} ((f , g) : A ↔ B) → - fiber (iff-equiv) (f , g) ≃ Σ (is-equiv f) (λ f' → map-inv-is-equiv f' ~ g) -compute-fiber-iff-equiv {A = A} {B} (f , g) = - ( equiv-tot (λ _ → equiv-funext)) ∘e - ( left-unit-law-Σ-is-contr (is-torsorial-Id' f) (f , refl)) ∘e - ( inv-associative-Σ (A → B) (_＝ f) _) ∘e - ( equiv-tot (λ _ → equiv-left-swap-Σ)) ∘e - ( associative-Σ (A → B) _ _) ∘e - ( equiv-tot (λ e → equiv-pair-eq (iff-equiv e) (f , g))) -``` - -### Two equal propositions are logically equivalent - -```agda -iff-eq : {l1 : Level} {P Q : Prop l1} → P ＝ Q → type-Prop (P ⇔ Q) -pr1 (iff-eq refl) = id -pr2 (iff-eq refl) = id -``` - ### Logical equivalence of propositions is equivalent to equivalence of propositions ```agda @@ -269,43 +127,12 @@ pr1 (equiv-equiv-iff P Q) = equiv-iff' P Q pr2 (equiv-equiv-iff P Q) = is-equiv-equiv-iff P Q ``` -## Logical equivalences between dependent function types - -```agda -module _ - {l1 l2 l3 : Level} {I : UU l1} {A : I → UU l2} {B : I → UU l3} - where - - iff-Π-iff-family : ((i : I) → A i ↔ B i) → ((i : I) → A i) ↔ ((i : I) → B i) - pr1 (iff-Π-iff-family e) a i = forward-implication (e i) (a i) - pr2 (iff-Π-iff-family e) b i = backward-implication (e i) (b i) -``` - -## Reasoning with logical equivalences - -Logical equivalences can be constructed by equational reasoning in the following -way: - -```text -logical-equivalence-reasoning - X ↔ Y by equiv-1 - ↔ Z by equiv-2 - ↔ V by equiv-3 -``` +### Equivalences are logical equivalences ```agda -infixl 1 logical-equivalence-reasoning_ -infixl 0 step-logical-equivalence-reasoning - -logical-equivalence-reasoning_ : - {l1 : Level} (X : UU l1) → X ↔ X -pr1 (logical-equivalence-reasoning X) = id -pr2 (logical-equivalence-reasoning X) = id - -step-logical-equivalence-reasoning : - {l1 l2 l3 : Level} {X : UU l1} {Y : UU l2} → - (X ↔ Y) → (Z : UU l3) → (Y ↔ Z) → (X ↔ Z) -step-logical-equivalence-reasoning e Z f = f ∘iff e - -syntax step-logical-equivalence-reasoning e Z f = e ↔ Z by f +compute-fiber-iff-equiv : + {l1 l2 : Level} {A : UU l1} {B : UU l2} ((f , g) : A ↔ B) → + fiber (iff-equiv) (f , g) ≃ Σ (is-equiv f) (λ f' → map-inv-is-equiv f' ~ g) +compute-fiber-iff-equiv {A = A} {B} e = + equiv-tot (λ _ → equiv-funext) ∘e compute-fiber-iff-equiv' e ``` diff --git a/src/foundation/negation.lagda.md b/src/foundation/negation.lagda.md index 18aab537b4..6e01b1d0a1 100644 --- a/src/foundation/negation.lagda.md +++ b/src/foundation/negation.lagda.md @@ -56,13 +56,6 @@ eq-neg : {l : Level} {A : UU l} {p q : ¬ A} → p ＝ q eq-neg = eq-is-prop is-prop-neg ``` -### Reductio ad absurdum - -```agda -reductio-ad-absurdum : {l1 l2 : Level} {P : UU l1} {Q : UU l2} → P → ¬ P → Q -reductio-ad-absurdum p np = ex-falso (np p) -``` - ### Logically equivalent types have logically equivalent negations ```agda @@ -92,11 +85,6 @@ module _ ### Negation has no fixed points ```agda -no-fixed-points-neg : - {l : Level} (A : UU l) → ¬ (A ↔ ¬ A) -no-fixed-points-neg A (f , g) = - ( λ (h : ¬ A) → h (g h)) (λ (a : A) → f a a) - abstract no-fixed-points-neg-Prop : {l : Level} (P : Prop l) → ¬ (type-Prop P ↔ ¬ (type-Prop P)) From 2b54978af8237c301b7ee96cd01ce2a1feb0d2bc Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 17:21:47 +0000 Subject: [PATCH 12/39] `foundation.dependent-products-truncated-types` --- src/foundation-core/endomorphisms.lagda.md | 1 + src/foundation-core/sets.lagda.md | 1 + src/foundation-core/truncated-types.lagda.md | 155 -------------- .../universal-property-truncation.lagda.md | 1 + src/foundation.lagda.md | 1 + src/foundation/1-types.lagda.md | 1 + ...ependent-products-truncated-types.lagda.md | 192 ++++++++++++++++++ src/foundation/fibered-maps.lagda.md | 1 + ...oriality-dependent-function-types.lagda.md | 1 + .../identity-truncated-types.lagda.md | 1 + src/foundation/invertible-maps.lagda.md | 1 + src/foundation/involutions.lagda.md | 1 + .../iterated-dependent-product-types.lagda.md | 1 + src/foundation/locally-small-types.lagda.md | 1 + src/foundation/mere-equivalences.lagda.md | 1 + src/foundation/path-cosplit-maps.lagda.md | 1 + src/foundation/retractions.lagda.md | 1 + src/foundation/sets.lagda.md | 1 + src/foundation/truncated-maps.lagda.md | 1 + src/foundation/truncated-types.lagda.md | 1 + .../truncation-equivalences.lagda.md | 1 + ...uniformly-decidable-type-families.lagda.md | 1 + src/foundation/uniqueness-truncation.lagda.md | 1 + src/foundation/unordered-tuples.lagda.md | 1 + ...homomorphisms-generated-subgroups.lagda.md | 1 + src/linear-algebra/vectors.lagda.md | 1 + .../extensions-maps.lagda.md | 1 + .../lifts-maps.lagda.md | 1 + src/trees/functoriality-w-types.lagda.md | 1 + src/trees/w-types.lagda.md | 1 + 30 files changed, 220 insertions(+), 155 deletions(-) create mode 100644 src/foundation/dependent-products-truncated-types.lagda.md diff --git a/src/foundation-core/endomorphisms.lagda.md b/src/foundation-core/endomorphisms.lagda.md index 0f59be9040..b374c58abd 100644 --- a/src/foundation-core/endomorphisms.lagda.md +++ b/src/foundation-core/endomorphisms.lagda.md @@ -8,6 +8,7 @@ module foundation-core.endomorphisms where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.sets open import foundation.universe-levels diff --git a/src/foundation-core/sets.lagda.md b/src/foundation-core/sets.lagda.md index def449a7a1..58eb572a12 100644 --- a/src/foundation-core/sets.lagda.md +++ b/src/foundation-core/sets.lagda.md @@ -8,6 +8,7 @@ module foundation-core.sets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation-core/truncated-types.lagda.md b/src/foundation-core/truncated-types.lagda.md index aab89dd8cf..a0c1773090 100644 --- a/src/foundation-core/truncated-types.lagda.md +++ b/src/foundation-core/truncated-types.lagda.md @@ -10,10 +10,7 @@ module foundation-core.truncated-types where open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -21,9 +18,7 @@ open import foundation-core.contractible-types open import foundation-core.embeddings open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences -open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.propositions open import foundation-core.retracts-of-types open import foundation-core.transport-along-identifications open import foundation-core.truncation-levels @@ -294,153 +289,3 @@ is-trunc-right-factor-product (succ-𝕋 k) {A} {B} H a b b' = ( H (pair a b) (pair a b'))) ( refl) ``` - -### Products of families of truncated types are truncated - -```agda -abstract - is-trunc-Π : - {l1 l2 : Level} (k : 𝕋) {A : UU l1} {B : A → UU l2} → - ((x : A) → is-trunc k (B x)) → is-trunc k ((x : A) → B x) - is-trunc-Π neg-two-𝕋 is-trunc-B = is-contr-Π is-trunc-B - is-trunc-Π (succ-𝕋 k) is-trunc-B f g = - is-trunc-is-equiv k (f ~ g) htpy-eq - ( funext f g) - ( is-trunc-Π k (λ x → is-trunc-B x (f x) (g x))) - -type-Π-Truncated-Type' : - (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → - UU (l1 ⊔ l2) -type-Π-Truncated-Type' k A B = (x : A) → type-Truncated-Type (B x) - -is-trunc-type-Π-Truncated-Type' : - (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → - is-trunc k (type-Π-Truncated-Type' k A B) -is-trunc-type-Π-Truncated-Type' k A B = - is-trunc-Π k (λ x → is-trunc-type-Truncated-Type (B x)) - -Π-Truncated-Type' : - (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → - Truncated-Type (l1 ⊔ l2) k -pr1 (Π-Truncated-Type' k A B) = type-Π-Truncated-Type' k A B -pr2 (Π-Truncated-Type' k A B) = is-trunc-type-Π-Truncated-Type' k A B - -type-Π-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : type-Truncated-Type A → Truncated-Type l2 k) → - UU (l1 ⊔ l2) -type-Π-Truncated-Type k A B = - type-Π-Truncated-Type' k (type-Truncated-Type A) B - -is-trunc-type-Π-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : type-Truncated-Type A → Truncated-Type l2 k) → - is-trunc k (type-Π-Truncated-Type k A B) -is-trunc-type-Π-Truncated-Type k A B = - is-trunc-type-Π-Truncated-Type' k (type-Truncated-Type A) B - -Π-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : type-Truncated-Type A → Truncated-Type l2 k) → - Truncated-Type (l1 ⊔ l2) k -Π-Truncated-Type k A B = - Π-Truncated-Type' k (type-Truncated-Type A) B -``` - -### The type of functions into a truncated type is truncated - -```agda -abstract - is-trunc-function-type : - {l1 l2 : Level} (k : 𝕋) {A : UU l1} {B : UU l2} → - is-trunc k B → is-trunc k (A → B) - is-trunc-function-type k {A} {B} is-trunc-B = - is-trunc-Π k {B = λ (x : A) → B} (λ x → is-trunc-B) - -function-type-Truncated-Type : - {l1 l2 : Level} {k : 𝕋} (A : UU l1) (B : Truncated-Type l2 k) → - Truncated-Type (l1 ⊔ l2) k -pr1 (function-type-Truncated-Type A B) = A → type-Truncated-Type B -pr2 (function-type-Truncated-Type A B) = - is-trunc-function-type _ (is-trunc-type-Truncated-Type B) - -type-hom-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : Truncated-Type l2 k) → UU (l1 ⊔ l2) -type-hom-Truncated-Type k A B = - type-Truncated-Type A → type-Truncated-Type B - -is-trunc-type-hom-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : Truncated-Type l2 k) → - is-trunc k (type-hom-Truncated-Type k A B) -is-trunc-type-hom-Truncated-Type k A B = - is-trunc-function-type k (is-trunc-type-Truncated-Type B) - -hom-Truncated-Type : - (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) - (B : Truncated-Type l2 k) → Truncated-Type (l1 ⊔ l2) k -pr1 (hom-Truncated-Type k A B) = type-hom-Truncated-Type k A B -pr2 (hom-Truncated-Type k A B) = is-trunc-type-hom-Truncated-Type k A B -``` - -### Being truncated is a property - -```agda -abstract - is-prop-is-trunc : - {l : Level} (k : 𝕋) (A : UU l) → is-prop (is-trunc k A) - is-prop-is-trunc neg-two-𝕋 A = is-property-is-contr - is-prop-is-trunc (succ-𝕋 k) A = - is-trunc-Π neg-one-𝕋 - ( λ x → is-trunc-Π neg-one-𝕋 (λ y → is-prop-is-trunc k (x ＝ y))) - -is-trunc-Prop : {l : Level} (k : 𝕋) (A : UU l) → Σ (UU l) (is-trunc neg-one-𝕋) -pr1 (is-trunc-Prop k A) = is-trunc k A -pr2 (is-trunc-Prop k A) = is-prop-is-trunc k A -``` - -### The type of equivalences between truncated types is truncated - -```agda -module _ - {l1 l2 : Level} {A : UU l1} {B : UU l2} - where - - is-trunc-equiv-is-trunc : - (k : 𝕋) → is-trunc k A → is-trunc k B → is-trunc k (A ≃ B) - is-trunc-equiv-is-trunc k H K = - is-trunc-Σ - ( is-trunc-function-type k K) - ( λ f → - is-trunc-Σ - ( is-trunc-Σ - ( is-trunc-function-type k H) - ( λ g → - is-trunc-Π k (λ y → is-trunc-Id K (f (g y)) y))) - ( λ _ → - is-trunc-Σ - ( is-trunc-function-type k H) - ( λ h → - is-trunc-Π k (λ x → is-trunc-Id H (h (f x)) x)))) - -type-equiv-Truncated-Type : - {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → - UU (l1 ⊔ l2) -type-equiv-Truncated-Type A B = - type-Truncated-Type A ≃ type-Truncated-Type B - -is-trunc-type-equiv-Truncated-Type : - {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → - is-trunc k (type-equiv-Truncated-Type A B) -is-trunc-type-equiv-Truncated-Type A B = - is-trunc-equiv-is-trunc _ - ( is-trunc-type-Truncated-Type A) - ( is-trunc-type-Truncated-Type B) - -equiv-Truncated-Type : - {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → - Truncated-Type (l1 ⊔ l2) k -pr1 (equiv-Truncated-Type A B) = type-equiv-Truncated-Type A B -pr2 (equiv-Truncated-Type A B) = is-trunc-type-equiv-Truncated-Type A B -``` diff --git a/src/foundation-core/universal-property-truncation.lagda.md b/src/foundation-core/universal-property-truncation.lagda.md index 1f7366ca3a..875fd1d2ba 100644 --- a/src/foundation-core/universal-property-truncation.lagda.md +++ b/src/foundation-core/universal-property-truncation.lagda.md @@ -8,6 +8,7 @@ module foundation-core.universal-property-truncation where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.function-extensionality open import foundation.universal-property-equivalences open import foundation.universe-levels diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index 0639393861..05fc7bc087 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -123,6 +123,7 @@ open import foundation.dependent-pair-types public open import foundation.dependent-products-contractible-types public open import foundation.dependent-products-propositions public open import foundation.dependent-products-pullbacks public +open import foundation.dependent-products-truncated-types public open import foundation.dependent-sequences public open import foundation.dependent-sums-pullbacks public open import foundation.dependent-telescopes public diff --git a/src/foundation/1-types.lagda.md b/src/foundation/1-types.lagda.md index cdce9dfe87..9a4b7da289 100644 --- a/src/foundation/1-types.lagda.md +++ b/src/foundation/1-types.lagda.md @@ -10,6 +10,7 @@ open import foundation-core.1-types public ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.subuniverses open import foundation.truncated-types open import foundation.universe-levels diff --git a/src/foundation/dependent-products-truncated-types.lagda.md b/src/foundation/dependent-products-truncated-types.lagda.md new file mode 100644 index 0000000000..52960698b7 --- /dev/null +++ b/src/foundation/dependent-products-truncated-types.lagda.md @@ -0,0 +1,192 @@ +# Dependent products truncated types + +```agda +module foundation.dependent-products-truncated-types where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-dependent-functions +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.equality-cartesian-product-types +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.universe-levels + +open import foundation-core.cartesian-product-types +open import foundation-core.contractible-types +open import foundation-core.embeddings +open import foundation-core.equality-dependent-pair-types +open import foundation-core.equivalences +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.propositions +open import foundation-core.retracts-of-types +open import foundation-core.transport-along-identifications +open import foundation-core.truncated-types +open import foundation-core.truncation-levels +``` + +
+ +## Idea + +The truncatedness of a type is a measure of the complexity of its identity +types. The simplest case is a contractible type. This is the base case of the +inductive definition of truncatedness for types. A type is `k+1`-truncated if +its identity types are `k`-truncated. + +## Properties + +### Products of families of truncated types are truncated + +```agda +abstract + is-trunc-Π : + {l1 l2 : Level} (k : 𝕋) {A : UU l1} {B : A → UU l2} → + ((x : A) → is-trunc k (B x)) → is-trunc k ((x : A) → B x) + is-trunc-Π neg-two-𝕋 is-trunc-B = is-contr-Π is-trunc-B + is-trunc-Π (succ-𝕋 k) is-trunc-B f g = + is-trunc-is-equiv k (f ~ g) htpy-eq + ( funext f g) + ( is-trunc-Π k (λ x → is-trunc-B x (f x) (g x))) + +type-Π-Truncated-Type' : + (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → + UU (l1 ⊔ l2) +type-Π-Truncated-Type' k A B = (x : A) → type-Truncated-Type (B x) + +is-trunc-type-Π-Truncated-Type' : + (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → + is-trunc k (type-Π-Truncated-Type' k A B) +is-trunc-type-Π-Truncated-Type' k A B = + is-trunc-Π k (λ x → is-trunc-type-Truncated-Type (B x)) + +Π-Truncated-Type' : + (k : 𝕋) {l1 l2 : Level} (A : UU l1) (B : A → Truncated-Type l2 k) → + Truncated-Type (l1 ⊔ l2) k +pr1 (Π-Truncated-Type' k A B) = type-Π-Truncated-Type' k A B +pr2 (Π-Truncated-Type' k A B) = is-trunc-type-Π-Truncated-Type' k A B + +type-Π-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : type-Truncated-Type A → Truncated-Type l2 k) → + UU (l1 ⊔ l2) +type-Π-Truncated-Type k A B = + type-Π-Truncated-Type' k (type-Truncated-Type A) B + +is-trunc-type-Π-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : type-Truncated-Type A → Truncated-Type l2 k) → + is-trunc k (type-Π-Truncated-Type k A B) +is-trunc-type-Π-Truncated-Type k A B = + is-trunc-type-Π-Truncated-Type' k (type-Truncated-Type A) B + +Π-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : type-Truncated-Type A → Truncated-Type l2 k) → + Truncated-Type (l1 ⊔ l2) k +Π-Truncated-Type k A B = + Π-Truncated-Type' k (type-Truncated-Type A) B +``` + +### The type of functions into a truncated type is truncated + +```agda +abstract + is-trunc-function-type : + {l1 l2 : Level} (k : 𝕋) {A : UU l1} {B : UU l2} → + is-trunc k B → is-trunc k (A → B) + is-trunc-function-type k {A} {B} is-trunc-B = + is-trunc-Π k {B = λ (x : A) → B} (λ x → is-trunc-B) + +function-type-Truncated-Type : + {l1 l2 : Level} {k : 𝕋} (A : UU l1) (B : Truncated-Type l2 k) → + Truncated-Type (l1 ⊔ l2) k +pr1 (function-type-Truncated-Type A B) = A → type-Truncated-Type B +pr2 (function-type-Truncated-Type A B) = + is-trunc-function-type _ (is-trunc-type-Truncated-Type B) + +type-hom-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : Truncated-Type l2 k) → UU (l1 ⊔ l2) +type-hom-Truncated-Type k A B = + type-Truncated-Type A → type-Truncated-Type B + +is-trunc-type-hom-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : Truncated-Type l2 k) → + is-trunc k (type-hom-Truncated-Type k A B) +is-trunc-type-hom-Truncated-Type k A B = + is-trunc-function-type k (is-trunc-type-Truncated-Type B) + +hom-Truncated-Type : + (k : 𝕋) {l1 l2 : Level} (A : Truncated-Type l1 k) + (B : Truncated-Type l2 k) → Truncated-Type (l1 ⊔ l2) k +pr1 (hom-Truncated-Type k A B) = type-hom-Truncated-Type k A B +pr2 (hom-Truncated-Type k A B) = is-trunc-type-hom-Truncated-Type k A B +``` + +### Being truncated is a property + +```agda +abstract + is-prop-is-trunc : + {l : Level} (k : 𝕋) (A : UU l) → is-prop (is-trunc k A) + is-prop-is-trunc neg-two-𝕋 A = is-property-is-contr + is-prop-is-trunc (succ-𝕋 k) A = + is-trunc-Π neg-one-𝕋 + ( λ x → is-trunc-Π neg-one-𝕋 (λ y → is-prop-is-trunc k (x ＝ y))) + +is-trunc-Prop : {l : Level} (k : 𝕋) (A : UU l) → Σ (UU l) (is-trunc neg-one-𝕋) +pr1 (is-trunc-Prop k A) = is-trunc k A +pr2 (is-trunc-Prop k A) = is-prop-is-trunc k A +``` + +### The type of equivalences between truncated types is truncated + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + is-trunc-equiv-is-trunc : + (k : 𝕋) → is-trunc k A → is-trunc k B → is-trunc k (A ≃ B) + is-trunc-equiv-is-trunc k H K = + is-trunc-Σ + ( is-trunc-function-type k K) + ( λ f → + is-trunc-Σ + ( is-trunc-Σ + ( is-trunc-function-type k H) + ( λ g → + is-trunc-Π k (λ y → is-trunc-Id K (f (g y)) y))) + ( λ _ → + is-trunc-Σ + ( is-trunc-function-type k H) + ( λ h → + is-trunc-Π k (λ x → is-trunc-Id H (h (f x)) x)))) + +type-equiv-Truncated-Type : + {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → + UU (l1 ⊔ l2) +type-equiv-Truncated-Type A B = + type-Truncated-Type A ≃ type-Truncated-Type B + +is-trunc-type-equiv-Truncated-Type : + {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → + is-trunc k (type-equiv-Truncated-Type A B) +is-trunc-type-equiv-Truncated-Type A B = + is-trunc-equiv-is-trunc _ + ( is-trunc-type-Truncated-Type A) + ( is-trunc-type-Truncated-Type B) + +equiv-Truncated-Type : + {l1 l2 : Level} {k : 𝕋} (A : Truncated-Type l1 k) (B : Truncated-Type l2 k) → + Truncated-Type (l1 ⊔ l2) k +pr1 (equiv-Truncated-Type A B) = type-equiv-Truncated-Type A B +pr2 (equiv-Truncated-Type A B) = is-trunc-type-equiv-Truncated-Type A B +``` diff --git a/src/foundation/fibered-maps.lagda.md b/src/foundation/fibered-maps.lagda.md index 2e4565e278..1ba4249488 100644 --- a/src/foundation/fibered-maps.lagda.md +++ b/src/foundation/fibered-maps.lagda.md @@ -10,6 +10,7 @@ module foundation.fibered-maps where open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-truncated-types open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction diff --git a/src/foundation/functoriality-dependent-function-types.lagda.md b/src/foundation/functoriality-dependent-function-types.lagda.md index 9fc8e6c98c..290c471228 100644 --- a/src/foundation/functoriality-dependent-function-types.lagda.md +++ b/src/foundation/functoriality-dependent-function-types.lagda.md @@ -11,6 +11,7 @@ open import foundation-core.functoriality-dependent-function-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.dependent-universal-property-equivalences open import foundation.equivalence-extensionality open import foundation.function-extensionality diff --git a/src/foundation/identity-truncated-types.lagda.md b/src/foundation/identity-truncated-types.lagda.md index 3da3145597..0201dea2e3 100644 --- a/src/foundation/identity-truncated-types.lagda.md +++ b/src/foundation/identity-truncated-types.lagda.md @@ -7,6 +7,7 @@ module foundation.identity-truncated-types where
Imports ```agda +open import foundation.dependent-products-truncated-types open import foundation.univalence open import foundation.universe-levels diff --git a/src/foundation/invertible-maps.lagda.md b/src/foundation/invertible-maps.lagda.md index 47fb7cca31..3edb105808 100644 --- a/src/foundation/invertible-maps.lagda.md +++ b/src/foundation/invertible-maps.lagda.md @@ -12,6 +12,7 @@ open import foundation-core.invertible-maps public open import foundation.action-on-identifications-functions open import foundation.commuting-triangles-of-homotopies open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.equality-cartesian-product-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/foundation/involutions.lagda.md b/src/foundation/involutions.lagda.md index df78de65a1..8f2ad4d544 100644 --- a/src/foundation/involutions.lagda.md +++ b/src/foundation/involutions.lagda.md @@ -9,6 +9,7 @@ module foundation.involutions where ```agda open import foundation.automorphisms open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/foundation/iterated-dependent-product-types.lagda.md b/src/foundation/iterated-dependent-product-types.lagda.md index 80ace77d32..1937e04f5f 100644 --- a/src/foundation/iterated-dependent-product-types.lagda.md +++ b/src/foundation/iterated-dependent-product-types.lagda.md @@ -13,6 +13,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation/locally-small-types.lagda.md b/src/foundation/locally-small-types.lagda.md index 3640cd7534..2c54ced78e 100644 --- a/src/foundation/locally-small-types.lagda.md +++ b/src/foundation/locally-small-types.lagda.md @@ -9,6 +9,7 @@ module foundation.locally-small-types where ```agda open import foundation.dependent-pair-types open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.equivalences open import foundation.function-extensionality open import foundation.inhabited-subtypes diff --git a/src/foundation/mere-equivalences.lagda.md b/src/foundation/mere-equivalences.lagda.md index 663c8f4d24..27fecbd0f1 100644 --- a/src/foundation/mere-equivalences.lagda.md +++ b/src/foundation/mere-equivalences.lagda.md @@ -9,6 +9,7 @@ module foundation.mere-equivalences where ```agda open import foundation.binary-relations open import foundation.decidable-equality +open import foundation.dependent-products-truncated-types open import foundation.functoriality-propositional-truncation open import foundation.mere-equality open import foundation.propositional-truncations diff --git a/src/foundation/path-cosplit-maps.lagda.md b/src/foundation/path-cosplit-maps.lagda.md index 602902e4a9..cf0e458b12 100644 --- a/src/foundation/path-cosplit-maps.lagda.md +++ b/src/foundation/path-cosplit-maps.lagda.md @@ -15,6 +15,7 @@ open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.empty-types open import foundation.equality-cartesian-product-types open import foundation.equality-coproduct-types diff --git a/src/foundation/retractions.lagda.md b/src/foundation/retractions.lagda.md index cf513e7240..afabb0426b 100644 --- a/src/foundation/retractions.lagda.md +++ b/src/foundation/retractions.lagda.md @@ -12,6 +12,7 @@ open import foundation-core.retractions public open import foundation.action-on-identifications-functions open import foundation.coslice open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/sets.lagda.md b/src/foundation/sets.lagda.md index 32edfb667b..e1d105beab 100644 --- a/src/foundation/sets.lagda.md +++ b/src/foundation/sets.lagda.md @@ -11,6 +11,7 @@ open import foundation-core.sets public ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.logical-equivalences open import foundation.subuniverses open import foundation.truncated-types diff --git a/src/foundation/truncated-maps.lagda.md b/src/foundation/truncated-maps.lagda.md index 5d640a4f3c..05f95a7187 100644 --- a/src/foundation/truncated-maps.lagda.md +++ b/src/foundation/truncated-maps.lagda.md @@ -3,6 +3,7 @@ ```agda module foundation.truncated-maps where +open import foundation.dependent-products-truncated-types public open import foundation-core.truncated-maps public ``` diff --git a/src/foundation/truncated-types.lagda.md b/src/foundation/truncated-types.lagda.md index d2248f9dab..4233ee729d 100644 --- a/src/foundation/truncated-types.lagda.md +++ b/src/foundation/truncated-types.lagda.md @@ -4,6 +4,7 @@ module foundation.truncated-types where open import foundation-core.truncated-types public +open import foundation.dependent-products-truncated-types public ```
Imports diff --git a/src/foundation/truncation-equivalences.lagda.md b/src/foundation/truncation-equivalences.lagda.md index 5462a0bf32..95d6169280 100644 --- a/src/foundation/truncation-equivalences.lagda.md +++ b/src/foundation/truncation-equivalences.lagda.md @@ -12,6 +12,7 @@ open import foundation.connected-maps open import foundation.connected-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.functoriality-truncation open import foundation.identity-types open import foundation.precomposition-functions-into-subuniverses diff --git a/src/foundation/uniformly-decidable-type-families.lagda.md b/src/foundation/uniformly-decidable-type-families.lagda.md index 0d848563b6..9beb5f6b51 100644 --- a/src/foundation/uniformly-decidable-type-families.lagda.md +++ b/src/foundation/uniformly-decidable-type-families.lagda.md @@ -12,6 +12,7 @@ open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-truncated-types open import foundation.equality-coproduct-types open import foundation.inhabited-types open import foundation.negation diff --git a/src/foundation/uniqueness-truncation.lagda.md b/src/foundation/uniqueness-truncation.lagda.md index 25971b85f3..d14c70219d 100644 --- a/src/foundation/uniqueness-truncation.lagda.md +++ b/src/foundation/uniqueness-truncation.lagda.md @@ -7,6 +7,7 @@ module foundation.uniqueness-truncation where
Imports ```agda +open import foundation.dependent-products-truncated-types open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/unordered-tuples.lagda.md b/src/foundation/unordered-tuples.lagda.md index 69977f8b8e..d3ce033256 100644 --- a/src/foundation/unordered-tuples.lagda.md +++ b/src/foundation/unordered-tuples.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.1-types open import foundation.decidable-equality open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction open import foundation.postcomposition-functions diff --git a/src/group-theory/homomorphisms-generated-subgroups.lagda.md b/src/group-theory/homomorphisms-generated-subgroups.lagda.md index dfebd1378a..4f2f8359a6 100644 --- a/src/group-theory/homomorphisms-generated-subgroups.lagda.md +++ b/src/group-theory/homomorphisms-generated-subgroups.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.embeddings open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/linear-algebra/vectors.lagda.md b/src/linear-algebra/vectors.lagda.md index 63c0566a42..5a2c7b7ed0 100644 --- a/src/linear-algebra/vectors.lagda.md +++ b/src/linear-algebra/vectors.lagda.md @@ -14,6 +14,7 @@ open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/orthogonal-factorization-systems/extensions-maps.lagda.md b/src/orthogonal-factorization-systems/extensions-maps.lagda.md index ccdc296bd0..1afb566035 100644 --- a/src/orthogonal-factorization-systems/extensions-maps.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-maps.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/orthogonal-factorization-systems/lifts-maps.lagda.md b/src/orthogonal-factorization-systems/lifts-maps.lagda.md index 9d2fe4746b..60cb9ba46c 100644 --- a/src/orthogonal-factorization-systems/lifts-maps.lagda.md +++ b/src/orthogonal-factorization-systems/lifts-maps.lagda.md @@ -10,6 +10,7 @@ module orthogonal-factorization-systems.lifts-maps where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/trees/functoriality-w-types.lagda.md b/src/trees/functoriality-w-types.lagda.md index 6a32e1a93e..b664531fd5 100644 --- a/src/trees/functoriality-w-types.lagda.md +++ b/src/trees/functoriality-w-types.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.contractible-maps open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.embeddings open import foundation.equivalences open import foundation.fibers-of-maps diff --git a/src/trees/w-types.lagda.md b/src/trees/w-types.lagda.md index cf2df81dea..9e3ae175b9 100644 --- a/src/trees/w-types.lagda.md +++ b/src/trees/w-types.lagda.md @@ -10,6 +10,7 @@ module trees.w-types where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.empty-types open import foundation.equivalences open import foundation.function-extensionality From c62f26fa593217730dd5d99b687c531026822aa7 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 17:30:42 +0000 Subject: [PATCH 13/39] move `equiv-Set` --- src/foundation-core/sets.lagda.md | 20 -------------------- src/foundation/automorphisms.lagda.md | 2 +- src/foundation/sets.lagda.md | 22 ++++++++++++++++++++++ 3 files changed, 23 insertions(+), 21 deletions(-) diff --git a/src/foundation-core/sets.lagda.md b/src/foundation-core/sets.lagda.md index 58eb572a12..b05ea9bb42 100644 --- a/src/foundation-core/sets.lagda.md +++ b/src/foundation-core/sets.lagda.md @@ -8,12 +8,10 @@ module foundation-core.sets where ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels open import foundation-core.contractible-types -open import foundation-core.embeddings open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.injective-maps @@ -195,24 +193,6 @@ abstract {l1 l2 : Level} (A : UU l1) {B : UU l2} (e : A ≃ B) → is-set A → is-set B is-set-equiv' = is-trunc-equiv' zero-𝕋 - -abstract - is-set-equiv-is-set : - {l1 l2 : Level} {A : UU l1} {B : UU l2} → - is-set A → is-set B → is-set (A ≃ B) - is-set-equiv-is-set = is-trunc-equiv-is-trunc zero-𝕋 - -module _ - {l1 l2 : Level} (A : Set l1) (B : Set l2) - where - - equiv-Set : UU (l1 ⊔ l2) - equiv-Set = type-Set A ≃ type-Set B - - equiv-set-Set : Set (l1 ⊔ l2) - pr1 equiv-set-Set = equiv-Set - pr2 equiv-set-Set = - is-set-equiv-is-set (is-set-type-Set A) (is-set-type-Set B) ``` ### If a type injects into a set, then it is a set diff --git a/src/foundation/automorphisms.lagda.md b/src/foundation/automorphisms.lagda.md index 183752d129..2a1f0e7a55 100644 --- a/src/foundation/automorphisms.lagda.md +++ b/src/foundation/automorphisms.lagda.md @@ -11,7 +11,7 @@ open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation-core.equivalences -open import foundation-core.sets +open import foundation.sets open import structured-types.pointed-types ``` diff --git a/src/foundation/sets.lagda.md b/src/foundation/sets.lagda.md index e1d105beab..f486be35a9 100644 --- a/src/foundation/sets.lagda.md +++ b/src/foundation/sets.lagda.md @@ -178,6 +178,28 @@ precomp-Set : precomp-Set f C = precomp f (type-Set C) ``` +### The type of equivalences between sets is a set + +```agda +abstract + is-set-equiv-is-set : + {l1 l2 : Level} {A : UU l1} {B : UU l2} → + is-set A → is-set B → is-set (A ≃ B) + is-set-equiv-is-set = is-trunc-equiv-is-trunc zero-𝕋 + +module _ + {l1 l2 : Level} (A : Set l1) (B : Set l2) + where + + equiv-Set : UU (l1 ⊔ l2) + equiv-Set = type-Set A ≃ type-Set B + + equiv-set-Set : Set (l1 ⊔ l2) + pr1 equiv-set-Set = equiv-Set + pr2 equiv-set-Set = + is-set-equiv-is-set (is-set-type-Set A) (is-set-type-Set B) +``` + ### Extensionality of sets ```agda From 0ed41ca3f3c0d2f2b4f4975d73c7facc59e6f783 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 17:30:58 +0000 Subject: [PATCH 14/39] script --- scripts/build_definition_graph.py | 665 ++++++++++++++++++++++++++++++ 1 file changed, 665 insertions(+) create mode 100644 scripts/build_definition_graph.py diff --git a/scripts/build_definition_graph.py b/scripts/build_definition_graph.py new file mode 100644 index 0000000000..85732c8a43 --- /dev/null +++ b/scripts/build_definition_graph.py @@ -0,0 +1,665 @@ +#!/usr/bin/env python3 + +import os +import re +import argparse +import json +from collections import defaultdict, deque +from pathlib import Path + +# Import utils for Git-related functionality +import sys +import os.path +sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) +from scripts.utils import get_git_tracked_files + +def find_agda_files(root_dir): + """Find all Git-tracked Agda source files in the given directory tree.""" + # Get all Git-tracked files + git_tracked_files = get_git_tracked_files() + + # Filter to keep only Agda files that are tracked by Git + agda_files = [] + root_path = Path(root_dir).resolve() + + for file_path in git_tracked_files: + full_path = Path(file_path) + # Check if the file is in the specified root directory + if root_path in full_path.resolve().parents or root_path == full_path.resolve().parent: + if file_path.suffix == '.agda' or (file_path.suffix == '.md' and file_path.stem.endswith('.lagda')): + agda_files.append(str(file_path)) + + return agda_files + +def extract_module_name(file_path, root_dir): + """Extract the module name from a file path.""" + rel_path = os.path.relpath(file_path, root_dir) + if rel_path.endswith('.lagda.md'): + module_name = rel_path[:-9] + else: # .agda + module_name = rel_path[:-5] + module_name = module_name.replace('/', '.') + return module_name + +def extract_definitions(file_path): + """ + Extract all definitions from a file. + Returns a list of tuples (definition_name, line_number, line_content) + """ + # Define a blacklist of regex patterns for definition names to exclude + definition_blacklist_patterns = [ + r'^[a-zA-Z]$', # Single letter names + r'^l\d+$', # 'l' followed by a number + ] + + with open(file_path, 'r', encoding='utf-8') as f: + content = f.read() + + # Determine if this is a literate Agda file (.lagda.md) + is_literate_agda = file_path.endswith('.lagda.md') + + # For literate Agda files, extract only content within code blocks + if is_literate_agda: + # Extract Agda code blocks (```agda ... ```) + code_blocks = re.findall(r'```agda\n(.*?)```', content, re.DOTALL) + # Combine all code blocks into a single string with line numbers preserved + processed_lines = [] + line_num = 0 + for block in code_blocks: + block_lines = block.split('\n') + processed_lines.extend([(line_num + i, line) for i, line in enumerate(block_lines)]) + # Update line_num to account for the block and the delimiters + line_num += len(block_lines) + 2 # +2 for ```agda and ``` + else: + # For regular .agda files, process all lines + lines = content.split('\n') + processed_lines = [(i, line) for i, line in enumerate(lines)] + + # Look for lines of the form "identifier : type" + pattern = r'^\s*([^\s;{}()@"]+)\s+:(?=$|\s)' + + # Add pattern for data and record definitions + data_record_pattern = r'^\s*(data|record)\s*\n?\s+(\S+)(?:$|\!\}|[\s;{}()@"._])' + + definitions = [] + + # Process regular definitions + for line_num, line in processed_lines: + match = re.search(pattern, line) + if match: + definition_name = match.group(1) + # Skip if it's a comment line or matches a blacklist pattern + if not line.strip().startswith('--') and not any(re.match(pattern, definition_name) for pattern in definition_blacklist_patterns): + # Remove underscores from definition name + definition_name = definition_name.replace('_', '') + definitions.append((definition_name, line_num, line)) + + # Process data and record definitions + i = 0 + while i < len(processed_lines): + line_num, line = processed_lines[i] + + # Check for data or record declarations that might span multiple lines + if re.match(r'^\s*(data|record)\s*$', line): + # If the keyword is alone on a line, check the next line + if i + 1 < len(processed_lines): + next_line_num, next_line = processed_lines[i+1] + combined_line = line + ' ' + next_line + match = re.search(data_record_pattern, combined_line) + if match: + definition_name = match.group(2) + if not any(re.match(pattern, definition_name) for pattern in definition_blacklist_patterns): + definition_name = definition_name.replace('_', '') + definitions.append((definition_name, line_num, combined_line)) + else: + # Check for data or record declarations on the same line + match = re.search(data_record_pattern, line) + if match: + definition_name = match.group(2) + if not line.strip().startswith('--') and not any(re.match(pattern, definition_name) for pattern in definition_blacklist_patterns): + definition_name = definition_name.replace('_', '') + definitions.append((definition_name, line_num, line)) + + i += 1 + + return definitions + +def extract_definition_bodies(file_path, definitions): + """ + Extract the body of each definition. + Returns a dictionary mapping definition names to their bodies. + """ + with open(file_path, 'r', encoding='utf-8') as f: + content = f.read() + + # Determine if this is a literate Agda file (.lagda.md) + is_literate_agda = file_path.endswith('.lagda.md') + + # Process content depending on file type + if is_literate_agda: + # Extract Agda code blocks + code_blocks = re.findall(r'```agda\n(.*?)```', content, re.DOTALL) + # Create a mapping from line numbers in original file to line content + line_to_content = {} + line_num = 0 + for block in code_blocks: + block_lines = block.split('\n') + for i, line in enumerate(block_lines): + line_to_content[line_num + i] = line + line_num += len(block_lines) + 2 # +2 for ```agda and ``` + + # Create a list of (line_number, line) for all code blocks + lines = [] + for i in sorted(line_to_content.keys()): + lines.append((i, line_to_content[i])) + else: + # For regular .agda files, process all lines + lines = [(i, line) for i, line in enumerate(content.split('\n'))] + + definition_bodies = {} + + for i, (definition_name, def_line_num, _) in enumerate(definitions): + # Find the start of the body (the first top-level colon after the definition name) + body_start = None + + # Find the line index in our processed lines list that corresponds to the definition line + def_idx = None + for idx, (line_num, _) in enumerate(lines): + if line_num == def_line_num: + def_idx = idx + break + + if def_idx is None: + continue # Skip if we couldn't find the definition line + + # Look for the first top-level colon after the definition name + current_idx = def_idx + paren_level = 0 # Track the nesting level of parentheses + + while current_idx < len(lines) and body_start is None: + line_num, line = lines[current_idx] + + # Process character by character to track parentheses nesting + for char_idx, char in enumerate(line): + if char == '(': + paren_level += 1 + elif char == ')': + paren_level = max(0, paren_level - 1) # Ensure we don't go negative + elif char == ':' and paren_level == 0: + # Found a top-level colon + body_start = (current_idx, char_idx + 1) # Start after the colon + break + + current_idx += 1 + + if body_start is None: + continue # No body found or constructor/postulate without implementation + + # Find the end of the body (the next definition or end of code block) + body_end = None + if i < len(definitions) - 1: + next_def_idx = None + for idx, (line_num, _) in enumerate(lines): + if line_num == definitions[i + 1][1]: + next_def_idx = idx + break + if next_def_idx is not None: + body_end = (next_def_idx, 0) + + if body_end is None: + body_end = (len(lines), 0) # End of file + + # Extract the body + body = "" + if body_start[0] == body_end[0]: + # Body is on the same line + body = lines[body_start[0]][1][body_start[1]:body_end[1]] + else: + # Body spans multiple lines + body = lines[body_start[0]][1][body_start[1]:] + for j in range(body_start[0] + 1, body_end[0]): + if j < len(lines): + body += '\n' + lines[j][1] + if body_end[1] > 0 and body_end[0] < len(lines): + body += '\n' + lines[body_end[0]][1][:body_end[1]] + + definition_bodies[definition_name] = body + + return definition_bodies + +def build_definition_graph(root_dir): + """ + Build a dependency graph of definitions from all Git-tracked Agda files. + """ + agda_files = find_agda_files(root_dir) + + # Dictionary to store all definitions across all files + all_definitions = {} # Maps definition_name -> (module_name, file_path) + module_definitions = defaultdict(list) # Maps module_name -> list of def_names + all_definition_bodies = {} # Maps definition_name -> body + + print(f"Processing {len(agda_files)} Agda files...") + + # First pass: collect all definitions + for file_path in agda_files: + try: + module_name = extract_module_name(file_path, root_dir) + definitions = extract_definitions(file_path) + + for def_name, _, _ in definitions: + # Store with module name to avoid name collisions across modules + qualified_name = f"{module_name}.{def_name}" + all_definitions[qualified_name] = (module_name, file_path) + module_definitions[module_name].append(def_name) + except Exception as e: + print(f"Error processing definitions in {file_path}: {e}") + + print(f"Found {len(all_definitions)} unique qualified definitions") + + # Second pass: extract bodies and build the dependency graph + for file_path in agda_files: + try: + module_name = extract_module_name(file_path, root_dir) + definitions = extract_definitions(file_path) + definition_bodies = extract_definition_bodies(file_path, definitions) + + for def_name, body in definition_bodies.items(): + qualified_name = f"{module_name}.{def_name}" + all_definition_bodies[qualified_name] = body + except Exception as e: + print(f"Error processing definition bodies in {file_path}: {e}") + + # Build the dependency graph + graph = defaultdict(list) + + # Create a reverse lookup from bare definition name to qualified names + # This will help us find all possible qualified definitions for a given bare name + bare_to_qualified = defaultdict(list) + for qualified_name in all_definitions: + bare_name = qualified_name.split('.')[-1] + bare_to_qualified[bare_name].append(qualified_name) + + # Define a blacklist of regex patterns to ignore when finding dependencies + token_blacklist_patterns = [ + r'^[a-zA-Z]$', # Single letter names + r'^l\d+$', # 'l' followed by a number + ] + + # For each definition body, check if it contains references to other definitions + for def_name, body in all_definition_bodies.items(): + module_name = def_name.rsplit('.', 1)[0] # Extract module name from qualified definition name + bare_def_name = def_name.split('.')[-1] # Extract the bare definition name + + # Split the body into tokens (only identifiers, not qualified) + + # The regex uses lookbehind and lookahead to match identifiers surrounded by separators + # but only captures the identifier itself + tokens = [] + pattern = r"""(?:^|\{\!|\{-\#|[\s;{}()@"._])(?!'|--)([^\s;{}()@"._]+)(?:$|\!\}|[\s;{}()@"._])""" + matches = re.finditer(pattern, ' ' + body + ' ') # Add spaces to ensure boundary matching + for match in matches: + tokens.append(match.group(1)) + + # Track unique dependencies to avoid duplicates + unique_deps = set() + + # Check if any token matches a known definition name (ignore qualified parts) + for token in tokens: + # Remove underscores from the token for matching + clean_token = token.replace('_', '') + + # Skip tokens that are the definition itself + if clean_token == bare_def_name: + continue + + # Skip tokens that match any regex in the blacklist + if any(re.match(pattern, clean_token) for pattern in token_blacklist_patterns): + continue + + # Check if it's a reference to a definition in the same module first + if clean_token in module_definitions[module_name]: + qualified_token = f"{module_name}.{clean_token}" + unique_deps.add(qualified_token) + # Otherwise, it might be a reference to an imported definition + # For now, we'll just consider all possible matches to be conservative + elif clean_token in bare_to_qualified and len(bare_to_qualified[clean_token]) > 0: + # Add potential dependencies + # For simplicity and to avoid false positives with common names, + # we'll only consider it a dependency if there's exactly one definition with this name + if len(bare_to_qualified[clean_token]) == 1: + unique_deps.add(bare_to_qualified[clean_token][0]) + + # Add all unique dependencies to the graph + graph[def_name] = list(unique_deps) + + return graph, all_definitions + +def compute_transitive_closure(graph): + """ + Compute the transitive closure of the dependency graph. + Returns a new graph where each definition has a list of all its + direct and indirect dependencies. + """ + transitive_closure = defaultdict(set) + + # For each definition, perform BFS to find all dependencies + for definition in graph: + queue = deque(graph[definition]) + visited = set(graph[definition]) + + while queue: + dep = queue.popleft() + transitive_closure[definition].add(dep) + + # Add any dependencies of this dependency that we haven't seen yet + for next_dep in graph.get(dep, []): + if next_dep not in visited: + visited.add(next_dep) + queue.append(next_dep) + + # Convert sets back to lists for consistent output + return {definition: list(deps) for definition, deps in transitive_closure.items()} + +def export_to_dot(graph, output_file): + """Export the graph to DOT format for visualization with Graphviz.""" + with open(output_file, 'w') as f: + f.write('digraph Dependencies {\n') + f.write(' node [shape=box];\n') + + for definition, deps in graph.items(): + for dep in deps: + f.write(f' "{definition}" -> "{dep}";\n') + + f.write('}\n') + +def export_to_json(graph, output_file): + """Export the graph to JSON format.""" + with open(output_file, 'w') as f: + json.dump(graph, f, indent=2) + +def find_dependent_definitions(graph, target_definition): + """ + Find all definitions that depend on the target definition. + + If the target_definition is not fully qualified, it will match any definition + that ends with this name (i.e., any module's definition with this bare name). + """ + dependent_definitions = [] + + # Check if the target is a fully qualified name or just a bare name + is_qualified = '.' in target_definition + + for definition, dependencies in graph.items(): + if is_qualified: + # Direct match for fully qualified names + if target_definition in dependencies: + dependent_definitions.append(definition) + else: + # For bare names, check if any dependency ends with the target + for dep in dependencies: + if dep.endswith('.' + target_definition): + dependent_definitions.append(definition) + break + + return dependent_definitions + +def find_module_dependent_definitions(graph, all_definitions, module_name): + """ + Find all definitions that transitively depend on any definition in the specified module. + + Args: + graph: The dependency graph + all_definitions: Dictionary mapping qualified definition names to (module_name, file_path) + module_name: The name of the module to find dependents of + + Returns: + A list of definition names that depend on any definition in the module + """ + # Find all definitions in the target module + module_definitions = [] + for qualified_name, (def_module, _) in all_definitions.items(): + if def_module == module_name: + module_definitions.append(qualified_name) + + if not module_definitions: + return [] + + # Find all definitions that depend on any definition in the module + dependent_definitions = set() + for definition in module_definitions: + dependents = find_dependent_definitions(graph, definition) + dependent_definitions.update(dependents) + + return list(dependent_definitions) + +def find_module_direct_dependencies(graph, all_definitions, module_name): + """ + Find all modules that directly depend on any definition in the specified module. + + Args: + graph: The dependency graph + all_definitions: Dictionary mapping qualified definition names to (module_name, file_path) + module_name: The name of the module to find direct dependents of + + Returns: + A list of module names that directly depend on any definition in the specified module + """ + # Find all definitions in the target module + module_definitions = [] + for qualified_name, (def_module, _) in all_definitions.items(): + if def_module == module_name: + module_definitions.append(qualified_name) + + if not module_definitions: + return [] + + # Find all definitions that depend on any definition in the module + dependent_modules = set() + for source_def, dependencies in graph.items(): + source_module = source_def.rsplit('.', 1)[0] # Extract module name from qualified definition name + + # Skip if the source is the same module we're checking dependencies for + if source_module == module_name: + continue + + # Check if this definition depends on any definition from our target module + for dep in dependencies: + if any(dep == target_def for target_def in module_definitions): + dependent_modules.add(source_module) + break + + return list(dependent_modules) + +def main(): + parser = argparse.ArgumentParser(description='Build dependency graph of Agda definitions') + parser.add_argument('root_dir', help='Root directory of the Agda library') + parser.add_argument('--dot', help='Output file for DOT graph') + parser.add_argument('--json', help='Output file for JSON representation') + parser.add_argument('--transitive', action='store_true', + help='Compute transitive closure of dependencies') + parser.add_argument('--transitive-dot', help='Output file for transitive closure DOT graph') + parser.add_argument('--transitive-json', help='Output file for transitive closure JSON') + parser.add_argument('--top-dependent', type=int, default=10, + help='Print top N definitions with most dependencies (default: 10)') + parser.add_argument('--find-dependents', metavar='DEFINITION', + help='Find all definitions that depend on the specified definition') + parser.add_argument('--find-module-dependents', metavar='MODULE', + help='Find all definitions that depend on any definition in the specified module') + parser.add_argument('--find-module-deps', metavar='MODULE', + help='Find all modules that directly depend on any definition in the specified module') + parser.add_argument('--quiet', action='store_true', + help='Suppress informational output, only show requested results') + args = parser.parse_args() + + # If find_dependents, find_module_dependents, or find_module_deps is used, enable quiet mode by default + quiet_mode = args.quiet or ((args.find_dependents or args.find_module_dependents or args.find_module_deps) and + not any([args.transitive, args.dot, args.json, args.transitive_dot, args.transitive_json])) + + if not quiet_mode: + print(f"Analyzing Git-tracked Agda files in {args.root_dir}...") + + try: + graph, all_definitions = build_definition_graph(args.root_dir) + except Exception as e: + print(f"Error building definition graph: {e}") + return + + # No need for duplicate filtering as we're being more careful above + # Just keep the graph as is + + if not quiet_mode: + print(f"Found {len(graph)} tracked definitions with dependencies.") + total_deps = sum(len(deps) for deps in graph.values()) + print(f"Total dependencies: {total_deps}") + + if args.dot: + export_to_dot(graph, args.dot) + if not quiet_mode: + print(f"DOT graph exported to {args.dot}") + + if args.json: + export_to_json(graph, args.json) + if not quiet_mode: + print(f"JSON data exported to {args.json}") + + # Compute transitive closure if needed + transitive_graph = None + if args.transitive or args.transitive_dot or args.transitive_json or args.find_dependents or args.find_module_dependents: + if not quiet_mode: + print("Computing transitive closure of dependencies...") + transitive_graph = compute_transitive_closure(graph) + + if args.transitive_dot: + export_to_dot(transitive_graph, args.transitive_dot) + if not quiet_mode: + print(f"Transitive closure DOT graph exported to {args.transitive_dot}") + + if args.transitive_json: + export_to_json(transitive_graph, args.transitive_json) + if not quiet_mode: + print(f"Transitive closure JSON exported to {args.transitive_json}") + + if args.transitive and not (args.transitive_dot or args.transitive_json) and not quiet_mode: + # Print some statistics about the transitive closure + avg_deps = sum(len(deps) for deps in transitive_graph.values()) / len(transitive_graph) if transitive_graph else 0 + max_deps = max(len(deps) for deps in transitive_graph.values()) if transitive_graph else 0 + + print(f"\nTransitive closure statistics:") + print(f" Average dependencies per definition: {avg_deps:.2f}") + print(f" Maximum dependencies for a definition: {max_deps}") + + # Check for definitions that depend on a specific definition + if args.find_dependents: + if not transitive_graph: + if not quiet_mode: + print("Computing transitive closure of dependencies...") + transitive_graph = compute_transitive_closure(graph) + + dependent_definitions = find_dependent_definitions(transitive_graph, args.find_dependents) + + # If no results with the input as provided, check if we need to look for it as a bare name + if not dependent_definitions and '.' not in args.find_dependents: + # Print possible fully qualified names that match this bare name + matching_qualified_names = [] + for qualified_name in all_definitions: + if qualified_name.endswith('.' + args.find_dependents): + matching_qualified_names.append(qualified_name) + + if matching_qualified_names: + print(f"\nFound {len(matching_qualified_names)} definitions named '{args.find_dependents}':") + for name in sorted(matching_qualified_names): + print(f" {name}") + print(f"\nTry searching with a fully qualified name like '--find-dependents {matching_qualified_names[0]}'") + + print(f"\nDefinitions that depend on '{args.find_dependents}':") + print(f"Found {len(dependent_definitions)} dependent definitions") + + if dependent_definitions: + # Sort alphabetically for easier reading + for definition in sorted(dependent_definitions): + print(f" {definition}") + + # Optionally export to a file if requested + if args.json: + dependents_json = os.path.splitext(args.json)[0] + f"-dependents-of-{args.find_dependents.replace('.', '-')}.json" + with open(dependents_json, 'w') as f: + json.dump(dependent_definitions, f, indent=2) + print(f"Dependent definitions exported to {dependents_json}") + else: + print(" No definitions depend on this definition") + + # Check for definitions that depend on any definition in a module + if args.find_module_dependents: + if not transitive_graph: + if not quiet_mode: + print("Computing transitive closure of dependencies...") + transitive_graph = compute_transitive_closure(graph) + + module_dependent_definitions = find_module_dependent_definitions(transitive_graph, all_definitions, args.find_module_dependents) + + print(f"\nDefinitions that depend on module '{args.find_module_dependents}':") + print(f"Found {len(module_dependent_definitions)} dependent definitions") + + if module_dependent_definitions: + # Sort alphabetically for easier reading + for definition in sorted(module_dependent_definitions): + print(f" {definition}") + + # Optionally export to a file if requested + if args.json: + module_dependents_json = os.path.splitext(args.json)[0] + f"-dependents-of-module-{args.find_module_dependents.replace('.', '-')}.json" + with open(module_dependents_json, 'w') as f: + json.dump(module_dependent_definitions, f, indent=2) + print(f"Module dependent definitions exported to {module_dependents_json}") + else: + print(f" No definitions depend on any definition in module '{args.find_module_dependents}'") + + # Check for modules that directly depend on a module + if args.find_module_deps: + module_dependencies = find_module_direct_dependencies(graph, all_definitions, args.find_module_deps) + + print(f"\nModules that directly depend on module '{args.find_module_deps}':") + print(f"Found {len(module_dependencies)} dependent modules") + + if module_dependencies: + # Sort alphabetically for easier reading + for module in sorted(module_dependencies): + print(f" {module}") + + # Optionally export to a file if requested + if args.json: + module_deps_json = os.path.splitext(args.json)[0] + f"-modules-depend-on-{args.find_module_deps.replace('.', '-')}.json" + with open(module_deps_json, 'w') as f: + json.dump(module_dependencies, f, indent=2) + print(f"Module dependencies exported to {module_deps_json}") + else: + print(f" No modules directly depend on module '{args.find_module_deps}'") + + # Only print remaining statistics if not in quiet mode + if not quiet_mode: + # Print top definitions with most direct dependencies + direct_dep_count = {definition: len(deps) for definition, deps in graph.items()} + + if direct_dep_count: + print(f"\nTop {args.top_dependent} definitions with most direct dependencies:") + for i, (definition, count) in enumerate(sorted(direct_dep_count.items(), key=lambda x: x[1], reverse=True)[:args.top_dependent], 1): + print(f" {i}. {definition}: {count} direct dependencies") + else: + print("\nNo definitions found for direct dependency analysis.") + + if not any([args.dot, args.json, args.transitive, args.transitive_dot, args.transitive_json, args.find_dependents]): + # Calculate the most depended upon definitions + most_depended = defaultdict(int) + for _, deps in graph.items(): + for dep in deps: + most_depended[dep] += 1 + + if most_depended: + print("\nTop 10 most used definitions:") + for definition, count in sorted(most_depended.items(), key=lambda x: x[1], reverse=True)[:10]: + print(f" {definition}: {count} usages") + else: + print("\nNo definitions found for usage analysis.") + +if __name__ == "__main__": + main() From edec29ff56af9dc8afddf0ed4be9e5eb314a33d9 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 18:13:03 +0000 Subject: [PATCH 15/39] import telescope --- .../composition-operations-on-binary-families-of-sets.lagda.md | 1 + .../conservative-functors-precategories.lagda.md | 1 + src/category-theory/coproducts-in-precategories.lagda.md | 1 + ...ependent-composition-operations-over-precategories.lagda.md | 1 + src/category-theory/faithful-maps-precategories.lagda.md | 1 + src/category-theory/full-maps-precategories.lagda.md | 1 + src/category-theory/fully-faithful-maps-precategories.lagda.md | 1 + src/category-theory/functors-set-magmoids.lagda.md | 1 + src/category-theory/groupoids.lagda.md | 1 + src/category-theory/indiscrete-precategories.lagda.md | 1 + src/category-theory/pregroupoids.lagda.md | 1 + src/category-theory/products-in-precategories.lagda.md | 1 + .../pseudomonic-functors-precategories.lagda.md | 1 + src/category-theory/pullbacks-in-precategories.lagda.md | 1 + src/category-theory/replete-subprecategories.lagda.md | 1 + .../structure-equivalences-set-magmoids.lagda.md | 1 + src/category-theory/subprecategories.lagda.md | 1 + src/category-theory/wide-subcategories.lagda.md | 1 + src/category-theory/wide-subprecategories.lagda.md | 1 + src/commutative-algebra/commutative-semirings.lagda.md | 1 + src/foundation/automorphisms.lagda.md | 2 +- src/foundation/binary-relations.lagda.md | 1 + src/foundation/binary-type-duality.lagda.md | 1 + src/foundation/cones-over-cospan-diagrams.lagda.md | 1 + src/foundation/equivalence-injective-type-families.lagda.md | 1 + src/foundation/global-subuniverses.lagda.md | 1 + src/foundation/iterated-dependent-pair-types.lagda.md | 3 +-- src/foundation/iterated-dependent-product-types.lagda.md | 3 +-- src/foundation/multivariable-homotopies.lagda.md | 3 +-- src/foundation/multivariable-sections.lagda.md | 3 +-- src/foundation/path-split-maps.lagda.md | 1 + src/foundation/perfect-images.lagda.md | 1 + src/foundation/strictly-involutive-identity-types.lagda.md | 1 + src/foundation/transport-split-type-families.lagda.md | 1 + src/foundation/univalent-type-families.lagda.md | 1 + src/foundation/weakly-constant-maps.lagda.md | 1 + src/foundation/yoneda-identity-types.lagda.md | 1 + src/group-theory/commutative-monoids.lagda.md | 1 + src/group-theory/homomorphisms-group-actions.lagda.md | 1 + .../factorization-operations-function-classes.lagda.md | 1 + src/orthogonal-factorization-systems/function-classes.lagda.md | 1 + src/orthogonal-factorization-systems/modal-induction.lagda.md | 1 + .../modal-subuniverse-induction.lagda.md | 1 + src/ring-theory/isomorphisms-rings.lagda.md | 1 + 44 files changed, 44 insertions(+), 9 deletions(-) diff --git a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md index d4e50dfdf4..49fbe79018 100644 --- a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md +++ b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md @@ -16,6 +16,7 @@ open import foundation.propositions open import foundation.sets open import foundation.strictly-involutive-identity-types open import foundation.subtypes +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/conservative-functors-precategories.lagda.md b/src/category-theory/conservative-functors-precategories.lagda.md index bdbd787dcb..e3b24903e9 100644 --- a/src/category-theory/conservative-functors-precategories.lagda.md +++ b/src/category-theory/conservative-functors-precategories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.precategories open import foundation.dependent-pair-types open import foundation.iterated-dependent-product-types open import foundation.propositions +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/coproducts-in-precategories.lagda.md b/src/category-theory/coproducts-in-precategories.lagda.md index cc72f57907..89a697bd01 100644 --- a/src/category-theory/coproducts-in-precategories.lagda.md +++ b/src/category-theory/coproducts-in-precategories.lagda.md @@ -16,6 +16,7 @@ open import foundation.dependent-pair-types open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions +open import foundation.telescopes open import foundation.uniqueness-quantification open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md index 8f663b706e..cd698e7403 100644 --- a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md +++ b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md @@ -20,6 +20,7 @@ open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.sets +open import foundation.telescopes open import foundation.transport-along-identifications open import foundation.truncated-types open import foundation.truncation-levels diff --git a/src/category-theory/faithful-maps-precategories.lagda.md b/src/category-theory/faithful-maps-precategories.lagda.md index 69cc0cd483..092f8cb396 100644 --- a/src/category-theory/faithful-maps-precategories.lagda.md +++ b/src/category-theory/faithful-maps-precategories.lagda.md @@ -19,6 +19,7 @@ open import foundation.iterated-dependent-product-types open import foundation.logical-equivalences open import foundation.propositions open import foundation.sets +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/full-maps-precategories.lagda.md b/src/category-theory/full-maps-precategories.lagda.md index 8b9755fe96..0e88643319 100644 --- a/src/category-theory/full-maps-precategories.lagda.md +++ b/src/category-theory/full-maps-precategories.lagda.md @@ -15,6 +15,7 @@ open import foundation.function-types open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.surjective-maps +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/fully-faithful-maps-precategories.lagda.md b/src/category-theory/fully-faithful-maps-precategories.lagda.md index 3716c27af4..2317e1536a 100644 --- a/src/category-theory/fully-faithful-maps-precategories.lagda.md +++ b/src/category-theory/fully-faithful-maps-precategories.lagda.md @@ -18,6 +18,7 @@ open import foundation.function-types open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.surjective-maps +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-set-magmoids.lagda.md b/src/category-theory/functors-set-magmoids.lagda.md index e3fcc50185..340252ac73 100644 --- a/src/category-theory/functors-set-magmoids.lagda.md +++ b/src/category-theory/functors-set-magmoids.lagda.md @@ -20,6 +20,7 @@ open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.subtypes +open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/groupoids.lagda.md b/src/category-theory/groupoids.lagda.md index 2fb548ee06..b137946933 100644 --- a/src/category-theory/groupoids.lagda.md +++ b/src/category-theory/groupoids.lagda.md @@ -26,6 +26,7 @@ open import foundation.iterated-dependent-pair-types open import foundation.propositions open import foundation.sets open import foundation.strictly-involutive-identity-types +open import foundation.telescopes open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/indiscrete-precategories.lagda.md b/src/category-theory/indiscrete-precategories.lagda.md index 68479adbd5..7692b84a17 100644 --- a/src/category-theory/indiscrete-precategories.lagda.md +++ b/src/category-theory/indiscrete-precategories.lagda.md @@ -23,6 +23,7 @@ open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.sets +open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/pregroupoids.lagda.md b/src/category-theory/pregroupoids.lagda.md index e5cd73ad42..6acee12a3c 100644 --- a/src/category-theory/pregroupoids.lagda.md +++ b/src/category-theory/pregroupoids.lagda.md @@ -17,6 +17,7 @@ open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.sets open import foundation.strictly-involutive-identity-types +open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/products-in-precategories.lagda.md b/src/category-theory/products-in-precategories.lagda.md index 78e0668af4..69fc1f4b93 100644 --- a/src/category-theory/products-in-precategories.lagda.md +++ b/src/category-theory/products-in-precategories.lagda.md @@ -16,6 +16,7 @@ open import foundation.dependent-pair-types open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions +open import foundation.telescopes open import foundation.uniqueness-quantification open import foundation.universe-levels ``` diff --git a/src/category-theory/pseudomonic-functors-precategories.lagda.md b/src/category-theory/pseudomonic-functors-precategories.lagda.md index 12821ec3b4..f5127417ad 100644 --- a/src/category-theory/pseudomonic-functors-precategories.lagda.md +++ b/src/category-theory/pseudomonic-functors-precategories.lagda.md @@ -22,6 +22,7 @@ open import foundation.iterated-dependent-product-types open import foundation.propositional-truncations open import foundation.propositions open import foundation.surjective-maps +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/pullbacks-in-precategories.lagda.md b/src/category-theory/pullbacks-in-precategories.lagda.md index aaefb61ec6..2ade1aec32 100644 --- a/src/category-theory/pullbacks-in-precategories.lagda.md +++ b/src/category-theory/pullbacks-in-precategories.lagda.md @@ -16,6 +16,7 @@ open import foundation.dependent-pair-types open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions +open import foundation.telescopes open import foundation.uniqueness-quantification open import foundation.universe-levels ``` diff --git a/src/category-theory/replete-subprecategories.lagda.md b/src/category-theory/replete-subprecategories.lagda.md index 50d39bd9b3..4f15777ab4 100644 --- a/src/category-theory/replete-subprecategories.lagda.md +++ b/src/category-theory/replete-subprecategories.lagda.md @@ -22,6 +22,7 @@ open import foundation.logical-equivalences open import foundation.propositions open import foundation.subsingleton-induction open import foundation.subtypes +open import foundation.telescopes open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/structure-equivalences-set-magmoids.lagda.md b/src/category-theory/structure-equivalences-set-magmoids.lagda.md index 97006c2dcd..38be07d265 100644 --- a/src/category-theory/structure-equivalences-set-magmoids.lagda.md +++ b/src/category-theory/structure-equivalences-set-magmoids.lagda.md @@ -18,6 +18,7 @@ open import foundation.functoriality-dependent-pair-types open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions +open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels diff --git a/src/category-theory/subprecategories.lagda.md b/src/category-theory/subprecategories.lagda.md index 684e900afc..9d2ff28504 100644 --- a/src/category-theory/subprecategories.lagda.md +++ b/src/category-theory/subprecategories.lagda.md @@ -21,6 +21,7 @@ open import foundation.propositions open import foundation.sets open import foundation.strictly-involutive-identity-types open import foundation.subtypes +open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/wide-subcategories.lagda.md b/src/category-theory/wide-subcategories.lagda.md index 8b3b4631fd..7c10b8b282 100644 --- a/src/category-theory/wide-subcategories.lagda.md +++ b/src/category-theory/wide-subcategories.lagda.md @@ -30,6 +30,7 @@ open import foundation.propositions open import foundation.sets open import foundation.strictly-involutive-identity-types open import foundation.subtypes +open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/wide-subprecategories.lagda.md b/src/category-theory/wide-subprecategories.lagda.md index 598da33856..9c22aab29a 100644 --- a/src/category-theory/wide-subprecategories.lagda.md +++ b/src/category-theory/wide-subprecategories.lagda.md @@ -23,6 +23,7 @@ open import foundation.propositions open import foundation.sets open import foundation.strictly-involutive-identity-types open import foundation.subtypes +open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/commutative-semirings.lagda.md b/src/commutative-algebra/commutative-semirings.lagda.md index 78e21f5b30..9f261db26a 100644 --- a/src/commutative-algebra/commutative-semirings.lagda.md +++ b/src/commutative-algebra/commutative-semirings.lagda.md @@ -15,6 +15,7 @@ open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.sets +open import foundation.telescopes open import foundation.universe-levels open import group-theory.commutative-monoids diff --git a/src/foundation/automorphisms.lagda.md b/src/foundation/automorphisms.lagda.md index 2a1f0e7a55..bc5d12d351 100644 --- a/src/foundation/automorphisms.lagda.md +++ b/src/foundation/automorphisms.lagda.md @@ -8,10 +8,10 @@ module foundation.automorphisms where ```agda open import foundation.dependent-pair-types +open import foundation.sets open import foundation.universe-levels open import foundation-core.equivalences -open import foundation.sets open import structured-types.pointed-types ``` diff --git a/src/foundation/binary-relations.lagda.md b/src/foundation/binary-relations.lagda.md index 7c18b153ba..d564eebeb0 100644 --- a/src/foundation/binary-relations.lagda.md +++ b/src/foundation/binary-relations.lagda.md @@ -13,6 +13,7 @@ open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.iterated-dependent-product-types open import foundation.subtypes +open import foundation.telescopes open import foundation.univalence open import foundation.universe-levels diff --git a/src/foundation/binary-type-duality.lagda.md b/src/foundation/binary-type-duality.lagda.md index 0365d3b368..5a4cfa15a6 100644 --- a/src/foundation/binary-type-duality.lagda.md +++ b/src/foundation/binary-type-duality.lagda.md @@ -15,6 +15,7 @@ open import foundation.multivariable-homotopies open import foundation.retractions open import foundation.sections open import foundation.spans +open import foundation.telescopes open import foundation.univalence open import foundation.universe-levels diff --git a/src/foundation/cones-over-cospan-diagrams.lagda.md b/src/foundation/cones-over-cospan-diagrams.lagda.md index 56fa968cec..8bc7769426 100644 --- a/src/foundation/cones-over-cospan-diagrams.lagda.md +++ b/src/foundation/cones-over-cospan-diagrams.lagda.md @@ -17,6 +17,7 @@ open import foundation.homotopy-induction open import foundation.identity-types open import foundation.multivariable-homotopies open import foundation.structure-identity-principle +open import foundation.telescopes open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/equivalence-injective-type-families.lagda.md b/src/foundation/equivalence-injective-type-families.lagda.md index 3fcc142fd6..f204fe7573 100644 --- a/src/foundation/equivalence-injective-type-families.lagda.md +++ b/src/foundation/equivalence-injective-type-families.lagda.md @@ -11,6 +11,7 @@ open import foundation.dependent-pair-types open import foundation.dependent-products-propositions open import foundation.functoriality-dependent-function-types open import foundation.iterated-dependent-product-types +open import foundation.telescopes open import foundation.univalence open import foundation.universal-property-equivalences open import foundation.universe-levels diff --git a/src/foundation/global-subuniverses.lagda.md b/src/foundation/global-subuniverses.lagda.md index fffb54617f..375ab98286 100644 --- a/src/foundation/global-subuniverses.lagda.md +++ b/src/foundation/global-subuniverses.lagda.md @@ -10,6 +10,7 @@ module foundation.global-subuniverses where open import foundation.dependent-pair-types open import foundation.iterated-dependent-product-types open import foundation.subuniverses +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/iterated-dependent-pair-types.lagda.md b/src/foundation/iterated-dependent-pair-types.lagda.md index ee7b8b853f..cf0e985ca9 100644 --- a/src/foundation/iterated-dependent-pair-types.lagda.md +++ b/src/foundation/iterated-dependent-pair-types.lagda.md @@ -2,8 +2,6 @@ ```agda module foundation.iterated-dependent-pair-types where - -open import foundation.telescopes public ```
Imports @@ -12,6 +10,7 @@ open import foundation.telescopes public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/iterated-dependent-product-types.lagda.md b/src/foundation/iterated-dependent-product-types.lagda.md index 1937e04f5f..a5cada2333 100644 --- a/src/foundation/iterated-dependent-product-types.lagda.md +++ b/src/foundation/iterated-dependent-product-types.lagda.md @@ -2,8 +2,6 @@ ```agda module foundation.iterated-dependent-product-types where - -open import foundation.telescopes public ```
Imports @@ -15,6 +13,7 @@ open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.dependent-products-truncated-types open import foundation.implicit-function-types +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/multivariable-homotopies.lagda.md b/src/foundation/multivariable-homotopies.lagda.md index 01d544c5ba..3d3588b02c 100644 --- a/src/foundation/multivariable-homotopies.lagda.md +++ b/src/foundation/multivariable-homotopies.lagda.md @@ -2,8 +2,6 @@ ```agda module foundation.multivariable-homotopies where - -open import foundation.telescopes public ```
Imports @@ -17,6 +15,7 @@ open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.implicit-function-types open import foundation.iterated-dependent-product-types +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/multivariable-sections.lagda.md b/src/foundation/multivariable-sections.lagda.md index 08d12e5bd9..f3fd8820d7 100644 --- a/src/foundation/multivariable-sections.lagda.md +++ b/src/foundation/multivariable-sections.lagda.md @@ -2,8 +2,6 @@ ```agda module foundation.multivariable-sections where - -open import foundation.telescopes public ```
Imports @@ -14,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.iterated-dependent-product-types open import foundation.multivariable-homotopies +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/path-split-maps.lagda.md b/src/foundation/path-split-maps.lagda.md index 7c985434d4..28223aec36 100644 --- a/src/foundation/path-split-maps.lagda.md +++ b/src/foundation/path-split-maps.lagda.md @@ -13,6 +13,7 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.iterated-dependent-product-types open import foundation.logical-equivalences +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/perfect-images.lagda.md b/src/foundation/perfect-images.lagda.md index 73b8c53e54..2a0569e866 100644 --- a/src/foundation/perfect-images.lagda.md +++ b/src/foundation/perfect-images.lagda.md @@ -18,6 +18,7 @@ open import foundation.iterating-functions open import foundation.law-of-excluded-middle open import foundation.negated-equality open import foundation.negation +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/strictly-involutive-identity-types.lagda.md b/src/foundation/strictly-involutive-identity-types.lagda.md index fe946180d7..f6cd949dd5 100644 --- a/src/foundation/strictly-involutive-identity-types.lagda.md +++ b/src/foundation/strictly-involutive-identity-types.lagda.md @@ -15,6 +15,7 @@ open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.multivariable-homotopies open import foundation.strictly-right-unital-concatenation-identifications +open import foundation.telescopes open import foundation.univalence open import foundation.universal-property-identity-systems open import foundation.universe-levels diff --git a/src/foundation/transport-split-type-families.lagda.md b/src/foundation/transport-split-type-families.lagda.md index 0b2e91bc07..ff883a366f 100644 --- a/src/foundation/transport-split-type-families.lagda.md +++ b/src/foundation/transport-split-type-families.lagda.md @@ -11,6 +11,7 @@ open import foundation.equivalence-injective-type-families open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.iterated-dependent-product-types +open import foundation.telescopes open import foundation.transport-along-identifications open import foundation.univalent-type-families open import foundation.universal-property-identity-systems diff --git a/src/foundation/univalent-type-families.lagda.md b/src/foundation/univalent-type-families.lagda.md index 9a7c109a9a..0a3999846c 100644 --- a/src/foundation/univalent-type-families.lagda.md +++ b/src/foundation/univalent-type-families.lagda.md @@ -16,6 +16,7 @@ open import foundation.identity-systems open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.subuniverses +open import foundation.telescopes open import foundation.transport-along-identifications open import foundation.univalence open import foundation.universal-property-identity-systems diff --git a/src/foundation/weakly-constant-maps.lagda.md b/src/foundation/weakly-constant-maps.lagda.md index 741e4c32c8..e2d2c88d58 100644 --- a/src/foundation/weakly-constant-maps.lagda.md +++ b/src/foundation/weakly-constant-maps.lagda.md @@ -12,6 +12,7 @@ open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions open import foundation.identity-types open import foundation.iterated-dependent-product-types +open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/yoneda-identity-types.lagda.md b/src/foundation/yoneda-identity-types.lagda.md index d35e342324..f9064f5122 100644 --- a/src/foundation/yoneda-identity-types.lagda.md +++ b/src/foundation/yoneda-identity-types.lagda.md @@ -13,6 +13,7 @@ open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.multivariable-homotopies open import foundation.strictly-right-unital-concatenation-identifications +open import foundation.telescopes open import foundation.transport-along-identifications open import foundation.univalence open import foundation.universal-property-identity-systems diff --git a/src/group-theory/commutative-monoids.lagda.md b/src/group-theory/commutative-monoids.lagda.md index 89b8b3f6aa..ad42cb9e4f 100644 --- a/src/group-theory/commutative-monoids.lagda.md +++ b/src/group-theory/commutative-monoids.lagda.md @@ -14,6 +14,7 @@ open import foundation.interchange-law open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.sets +open import foundation.telescopes open import foundation.unital-binary-operations open import foundation.universe-levels diff --git a/src/group-theory/homomorphisms-group-actions.lagda.md b/src/group-theory/homomorphisms-group-actions.lagda.md index b9f76c3392..7c488f7072 100644 --- a/src/group-theory/homomorphisms-group-actions.lagda.md +++ b/src/group-theory/homomorphisms-group-actions.lagda.md @@ -19,6 +19,7 @@ open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.sets open import foundation.subtype-identity-principle +open import foundation.telescopes open import foundation.torsorial-type-families open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md index 4f01d8a991..1d51743a99 100644 --- a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md @@ -22,6 +22,7 @@ open import foundation.inhabited-types open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.subtypes +open import foundation.telescopes open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/function-classes.lagda.md b/src/orthogonal-factorization-systems/function-classes.lagda.md index db1a440376..821f6aa51e 100644 --- a/src/orthogonal-factorization-systems/function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/function-classes.lagda.md @@ -20,6 +20,7 @@ open import foundation.logical-equivalences open import foundation.propositions open import foundation.pullbacks open import foundation.subtypes +open import foundation.telescopes open import foundation.transport-along-identifications open import foundation.univalence open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/modal-induction.lagda.md b/src/orthogonal-factorization-systems/modal-induction.lagda.md index 207aa7c89a..9329a93810 100644 --- a/src/orthogonal-factorization-systems/modal-induction.lagda.md +++ b/src/orthogonal-factorization-systems/modal-induction.lagda.md @@ -21,6 +21,7 @@ open import foundation.precomposition-dependent-functions open import foundation.precomposition-functions open import foundation.retractions open import foundation.sections +open import foundation.telescopes open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md b/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md index 898c4cc4ea..32cc226bd3 100644 --- a/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md +++ b/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md @@ -18,6 +18,7 @@ open import foundation.multivariable-sections open import foundation.precomposition-dependent-functions open import foundation.precomposition-functions open import foundation.retractions +open import foundation.telescopes open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels diff --git a/src/ring-theory/isomorphisms-rings.lagda.md b/src/ring-theory/isomorphisms-rings.lagda.md index 5a982e30d8..9ca0051cd9 100644 --- a/src/ring-theory/isomorphisms-rings.lagda.md +++ b/src/ring-theory/isomorphisms-rings.lagda.md @@ -28,6 +28,7 @@ open import foundation.propositions open import foundation.structure-identity-principle open import foundation.subtype-identity-principle open import foundation.subtypes +open import foundation.telescopes open import foundation.torsorial-type-families open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types From ef7655b64d839f551a2a1bfeee5d47a1cd355895 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 18:51:27 +0000 Subject: [PATCH 16/39] move raising universe levels unit type --- .../copresheaf-categories.lagda.md | 1 + .../full-ideals-commutative-rings.lagda.md | 1 + ...fundamental-theorem-of-arithmetic.lagda.md | 1 + .../equivalence-relations.lagda.md | 1 + src/foundation-core/small-types.lagda.md | 1 + src/foundation.lagda.md | 1 + src/foundation/category-of-sets.lagda.md | 1 + src/foundation/contractible-types.lagda.md | 1 + .../decidable-propositions.lagda.md | 1 + ...ndent-inverse-sequential-diagrams.lagda.md | 1 + ...rete-relaxed-sigma-decompositions.lagda.md | 1 + .../discrete-sigma-decompositions.lagda.md | 1 + ...epimorphisms-with-respect-to-sets.lagda.md | 1 + src/foundation/fiber-inclusions.lagda.md | 1 + src/foundation/full-subtypes.lagda.md | 1 + .../inverse-sequential-diagrams.lagda.md | 1 + .../iterated-cartesian-product-types.lagda.md | 1 + .../locale-of-propositions.lagda.md | 1 + .../multivariable-operations.lagda.md | 1 + src/foundation/powersets.lagda.md | 1 + ...roduct-decompositions-subuniverse.lagda.md | 1 + .../propositional-extensionality.lagda.md | 1 + ...raising-universe-levels-unit-type.lagda.md | 121 ++++++++++++++++++ ...vial-relaxed-sigma-decompositions.lagda.md | 1 + .../trivial-sigma-decompositions.lagda.md | 1 + src/foundation/type-duality.lagda.md | 1 + src/foundation/unit-type.lagda.md | 76 ----------- src/foundation/vectors-set-quotients.lagda.md | 1 + .../generating-elements-groups.lagda.md | 1 + ...artesian-products-concrete-groups.lagda.md | 1 + .../trivial-concrete-groups.lagda.md | 1 + ...-cartesian-products-higher-groups.lagda.md | 1 + .../trivial-higher-groups.lagda.md | 1 + src/linear-algebra/vectors.lagda.md | 1 + src/lists/lists-discrete-types.lagda.md | 1 + src/lists/lists.lagda.md | 1 + src/lists/predicates-on-lists.lagda.md | 1 + src/lists/sort-by-insertion-vectors.lagda.md | 1 + src/lists/sorted-lists.lagda.md | 1 + src/lists/sorted-vectors.lagda.md | 1 + .../lawvere-tierney-topologies.lagda.md | 1 + .../zero-modality.lagda.md | 1 + src/polytopes/abstract-polytopes.lagda.md | 1 + src/ring-theory/full-ideals-rings.lagda.md | 1 + src/set-theory/cumulative-hierarchy.lagda.md | 1 + ...-species-of-types-in-subuniverses.lagda.md | 1 + ...-species-of-types-in-subuniverses.lagda.md | 1 + ...species-of-finite-inhabited-types.lagda.md | 1 + ...-species-of-types-in-subuniverses.lagda.md | 1 + ...d-pointed-cartesian-product-types.lagda.md | 1 + ...types-equipped-with-endomorphisms.lagda.md | 1 + .../suspensions-of-propositions.lagda.md | 1 + src/trees/w-type-of-propositions.lagda.md | 1 + .../binomial-types.lagda.md | 1 + .../discrete-sigma-decompositions.lagda.md | 1 + .../finite-types.lagda.md | 1 + .../trivial-sigma-decompositions.lagda.md | 1 + ...al-property-standard-finite-types.lagda.md | 1 + src/universal-algebra/congruences.lagda.md | 1 + .../quotient-algebras.lagda.md | 1 + .../terms-over-signatures.lagda.md | 1 + 61 files changed, 180 insertions(+), 76 deletions(-) create mode 100644 src/foundation/raising-universe-levels-unit-type.lagda.md diff --git a/src/category-theory/copresheaf-categories.lagda.md b/src/category-theory/copresheaf-categories.lagda.md index f0082a5143..71e72eff00 100644 --- a/src/category-theory/copresheaf-categories.lagda.md +++ b/src/category-theory/copresheaf-categories.lagda.md @@ -34,6 +34,7 @@ open import foundation.homotopies open import foundation.identity-types open import foundation.propositions open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.unit-type open import foundation.universe-levels diff --git a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md index 74e4efd94e..762bbd4709 100644 --- a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md @@ -16,6 +16,7 @@ open import commutative-algebra.subsets-commutative-rings open import foundation.dependent-pair-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md index 6badd26e4b..9b880f9d1a 100644 --- a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md +++ b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md @@ -34,6 +34,7 @@ open import foundation.dependent-pair-types open import foundation.empty-types open import foundation.identity-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.type-arithmetic-empty-type diff --git a/src/foundation-core/equivalence-relations.lagda.md b/src/foundation-core/equivalence-relations.lagda.md index 28396e95f5..cf970f3056 100644 --- a/src/foundation-core/equivalence-relations.lagda.md +++ b/src/foundation-core/equivalence-relations.lagda.md @@ -13,6 +13,7 @@ open import foundation.fundamental-theorem-of-identity-types open import foundation.inhabited-subtypes open import foundation.logical-equivalences open import foundation.propositional-truncations +open import foundation.raising-universe-levels-unit-type open import foundation.subtype-identity-principle open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation-core/small-types.lagda.md b/src/foundation-core/small-types.lagda.md index 96a3cd8d75..adb78b9475 100644 --- a/src/foundation-core/small-types.lagda.md +++ b/src/foundation-core/small-types.lagda.md @@ -15,6 +15,7 @@ open import foundation.logical-equivalences open import foundation.mere-equivalences open import foundation.propositional-truncations open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index 05fc7bc087..6965be4664 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -360,6 +360,7 @@ open import foundation.pullbacks public open import foundation.pullbacks-subtypes public open import foundation.quasicoherently-idempotent-maps public open import foundation.raising-universe-levels public +open import foundation.raising-universe-levels-unit-type public open import foundation.reflecting-maps-equivalence-relations public open import foundation.reflexive-relations public open import foundation.regensburg-extension-fundamental-theorem-of-identity-types public diff --git a/src/foundation/category-of-sets.lagda.md b/src/foundation/category-of-sets.lagda.md index 05ad4d10cd..23f7b9be68 100644 --- a/src/foundation/category-of-sets.lagda.md +++ b/src/foundation/category-of-sets.lagda.md @@ -28,6 +28,7 @@ open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types open import foundation.isomorphisms-of-sets open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.retractions open import foundation.sections open import foundation.sets diff --git a/src/foundation/contractible-types.lagda.md b/src/foundation/contractible-types.lagda.md index 6491e0a1ed..52cc6fd388 100644 --- a/src/foundation/contractible-types.lagda.md +++ b/src/foundation/contractible-types.lagda.md @@ -16,6 +16,7 @@ open import foundation.diagonal-maps-of-types open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.logical-equivalences +open import foundation.raising-universe-levels-unit-type open import foundation.subuniverses open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/decidable-propositions.lagda.md b/src/foundation/decidable-propositions.lagda.md index ef885f24e7..5a6cc27816 100644 --- a/src/foundation/decidable-propositions.lagda.md +++ b/src/foundation/decidable-propositions.lagda.md @@ -22,6 +22,7 @@ open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type diff --git a/src/foundation/dependent-inverse-sequential-diagrams.lagda.md b/src/foundation/dependent-inverse-sequential-diagrams.lagda.md index f48ea9d065..7fa699aa8e 100644 --- a/src/foundation/dependent-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/dependent-inverse-sequential-diagrams.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.inverse-sequential-diagrams open import foundation.iterating-families-of-maps +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md index 349b82ae5a..5c88106f31 100644 --- a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md @@ -12,6 +12,7 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.dependent-products-propositions open import foundation.equivalences +open import foundation.raising-universe-levels-unit-type open import foundation.relaxed-sigma-decompositions open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type diff --git a/src/foundation/discrete-sigma-decompositions.lagda.md b/src/foundation/discrete-sigma-decompositions.lagda.md index 9b44f7a2e0..4f46918e5b 100644 --- a/src/foundation/discrete-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-sigma-decompositions.lagda.md @@ -13,6 +13,7 @@ open import foundation.dependent-pair-types open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.propositional-truncations +open import foundation.raising-universe-levels-unit-type open import foundation.sigma-decompositions open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type diff --git a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md index 85011ac449..63bd907d28 100644 --- a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md +++ b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md @@ -16,6 +16,7 @@ open import foundation.identity-types open import foundation.injective-maps open import foundation.propositional-extensionality open import foundation.propositional-truncations +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.surjective-maps open import foundation.unit-type diff --git a/src/foundation/fiber-inclusions.lagda.md b/src/foundation/fiber-inclusions.lagda.md index fb33d403c9..ca0e8f0ac8 100644 --- a/src/foundation/fiber-inclusions.lagda.md +++ b/src/foundation/fiber-inclusions.lagda.md @@ -12,6 +12,7 @@ open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types open import foundation.faithful-maps open import foundation.fibers-of-maps +open import foundation.raising-universe-levels-unit-type open import foundation.standard-pullbacks open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/full-subtypes.lagda.md b/src/foundation/full-subtypes.lagda.md index 565bd3f72b..c2cb38a34f 100644 --- a/src/foundation/full-subtypes.lagda.md +++ b/src/foundation/full-subtypes.lagda.md @@ -10,6 +10,7 @@ module foundation.full-subtypes where open import foundation.decidable-subtypes open import foundation.dependent-pair-types open import foundation.dependent-products-propositions +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/inverse-sequential-diagrams.lagda.md b/src/foundation/inverse-sequential-diagrams.lagda.md index 28053d466e..553548e870 100644 --- a/src/foundation/inverse-sequential-diagrams.lagda.md +++ b/src/foundation/inverse-sequential-diagrams.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.iterating-functions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/iterated-cartesian-product-types.lagda.md b/src/foundation/iterated-cartesian-product-types.lagda.md index ab1849056b..8a20d00913 100644 --- a/src/foundation/iterated-cartesian-product-types.lagda.md +++ b/src/foundation/iterated-cartesian-product-types.lagda.md @@ -15,6 +15,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.functoriality-cartesian-product-types open import foundation.functoriality-dependent-function-types +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-function-types open import foundation.unit-type diff --git a/src/foundation/locale-of-propositions.lagda.md b/src/foundation/locale-of-propositions.lagda.md index daef5de811..dd65321505 100644 --- a/src/foundation/locale-of-propositions.lagda.md +++ b/src/foundation/locale-of-propositions.lagda.md @@ -12,6 +12,7 @@ open import foundation.dependent-pair-types open import foundation.existential-quantification open import foundation.large-locale-of-propositions open import foundation.logical-equivalences +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/multivariable-operations.lagda.md b/src/foundation/multivariable-operations.lagda.md index fe71b9e834..fd82bdc4d4 100644 --- a/src/foundation/multivariable-operations.lagda.md +++ b/src/foundation/multivariable-operations.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/powersets.lagda.md b/src/foundation/powersets.lagda.md index e40e0a8090..e195cf37f9 100644 --- a/src/foundation/powersets.lagda.md +++ b/src/foundation/powersets.lagda.md @@ -13,6 +13,7 @@ open import foundation.identity-types open import foundation.large-locale-of-propositions open import foundation.logical-equivalences open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/product-decompositions-subuniverse.lagda.md b/src/foundation/product-decompositions-subuniverse.lagda.md index beb392b79c..cb4513fe87 100644 --- a/src/foundation/product-decompositions-subuniverse.lagda.md +++ b/src/foundation/product-decompositions-subuniverse.lagda.md @@ -12,6 +12,7 @@ open import foundation.dependent-pair-types open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.equivalences +open import foundation.raising-universe-levels-unit-type open import foundation.subuniverses open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/propositional-extensionality.lagda.md b/src/foundation/propositional-extensionality.lagda.md index 495e07ec8a..3d3e72c471 100644 --- a/src/foundation/propositional-extensionality.lagda.md +++ b/src/foundation/propositional-extensionality.lagda.md @@ -16,6 +16,7 @@ open import foundation.logical-equivalences open import foundation.negation open import foundation.postcomposition-functions open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.subtype-identity-principle open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types diff --git a/src/foundation/raising-universe-levels-unit-type.lagda.md b/src/foundation/raising-universe-levels-unit-type.lagda.md new file mode 100644 index 0000000000..c8315fa606 --- /dev/null +++ b/src/foundation/raising-universe-levels-unit-type.lagda.md @@ -0,0 +1,121 @@ +# Raising universe levels for the unit type + +```agda +module foundation.raising-universe-levels-unit-type where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.raising-universe-levels +open import foundation.unit-type +open import foundation.universe-levels + +open import foundation-core.constant-maps +open import foundation-core.contractible-types +open import foundation-core.equivalences +open import foundation-core.identity-types +open import foundation-core.propositions +open import foundation-core.retractions +open import foundation-core.sets +open import foundation-core.truncated-types +open import foundation-core.truncation-levels +``` + +
+ +## Idea + +The **unit type** is a type inductively generated by a single point. + +## Definition + +### Raising the universe level of the unit type + +```agda +raise-unit : (l : Level) → UU l +raise-unit l = raise l unit + +raise-star : {l : Level} → raise l unit +raise-star = map-raise star + +raise-terminal-map : {l1 l2 : Level} (A : UU l1) → A → raise-unit l2 +raise-terminal-map {l2 = l2} A = const A raise-star + +compute-raise-unit : (l : Level) → unit ≃ raise-unit l +compute-raise-unit l = compute-raise l unit + +inv-compute-raise-unit : (l : Level) → raise-unit l ≃ unit +inv-compute-raise-unit l = inv-compute-raise l unit +``` + +## Properties + +### The raised unit type is contractible + +```agda +abstract + is-contr-raise-unit : {l1 : Level} → is-contr (raise-unit l1) + is-contr-raise-unit {l1} = + is-contr-equiv' unit (compute-raise l1 unit) is-contr-unit +``` + +### Any contractible type is equivalent to the raised unit type + +```agda +module _ + {l1 l2 : Level} {A : UU l1} + where + + is-equiv-raise-terminal-map-is-contr : + is-contr A → is-equiv (raise-terminal-map {l2 = l2} A) + is-equiv-raise-terminal-map-is-contr H = + is-equiv-is-invertible + ( λ _ → center H) + ( λ where (map-raise x) → refl) + ( contraction H) + + equiv-raise-unit-is-contr : is-contr A → A ≃ raise-unit l2 + equiv-raise-unit-is-contr H = + raise-terminal-map A , is-equiv-raise-terminal-map-is-contr H + + is-contr-retraction-raise-terminal-map : + retraction (raise-terminal-map {l2 = l2} A) → is-contr A + is-contr-retraction-raise-terminal-map (h , H) = h raise-star , H + + is-contr-is-equiv-raise-terminal-map : + is-equiv (raise-terminal-map {l2 = l2} A) → is-contr A + is-contr-is-equiv-raise-terminal-map H = + is-contr-retraction-raise-terminal-map (retraction-is-equiv H) + + is-contr-equiv-raise-unit : A ≃ raise-unit l2 → is-contr A + is-contr-equiv-raise-unit e = + ( map-inv-equiv e raise-star) , + ( λ x → + ap (map-inv-equiv e) (eq-is-contr is-contr-raise-unit) ∙ + is-retraction-map-inv-equiv e x) +``` + +### The raised unit type is a proposition + +```agda +abstract + is-prop-raise-unit : {l1 : Level} → is-prop (raise-unit l1) + is-prop-raise-unit {l1} = is-prop-equiv' (compute-raise l1 unit) is-prop-unit + +raise-unit-Prop : (l1 : Level) → Prop l1 +raise-unit-Prop l1 = raise-unit l1 , is-prop-raise-unit +``` + +### The raised unit type is a set + +```agda +abstract + is-set-raise-unit : {l1 : Level} → is-set (raise-unit l1) + is-set-raise-unit = is-trunc-succ-is-trunc neg-one-𝕋 is-prop-raise-unit + +raise-unit-Set : (l1 : Level) → Set l1 +raise-unit-Set l1 = raise-unit l1 , is-set-raise-unit +``` diff --git a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md index 8ab55c81ac..905d56a633 100644 --- a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md @@ -9,6 +9,7 @@ module foundation.trivial-relaxed-sigma-decompositions where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.raising-universe-levels-unit-type open import foundation.relaxed-sigma-decompositions open import foundation.transposition-identifications-along-equivalences open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/trivial-sigma-decompositions.lagda.md b/src/foundation/trivial-sigma-decompositions.lagda.md index e50fa85044..d7a099583f 100644 --- a/src/foundation/trivial-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-sigma-decompositions.lagda.md @@ -11,6 +11,7 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.functoriality-propositional-truncation open import foundation.inhabited-types +open import foundation.raising-universe-levels-unit-type open import foundation.sigma-decompositions open import foundation.transposition-identifications-along-equivalences open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/type-duality.lagda.md b/src/foundation/type-duality.lagda.md index c2beea330e..50d1ca1b70 100644 --- a/src/foundation/type-duality.lagda.md +++ b/src/foundation/type-duality.lagda.md @@ -13,6 +13,7 @@ open import foundation.equivalences open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.locally-small-types +open import foundation.raising-universe-levels-unit-type open import foundation.slice open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type diff --git a/src/foundation/unit-type.lagda.md b/src/foundation/unit-type.lagda.md index d1246282e0..53797ac8f5 100644 --- a/src/foundation/unit-type.lagda.md +++ b/src/foundation/unit-type.lagda.md @@ -7,10 +7,8 @@ module foundation.unit-type where
Imports ```agda -open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.diagonal-maps-of-types -open import foundation.raising-universe-levels open import foundation.universe-levels open import foundation-core.constant-maps @@ -72,25 +70,6 @@ module _ point = diagonal-exponential A unit ``` -### Raising the universe level of the unit type - -```agda -raise-unit : (l : Level) → UU l -raise-unit l = raise l unit - -raise-star : {l : Level} → raise l unit -raise-star = map-raise star - -raise-terminal-map : {l1 l2 : Level} (A : UU l1) → A → raise-unit l2 -raise-terminal-map {l2 = l2} A = const A raise-star - -compute-raise-unit : (l : Level) → unit ≃ raise-unit l -compute-raise-unit l = compute-raise l unit - -inv-compute-raise-unit : (l : Level) → raise-unit l ≃ unit -inv-compute-raise-unit l = inv-compute-raise l unit -``` - ## Properties ### The unit type is contractible @@ -100,11 +79,6 @@ abstract is-contr-unit : is-contr unit pr1 is-contr-unit = star pr2 is-contr-unit _ = refl - -abstract - is-contr-raise-unit : {l1 : Level} → is-contr (raise-unit l1) - is-contr-raise-unit {l1} = - is-contr-equiv' unit (compute-raise l1 unit) is-contr-unit ``` ### Any contractible type is equivalent to the unit type @@ -135,42 +109,6 @@ module _ is-contr-equiv-unit' e = (map-equiv e star , is-section-map-inv-equiv e) ``` -### Any contractible type is equivalent to the raised unit type - -```agda -module _ - {l1 l2 : Level} {A : UU l1} - where - - is-equiv-raise-terminal-map-is-contr : - is-contr A → is-equiv (raise-terminal-map {l2 = l2} A) - is-equiv-raise-terminal-map-is-contr H = - is-equiv-is-invertible - ( λ _ → center H) - ( λ where (map-raise x) → refl) - ( contraction H) - - equiv-raise-unit-is-contr : is-contr A → A ≃ raise-unit l2 - equiv-raise-unit-is-contr H = - raise-terminal-map A , is-equiv-raise-terminal-map-is-contr H - - is-contr-retraction-raise-terminal-map : - retraction (raise-terminal-map {l2 = l2} A) → is-contr A - is-contr-retraction-raise-terminal-map (h , H) = h raise-star , H - - is-contr-is-equiv-raise-terminal-map : - is-equiv (raise-terminal-map {l2 = l2} A) → is-contr A - is-contr-is-equiv-raise-terminal-map H = - is-contr-retraction-raise-terminal-map (retraction-is-equiv H) - - is-contr-equiv-raise-unit : A ≃ raise-unit l2 → is-contr A - is-contr-equiv-raise-unit e = - ( map-inv-equiv e raise-star) , - ( λ x → - ap (map-inv-equiv e) (eq-is-contr is-contr-raise-unit) ∙ - is-retraction-map-inv-equiv e x) -``` - ### The unit type is a proposition ```agda @@ -180,13 +118,6 @@ abstract unit-Prop : Prop lzero unit-Prop = unit , is-prop-unit - -abstract - is-prop-raise-unit : {l1 : Level} → is-prop (raise-unit l1) - is-prop-raise-unit {l1} = is-prop-equiv' (compute-raise l1 unit) is-prop-unit - -raise-unit-Prop : (l1 : Level) → Prop l1 -raise-unit-Prop l1 = raise-unit l1 , is-prop-raise-unit ``` ### The unit type is a set @@ -198,13 +129,6 @@ abstract unit-Set : Set lzero unit-Set = unit , is-set-unit - -abstract - is-set-raise-unit : {l1 : Level} → is-set (raise-unit l1) - is-set-raise-unit = is-trunc-succ-is-trunc neg-one-𝕋 is-prop-raise-unit - -raise-unit-Set : (l1 : Level) → Set l1 -raise-unit-Set l1 = raise-unit l1 , is-set-raise-unit ``` ### All parallel maps into `unit` are equal diff --git a/src/foundation/vectors-set-quotients.lagda.md b/src/foundation/vectors-set-quotients.lagda.md index 57d80affe9..d9652fc385 100644 --- a/src/foundation/vectors-set-quotients.lagda.md +++ b/src/foundation/vectors-set-quotients.lagda.md @@ -20,6 +20,7 @@ open import foundation.function-extensionality-axiom open import foundation.multivariable-operations open import foundation.products-equivalence-relations open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.reflecting-maps-equivalence-relations open import foundation.set-quotients open import foundation.sets diff --git a/src/group-theory/generating-elements-groups.lagda.md b/src/group-theory/generating-elements-groups.lagda.md index 41643d2ee7..f0b26019b2 100644 --- a/src/group-theory/generating-elements-groups.lagda.md +++ b/src/group-theory/generating-elements-groups.lagda.md @@ -21,6 +21,7 @@ open import foundation.injective-maps open import foundation.propositional-maps open import foundation.propositional-truncations open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.subtypes open import foundation.surjective-maps diff --git a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md index db2815fc12..d189124e89 100644 --- a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md +++ b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md @@ -22,6 +22,7 @@ open import foundation.iterated-cartesian-product-types open import foundation.mere-equality open import foundation.propositional-truncations open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.truncated-types open import foundation.truncation-levels diff --git a/src/group-theory/trivial-concrete-groups.lagda.md b/src/group-theory/trivial-concrete-groups.lagda.md index 0c939f55de..5c20a531f4 100644 --- a/src/group-theory/trivial-concrete-groups.lagda.md +++ b/src/group-theory/trivial-concrete-groups.lagda.md @@ -10,6 +10,7 @@ module group-theory.trivial-concrete-groups where open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels diff --git a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md index e9a5b7aaab..d8ae507260 100644 --- a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md +++ b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md @@ -20,6 +20,7 @@ open import foundation.identity-types open import foundation.iterated-cartesian-product-types open import foundation.mere-equality open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.unit-type open import foundation.universe-levels diff --git a/src/higher-group-theory/trivial-higher-groups.lagda.md b/src/higher-group-theory/trivial-higher-groups.lagda.md index 18edbed574..32e453fac8 100644 --- a/src/higher-group-theory/trivial-higher-groups.lagda.md +++ b/src/higher-group-theory/trivial-higher-groups.lagda.md @@ -11,6 +11,7 @@ open import foundation.0-connected-types open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/linear-algebra/vectors.lagda.md b/src/linear-algebra/vectors.lagda.md index 5a2c7b7ed0..4a6be035b9 100644 --- a/src/linear-algebra/vectors.lagda.md +++ b/src/linear-algebra/vectors.lagda.md @@ -23,6 +23,7 @@ open import foundation.function-types open import foundation.homotopies open import foundation.identity-types open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.transport-along-identifications open import foundation.truncated-types diff --git a/src/lists/lists-discrete-types.lagda.md b/src/lists/lists-discrete-types.lagda.md index d0b8cd7b4b..1675657885 100644 --- a/src/lists/lists-discrete-types.lagda.md +++ b/src/lists/lists-discrete-types.lagda.md @@ -17,6 +17,7 @@ open import foundation.empty-types open import foundation.function-types open import foundation.identity-types open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/lists/lists.lagda.md b/src/lists/lists.lagda.md index dfa10f3084..f7922f6274 100644 --- a/src/lists/lists.lagda.md +++ b/src/lists/lists.lagda.md @@ -25,6 +25,7 @@ open import foundation.identity-types open import foundation.maybe open import foundation.negation open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.torsorial-type-families open import foundation.truncated-types diff --git a/src/lists/predicates-on-lists.lagda.md b/src/lists/predicates-on-lists.lagda.md index 4d52edb669..69fb45c9a5 100644 --- a/src/lists/predicates-on-lists.lagda.md +++ b/src/lists/predicates-on-lists.lagda.md @@ -8,6 +8,7 @@ module lists.predicates-on-lists where ```agda open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/lists/sort-by-insertion-vectors.lagda.md b/src/lists/sort-by-insertion-vectors.lagda.md index 56d1870c3a..0624942846 100644 --- a/src/lists/sort-by-insertion-vectors.lagda.md +++ b/src/lists/sort-by-insertion-vectors.lagda.md @@ -18,6 +18,7 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.functoriality-coproduct-types open import foundation.identity-types +open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/lists/sorted-lists.lagda.md b/src/lists/sorted-lists.lagda.md index dbd5f1f37e..fb82aebedd 100644 --- a/src/lists/sorted-lists.lagda.md +++ b/src/lists/sorted-lists.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/lists/sorted-vectors.lagda.md b/src/lists/sorted-vectors.lagda.md index dbb2353d4f..0aeb41d303 100644 --- a/src/lists/sorted-vectors.lagda.md +++ b/src/lists/sorted-vectors.lagda.md @@ -16,6 +16,7 @@ open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.function-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md index 93fdf8ad66..8976f0993e 100644 --- a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md +++ b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md @@ -14,6 +14,7 @@ open import foundation.function-types open import foundation.logical-equivalences open import foundation.propositional-extensionality open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.subtypes open import foundation.unit-type diff --git a/src/orthogonal-factorization-systems/zero-modality.lagda.md b/src/orthogonal-factorization-systems/zero-modality.lagda.md index 6395eb912e..7725c93fb4 100644 --- a/src/orthogonal-factorization-systems/zero-modality.lagda.md +++ b/src/orthogonal-factorization-systems/zero-modality.lagda.md @@ -7,6 +7,7 @@ module orthogonal-factorization-systems.zero-modality where
Imports ```agda +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/polytopes/abstract-polytopes.lagda.md b/src/polytopes/abstract-polytopes.lagda.md index 429d52d3ab..b2a62140af 100644 --- a/src/polytopes/abstract-polytopes.lagda.md +++ b/src/polytopes/abstract-polytopes.lagda.md @@ -18,6 +18,7 @@ open import foundation.disjunction open import foundation.identity-types open import foundation.propositional-truncations open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.transport-along-identifications open import foundation.unit-type diff --git a/src/ring-theory/full-ideals-rings.lagda.md b/src/ring-theory/full-ideals-rings.lagda.md index a415b1eeeb..145fc154fa 100644 --- a/src/ring-theory/full-ideals-rings.lagda.md +++ b/src/ring-theory/full-ideals-rings.lagda.md @@ -10,6 +10,7 @@ module ring-theory.full-ideals-rings where open import foundation.dependent-pair-types open import foundation.full-subtypes open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels diff --git a/src/set-theory/cumulative-hierarchy.lagda.md b/src/set-theory/cumulative-hierarchy.lagda.md index 4d4ae93868..8af1c9e172 100644 --- a/src/set-theory/cumulative-hierarchy.lagda.md +++ b/src/set-theory/cumulative-hierarchy.lagda.md @@ -26,6 +26,7 @@ open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.transport-along-identifications open import foundation.truncated-types diff --git a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md index 65183258e0..d3642b399f 100644 --- a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -19,6 +19,7 @@ open import foundation.functoriality-dependent-pair-types open import foundation.global-subuniverses open import foundation.homotopies open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.relaxed-sigma-decompositions open import foundation.sigma-closed-subuniverses open import foundation.sigma-decomposition-subuniverse diff --git a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md index 1c966ec39c..b2e6b43e7c 100644 --- a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md @@ -18,6 +18,7 @@ open import foundation.identity-types open import foundation.product-decompositions open import foundation.product-decompositions-subuniverse open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types diff --git a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md index 32e27e77d0..2b7b0202fd 100644 --- a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md +++ b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md @@ -18,6 +18,7 @@ open import foundation.functoriality-dependent-pair-types open import foundation.identity-types open import foundation.inhabited-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.relaxed-sigma-decompositions open import foundation.sigma-closed-subuniverses open import foundation.sigma-decomposition-subuniverse diff --git a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md index 78eac4cbc1..22cb26f896 100644 --- a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -17,6 +17,7 @@ open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types open import foundation.identity-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.relaxed-sigma-decompositions open import foundation.sigma-closed-subuniverses open import foundation.sigma-decomposition-subuniverse diff --git a/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md b/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md index 085abff691..305993ecf4 100644 --- a/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md +++ b/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md @@ -8,6 +8,7 @@ module structured-types.iterated-pointed-cartesian-product-types where ```agda open import foundation.dependent-pair-types +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/structured-types/types-equipped-with-endomorphisms.lagda.md b/src/structured-types/types-equipped-with-endomorphisms.lagda.md index f9e9a9b3d5..198947f526 100644 --- a/src/structured-types/types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/types-equipped-with-endomorphisms.lagda.md @@ -10,6 +10,7 @@ module structured-types.types-equipped-with-endomorphisms where open import foundation.dependent-pair-types open import foundation.endomorphisms open import foundation.function-types +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md index a5430e4847..511ff1e9b6 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md @@ -19,6 +19,7 @@ open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies open import foundation.identity-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.subsingleton-induction open import foundation.surjective-maps diff --git a/src/trees/w-type-of-propositions.lagda.md b/src/trees/w-type-of-propositions.lagda.md index 0b9f78bdb3..8b460d8d29 100644 --- a/src/trees/w-type-of-propositions.lagda.md +++ b/src/trees/w-type-of-propositions.lagda.md @@ -12,6 +12,7 @@ open import foundation.dependent-pair-types open import foundation.empty-types open import foundation.propositional-extensionality open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.unit-type open import foundation.universe-levels diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index 30cfb287ac..7effe481d3 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -37,6 +37,7 @@ open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md index cb68b48e7d..3eb65dbffb 100644 --- a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md @@ -13,6 +13,7 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.identity-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.subtypes open import foundation.universe-levels diff --git a/src/univalent-combinatorics/finite-types.lagda.md b/src/univalent-combinatorics/finite-types.lagda.md index 747292e801..ca162f16ce 100644 --- a/src/univalent-combinatorics/finite-types.lagda.md +++ b/src/univalent-combinatorics/finite-types.lagda.md @@ -30,6 +30,7 @@ open import foundation.mere-equivalences open import foundation.propositional-truncations open import foundation.propositions open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.subtypes open import foundation.subuniverses diff --git a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md index 4bace31233..5816c35f0e 100644 --- a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md @@ -14,6 +14,7 @@ open import foundation.dependent-pair-types open import foundation.identity-types open import foundation.inhabited-types open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.subtypes open import foundation.universe-levels diff --git a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md index 087aa5e436..707c60a123 100644 --- a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md @@ -19,6 +19,7 @@ open import foundation.function-types open import foundation.functoriality-cartesian-product-types open import foundation.homotopies open import foundation.identity-types +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universal-property-contractible-types open import foundation.universal-property-empty-type diff --git a/src/universal-algebra/congruences.lagda.md b/src/universal-algebra/congruences.lagda.md index 811e9e865c..d8951087da 100644 --- a/src/universal-algebra/congruences.lagda.md +++ b/src/universal-algebra/congruences.lagda.md @@ -13,6 +13,7 @@ open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.equivalence-relations open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/universal-algebra/quotient-algebras.lagda.md b/src/universal-algebra/quotient-algebras.lagda.md index 6a031ee6f2..94bfede7ee 100644 --- a/src/universal-algebra/quotient-algebras.lagda.md +++ b/src/universal-algebra/quotient-algebras.lagda.md @@ -18,6 +18,7 @@ open import foundation.multivariable-functoriality-set-quotients open import foundation.multivariable-operations open import foundation.propositional-truncations open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.set-quotients open import foundation.sets open import foundation.unit-type diff --git a/src/universal-algebra/terms-over-signatures.lagda.md b/src/universal-algebra/terms-over-signatures.lagda.md index 8a5cf6febf..6ecf7d9351 100644 --- a/src/universal-algebra/terms-over-signatures.lagda.md +++ b/src/universal-algebra/terms-over-signatures.lagda.md @@ -14,6 +14,7 @@ open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.identity-types +open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels From 84e962847514330b42398373dcb564a0b0453915 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 19:04:33 +0000 Subject: [PATCH 17/39] `foundation-core.diagonal-maps-of-types` --- src/foundation-core.lagda.md | 1 + .../diagonal-maps-of-types.lagda.md | 92 +++++++++++++++++++ src/foundation/connected-types.lagda.md | 2 +- src/foundation/contractible-types.lagda.md | 2 +- .../diagonal-maps-of-types.lagda.md | 57 +----------- src/foundation/surjective-maps.lagda.md | 2 +- src/foundation/unit-type.lagda.md | 2 +- ...property-family-of-fibers-of-maps.lagda.md | 2 +- .../universal-property-unit-type.lagda.md | 2 +- .../null-families-of-types.lagda.md | 2 +- .../null-maps.lagda.md | 3 +- .../null-types.lagda.md | 2 +- 12 files changed, 106 insertions(+), 63 deletions(-) create mode 100644 src/foundation-core/diagonal-maps-of-types.lagda.md diff --git a/src/foundation-core.lagda.md b/src/foundation-core.lagda.md index 833226f9fd..d481c784f4 100644 --- a/src/foundation-core.lagda.md +++ b/src/foundation-core.lagda.md @@ -20,6 +20,7 @@ open import foundation-core.coproduct-types public open import foundation-core.decidable-propositions public open import foundation-core.dependent-identifications public open import foundation-core.diagonal-maps-cartesian-products-of-types public +open import foundation-core.diagonal-maps-of-types public open import foundation-core.discrete-types public open import foundation-core.embeddings public open import foundation-core.empty-types public diff --git a/src/foundation-core/diagonal-maps-of-types.lagda.md b/src/foundation-core/diagonal-maps-of-types.lagda.md new file mode 100644 index 0000000000..3e09e621f5 --- /dev/null +++ b/src/foundation-core/diagonal-maps-of-types.lagda.md @@ -0,0 +1,92 @@ +# Diagonal maps of types + +```agda +module foundation-core.diagonal-maps-of-types where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.function-extensionality-axiom +open import foundation.universe-levels + +open import foundation-core.constant-maps +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.injective-maps +``` + +
+ +## Idea + +The +{{#concept "diagonal map" Disambiguation="of a type into exponentials" Agda=diagonal-exponential}} +of a type `A` is the map that includes the points of `A` into the exponential +`X → A`. + +## Definitions + +```agda +module _ + {l1 l2 : Level} (A : UU l1) (X : UU l2) + where + + diagonal-exponential : A → X → A + diagonal-exponential = const X +``` + +## Properties + +### The action on identifications of a diagonal map is another diagonal map + +```agda +module _ + {l1 l2 : Level} {A : UU l1} (x y : A) (B : UU l2) + where + + htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq : + htpy-eq ∘ ap (diagonal-exponential A B) ~ diagonal-exponential (x ＝ y) B + htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq refl = refl + + htpy-ap-diagonal-exponential-htpy-eq-diagonal-exponential-Id : + diagonal-exponential (x ＝ y) B ~ htpy-eq ∘ ap (diagonal-exponential A B) + htpy-ap-diagonal-exponential-htpy-eq-diagonal-exponential-Id = + inv-htpy htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq +``` + +### Given an element of the exponent the diagonal map is injective + +```agda +module _ + {l1 l2 : Level} (A : UU l1) (B : UU l2) (b : B) + where + + is-injective-diagonal-exponential : + is-injective (diagonal-exponential A B) + is-injective-diagonal-exponential p = htpy-eq p b + + diagonal-exponential-injection : injection A (B → A) + pr1 diagonal-exponential-injection = diagonal-exponential A B + pr2 diagonal-exponential-injection = is-injective-diagonal-exponential +``` + +### The action on identifications of an (exponential) diagonal is a diagonal + +```agda +module _ + {l1 l2 : Level} (A : UU l1) {B : UU l2} (x y : B) + where + + compute-htpy-eq-ap-diagonal-exponential : + htpy-eq ∘ ap (diagonal-exponential B A) ~ diagonal-exponential (x ＝ y) A + compute-htpy-eq-ap-diagonal-exponential refl = refl + + inv-compute-htpy-eq-ap-diagonal-exponential : + diagonal-exponential (x ＝ y) A ~ htpy-eq ∘ ap (diagonal-exponential B A) + inv-compute-htpy-eq-ap-diagonal-exponential = + inv-htpy compute-htpy-eq-ap-diagonal-exponential +``` diff --git a/src/foundation/connected-types.lagda.md b/src/foundation/connected-types.lagda.md index cc22ef2f73..433b38821f 100644 --- a/src/foundation/connected-types.lagda.md +++ b/src/foundation/connected-types.lagda.md @@ -9,7 +9,6 @@ module foundation.connected-types where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types open import foundation.function-extensionality-axiom open import foundation.functoriality-truncation open import foundation.inhabited-types @@ -20,6 +19,7 @@ open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation-core.contractible-maps +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types diff --git a/src/foundation/contractible-types.lagda.md b/src/foundation/contractible-types.lagda.md index 52cc6fd388..0a1a3f297f 100644 --- a/src/foundation/contractible-types.lagda.md +++ b/src/foundation/contractible-types.lagda.md @@ -12,7 +12,6 @@ open import foundation.dependent-products-contractible-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.logical-equivalences @@ -22,6 +21,7 @@ open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-maps +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types diff --git a/src/foundation/diagonal-maps-of-types.lagda.md b/src/foundation/diagonal-maps-of-types.lagda.md index 8876d05884..ed122f9939 100644 --- a/src/foundation/diagonal-maps-of-types.lagda.md +++ b/src/foundation/diagonal-maps-of-types.lagda.md @@ -2,6 +2,8 @@ ```agda module foundation.diagonal-maps-of-types where + +open import foundation-core.diagonal-maps-of-types public ```
Imports @@ -33,52 +35,8 @@ The of a type `A` is the map that includes the points of `A` into the exponential `X → A`. -## Definitions - -```agda -module _ - {l1 l2 : Level} (A : UU l1) (X : UU l2) - where - - diagonal-exponential : A → X → A - diagonal-exponential = const X -``` - ## Properties -### The action on identifications of a diagonal map is another diagonal map - -```agda -module _ - {l1 l2 : Level} {A : UU l1} (x y : A) (B : UU l2) - where - - htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq : - htpy-eq ∘ ap (diagonal-exponential A B) ~ diagonal-exponential (x ＝ y) B - htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq refl = refl - - htpy-ap-diagonal-exponential-htpy-eq-diagonal-exponential-Id : - diagonal-exponential (x ＝ y) B ~ htpy-eq ∘ ap (diagonal-exponential A B) - htpy-ap-diagonal-exponential-htpy-eq-diagonal-exponential-Id = - inv-htpy htpy-diagonal-exponential-Id-ap-diagonal-exponential-htpy-eq -``` - -### Given an element of the exponent the diagonal map is injective - -```agda -module _ - {l1 l2 : Level} (A : UU l1) (B : UU l2) (b : B) - where - - is-injective-diagonal-exponential : - is-injective (diagonal-exponential A B) - is-injective-diagonal-exponential p = htpy-eq p b - - diagonal-exponential-injection : injection A (B → A) - pr1 diagonal-exponential-injection = diagonal-exponential A B - pr2 diagonal-exponential-injection = is-injective-diagonal-exponential -``` - ### The action on identifications of an (exponential) diagonal is a diagonal ```agda @@ -86,21 +44,12 @@ module _ {l1 l2 : Level} (A : UU l1) {B : UU l2} (x y : B) where - compute-htpy-eq-ap-diagonal-exponential : - htpy-eq ∘ ap (diagonal-exponential B A) ~ diagonal-exponential (x ＝ y) A - compute-htpy-eq-ap-diagonal-exponential refl = refl - - inv-compute-htpy-eq-ap-diagonal-exponential : - diagonal-exponential (x ＝ y) A ~ htpy-eq ∘ ap (diagonal-exponential B A) - inv-compute-htpy-eq-ap-diagonal-exponential = - inv-htpy compute-htpy-eq-ap-diagonal-exponential - compute-eq-htpy-ap-diagonal-exponential : ap (diagonal-exponential B A) ~ eq-htpy ∘ diagonal-exponential (x ＝ y) A compute-eq-htpy-ap-diagonal-exponential p = map-eq-transpose-equiv ( equiv-funext) - ( compute-htpy-eq-ap-diagonal-exponential p) + ( compute-htpy-eq-ap-diagonal-exponential A x y p) ``` ### Computing the fibers of diagonal maps diff --git a/src/foundation/surjective-maps.lagda.md b/src/foundation/surjective-maps.lagda.md index 57a649a995..6296eb39df 100644 --- a/src/foundation/surjective-maps.lagda.md +++ b/src/foundation/surjective-maps.lagda.md @@ -12,7 +12,6 @@ open import foundation.connected-maps open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.dependent-products-propositions -open import foundation.diagonal-maps-of-types open import foundation.embeddings open import foundation.equality-cartesian-product-types open import foundation.functoriality-cartesian-product-types @@ -34,6 +33,7 @@ open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.constant-maps open import foundation-core.contractible-maps +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types diff --git a/src/foundation/unit-type.lagda.md b/src/foundation/unit-type.lagda.md index 53797ac8f5..87b935b6db 100644 --- a/src/foundation/unit-type.lagda.md +++ b/src/foundation/unit-type.lagda.md @@ -8,11 +8,11 @@ module foundation.unit-type where ```agda open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types open import foundation.universe-levels open import foundation-core.constant-maps open import foundation-core.contractible-types +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md index b67eb5fad9..82c10540aa 100644 --- a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md +++ b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md @@ -9,7 +9,6 @@ module foundation.universal-property-family-of-fibers-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types open import foundation.families-of-equivalences open import foundation.function-extensionality open import foundation.function-extensionality-axiom @@ -18,6 +17,7 @@ open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types diff --git a/src/foundation/universal-property-unit-type.lagda.md b/src/foundation/universal-property-unit-type.lagda.md index 6d066ead4f..20149383b1 100644 --- a/src/foundation/universal-property-unit-type.lagda.md +++ b/src/foundation/universal-property-unit-type.lagda.md @@ -8,7 +8,6 @@ module foundation.universal-property-unit-type where ```agda open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types open import foundation.unit-type open import foundation.universal-property-contractible-types open import foundation.universal-property-equivalences @@ -16,6 +15,7 @@ open import foundation.universe-levels open import foundation-core.constant-maps open import foundation-core.contractible-types +open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.precomposition-functions diff --git a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md index 9a6dfa29eb..1ea050536a 100644 --- a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md @@ -25,7 +25,7 @@ open import orthogonal-factorization-systems.orthogonal-maps A family of types `B : A → UU l` is said to be {{#concept "null" Disambiguation="family of types" Agda=is-null-family}} at `Y`, or **`Y`-null**, if every fiber is. I.e., if the -[diagonal map](foundation.diagonal-maps-of-types.md) +[diagonal map](foundation-core.diagonal-maps-of-types.md) ```text Δ : B x → (Y → B x) diff --git a/src/orthogonal-factorization-systems/null-maps.lagda.md b/src/orthogonal-factorization-systems/null-maps.lagda.md index af001e1fc2..abce4f90c5 100644 --- a/src/orthogonal-factorization-systems/null-maps.lagda.md +++ b/src/orthogonal-factorization-systems/null-maps.lagda.md @@ -9,7 +9,6 @@ module orthogonal-factorization-systems.null-maps where ```agda open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types open import foundation.equivalences open import foundation.equivalences-arrows open import foundation.families-of-equivalences @@ -30,6 +29,8 @@ open import foundation.unit-type open import foundation.universal-property-family-of-fibers-of-maps open import foundation.universe-levels +open import foundation-core.diagonal-maps-of-types + open import orthogonal-factorization-systems.maps-local-at-maps open import orthogonal-factorization-systems.null-families-of-types open import orthogonal-factorization-systems.null-types diff --git a/src/orthogonal-factorization-systems/null-types.lagda.md b/src/orthogonal-factorization-systems/null-types.lagda.md index d47b2a74fd..f6b07a4409 100644 --- a/src/orthogonal-factorization-systems/null-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-types.lagda.md @@ -48,7 +48,7 @@ open import orthogonal-factorization-systems.types-local-at-maps A type `A` is said to be {{#concept "null at" Disambiguation="type" Agda=is-null}} `Y`, or {{#concept "`Y`-null" Disambiguation="type" Agda=is-null}}, if the -[diagonal map](foundation.diagonal-maps-of-types.md) +[diagonal map](foundation-core.diagonal-maps-of-types.md) ```text Δ : A → (Y → A) From 35ac679bd108f8aa67eb719e6cefe921e44933ce Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 19:19:19 +0000 Subject: [PATCH 18/39] raising universe levels of booleans --- src/foundation/booleans.lagda.md | 17 -------- .../raising-universe-levels-booleans.lagda.md | 42 +++++++++++++++++++ .../raising-universe-levels.lagda.md | 7 +--- src/reflection/definitions.lagda.md | 5 ++- src/reflection/fixity.lagda.md | 3 +- src/reflection/group-solver.lagda.md | 5 ++- src/reflection/metavariables.lagda.md | 3 +- src/reflection/names.lagda.md | 3 +- src/reflection/precategory-solver.lagda.md | 3 +- src/reflection/type-checking-monad.lagda.md | 3 +- src/set-theory/cumulative-hierarchy.lagda.md | 1 + 11 files changed, 61 insertions(+), 31 deletions(-) create mode 100644 src/foundation/raising-universe-levels-booleans.lagda.md diff --git a/src/foundation/booleans.lagda.md b/src/foundation/booleans.lagda.md index eedc11aacd..0f43837d04 100644 --- a/src/foundation/booleans.lagda.md +++ b/src/foundation/booleans.lagda.md @@ -12,7 +12,6 @@ open import foundation.dependent-pair-types open import foundation.discrete-types open import foundation.involutions open import foundation.negated-equality -open import foundation.raising-universe-levels open import foundation.unit-type open import foundation.universe-levels @@ -88,22 +87,6 @@ module _ if b then x else y = rec-bool x y b ``` -### Raising universe levels of the booleans - -```agda -raise-bool : (l : Level) → UU l -raise-bool l = raise l bool - -raise-true : (l : Level) → raise-bool l -raise-true l = map-raise true - -raise-false : (l : Level) → raise-bool l -raise-false l = map-raise false - -compute-raise-bool : (l : Level) → bool ≃ raise-bool l -compute-raise-bool l = compute-raise l bool -``` - ### The standard propositions associated to the constructors of bool ```agda diff --git a/src/foundation/raising-universe-levels-booleans.lagda.md b/src/foundation/raising-universe-levels-booleans.lagda.md new file mode 100644 index 0000000000..3fca40fc4d --- /dev/null +++ b/src/foundation/raising-universe-levels-booleans.lagda.md @@ -0,0 +1,42 @@ +# Raising universe levels of the booleans + +```agda +module foundation.raising-universe-levels-booleans where +``` + +
Imports + +```agda +open import foundation.booleans +open import foundation.raising-universe-levels +open import foundation.universe-levels + +open import foundation-core.equivalences +``` + +
+ +## Idea + +The type of **booleans** is a +[2-element type](univalent-combinatorics.2-element-types.md) with elements +`true false : bool`, which is used for reasoning with +[decidable propositions](foundation-core.decidable-propositions.md). + +## Definition + +### Raising universe levels of the booleans + +```agda +raise-bool : (l : Level) → UU l +raise-bool l = raise l bool + +raise-true : (l : Level) → raise-bool l +raise-true l = map-raise true + +raise-false : (l : Level) → raise-bool l +raise-false l = map-raise false + +compute-raise-bool : (l : Level) → bool ≃ raise-bool l +compute-raise-bool l = compute-raise l bool +``` diff --git a/src/foundation/raising-universe-levels.lagda.md b/src/foundation/raising-universe-levels.lagda.md index 81c3676716..052c944420 100644 --- a/src/foundation/raising-universe-levels.lagda.md +++ b/src/foundation/raising-universe-levels.lagda.md @@ -102,11 +102,8 @@ pr2 (raise-Set l A) = ```agda raise-subtype : - (l : Level) → - {l1 l2 : Level} → - {A : UU l1} → - subtype l2 A → - subtype (l2 ⊔ l) A + (l : Level) {l1 l2 : Level} {A : UU l1} → + subtype l2 A → subtype (l2 ⊔ l) A raise-subtype l B x = raise-Prop l (B x) ``` diff --git a/src/reflection/definitions.lagda.md b/src/reflection/definitions.lagda.md index 3e0615a316..bea9353b8b 100644 --- a/src/reflection/definitions.lagda.md +++ b/src/reflection/definitions.lagda.md @@ -10,11 +10,12 @@ module reflection.definitions where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types open import foundation.propositional-truncations open import foundation.universe-levels +open import foundation-core.empty-types +open import foundation-core.identity-types + open import lists.lists open import reflection.abstractions diff --git a/src/reflection/fixity.lagda.md b/src/reflection/fixity.lagda.md index 52e0174190..6f7961f5ce 100644 --- a/src/reflection/fixity.lagda.md +++ b/src/reflection/fixity.lagda.md @@ -9,9 +9,10 @@ module reflection.fixity where ```agda open import elementary-number-theory.addition-integers -open import foundation.identity-types open import foundation.universe-levels +open import foundation-core.identity-types + open import primitives.floats open import reflection.names diff --git a/src/reflection/group-solver.lagda.md b/src/reflection/group-solver.lagda.md index 2f6e85638e..6fb762b69b 100644 --- a/src/reflection/group-solver.lagda.md +++ b/src/reflection/group-solver.lagda.md @@ -10,12 +10,13 @@ module reflection.group-solver where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types open import foundation.decidable-types -open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels +open import foundation-core.coproduct-types +open import foundation-core.identity-types + open import group-theory.groups open import linear-algebra.vectors diff --git a/src/reflection/metavariables.lagda.md b/src/reflection/metavariables.lagda.md index 17e3ac21c1..65baaca3e4 100644 --- a/src/reflection/metavariables.lagda.md +++ b/src/reflection/metavariables.lagda.md @@ -10,9 +10,10 @@ module reflection.metavariables where open import elementary-number-theory.natural-numbers open import foundation.booleans -open import foundation.identity-types open import foundation.universe-levels +open import foundation-core.identity-types + open import lists.lists open import primitives.strings diff --git a/src/reflection/names.lagda.md b/src/reflection/names.lagda.md index 8b971a32c0..7e10dbdd4b 100644 --- a/src/reflection/names.lagda.md +++ b/src/reflection/names.lagda.md @@ -9,10 +9,11 @@ module reflection.names where ```agda open import foundation.booleans open import foundation.cartesian-product-types -open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.identity-types + open import primitives.machine-integers open import primitives.strings ``` diff --git a/src/reflection/precategory-solver.lagda.md b/src/reflection/precategory-solver.lagda.md index c0d90a380a..dd11d6389c 100644 --- a/src/reflection/precategory-solver.lagda.md +++ b/src/reflection/precategory-solver.lagda.md @@ -14,10 +14,11 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.function-types -open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.identity-types + open import lists.concatenation-lists open import lists.lists diff --git a/src/reflection/type-checking-monad.lagda.md b/src/reflection/type-checking-monad.lagda.md index 66e434811d..e1524ac71b 100644 --- a/src/reflection/type-checking-monad.lagda.md +++ b/src/reflection/type-checking-monad.lagda.md @@ -15,10 +15,11 @@ open import elementary-number-theory.natural-numbers open import foundation.booleans open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.identity-types + open import lists.lists open import primitives.strings diff --git a/src/set-theory/cumulative-hierarchy.lagda.md b/src/set-theory/cumulative-hierarchy.lagda.md index 8af1c9e172..f2458ffdc1 100644 --- a/src/set-theory/cumulative-hierarchy.lagda.md +++ b/src/set-theory/cumulative-hierarchy.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.booleans +open import foundation.raising-universe-levels-booleans open import foundation.cartesian-product-types open import foundation.constant-type-families open import foundation.coproduct-types From d3f695aa289385bd184a631357b7f0438edbea35 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 21:25:22 +0000 Subject: [PATCH 19/39] `foundation-core.maybe` --- .../conatural-numbers.lagda.md | 2 +- .../equality-conatural-numbers.lagda.md | 3 +- .../inequality-conatural-numbers.lagda.md | 3 +- .../positive-conatural-numbers.lagda.md | 2 +- ...versal-property-conatural-numbers.lagda.md | 2 +- .../zero-conatural-numbers.lagda.md | 2 +- src/foundation-core.lagda.md | 1 + src/foundation-core/maybe.lagda.md | 212 ++++++++++++++++++ src/foundation.lagda.md | 1 + src/foundation/coalgebras-maybe.lagda.md | 3 +- ...ecidable-dependent-function-types.lagda.md | 2 +- .../decidable-dependent-pair-types.lagda.md | 2 +- src/foundation/isolated-elements.lagda.md | 2 +- src/foundation/maybe.lagda.md | 179 ++------------- .../morphisms-coalgebras-maybe.lagda.md | 7 +- .../universal-property-maybe.lagda.md | 2 +- src/lists/lists.lagda.md | 7 +- src/primitives/floats.lagda.md | 3 +- src/primitives/strings.lagda.md | 3 +- src/set-theory/cumulative-hierarchy.lagda.md | 2 +- .../counting-maybe.lagda.md | 5 +- src/univalent-combinatorics/maybe.lagda.md | 2 +- 22 files changed, 259 insertions(+), 188 deletions(-) create mode 100644 src/foundation-core/maybe.lagda.md diff --git a/src/elementary-number-theory/conatural-numbers.lagda.md b/src/elementary-number-theory/conatural-numbers.lagda.md index 3a263db97d..54310d096a 100644 --- a/src/elementary-number-theory/conatural-numbers.lagda.md +++ b/src/elementary-number-theory/conatural-numbers.lagda.md @@ -14,7 +14,6 @@ open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.homotopies open import foundation.injective-maps -open import foundation.maybe open import foundation.negated-equality open import foundation.retractions open import foundation.sections @@ -22,6 +21,7 @@ open import foundation.unit-type open import foundation.universe-levels open import foundation-core.identity-types +open import foundation-core.maybe ```
diff --git a/src/elementary-number-theory/equality-conatural-numbers.lagda.md b/src/elementary-number-theory/equality-conatural-numbers.lagda.md index 9231d89474..eb8d842c46 100644 --- a/src/elementary-number-theory/equality-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/equality-conatural-numbers.lagda.md @@ -25,7 +25,6 @@ open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies open import foundation.identity-types open import foundation.injective-maps -open import foundation.maybe open import foundation.negation open import foundation.retractions open import foundation.retracts-of-types @@ -36,6 +35,8 @@ open import foundation.torsorial-type-families open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.maybe + open import logic.double-negation-elimination ``` diff --git a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md index a3aa5e7a0f..5a90091ea9 100644 --- a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md @@ -21,12 +21,13 @@ open import foundation.empty-types open import foundation.function-types open import foundation.functoriality-coproduct-types open import foundation.identity-types -open import foundation.maybe open import foundation.negation open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.maybe + open import order-theory.posets open import order-theory.preorders ``` diff --git a/src/elementary-number-theory/positive-conatural-numbers.lagda.md b/src/elementary-number-theory/positive-conatural-numbers.lagda.md index d50eb34f27..4d2dd9340a 100644 --- a/src/elementary-number-theory/positive-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/positive-conatural-numbers.lagda.md @@ -15,12 +15,12 @@ open import elementary-number-theory.zero-conatural-numbers open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.maybe open import foundation.negation open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.identity-types +open import foundation-core.maybe ```
diff --git a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md index c593269a23..54e612e108 100644 --- a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md @@ -23,7 +23,7 @@ enjoys many universal properties, among others: 1. It is the one-point compactification of the [natural numbers](elementary-number-theory.natural-numbers.md). 2. It classifies downward-stable subsets of the natural numbers. -3. It is the final coalgebra of the [maybe monad](foundation.maybe.md). +3. It is the final coalgebra of the [maybe monad](foundation-core.maybe.md). On this page we consider the last of these. Thus, a `Maybe`-[coalgebra](foundation.coalgebras-maybe.md) `η : X → Maybe X` satisfies diff --git a/src/elementary-number-theory/zero-conatural-numbers.lagda.md b/src/elementary-number-theory/zero-conatural-numbers.lagda.md index ea40798173..0daa319c80 100644 --- a/src/elementary-number-theory/zero-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/zero-conatural-numbers.lagda.md @@ -14,11 +14,11 @@ open import elementary-number-theory.conatural-numbers open import foundation.coproduct-types open import foundation.decidable-types open import foundation.function-types -open import foundation.maybe open import foundation.negation open import foundation.universe-levels open import foundation-core.identity-types +open import foundation-core.maybe open import foundation-core.propositions ``` diff --git a/src/foundation-core.lagda.md b/src/foundation-core.lagda.md index d481c784f4..850d3ef2e1 100644 --- a/src/foundation-core.lagda.md +++ b/src/foundation-core.lagda.md @@ -38,6 +38,7 @@ open import foundation-core.identity-types public open import foundation-core.injective-maps public open import foundation-core.invertible-maps public open import foundation-core.logical-equivalences public +open import foundation-core.maybe public open import foundation-core.negation public open import foundation-core.operations-span-diagrams public open import foundation-core.operations-spans public diff --git a/src/foundation-core/maybe.lagda.md b/src/foundation-core/maybe.lagda.md new file mode 100644 index 0000000000..ca3502824d --- /dev/null +++ b/src/foundation-core/maybe.lagda.md @@ -0,0 +1,212 @@ +# The maybe monad + +```agda +module foundation-core.maybe where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.unit-type +open import foundation.universe-levels + +open import foundation-core.cartesian-product-types +open import foundation-core.coproduct-types +open import foundation-core.equivalences +open import foundation-core.identity-types +open import foundation-core.negation +open import foundation-core.propositions +open import foundation-core.retractions +open import foundation-core.sections +``` + +
+ +## Idea + +The +{{#concept "maybe monad" Disambiguation="on types" Agda=Maybe WD="option type" WDID=Q7099015}} +is an operation on types that adds one point. This is used, for example, to +define [partial functions](foundation.partial-functions.md), where a partial +function `f : X ⇀ Y` is a map `f : X → Maybe Y`. + +The maybe monad is an example of a monad that is not a +[modality](orthogonal-factorization-systems.higher-modalities.md), since it is +not [idempotent](foundation.idempotent-maps.md). + +## Definitions + +### The maybe monad + +```agda +Maybe : {l : Level} → UU l → UU l +Maybe X = X + unit + +unit-Maybe : {l : Level} {X : UU l} → X → Maybe X +unit-Maybe = inl + +exception-Maybe : {l : Level} {X : UU l} → Maybe X +exception-Maybe = inr star + +extend-Maybe : + {l1 l2 : Level} {X : UU l1} {Y : UU l2} → (X → Maybe Y) → Maybe X → Maybe Y +extend-Maybe f (inl x) = f x +extend-Maybe f (inr *) = inr * + +map-Maybe : + {l1 l2 : Level} {X : UU l1} {Y : UU l2} → (X → Y) → Maybe X → Maybe Y +map-Maybe f (inl x) = inl (f x) +map-Maybe f (inr *) = inr * +``` + +### The inductive definition of the maybe monad + +```agda +data Maybe' {l : Level} (X : UU l) : UU l where + unit-Maybe' : X → Maybe' X + exception-Maybe' : Maybe' X + +{-# BUILTIN MAYBE Maybe' #-} +``` + +### The predicate of being an exception + +```agda +is-exception-Maybe : {l : Level} {X : UU l} → Maybe X → UU l +is-exception-Maybe {l} {X} x = (x ＝ exception-Maybe) + +is-not-exception-Maybe : {l : Level} {X : UU l} → Maybe X → UU l +is-not-exception-Maybe x = ¬ (is-exception-Maybe x) + +abstract + is-prop-is-exception-Maybe : + {l : Level} {X : UU l} (x : Maybe X) → is-prop (is-exception-Maybe x) + is-prop-is-exception-Maybe (inl x) () + is-prop-is-exception-Maybe (inr star) refl refl = refl , (λ where refl → refl) +``` + +### The predicate of being a value + +```agda +is-value-Maybe : {l : Level} {X : UU l} → Maybe X → UU l +is-value-Maybe {l} {X} x = Σ X (λ y → inl y ＝ x) + +value-is-value-Maybe : + {l : Level} {X : UU l} (x : Maybe X) → is-value-Maybe x → X +value-is-value-Maybe x = pr1 + +eq-is-value-Maybe : + {l : Level} {X : UU l} (x : Maybe X) (H : is-value-Maybe x) → + inl (value-is-value-Maybe x H) ＝ x +eq-is-value-Maybe x H = pr2 H +``` + +### Maybe structure on a type + +```agda +maybe-structure : {l1 : Level} (X : UU l1) → UU (lsuc l1) +maybe-structure {l1} X = Σ (UU l1) (λ Y → Maybe Y ≃ X) +``` + +## Properties + +### The values of the unit of the `Maybe` monad are not exceptions + +```agda +abstract + is-not-exception-unit-Maybe : + {l : Level} {X : UU l} (x : X) → is-not-exception-Maybe (unit-Maybe x) + is-not-exception-unit-Maybe x () +``` + +### For any element of type `Maybe X` we can decide whether it is a value or an exception + +```agda +decide-Maybe : + {l : Level} {X : UU l} (x : Maybe X) → is-value-Maybe x + is-exception-Maybe x +decide-Maybe (inl x) = inl (x , refl) +decide-Maybe (inr star) = inr refl +``` + +### Values are not exceptions + +```agda +abstract + is-not-exception-is-value-Maybe : + {l1 : Level} {X : UU l1} (x : Maybe X) → + is-value-Maybe x → is-not-exception-Maybe x + is-not-exception-is-value-Maybe {l1} {X} .(inl x) (x , refl) = + is-not-exception-unit-Maybe x +``` + +### The two definitions of `Maybe` are equivalent + +```agda +module _ + {l1 l2 : Level} {X : UU l1} + where + + map-Maybe-Maybe' : Maybe X → Maybe' X + map-Maybe-Maybe' (inl x) = unit-Maybe' x + map-Maybe-Maybe' (inr _) = exception-Maybe' + + map-inv-Maybe-Maybe' : Maybe' X → Maybe X + map-inv-Maybe-Maybe' (unit-Maybe' x) = inl x + map-inv-Maybe-Maybe' exception-Maybe' = inr star + + is-section-map-inv-Maybe-Maybe' : + is-section map-Maybe-Maybe' map-inv-Maybe-Maybe' + is-section-map-inv-Maybe-Maybe' (unit-Maybe' x) = refl + is-section-map-inv-Maybe-Maybe' exception-Maybe' = refl + + is-retraction-map-inv-Maybe-Maybe' : + is-retraction map-Maybe-Maybe' map-inv-Maybe-Maybe' + is-retraction-map-inv-Maybe-Maybe' (inl x) = refl + is-retraction-map-inv-Maybe-Maybe' (inr x) = refl + + is-equiv-map-Maybe-Maybe' : is-equiv map-Maybe-Maybe' + is-equiv-map-Maybe-Maybe' = + is-equiv-is-invertible + ( map-inv-Maybe-Maybe') + ( is-section-map-inv-Maybe-Maybe') + ( is-retraction-map-inv-Maybe-Maybe') + + equiv-Maybe-Maybe' : Maybe X ≃ Maybe' X + equiv-Maybe-Maybe' = (map-Maybe-Maybe' , is-equiv-map-Maybe-Maybe') +``` + +### There is a surjection from `Maybe A + Maybe B` to `Maybe (A + B)` + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + map-maybe-coproduct : Maybe A + Maybe B → Maybe (A + B) + map-maybe-coproduct (inl (inl x)) = inl (inl x) + map-maybe-coproduct (inl (inr star)) = inr star + map-maybe-coproduct (inr (inl x)) = inl (inr x) + map-maybe-coproduct (inr (inr star)) = inr star +``` + +### There is a surjection from `Maybe A × Maybe B` to `Maybe (A × B)` + +```agda +module _ + {l1 l2 : Level} {A : UU l1} {B : UU l2} + where + + map-maybe-product : Maybe A × Maybe B → Maybe (A × B) + map-maybe-product (inl a , inl b) = inl (a , b) + map-maybe-product (inl a , inr star) = inr star + map-maybe-product (inr star , inl b) = inr star + map-maybe-product (inr star , inr star) = inr star +``` + +## External links + +- [maybe monad](https://ncatlab.org/nlab/show/maybe+monad) at $n$Lab +- [Monad (category theory)#The maybe monad]() + at Wikipedia +- [Option type](https://en.wikipedia.org/wiki/Option_type) at Wikipedia diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index 6965be4664..ebab239526 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -360,6 +360,7 @@ open import foundation.pullbacks public open import foundation.pullbacks-subtypes public open import foundation.quasicoherently-idempotent-maps public open import foundation.raising-universe-levels public +open import foundation.raising-universe-levels-booleans public open import foundation.raising-universe-levels-unit-type public open import foundation.reflecting-maps-equivalence-relations public open import foundation.reflexive-relations public diff --git a/src/foundation/coalgebras-maybe.lagda.md b/src/foundation/coalgebras-maybe.lagda.md index 855690a002..afca8c6ef1 100644 --- a/src/foundation/coalgebras-maybe.lagda.md +++ b/src/foundation/coalgebras-maybe.lagda.md @@ -8,9 +8,10 @@ module foundation.coalgebras-maybe where ```agda open import foundation.dependent-pair-types -open import foundation.maybe open import foundation.universe-levels +open import foundation-core.maybe + open import trees.polynomial-endofunctors ``` diff --git a/src/foundation/decidable-dependent-function-types.lagda.md b/src/foundation/decidable-dependent-function-types.lagda.md index c63c6ddeea..efc5cf4919 100644 --- a/src/foundation/decidable-dependent-function-types.lagda.md +++ b/src/foundation/decidable-dependent-function-types.lagda.md @@ -9,7 +9,6 @@ module foundation.decidable-dependent-function-types where ```agda open import foundation.decidable-types open import foundation.functoriality-dependent-function-types -open import foundation.maybe open import foundation.uniformly-decidable-type-families open import foundation.universal-property-coproduct-types open import foundation.universal-property-maybe @@ -19,6 +18,7 @@ open import foundation-core.coproduct-types open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types +open import foundation-core.maybe open import foundation-core.negation ``` diff --git a/src/foundation/decidable-dependent-pair-types.lagda.md b/src/foundation/decidable-dependent-pair-types.lagda.md index 4af4b5e568..eb012329f7 100644 --- a/src/foundation/decidable-dependent-pair-types.lagda.md +++ b/src/foundation/decidable-dependent-pair-types.lagda.md @@ -9,7 +9,6 @@ module foundation.decidable-dependent-pair-types where ```agda open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.maybe open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-unit-type open import foundation.uniformly-decidable-type-families @@ -19,6 +18,7 @@ open import foundation-core.coproduct-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types +open import foundation-core.maybe open import foundation-core.negation ``` diff --git a/src/foundation/isolated-elements.lagda.md b/src/foundation/isolated-elements.lagda.md index f4af701d09..994d1a5448 100644 --- a/src/foundation/isolated-elements.lagda.md +++ b/src/foundation/isolated-elements.lagda.md @@ -19,7 +19,6 @@ open import foundation.embeddings open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types open import foundation.injective-maps -open import foundation.maybe open import foundation.negated-equality open import foundation.negation open import foundation.sets @@ -35,6 +34,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies +open import foundation-core.maybe open import foundation-core.propositions open import foundation-core.subtypes open import foundation-core.torsorial-type-families diff --git a/src/foundation/maybe.lagda.md b/src/foundation/maybe.lagda.md index eb0267724d..a7c8ed3e01 100644 --- a/src/foundation/maybe.lagda.md +++ b/src/foundation/maybe.lagda.md @@ -2,13 +2,14 @@ ```agda module foundation.maybe where + +open import foundation-core.maybe public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types @@ -22,13 +23,10 @@ open import foundation.universe-levels open import foundation-core.embeddings open import foundation-core.empty-types -open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.negation open import foundation-core.propositions -open import foundation-core.retractions -open import foundation-core.sections ```
@@ -45,80 +43,6 @@ The maybe monad is an example of a monad that is not a [modality](orthogonal-factorization-systems.higher-modalities.md), since it is not [idempotent](foundation.idempotent-maps.md). -## Definitions - -### The maybe monad - -```agda -Maybe : {l : Level} → UU l → UU l -Maybe X = X + unit - -unit-Maybe : {l : Level} {X : UU l} → X → Maybe X -unit-Maybe = inl - -exception-Maybe : {l : Level} {X : UU l} → Maybe X -exception-Maybe = inr star - -extend-Maybe : - {l1 l2 : Level} {X : UU l1} {Y : UU l2} → (X → Maybe Y) → Maybe X → Maybe Y -extend-Maybe f (inl x) = f x -extend-Maybe f (inr *) = inr * - -map-Maybe : - {l1 l2 : Level} {X : UU l1} {Y : UU l2} → (X → Y) → Maybe X → Maybe Y -map-Maybe f (inl x) = inl (f x) -map-Maybe f (inr *) = inr * -``` - -### The inductive definition of the maybe monad - -```agda -data Maybe' {l : Level} (X : UU l) : UU l where - unit-Maybe' : X → Maybe' X - exception-Maybe' : Maybe' X - -{-# BUILTIN MAYBE Maybe' #-} -``` - -### The predicate of being an exception - -```agda -is-exception-Maybe : {l : Level} {X : UU l} → Maybe X → UU l -is-exception-Maybe {l} {X} x = (x ＝ exception-Maybe) - -is-not-exception-Maybe : {l : Level} {X : UU l} → Maybe X → UU l -is-not-exception-Maybe x = ¬ (is-exception-Maybe x) - -is-prop-is-exception-Maybe : - {l : Level} {X : UU l} (x : Maybe X) → is-prop (is-exception-Maybe x) -is-prop-is-exception-Maybe (inl x) () -is-prop-is-exception-Maybe (inr x) = - is-prop-equiv (compute-eq-coproduct-inr-inr x star) (is-set-unit x star) -``` - -### The predicate of being a value - -```agda -is-value-Maybe : {l : Level} {X : UU l} → Maybe X → UU l -is-value-Maybe {l} {X} x = Σ X (λ y → inl y ＝ x) - -value-is-value-Maybe : - {l : Level} {X : UU l} (x : Maybe X) → is-value-Maybe x → X -value-is-value-Maybe x = pr1 - -eq-is-value-Maybe : - {l : Level} {X : UU l} (x : Maybe X) (H : is-value-Maybe x) → - inl (value-is-value-Maybe x H) ＝ x -eq-is-value-Maybe x H = pr2 H -``` - -### Maybe structure on a type - -```agda -maybe-structure : {l1 : Level} (X : UU l1) → UU (lsuc l1) -maybe-structure {l1} X = Σ (UU l1) (λ Y → Maybe Y ≃ X) -``` - ## Properties ### The unit of `Maybe` is an embedding @@ -157,47 +81,6 @@ module _ is-decidable-neg (is-decidable-is-exception-Maybe x) ``` -### The values of the unit of the `Maybe` monad are not exceptions - -```agda -abstract - is-not-exception-unit-Maybe : - {l : Level} {X : UU l} (x : X) → is-not-exception-Maybe (unit-Maybe x) - is-not-exception-unit-Maybe x () -``` - -### The unit of `Maybe` is not surjective - -```agda -abstract - is-not-surjective-unit-Maybe : - {l : Level} {X : UU l} → ¬ (is-surjective (unit-Maybe {X = X})) - is-not-surjective-unit-Maybe H = - rec-trunc-Prop empty-Prop - ( λ p → is-not-exception-unit-Maybe (pr1 p) (pr2 p)) - ( H exception-Maybe) -``` - -### For any element of type `Maybe X` we can decide whether it is a value or an exception - -```agda -decide-Maybe : - {l : Level} {X : UU l} (x : Maybe X) → is-value-Maybe x + is-exception-Maybe x -decide-Maybe (inl x) = inl (x , refl) -decide-Maybe (inr star) = inr refl -``` - -### Values are not exceptions - -```agda -abstract - is-not-exception-is-value-Maybe : - {l1 : Level} {X : UU l1} (x : Maybe X) → - is-value-Maybe x → is-not-exception-Maybe x - is-not-exception-is-value-Maybe {l1} {X} .(inl x) (x , refl) = - is-not-exception-unit-Maybe x -``` - ### If a point is not an exception, then it is a value ```agda @@ -223,40 +106,16 @@ eq-is-not-exception-Maybe x H = eq-is-value-Maybe x (is-value-is-not-exception-Maybe x H) ``` -### The two definitions of `Maybe` are equivalent +### The unit of `Maybe` is not surjective ```agda -module _ - {l1 l2 : Level} {X : UU l1} - where - - map-Maybe-Maybe' : Maybe X → Maybe' X - map-Maybe-Maybe' (inl x) = unit-Maybe' x - map-Maybe-Maybe' (inr _) = exception-Maybe' - - map-inv-Maybe-Maybe' : Maybe' X → Maybe X - map-inv-Maybe-Maybe' (unit-Maybe' x) = inl x - map-inv-Maybe-Maybe' exception-Maybe' = inr star - - is-section-map-inv-Maybe-Maybe' : - is-section map-Maybe-Maybe' map-inv-Maybe-Maybe' - is-section-map-inv-Maybe-Maybe' (unit-Maybe' x) = refl - is-section-map-inv-Maybe-Maybe' exception-Maybe' = refl - - is-retraction-map-inv-Maybe-Maybe' : - is-retraction map-Maybe-Maybe' map-inv-Maybe-Maybe' - is-retraction-map-inv-Maybe-Maybe' (inl x) = refl - is-retraction-map-inv-Maybe-Maybe' (inr x) = refl - - is-equiv-map-Maybe-Maybe' : is-equiv map-Maybe-Maybe' - is-equiv-map-Maybe-Maybe' = - is-equiv-is-invertible - ( map-inv-Maybe-Maybe') - ( is-section-map-inv-Maybe-Maybe') - ( is-retraction-map-inv-Maybe-Maybe') - - equiv-Maybe-Maybe' : Maybe X ≃ Maybe' X - equiv-Maybe-Maybe' = (map-Maybe-Maybe' , is-equiv-map-Maybe-Maybe') +abstract + is-not-surjective-unit-Maybe : + {l : Level} {X : UU l} → ¬ (is-surjective (unit-Maybe {X = X})) + is-not-surjective-unit-Maybe H = + rec-trunc-Prop empty-Prop + ( λ p → is-not-exception-unit-Maybe (pr1 p) (pr2 p)) + ( H exception-Maybe) ``` ### The extension of surjective maps is surjective @@ -299,13 +158,8 @@ module _ {l1 l2 : Level} {A : UU l1} {B : UU l2} where - map-maybe-coproduct : Maybe A + Maybe B → Maybe (A + B) - map-maybe-coproduct (inl (inl x)) = inl (inl x) - map-maybe-coproduct (inl (inr star)) = inr star - map-maybe-coproduct (inr (inl x)) = inl (inr x) - map-maybe-coproduct (inr (inr star)) = inr star - - is-surjective-map-maybe-coproduct : is-surjective map-maybe-coproduct + is-surjective-map-maybe-coproduct : + is-surjective (map-maybe-coproduct {A = A} {B}) is-surjective-map-maybe-coproduct (inl (inl x)) = unit-trunc-Prop ((inl (inl x)) , refl) is-surjective-map-maybe-coproduct (inl (inr x)) = @@ -321,13 +175,8 @@ module _ {l1 l2 : Level} {A : UU l1} {B : UU l2} where - map-maybe-product : Maybe A × Maybe B → Maybe (A × B) - map-maybe-product (inl a , inl b) = inl (a , b) - map-maybe-product (inl a , inr star) = inr star - map-maybe-product (inr star , inl b) = inr star - map-maybe-product (inr star , inr star) = inr star - - is-surjective-map-maybe-product : is-surjective map-maybe-product + is-surjective-map-maybe-product : + is-surjective (map-maybe-product {A = A} {B}) is-surjective-map-maybe-product (inl (a , b)) = unit-trunc-Prop ((inl a , inl b) , refl) is-surjective-map-maybe-product (inr star) = diff --git a/src/foundation/morphisms-coalgebras-maybe.lagda.md b/src/foundation/morphisms-coalgebras-maybe.lagda.md index 356b8eba5b..41c03ed586 100644 --- a/src/foundation/morphisms-coalgebras-maybe.lagda.md +++ b/src/foundation/morphisms-coalgebras-maybe.lagda.md @@ -10,9 +10,10 @@ module foundation.morphisms-coalgebras-maybe where open import foundation.coalgebras-maybe open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.maybe open import foundation.universe-levels +open import foundation-core.maybe + open import trees.polynomial-endofunctors ``` @@ -21,8 +22,8 @@ open import trees.polynomial-endofunctors ## Idea Given two [coalgebras](foundation.coalgebras-maybe.md) of the -[maybe monad](foundation.maybe.md) `η : X → Maybe X`, `η' : Y → Maybe Y`, then a -map `f : X → Y` is a +[maybe monad](foundation-core.maybe.md) `η : X → Maybe X`, `η' : Y → Maybe Y`, +then a map `f : X → Y` is a {{#concept "morphism of coalgebras" Disambiguation="of the maybe monad" Agda=hom-coalgebra-Maybe}} if the square diff --git a/src/foundation/universal-property-maybe.lagda.md b/src/foundation/universal-property-maybe.lagda.md index 0c8afea5e1..f55128fdfa 100644 --- a/src/foundation/universal-property-maybe.lagda.md +++ b/src/foundation/universal-property-maybe.lagda.md @@ -9,7 +9,6 @@ module foundation.universal-property-maybe where ```agda open import foundation.dependent-pair-types open import foundation.function-extensionality -open import foundation.maybe open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -18,6 +17,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types +open import foundation-core.maybe ```
diff --git a/src/lists/lists.lagda.md b/src/lists/lists.lagda.md index f7922f6274..78993660a9 100644 --- a/src/lists/lists.lagda.md +++ b/src/lists/lists.lagda.md @@ -20,9 +20,6 @@ open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.maybe open import foundation.negation open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type @@ -32,6 +29,10 @@ open import foundation.truncated-types open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.maybe ```
diff --git a/src/primitives/floats.lagda.md b/src/primitives/floats.lagda.md index 902432e801..7c2e16d374 100644 --- a/src/primitives/floats.lagda.md +++ b/src/primitives/floats.lagda.md @@ -10,9 +10,10 @@ module primitives.floats where open import elementary-number-theory.natural-numbers open import foundation.booleans -open import foundation.maybe open import foundation.universe-levels +open import foundation-core.maybe + open import primitives.machine-integers open import primitives.strings ``` diff --git a/src/primitives/strings.lagda.md b/src/primitives/strings.lagda.md index d94ebd03e7..81996faa8c 100644 --- a/src/primitives/strings.lagda.md +++ b/src/primitives/strings.lagda.md @@ -11,9 +11,10 @@ open import elementary-number-theory.natural-numbers open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.maybe open import foundation.universe-levels +open import foundation-core.maybe + open import lists.lists open import primitives.characters diff --git a/src/set-theory/cumulative-hierarchy.lagda.md b/src/set-theory/cumulative-hierarchy.lagda.md index f2458ffdc1..baa1ddad21 100644 --- a/src/set-theory/cumulative-hierarchy.lagda.md +++ b/src/set-theory/cumulative-hierarchy.lagda.md @@ -11,7 +11,6 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.booleans -open import foundation.raising-universe-levels-booleans open import foundation.cartesian-product-types open import foundation.constant-type-families open import foundation.coproduct-types @@ -27,6 +26,7 @@ open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-booleans open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.transport-along-identifications diff --git a/src/univalent-combinatorics/counting-maybe.lagda.md b/src/univalent-combinatorics/counting-maybe.lagda.md index a77a6a7cfb..a69e71d84a 100644 --- a/src/univalent-combinatorics/counting-maybe.lagda.md +++ b/src/univalent-combinatorics/counting-maybe.lagda.md @@ -11,10 +11,11 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.equivalences-maybe -open import foundation.identity-types -open import foundation.maybe open import foundation.universe-levels +open import foundation-core.identity-types +open import foundation-core.maybe + open import univalent-combinatorics.coproduct-types open import univalent-combinatorics.counting ``` diff --git a/src/univalent-combinatorics/maybe.lagda.md b/src/univalent-combinatorics/maybe.lagda.md index 9a9c68812f..7ba870c33e 100644 --- a/src/univalent-combinatorics/maybe.lagda.md +++ b/src/univalent-combinatorics/maybe.lagda.md @@ -3,7 +3,7 @@ ```agda module univalent-combinatorics.maybe where -open import foundation.maybe public +open import foundation-core.maybe public ```
Imports From cf9ed8879fa3154fc8a01af37e9037b1532659d0 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 22:04:03 +0000 Subject: [PATCH 20/39] `foundation-core.booleans` --- .../representing-arrow-category.lagda.md | 5 +- src/foundation-core.lagda.md | 1 + src/foundation-core/booleans.lagda.md | 235 ++++++++++++++++++ src/foundation/booleans.lagda.md | 203 +-------------- src/foundation/diaconescus-theorem.lagda.md | 4 +- ...-limited-principle-of-omniscience.lagda.md | 8 +- .../limited-principle-of-omniscience.lagda.md | 2 +- .../raising-universe-levels-booleans.lagda.md | 2 +- .../type-arithmetic-booleans.lagda.md | 2 +- .../universal-property-booleans.lagda.md | 2 +- ...-limited-principle-of-omniscience.lagda.md | 2 +- src/logic/markovian-types.lagda.md | 6 +- src/logic/markovs-principle.lagda.md | 2 +- .../orthogonal-maps.lagda.md | 2 +- src/primitives/characters.lagda.md | 3 +- src/primitives/floats.lagda.md | 2 +- src/primitives/strings.lagda.md | 2 +- src/reflection/boolean-reflection.lagda.md | 2 +- src/reflection/metavariables.lagda.md | 2 +- src/reflection/names.lagda.md | 6 +- src/reflection/type-checking-monad.lagda.md | 2 +- 21 files changed, 267 insertions(+), 228 deletions(-) create mode 100644 src/foundation-core/booleans.lagda.md diff --git a/src/category-theory/representing-arrow-category.lagda.md b/src/category-theory/representing-arrow-category.lagda.md index dbdfec5962..a4259a4611 100644 --- a/src/category-theory/representing-arrow-category.lagda.md +++ b/src/category-theory/representing-arrow-category.lagda.md @@ -11,7 +11,6 @@ open import category-theory.categories open import category-theory.isomorphisms-in-precategories open import category-theory.precategories -open import foundation.booleans open import foundation.dependent-pair-types open import foundation.empty-types open import foundation.identity-types @@ -21,6 +20,8 @@ open import foundation.sets open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.booleans ```
@@ -30,7 +31,7 @@ open import foundation.universe-levels The **representing arrow** is the [category](category-theory.categories.md) that [represents](category-theory.representable-functors-categories.md) arrows in a ([pre-](category-theory.precategories.md))category. We model it after -implication on the [booleans](foundation.booleans.md). +implication on the [booleans](foundation-core.booleans.md). ## Definition diff --git a/src/foundation-core.lagda.md b/src/foundation-core.lagda.md index 850d3ef2e1..17d58ece65 100644 --- a/src/foundation-core.lagda.md +++ b/src/foundation-core.lagda.md @@ -6,6 +6,7 @@ module foundation-core where open import foundation-core.1-types public +open import foundation-core.booleans public open import foundation-core.cartesian-product-types public open import foundation-core.coherently-invertible-maps public open import foundation-core.commuting-prisms-of-maps public diff --git a/src/foundation-core/booleans.lagda.md b/src/foundation-core/booleans.lagda.md new file mode 100644 index 0000000000..c952e4b34a --- /dev/null +++ b/src/foundation-core/booleans.lagda.md @@ -0,0 +1,235 @@ +# The booleans + +```agda +module foundation-core.booleans where +``` + +
Imports + +```agda +open import foundation.dependent-pair-types +open import foundation.unit-type +open import foundation.universe-levels + +open import foundation-core.constant-maps +open import foundation-core.empty-types +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.identity-types +open import foundation-core.negation +open import foundation-core.propositions +open import foundation-core.sections +open import foundation-core.sets +``` + +
+ +## Idea + +The type of **booleans** is a +[2-element type](univalent-combinatorics.2-element-types.md) with elements +`true false : bool`, which is used for reasoning with +[decidable propositions](foundation-core.decidable-propositions.md). + +## Definition + +### The booleans + +```agda +data bool : UU lzero where + true false : bool + +{-# BUILTIN BOOL bool #-} +{-# BUILTIN TRUE true #-} +{-# BUILTIN FALSE false #-} +``` + +### The induction principle of the booleans + +```agda +module _ + {l : Level} (P : bool → UU l) + where + + ind-bool : P true → P false → (b : bool) → P b + ind-bool pt pf true = pt + ind-bool pt pf false = pf +``` + +### The recursion principle of the booleans + +```agda +module _ + {l : Level} {P : UU l} + where + + rec-bool : P → P → bool → P + rec-bool = ind-bool (λ _ → P) +``` + +### The `if_then_else` function + +```agda +module _ + {l : Level} {A : UU l} + where + + if_then_else_ : bool → A → A → A + if b then x else y = rec-bool x y b +``` + +### The standard propositions associated to the constructors of bool + +```agda +prop-bool : bool → Prop lzero +prop-bool true = unit-Prop +prop-bool false = empty-Prop + +type-prop-bool : bool → UU lzero +type-prop-bool = type-Prop ∘ prop-bool +``` + +### Equality on the booleans + +```agda +Eq-bool : bool → bool → UU lzero +Eq-bool true true = unit +Eq-bool true false = empty +Eq-bool false true = empty +Eq-bool false false = unit + +refl-Eq-bool : (x : bool) → Eq-bool x x +refl-Eq-bool true = star +refl-Eq-bool false = star + +Eq-eq-bool : + {x y : bool} → x ＝ y → Eq-bool x y +Eq-eq-bool {x = x} refl = refl-Eq-bool x + +eq-Eq-bool : + {x y : bool} → Eq-bool x y → x ＝ y +eq-Eq-bool {true} {true} star = refl +eq-Eq-bool {false} {false} star = refl + +neq-false-true-bool : ¬ (false ＝ true) +neq-false-true-bool () + +neq-true-false-bool : ¬ (true ＝ false) +neq-true-false-bool () +``` + +## Structure + +### The boolean operators + +```agda +neg-bool : bool → bool +neg-bool true = false +neg-bool false = true + +conjunction-bool : bool → bool → bool +conjunction-bool true true = true +conjunction-bool true false = false +conjunction-bool false true = false +conjunction-bool false false = false + +disjunction-bool : bool → bool → bool +disjunction-bool true true = true +disjunction-bool true false = true +disjunction-bool false true = true +disjunction-bool false false = false + +implication-bool : bool → bool → bool +implication-bool true true = true +implication-bool true false = false +implication-bool false true = true +implication-bool false false = true +``` + +## Properties + +### The booleans are a set + +```agda +abstract + is-prop-Eq-bool : (x y : bool) → is-prop (Eq-bool x y) + is-prop-Eq-bool true true = is-prop-unit + is-prop-Eq-bool true false = is-prop-empty + is-prop-Eq-bool false true = is-prop-empty + is-prop-Eq-bool false false = is-prop-unit + +abstract + is-set-bool : is-set bool + is-set-bool = + is-set-prop-in-id + ( Eq-bool) + ( is-prop-Eq-bool) + ( refl-Eq-bool) + ( λ x y → eq-Eq-bool) + +bool-Set : Set lzero +bool-Set = bool , is-set-bool +``` + +### The "is true" predicate on booleans + +```agda +is-true : bool → UU lzero +is-true = _＝ true + +is-prop-is-true : (b : bool) → is-prop (is-true b) +is-prop-is-true b = is-set-bool b true + +is-true-Prop : bool → Prop lzero +is-true-Prop b = is-true b , is-prop-is-true b +``` + +### The "is false" predicate on booleans + +```agda +is-false : bool → UU lzero +is-false = _＝ false + +is-prop-is-false : (b : bool) → is-prop (is-false b) +is-prop-is-false b = is-set-bool b false + +is-false-Prop : bool → Prop lzero +is-false-Prop b = is-false b , is-prop-is-false b +``` + +### A boolean cannot be both true and false + +```agda +not-is-false-is-true : (x : bool) → is-true x → ¬ (is-false x) +not-is-false-is-true true t () +not-is-false-is-true false () f + +not-is-true-is-false : (x : bool) → is-false x → ¬ (is-true x) +not-is-true-is-false true () f +not-is-true-is-false false t () +``` + +### Boolean negation has no fixed points + +```agda +neq-neg-bool : (b : bool) → ¬ (b ＝ neg-bool b) +neq-neg-bool true () +neq-neg-bool false () + +neq-neg-bool' : (b : bool) → ¬ (neg-bool b ＝ b) +neq-neg-bool' b = neq-neg-bool b ∘ inv +``` + +### The constant function `const bool b` is not an equivalence + +```agda +abstract + no-section-const-bool : (b : bool) → ¬ (section (const bool b)) + no-section-const-bool true (g , G) = neq-true-false-bool (G false) + no-section-const-bool false (g , G) = neq-false-true-bool (G true) + +abstract + is-not-equiv-const-bool : + (b : bool) → ¬ (is-equiv (const bool b)) + is-not-equiv-const-bool b e = no-section-const-bool b (section-is-equiv e) +``` diff --git a/src/foundation/booleans.lagda.md b/src/foundation/booleans.lagda.md index 0f43837d04..3ac9ef298c 100644 --- a/src/foundation/booleans.lagda.md +++ b/src/foundation/booleans.lagda.md @@ -2,6 +2,8 @@ ```agda module foundation.booleans where + +open import foundation-core.booleans public ```
Imports @@ -40,146 +42,8 @@ The type of **booleans** is a `true false : bool`, which is used for reasoning with [decidable propositions](foundation-core.decidable-propositions.md). -## Definition - -### The booleans - -```agda -data bool : UU lzero where - true false : bool - -{-# BUILTIN BOOL bool #-} -{-# BUILTIN TRUE true #-} -{-# BUILTIN FALSE false #-} -``` - -### The induction principle of the booleans - -```agda -module _ - {l : Level} (P : bool → UU l) - where - - ind-bool : P true → P false → (b : bool) → P b - ind-bool pt pf true = pt - ind-bool pt pf false = pf -``` - -### The recursion principle of the booleans - -```agda -module _ - {l : Level} {P : UU l} - where - - rec-bool : P → P → bool → P - rec-bool = ind-bool (λ _ → P) -``` - -### The `if_then_else` function - -```agda -module _ - {l : Level} {A : UU l} - where - - if_then_else_ : bool → A → A → A - if b then x else y = rec-bool x y b -``` - -### The standard propositions associated to the constructors of bool - -```agda -prop-bool : bool → Prop lzero -prop-bool true = unit-Prop -prop-bool false = empty-Prop - -type-prop-bool : bool → UU lzero -type-prop-bool = type-Prop ∘ prop-bool -``` - -### Equality on the booleans - -```agda -Eq-bool : bool → bool → UU lzero -Eq-bool true true = unit -Eq-bool true false = empty -Eq-bool false true = empty -Eq-bool false false = unit - -refl-Eq-bool : (x : bool) → Eq-bool x x -refl-Eq-bool true = star -refl-Eq-bool false = star - -Eq-eq-bool : - {x y : bool} → x ＝ y → Eq-bool x y -Eq-eq-bool {x = x} refl = refl-Eq-bool x - -eq-Eq-bool : - {x y : bool} → Eq-bool x y → x ＝ y -eq-Eq-bool {true} {true} star = refl -eq-Eq-bool {false} {false} star = refl - -neq-false-true-bool : false ≠ true -neq-false-true-bool () - -neq-true-false-bool : true ≠ false -neq-true-false-bool () -``` - -## Structure - -### The boolean operators - -```agda -neg-bool : bool → bool -neg-bool true = false -neg-bool false = true - -conjunction-bool : bool → bool → bool -conjunction-bool true true = true -conjunction-bool true false = false -conjunction-bool false true = false -conjunction-bool false false = false - -disjunction-bool : bool → bool → bool -disjunction-bool true true = true -disjunction-bool true false = true -disjunction-bool false true = true -disjunction-bool false false = false - -implication-bool : bool → bool → bool -implication-bool true true = true -implication-bool true false = false -implication-bool false true = true -implication-bool false false = true -``` - ## Properties -### The booleans are a set - -```agda -abstract - is-prop-Eq-bool : (x y : bool) → is-prop (Eq-bool x y) - is-prop-Eq-bool true true = is-prop-unit - is-prop-Eq-bool true false = is-prop-empty - is-prop-Eq-bool false true = is-prop-empty - is-prop-Eq-bool false false = is-prop-unit - -abstract - is-set-bool : is-set bool - is-set-bool = - is-set-prop-in-id - ( Eq-bool) - ( is-prop-Eq-bool) - ( refl-Eq-bool) - ( λ x y → eq-Eq-bool) - -bool-Set : Set lzero -bool-Set = bool , is-set-bool -``` - ### The booleans have decidable equality ```agda @@ -193,44 +57,6 @@ bool-Discrete-Type : Discrete-Type lzero bool-Discrete-Type = bool , has-decidable-equality-bool ``` -### The "is true" predicate on booleans - -```agda -is-true : bool → UU lzero -is-true = _＝ true - -is-prop-is-true : (b : bool) → is-prop (is-true b) -is-prop-is-true b = is-set-bool b true - -is-true-Prop : bool → Prop lzero -is-true-Prop b = is-true b , is-prop-is-true b -``` - -### The "is false" predicate on booleans - -```agda -is-false : bool → UU lzero -is-false = _＝ false - -is-prop-is-false : (b : bool) → is-prop (is-false b) -is-prop-is-false b = is-set-bool b false - -is-false-Prop : bool → Prop lzero -is-false-Prop b = is-false b , is-prop-is-false b -``` - -### A boolean cannot be both true and false - -```agda -not-is-false-is-true : (x : bool) → is-true x → ¬ (is-false x) -not-is-false-is-true true t () -not-is-false-is-true false () f - -not-is-true-is-false : (x : bool) → is-false x → ¬ (is-true x) -not-is-true-is-false true () f -not-is-true-is-false false t () -``` - ### The type of booleans is equivalent to `Fin 2` ```agda @@ -279,17 +105,6 @@ pr1 bool-Finite-Type = bool pr2 bool-Finite-Type = is-finite-bool ``` -### Boolean negation has no fixed points - -```agda -neq-neg-bool : (b : bool) → b ≠ neg-bool b -neq-neg-bool true () -neq-neg-bool false () - -neq-neg-bool' : (b : bool) → neg-bool b ≠ b -neq-neg-bool' b = neq-neg-bool b ∘ inv -``` - ### Boolean negation is an involution ```agda @@ -309,17 +124,3 @@ equiv-neg-bool : bool ≃ bool pr1 equiv-neg-bool = neg-bool pr2 equiv-neg-bool = is-equiv-neg-bool ``` - -### The constant function `const bool b` is not an equivalence - -```agda -abstract - no-section-const-bool : (b : bool) → ¬ (section (const bool b)) - no-section-const-bool true (g , G) = neq-true-false-bool (G false) - no-section-const-bool false (g , G) = neq-false-true-bool (G true) - -abstract - is-not-equiv-const-bool : - (b : bool) → ¬ (is-equiv (const bool b)) - is-not-equiv-const-bool b e = no-section-const-bool b (section-is-equiv e) -``` diff --git a/src/foundation/diaconescus-theorem.lagda.md b/src/foundation/diaconescus-theorem.lagda.md index adcacce8cc..246899fdd2 100644 --- a/src/foundation/diaconescus-theorem.lagda.md +++ b/src/foundation/diaconescus-theorem.lagda.md @@ -44,8 +44,8 @@ We follow the proof given under Theorem 10.1.14 in {{#cite UF13}}. [suspension](synthetic-homotopy-theory.suspensions-of-propositions.md) `ΣP` is a [set](foundation-core.sets.md) with the property that `(N ＝ S) ≃ ΣP`, where `N` and `S` are the _poles_ of `ΣP`. There is a surjection from the -[booleans](foundation.booleans.md) onto the suspension `f : bool ↠ ΣP` such that -`f true ≐ N` and `f false ≐ S`. Its +[booleans](foundation-core.booleans.md) onto the suspension `f : bool ↠ ΣP` such +that `f true ≐ N` and `f false ≐ S`. Its [fiber family](foundation-core.fibers-of-maps.md) is in other words an [inhabited](foundation.inhabited-types.md) family over `ΣP`. Applying the axiom of choice to this family, we obtain a diff --git a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md index a91743a9f5..5c9d5e9e71 100644 --- a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md +++ b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md @@ -10,13 +10,13 @@ module foundation.lesser-limited-principle-of-omniscience where open import elementary-number-theory.natural-numbers open import elementary-number-theory.parity-natural-numbers -open import foundation.booleans open import foundation.dependent-pair-types open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.universal-quantification open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.fibers-of-maps open import foundation-core.propositions open import foundation-core.sets @@ -28,9 +28,9 @@ open import foundation-core.sets The {{#concept "lesser limited principle of omniscience" Agda=LLPO}} (LLPO) asserts that for any [sequence](foundation.sequences.md) of -[booleans](foundation.booleans.md) `f : ℕ → bool` such that `f n` is true for -[at most one](foundation-core.propositions.md) `n`, then either `f n` is false -for all even `n` or `f n` is false for all odd `n`. +[booleans](foundation-core.booleans.md) `f : ℕ → bool` such that `f n` is true +for [at most one](foundation-core.propositions.md) `n`, then either `f n` is +false for all even `n` or `f n` is false for all odd `n`. ```agda prop-LLPO : Prop lzero diff --git a/src/foundation/limited-principle-of-omniscience.lagda.md b/src/foundation/limited-principle-of-omniscience.lagda.md index c9a3616681..58bfd6a8d7 100644 --- a/src/foundation/limited-principle-of-omniscience.lagda.md +++ b/src/foundation/limited-principle-of-omniscience.lagda.md @@ -9,7 +9,6 @@ module foundation.limited-principle-of-omniscience where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.dependent-products-propositions @@ -19,6 +18,7 @@ open import foundation.negation open import foundation.universal-quantification open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets diff --git a/src/foundation/raising-universe-levels-booleans.lagda.md b/src/foundation/raising-universe-levels-booleans.lagda.md index 3fca40fc4d..a94fd6c0e0 100644 --- a/src/foundation/raising-universe-levels-booleans.lagda.md +++ b/src/foundation/raising-universe-levels-booleans.lagda.md @@ -7,10 +7,10 @@ module foundation.raising-universe-levels-booleans where
Imports ```agda -open import foundation.booleans open import foundation.raising-universe-levels open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.equivalences ``` diff --git a/src/foundation/type-arithmetic-booleans.lagda.md b/src/foundation/type-arithmetic-booleans.lagda.md index 5d7dfaad12..0b455a3719 100644 --- a/src/foundation/type-arithmetic-booleans.lagda.md +++ b/src/foundation/type-arithmetic-booleans.lagda.md @@ -7,10 +7,10 @@ module foundation.type-arithmetic-booleans where
Imports ```agda -open import foundation.booleans open import foundation.dependent-pair-types open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.coproduct-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/universal-property-booleans.lagda.md b/src/foundation/universal-property-booleans.lagda.md index b976f49d78..bcb23bb57a 100644 --- a/src/foundation/universal-property-booleans.lagda.md +++ b/src/foundation/universal-property-booleans.lagda.md @@ -7,12 +7,12 @@ module foundation.universal-property-booleans where
Imports ```agda -open import foundation.booleans open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/weak-limited-principle-of-omniscience.lagda.md b/src/foundation/weak-limited-principle-of-omniscience.lagda.md index bc9b213e06..abef45248f 100644 --- a/src/foundation/weak-limited-principle-of-omniscience.lagda.md +++ b/src/foundation/weak-limited-principle-of-omniscience.lagda.md @@ -9,12 +9,12 @@ module foundation.weak-limited-principle-of-omniscience where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.disjunction open import foundation.negation open import foundation.universal-quantification open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.decidable-propositions open import foundation-core.propositions open import foundation-core.sets diff --git a/src/logic/markovian-types.lagda.md b/src/logic/markovian-types.lagda.md index cdf5521276..4add56697f 100644 --- a/src/logic/markovian-types.lagda.md +++ b/src/logic/markovian-types.lagda.md @@ -9,7 +9,6 @@ module logic.markovian-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.decidable-subtypes open import foundation.dependent-pair-types open import foundation.dependent-products-propositions @@ -21,6 +20,7 @@ open import foundation.negation open import foundation.universal-quantification open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets @@ -42,8 +42,8 @@ then there is an element of `A` that is ### The predicate of being Markovian -We phrase the condition using the [type of booleans](foundation.booleans.md) so -that the predicate is small. +We phrase the condition using the +[type of booleans](foundation-core.booleans.md) so that the predicate is small. ```agda is-markovian : {l : Level} → UU l → UU l diff --git a/src/logic/markovs-principle.lagda.md b/src/logic/markovs-principle.lagda.md index 51ef1a407f..66eeefbf91 100644 --- a/src/logic/markovs-principle.lagda.md +++ b/src/logic/markovs-principle.lagda.md @@ -9,7 +9,6 @@ module logic.markovs-principle where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.decidable-subtypes open import foundation.dependent-pair-types open import foundation.disjunction @@ -20,6 +19,7 @@ open import foundation.negation open import foundation.universal-quantification open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets diff --git a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md index ec37ad84de..0d98e6c2ea 100644 --- a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md @@ -997,7 +997,7 @@ under products. **Note:** This result can also be obtained as a special case of the previous one by taking the indexing type to be the -[two-element type](foundation.booleans.md). +[two-element type](foundation-core.booleans.md). ```agda module _ diff --git a/src/primitives/characters.lagda.md b/src/primitives/characters.lagda.md index 5a1d6a930b..8b083f21ed 100644 --- a/src/primitives/characters.lagda.md +++ b/src/primitives/characters.lagda.md @@ -9,8 +9,9 @@ module primitives.characters where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.universe-levels + +open import foundation-core.booleans ```
diff --git a/src/primitives/floats.lagda.md b/src/primitives/floats.lagda.md index 7c2e16d374..68f4246d71 100644 --- a/src/primitives/floats.lagda.md +++ b/src/primitives/floats.lagda.md @@ -9,9 +9,9 @@ module primitives.floats where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.maybe open import primitives.machine-integers diff --git a/src/primitives/strings.lagda.md b/src/primitives/strings.lagda.md index 81996faa8c..cfcb24c3cf 100644 --- a/src/primitives/strings.lagda.md +++ b/src/primitives/strings.lagda.md @@ -9,10 +9,10 @@ module primitives.strings where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.dependent-pair-types open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.maybe open import lists.lists diff --git a/src/reflection/boolean-reflection.lagda.md b/src/reflection/boolean-reflection.lagda.md index 6908c83cf5..e4602783c7 100644 --- a/src/reflection/boolean-reflection.lagda.md +++ b/src/reflection/boolean-reflection.lagda.md @@ -7,10 +7,10 @@ module reflection.boolean-reflection where
Imports ```agda -open import foundation.booleans open import foundation.decidable-types open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.coproduct-types open import foundation-core.empty-types open import foundation-core.identity-types diff --git a/src/reflection/metavariables.lagda.md b/src/reflection/metavariables.lagda.md index 65baaca3e4..bb2cf558a2 100644 --- a/src/reflection/metavariables.lagda.md +++ b/src/reflection/metavariables.lagda.md @@ -9,9 +9,9 @@ module reflection.metavariables where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.identity-types open import lists.lists diff --git a/src/reflection/names.lagda.md b/src/reflection/names.lagda.md index 7e10dbdd4b..40ee6f849e 100644 --- a/src/reflection/names.lagda.md +++ b/src/reflection/names.lagda.md @@ -7,11 +7,11 @@ module reflection.names where
Imports ```agda -open import foundation.booleans open import foundation.cartesian-product-types open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.identity-types open import primitives.machine-integers @@ -46,10 +46,10 @@ primitive ## Examples -```agda +```text _ : primQNameLess (quote bool) (quote unit) ＝ true _ = refl -_ : primShowQName (quote bool) ＝ "foundation.booleans.bool" +_ : primShowQName (quote bool) ＝ "foundation-core.booleans.bool" _ = refl ``` diff --git a/src/reflection/type-checking-monad.lagda.md b/src/reflection/type-checking-monad.lagda.md index e1524ac71b..34aef27c9f 100644 --- a/src/reflection/type-checking-monad.lagda.md +++ b/src/reflection/type-checking-monad.lagda.md @@ -12,12 +12,12 @@ module reflection.type-checking-monad where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.booleans open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.booleans open import foundation-core.identity-types open import lists.lists From 12eaf6855a74b2441951fcc1e50da866b339380a Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 22:07:54 +0000 Subject: [PATCH 21/39] import optimizations reflection --- src/primitives/machine-integers.lagda.md | 2 +- src/reflection/terms.lagda.md | 2 +- src/reflection/type-checking-monad.lagda.md | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/src/primitives/machine-integers.lagda.md b/src/primitives/machine-integers.lagda.md index 84db3aa726..0eaf9e84d7 100644 --- a/src/primitives/machine-integers.lagda.md +++ b/src/primitives/machine-integers.lagda.md @@ -9,7 +9,7 @@ module primitives.machine-integers where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation-core.identity-types open import foundation.universe-levels ``` diff --git a/src/reflection/terms.lagda.md b/src/reflection/terms.lagda.md index 5a823a2be2..1a13133edc 100644 --- a/src/reflection/terms.lagda.md +++ b/src/reflection/terms.lagda.md @@ -9,7 +9,7 @@ module reflection.terms where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation-core.cartesian-product-types open import foundation.universe-levels open import lists.lists diff --git a/src/reflection/type-checking-monad.lagda.md b/src/reflection/type-checking-monad.lagda.md index 34aef27c9f..9463e40ce3 100644 --- a/src/reflection/type-checking-monad.lagda.md +++ b/src/reflection/type-checking-monad.lagda.md @@ -12,7 +12,7 @@ module reflection.type-checking-monad where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation-core.cartesian-product-types open import foundation.dependent-pair-types open import foundation.unit-type open import foundation.universe-levels From 7e89f92aa126a97da491ce44deec920a3ee8e247 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 22:08:03 +0000 Subject: [PATCH 22/39] import optimizations reflection --- src/primitives/machine-integers.lagda.md | 3 ++- src/reflection/terms.lagda.md | 3 ++- src/reflection/type-checking-monad.lagda.md | 2 +- 3 files changed, 5 insertions(+), 3 deletions(-) diff --git a/src/primitives/machine-integers.lagda.md b/src/primitives/machine-integers.lagda.md index 0eaf9e84d7..af8fed1892 100644 --- a/src/primitives/machine-integers.lagda.md +++ b/src/primitives/machine-integers.lagda.md @@ -9,8 +9,9 @@ module primitives.machine-integers where ```agda open import elementary-number-theory.natural-numbers -open import foundation-core.identity-types open import foundation.universe-levels + +open import foundation-core.identity-types ```
diff --git a/src/reflection/terms.lagda.md b/src/reflection/terms.lagda.md index 1a13133edc..2e9e9b82c3 100644 --- a/src/reflection/terms.lagda.md +++ b/src/reflection/terms.lagda.md @@ -9,9 +9,10 @@ module reflection.terms where ```agda open import elementary-number-theory.natural-numbers -open import foundation-core.cartesian-product-types open import foundation.universe-levels +open import foundation-core.cartesian-product-types + open import lists.lists open import primitives.strings diff --git a/src/reflection/type-checking-monad.lagda.md b/src/reflection/type-checking-monad.lagda.md index 9463e40ce3..bcd6fe6e34 100644 --- a/src/reflection/type-checking-monad.lagda.md +++ b/src/reflection/type-checking-monad.lagda.md @@ -12,12 +12,12 @@ module reflection.type-checking-monad where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation-core.cartesian-product-types open import foundation.dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import foundation-core.booleans +open import foundation-core.cartesian-product-types open import foundation-core.identity-types open import lists.lists From 7c34b94912cc72c56424b71ade774aac0d2c43ae Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 22:18:46 +0000 Subject: [PATCH 23/39] optimize imports `lists.lists` --- ...fundamental-theorem-of-arithmetic.lagda.md | 1 + src/lists.lagda.md | 1 + src/lists/equality-lists.lagda.md | 147 ++++++++++++++++++ src/lists/functoriality-lists.lagda.md | 1 + src/lists/lists-discrete-types.lagda.md | 1 + src/lists/lists.lagda.md | 130 +--------------- 6 files changed, 157 insertions(+), 124 deletions(-) create mode 100644 src/lists/equality-lists.lagda.md diff --git a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md index 9b880f9d1a..770e230cd9 100644 --- a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md +++ b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md @@ -42,6 +42,7 @@ open import foundation.unit-type open import foundation.universe-levels open import lists.concatenation-lists +open import lists.equality-lists open import lists.functoriality-lists open import lists.lists open import lists.permutation-lists diff --git a/src/lists.lagda.md b/src/lists.lagda.md index 0263108995..612d0e6270 100644 --- a/src/lists.lagda.md +++ b/src/lists.lagda.md @@ -7,6 +7,7 @@ module lists where open import lists.arrays public open import lists.concatenation-lists public +open import lists.equality-lists public open import lists.flattening-lists public open import lists.functoriality-lists public open import lists.lists public diff --git a/src/lists/equality-lists.lagda.md b/src/lists/equality-lists.lagda.md new file mode 100644 index 0000000000..f5dfc68872 --- /dev/null +++ b/src/lists/equality-lists.lagda.md @@ -0,0 +1,147 @@ +# Equality of lists + +```agda +module lists.equality-lists where +``` + +
Imports + +```agda +open import elementary-number-theory.natural-numbers + +open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-identifications-functions +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.dependent-pair-types +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.negation +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type +open import foundation.sets +open import foundation.torsorial-type-families +open import foundation.truncated-types +open import foundation.truncation-levels +open import foundation.unit-type +open import foundation.universe-levels + +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.maybe +``` + +
+ +## Properties + +### Characterizing the identity type of lists + +```agda +Eq-list : {l1 : Level} {A : UU l1} → list A → list A → UU l1 +Eq-list {l1} nil nil = raise-unit l1 +Eq-list {l1} nil (cons x l') = raise-empty l1 +Eq-list {l1} (cons x l) nil = raise-empty l1 +Eq-list {l1} (cons x l) (cons x' l') = (Id x x') × Eq-list l l' + +refl-Eq-list : {l1 : Level} {A : UU l1} (l : list A) → Eq-list l l +refl-Eq-list nil = raise-star +refl-Eq-list (cons x l) = pair refl (refl-Eq-list l) + +Eq-eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) → Id l l' → Eq-list l l' +Eq-eq-list l .l refl = refl-Eq-list l + +eq-Eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) → Eq-list l l' → Id l l' +eq-Eq-list nil nil (map-raise star) = refl +eq-Eq-list nil (cons x l') (map-raise f) = ex-falso f +eq-Eq-list (cons x l) nil (map-raise f) = ex-falso f +eq-Eq-list (cons x l) (cons .x l') (pair refl e) = + ap (cons x) (eq-Eq-list l l' e) + +square-eq-Eq-list : + {l1 : Level} {A : UU l1} {x : A} {l l' : list A} (p : Id l l') → + Id + ( Eq-eq-list (cons x l) (cons x l') (ap (cons x) p)) + ( pair refl (Eq-eq-list l l' p)) +square-eq-Eq-list refl = refl + +is-section-eq-Eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) (e : Eq-list l l') → + Id (Eq-eq-list l l' (eq-Eq-list l l' e)) e +is-section-eq-Eq-list nil nil e = eq-is-contr is-contr-raise-unit +is-section-eq-Eq-list nil (cons x l') e = ex-falso (is-empty-raise-empty e) +is-section-eq-Eq-list (cons x l) nil e = ex-falso (is-empty-raise-empty e) +is-section-eq-Eq-list (cons x l) (cons .x l') (pair refl e) = + ( square-eq-Eq-list (eq-Eq-list l l' e)) ∙ + ( eq-pair-eq-fiber (is-section-eq-Eq-list l l' e)) + +eq-Eq-refl-Eq-list : + {l1 : Level} {A : UU l1} (l : list A) → + Id (eq-Eq-list l l (refl-Eq-list l)) refl +eq-Eq-refl-Eq-list nil = refl +eq-Eq-refl-Eq-list (cons x l) = ap² (cons x) (eq-Eq-refl-Eq-list l) + +is-retraction-eq-Eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) (p : Id l l') → + Id (eq-Eq-list l l' (Eq-eq-list l l' p)) p +is-retraction-eq-Eq-list nil .nil refl = refl +is-retraction-eq-Eq-list (cons x l) .(cons x l) refl = + eq-Eq-refl-Eq-list (cons x l) + +is-equiv-Eq-eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) → is-equiv (Eq-eq-list l l') +is-equiv-Eq-eq-list l l' = + is-equiv-is-invertible + ( eq-Eq-list l l') + ( is-section-eq-Eq-list l l') + ( is-retraction-eq-Eq-list l l') + +equiv-Eq-list : + {l1 : Level} {A : UU l1} (l l' : list A) → Id l l' ≃ Eq-list l l' +equiv-Eq-list l l' = + pair (Eq-eq-list l l') (is-equiv-Eq-eq-list l l') + +is-torsorial-Eq-list : + {l1 : Level} {A : UU l1} (l : list A) → + is-torsorial (Eq-list l) +is-torsorial-Eq-list {A = A} l = + is-contr-equiv' + ( Σ (list A) (Id l)) + ( equiv-tot (equiv-Eq-list l)) + ( is-torsorial-Id l) + +is-trunc-Eq-list : + (k : 𝕋) {l : Level} {A : UU l} → is-trunc (succ-𝕋 (succ-𝕋 k)) A → + (l l' : list A) → is-trunc (succ-𝕋 k) (Eq-list l l') +is-trunc-Eq-list k H nil nil = + is-trunc-is-contr (succ-𝕋 k) is-contr-raise-unit +is-trunc-Eq-list k H nil (cons x l') = + is-trunc-is-empty k is-empty-raise-empty +is-trunc-Eq-list k H (cons x l) nil = + is-trunc-is-empty k is-empty-raise-empty +is-trunc-Eq-list k H (cons x l) (cons y l') = + is-trunc-product (succ-𝕋 k) (H x y) (is-trunc-Eq-list k H l l') + +is-trunc-list : + (k : 𝕋) {l : Level} {A : UU l} → is-trunc (succ-𝕋 (succ-𝕋 k)) A → + is-trunc (succ-𝕋 (succ-𝕋 k)) (list A) +is-trunc-list k H l l' = + is-trunc-equiv + ( succ-𝕋 k) + ( Eq-list l l') + ( equiv-Eq-list l l') + ( is-trunc-Eq-list k H l l') + +is-set-list : + {l : Level} {A : UU l} → is-set A → is-set (list A) +is-set-list = is-trunc-list neg-two-𝕋 + +list-Set : {l : Level} → Set l → Set l +list-Set A = pair (list (type-Set A)) (is-set-list (is-set-type-Set A)) +``` diff --git a/src/lists/functoriality-lists.lagda.md b/src/lists/functoriality-lists.lagda.md index 5fca45b262..233992c6a0 100644 --- a/src/lists/functoriality-lists.lagda.md +++ b/src/lists/functoriality-lists.lagda.md @@ -25,6 +25,7 @@ open import linear-algebra.vectors open import lists.arrays open import lists.concatenation-lists +open import lists.equality-lists open import lists.lists ``` diff --git a/src/lists/lists-discrete-types.lagda.md b/src/lists/lists-discrete-types.lagda.md index 1675657885..64cecc520a 100644 --- a/src/lists/lists-discrete-types.lagda.md +++ b/src/lists/lists-discrete-types.lagda.md @@ -21,6 +21,7 @@ open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels +open import lists.equality-lists open import lists.lists ``` diff --git a/src/lists/lists.lagda.md b/src/lists/lists.lagda.md index 78993660a9..e9a1e4c030 100644 --- a/src/lists/lists.lagda.md +++ b/src/lists/lists.lagda.md @@ -9,30 +9,19 @@ module lists.lists where ```agda open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions -open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.negation -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type -open import foundation.sets -open import foundation.torsorial-type-families -open import foundation.truncated-types -open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.cartesian-product-types +open import foundation-core.coproduct-types +open import foundation-core.empty-types +open import foundation-core.equivalences +open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.maybe +open import foundation-core.negation ```
@@ -163,113 +152,6 @@ tail-is-nonnil-list l p = pr2 (pr1 (is-cons-is-nonnil-list l p)) ``` -### Characterizing the identity type of lists - -```agda -Eq-list : {l1 : Level} {A : UU l1} → list A → list A → UU l1 -Eq-list {l1} nil nil = raise-unit l1 -Eq-list {l1} nil (cons x l') = raise-empty l1 -Eq-list {l1} (cons x l) nil = raise-empty l1 -Eq-list {l1} (cons x l) (cons x' l') = (Id x x') × Eq-list l l' - -refl-Eq-list : {l1 : Level} {A : UU l1} (l : list A) → Eq-list l l -refl-Eq-list nil = raise-star -refl-Eq-list (cons x l) = pair refl (refl-Eq-list l) - -Eq-eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) → Id l l' → Eq-list l l' -Eq-eq-list l .l refl = refl-Eq-list l - -eq-Eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) → Eq-list l l' → Id l l' -eq-Eq-list nil nil (map-raise star) = refl -eq-Eq-list nil (cons x l') (map-raise f) = ex-falso f -eq-Eq-list (cons x l) nil (map-raise f) = ex-falso f -eq-Eq-list (cons x l) (cons .x l') (pair refl e) = - ap (cons x) (eq-Eq-list l l' e) - -square-eq-Eq-list : - {l1 : Level} {A : UU l1} {x : A} {l l' : list A} (p : Id l l') → - Id - ( Eq-eq-list (cons x l) (cons x l') (ap (cons x) p)) - ( pair refl (Eq-eq-list l l' p)) -square-eq-Eq-list refl = refl - -is-section-eq-Eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) (e : Eq-list l l') → - Id (Eq-eq-list l l' (eq-Eq-list l l' e)) e -is-section-eq-Eq-list nil nil e = eq-is-contr is-contr-raise-unit -is-section-eq-Eq-list nil (cons x l') e = ex-falso (is-empty-raise-empty e) -is-section-eq-Eq-list (cons x l) nil e = ex-falso (is-empty-raise-empty e) -is-section-eq-Eq-list (cons x l) (cons .x l') (pair refl e) = - ( square-eq-Eq-list (eq-Eq-list l l' e)) ∙ - ( eq-pair-eq-fiber (is-section-eq-Eq-list l l' e)) - -eq-Eq-refl-Eq-list : - {l1 : Level} {A : UU l1} (l : list A) → - Id (eq-Eq-list l l (refl-Eq-list l)) refl -eq-Eq-refl-Eq-list nil = refl -eq-Eq-refl-Eq-list (cons x l) = ap² (cons x) (eq-Eq-refl-Eq-list l) - -is-retraction-eq-Eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) (p : Id l l') → - Id (eq-Eq-list l l' (Eq-eq-list l l' p)) p -is-retraction-eq-Eq-list nil .nil refl = refl -is-retraction-eq-Eq-list (cons x l) .(cons x l) refl = - eq-Eq-refl-Eq-list (cons x l) - -is-equiv-Eq-eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) → is-equiv (Eq-eq-list l l') -is-equiv-Eq-eq-list l l' = - is-equiv-is-invertible - ( eq-Eq-list l l') - ( is-section-eq-Eq-list l l') - ( is-retraction-eq-Eq-list l l') - -equiv-Eq-list : - {l1 : Level} {A : UU l1} (l l' : list A) → Id l l' ≃ Eq-list l l' -equiv-Eq-list l l' = - pair (Eq-eq-list l l') (is-equiv-Eq-eq-list l l') - -is-torsorial-Eq-list : - {l1 : Level} {A : UU l1} (l : list A) → - is-torsorial (Eq-list l) -is-torsorial-Eq-list {A = A} l = - is-contr-equiv' - ( Σ (list A) (Id l)) - ( equiv-tot (equiv-Eq-list l)) - ( is-torsorial-Id l) - -is-trunc-Eq-list : - (k : 𝕋) {l : Level} {A : UU l} → is-trunc (succ-𝕋 (succ-𝕋 k)) A → - (l l' : list A) → is-trunc (succ-𝕋 k) (Eq-list l l') -is-trunc-Eq-list k H nil nil = - is-trunc-is-contr (succ-𝕋 k) is-contr-raise-unit -is-trunc-Eq-list k H nil (cons x l') = - is-trunc-is-empty k is-empty-raise-empty -is-trunc-Eq-list k H (cons x l) nil = - is-trunc-is-empty k is-empty-raise-empty -is-trunc-Eq-list k H (cons x l) (cons y l') = - is-trunc-product (succ-𝕋 k) (H x y) (is-trunc-Eq-list k H l l') - -is-trunc-list : - (k : 𝕋) {l : Level} {A : UU l} → is-trunc (succ-𝕋 (succ-𝕋 k)) A → - is-trunc (succ-𝕋 (succ-𝕋 k)) (list A) -is-trunc-list k H l l' = - is-trunc-equiv - ( succ-𝕋 k) - ( Eq-list l l') - ( equiv-Eq-list l l') - ( is-trunc-Eq-list k H l l') - -is-set-list : - {l : Level} {A : UU l} → is-set A → is-set (list A) -is-set-list = is-trunc-list neg-two-𝕋 - -list-Set : {l : Level} → Set l → Set l -list-Set A = pair (list (type-Set A)) (is-set-list (is-set-type-Set A)) -``` - ### The length operation behaves well with respect to the other list operations ```agda From 4588624202a8c6bbb1dbbe95bd9cd1a97f1e6d31 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 22:40:13 +0000 Subject: [PATCH 24/39] imports equality integers --- .../eisenstein-integers.lagda.md | 1 + .../gaussian-integers.lagda.md | 1 + .../equality-integers.lagda.md | 14 ++++++ .../group-of-integers.lagda.md | 7 +++ .../integers.lagda.md | 48 ++++++------------- .../negative-integers.lagda.md | 1 + .../nonnegative-integers.lagda.md | 1 + .../nonpositive-integers.lagda.md | 1 + .../positive-integers.lagda.md | 1 + .../relatively-prime-integers.lagda.md | 1 + src/group-theory/e8-lattice.lagda.md | 1 + src/lists/concatenation-lists.lagda.md | 1 + src/lists/equality-lists.lagda.md | 2 + src/set-theory/countable-sets.lagda.md | 1 + ...types-equipped-with-endomorphisms.lagda.md | 5 +- .../infinite-cyclic-types.lagda.md | 1 + .../universal-cover-circle.lagda.md | 1 + 17 files changed, 52 insertions(+), 36 deletions(-) diff --git a/src/commutative-algebra/eisenstein-integers.lagda.md b/src/commutative-algebra/eisenstein-integers.lagda.md index e7bdaf0e62..d0120575cd 100644 --- a/src/commutative-algebra/eisenstein-integers.lagda.md +++ b/src/commutative-algebra/eisenstein-integers.lagda.md @@ -10,6 +10,7 @@ module commutative-algebra.eisenstein-integers where open import commutative-algebra.commutative-rings open import elementary-number-theory.addition-integers +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.multiplication-integers diff --git a/src/commutative-algebra/gaussian-integers.lagda.md b/src/commutative-algebra/gaussian-integers.lagda.md index c4b999395d..2cbe987830 100644 --- a/src/commutative-algebra/gaussian-integers.lagda.md +++ b/src/commutative-algebra/gaussian-integers.lagda.md @@ -11,6 +11,7 @@ open import commutative-algebra.commutative-rings open import elementary-number-theory.addition-integers open import elementary-number-theory.difference-integers +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.multiplication-integers diff --git a/src/elementary-number-theory/equality-integers.lagda.md b/src/elementary-number-theory/equality-integers.lagda.md index 0638b0bb24..0ff7538a18 100644 --- a/src/elementary-number-theory/equality-integers.lagda.md +++ b/src/elementary-number-theory/equality-integers.lagda.md @@ -17,6 +17,7 @@ open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.discrete-types open import foundation.empty-types +open import foundation.equality-coproduct-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-types @@ -24,6 +25,7 @@ open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types open import foundation.propositions open import foundation.set-truncations +open import foundation.sets open import foundation.torsorial-type-families open import foundation.unit-type open import foundation.universe-levels @@ -92,6 +94,18 @@ pr1 ℤ-Discrete-Type = ℤ pr2 ℤ-Discrete-Type = has-decidable-equality-ℤ ``` +### The type of integers is a set + +```agda +abstract + is-set-ℤ : is-set ℤ + is-set-ℤ = is-set-coproduct is-set-ℕ (is-set-coproduct is-set-unit is-set-ℕ) + +ℤ-Set : Set lzero +pr1 ℤ-Set = ℤ +pr2 ℤ-Set = is-set-ℤ +``` + ### The type of integers is its own set truncation ```agda diff --git a/src/elementary-number-theory/group-of-integers.lagda.md b/src/elementary-number-theory/group-of-integers.lagda.md index 358f281d2d..e1c12a108d 100644 --- a/src/elementary-number-theory/group-of-integers.lagda.md +++ b/src/elementary-number-theory/group-of-integers.lagda.md @@ -8,6 +8,7 @@ module elementary-number-theory.group-of-integers where ```agda open import elementary-number-theory.addition-integers +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import foundation.dependent-pair-types @@ -16,6 +17,8 @@ open import foundation.universe-levels open import group-theory.abelian-groups open import group-theory.groups open import group-theory.semigroups + +open import structured-types.types-equipped-with-endomorphisms ```
@@ -28,6 +31,10 @@ forms a group. ## Definition ```agda +ℤ-Type-With-Endomorphism : Type-With-Endomorphism lzero +pr1 ℤ-Type-With-Endomorphism = ℤ +pr2 ℤ-Type-With-Endomorphism = succ-ℤ + ℤ-Semigroup : Semigroup lzero pr1 ℤ-Semigroup = ℤ-Set pr1 (pr2 ℤ-Semigroup) = add-ℤ diff --git a/src/elementary-number-theory/integers.lagda.md b/src/elementary-number-theory/integers.lagda.md index 2c1ea175d6..6b801f4787 100644 --- a/src/elementary-number-theory/integers.lagda.md +++ b/src/elementary-number-theory/integers.lagda.md @@ -7,30 +7,26 @@ module elementary-number-theory.integers where
Imports ```agda -open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import foundation-core.coproduct-types +open import foundation-core.embeddings +open import foundation-core.empty-types +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.injective-maps +open import foundation-core.negation +open import foundation-core.propositions +open import foundation-core.retractions +open import foundation-core.sections +open import foundation-core.sets ```
@@ -136,10 +132,6 @@ pred-ℤ (inl x) = inl (succ-ℕ x) pred-ℤ (inr (inl star)) = inl zero-ℕ pred-ℤ (inr (inr zero-ℕ)) = inr (inl star) pred-ℤ (inr (inr (succ-ℕ x))) = inr (inr x) - -ℤ-Type-With-Endomorphism : Type-With-Endomorphism lzero -pr1 ℤ-Type-With-Endomorphism = ℤ -pr2 ℤ-Type-With-Endomorphism = succ-ℤ ``` ### The negative of an integer @@ -153,18 +145,6 @@ neg-ℤ (inr (inr x)) = inl x ## Properties -### The type of integers is a set - -```agda -abstract - is-set-ℤ : is-set ℤ - is-set-ℤ = is-set-coproduct is-set-ℕ (is-set-coproduct is-set-unit is-set-ℕ) - -ℤ-Set : Set lzero -pr1 ℤ-Set = ℤ -pr2 ℤ-Set = is-set-ℤ -``` - ### The successor and predecessor functions on ℤ are mutual inverses ```agda @@ -214,7 +194,7 @@ abstract is-injective-succ-ℤ {x} {y} p = inv (is-retraction-pred-ℤ x) ∙ ap pred-ℤ p ∙ is-retraction-pred-ℤ y - has-no-fixed-points-succ-ℤ : (x : ℤ) → succ-ℤ x ≠ x + has-no-fixed-points-succ-ℤ : (x : ℤ) → ¬ (succ-ℤ x ＝ x) has-no-fixed-points-succ-ℤ (inl zero-ℕ) () has-no-fixed-points-succ-ℤ (inl (succ-ℕ x)) () has-no-fixed-points-succ-ℤ (inr (inl star)) () diff --git a/src/elementary-number-theory/negative-integers.lagda.md b/src/elementary-number-theory/negative-integers.lagda.md index a549a3ae37..86dd90ed11 100644 --- a/src/elementary-number-theory/negative-integers.lagda.md +++ b/src/elementary-number-theory/negative-integers.lagda.md @@ -7,6 +7,7 @@ module elementary-number-theory.negative-integers where
Imports ```agda +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import elementary-number-theory.nonzero-integers diff --git a/src/elementary-number-theory/nonnegative-integers.lagda.md b/src/elementary-number-theory/nonnegative-integers.lagda.md index 6f9d446eca..d9c2b50561 100644 --- a/src/elementary-number-theory/nonnegative-integers.lagda.md +++ b/src/elementary-number-theory/nonnegative-integers.lagda.md @@ -7,6 +7,7 @@ module elementary-number-theory.nonnegative-integers where
Imports ```agda +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers diff --git a/src/elementary-number-theory/nonpositive-integers.lagda.md b/src/elementary-number-theory/nonpositive-integers.lagda.md index 423216dbe2..e5a31ad753 100644 --- a/src/elementary-number-theory/nonpositive-integers.lagda.md +++ b/src/elementary-number-theory/nonpositive-integers.lagda.md @@ -7,6 +7,7 @@ module elementary-number-theory.nonpositive-integers where
Imports ```agda +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers diff --git a/src/elementary-number-theory/positive-integers.lagda.md b/src/elementary-number-theory/positive-integers.lagda.md index d122134e21..9070e78e0c 100644 --- a/src/elementary-number-theory/positive-integers.lagda.md +++ b/src/elementary-number-theory/positive-integers.lagda.md @@ -7,6 +7,7 @@ module elementary-number-theory.positive-integers where
Imports ```agda +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import elementary-number-theory.nonzero-integers diff --git a/src/elementary-number-theory/relatively-prime-integers.lagda.md b/src/elementary-number-theory/relatively-prime-integers.lagda.md index 56ab84992a..a3719203ab 100644 --- a/src/elementary-number-theory/relatively-prime-integers.lagda.md +++ b/src/elementary-number-theory/relatively-prime-integers.lagda.md @@ -8,6 +8,7 @@ module elementary-number-theory.relatively-prime-integers where ```agda open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.equality-integers open import elementary-number-theory.greatest-common-divisor-integers open import elementary-number-theory.integers open import elementary-number-theory.relatively-prime-natural-numbers diff --git a/src/group-theory/e8-lattice.lagda.md b/src/group-theory/e8-lattice.lagda.md index 004bb360a5..85b7ccc933 100644 --- a/src/group-theory/e8-lattice.lagda.md +++ b/src/group-theory/e8-lattice.lagda.md @@ -7,6 +7,7 @@ module group-theory.e8-lattice where
Imports ```agda +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import foundation.equality-coproduct-types diff --git a/src/lists/concatenation-lists.lagda.md b/src/lists/concatenation-lists.lagda.md index 1face70497..3471f3bcc5 100644 --- a/src/lists/concatenation-lists.lagda.md +++ b/src/lists/concatenation-lists.lagda.md @@ -19,6 +19,7 @@ open import foundation.universe-levels open import group-theory.monoids +open import lists.equality-lists open import lists.lists ``` diff --git a/src/lists/equality-lists.lagda.md b/src/lists/equality-lists.lagda.md index f5dfc68872..b2345f4801 100644 --- a/src/lists/equality-lists.lagda.md +++ b/src/lists/equality-lists.lagda.md @@ -33,6 +33,8 @@ open import foundation.universe-levels open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.maybe + +open import lists.lists ```
diff --git a/src/set-theory/countable-sets.lagda.md b/src/set-theory/countable-sets.lagda.md index 023911e269..ab92a803d5 100644 --- a/src/set-theory/countable-sets.lagda.md +++ b/src/set-theory/countable-sets.lagda.md @@ -7,6 +7,7 @@ module set-theory.countable-sets where
Imports ```agda +open import elementary-number-theory.equality-integers open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers diff --git a/src/structured-types/types-equipped-with-endomorphisms.lagda.md b/src/structured-types/types-equipped-with-endomorphisms.lagda.md index 198947f526..beffcc9d59 100644 --- a/src/structured-types/types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/types-equipped-with-endomorphisms.lagda.md @@ -8,11 +8,12 @@ module structured-types.types-equipped-with-endomorphisms where ```agda open import foundation.dependent-pair-types -open import foundation.endomorphisms -open import foundation.function-types open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.endomorphisms +open import foundation-core.function-types ```
diff --git a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md index 0714fee4d0..c651ce59fa 100644 --- a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md @@ -8,6 +8,7 @@ module synthetic-homotopy-theory.infinite-cyclic-types where ```agda open import elementary-number-theory.addition-integers +open import elementary-number-theory.group-of-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers diff --git a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md index 2d69b1844c..55603d9eb5 100644 --- a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.universal-cover-circle where
Imports ```agda +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.nonzero-integers open import elementary-number-theory.universal-property-integers From 2cfd6ff04bdc785414771ee4f4fe79a5533f59cd Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 22:44:31 +0000 Subject: [PATCH 25/39] imports reflection --- src/reflection/definitions.lagda.md | 19 +++++++++---------- src/reflection/names.lagda.md | 2 +- 2 files changed, 10 insertions(+), 11 deletions(-) diff --git a/src/reflection/definitions.lagda.md b/src/reflection/definitions.lagda.md index bea9353b8b..b95792be7d 100644 --- a/src/reflection/definitions.lagda.md +++ b/src/reflection/definitions.lagda.md @@ -10,7 +10,6 @@ module reflection.definitions where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.empty-types @@ -83,15 +82,15 @@ _ : ( visible-Argument-Agda (constructor-Term-Agda (quote zero-ℕ) nil))) _ = refl -_ : - {l : Level} {A : UU l} → - quoteTerm (type-trunc-Prop A) ＝ - definition-Term-Agda - ( quote type-trunc-Prop) - ( cons - ( hidden-Argument-Agda (variable-Term-Agda 1 nil)) - ( unit-list (visible-Argument-Agda (variable-Term-Agda 0 nil)))) -_ = refl +-- _ : +-- {l : Level} {A : UU l} → +-- quoteTerm (type-trunc-Prop A) ＝ +-- definition-Term-Agda +-- ( quote type-trunc-Prop) +-- ( cons +-- ( hidden-Argument-Agda (variable-Term-Agda 1 nil)) +-- ( unit-list (visible-Argument-Agda (variable-Term-Agda 0 nil)))) +-- _ = refl ``` ### Lambda abstractions diff --git a/src/reflection/names.lagda.md b/src/reflection/names.lagda.md index 40ee6f849e..b42117fb12 100644 --- a/src/reflection/names.lagda.md +++ b/src/reflection/names.lagda.md @@ -7,11 +7,11 @@ module reflection.names where
Imports ```agda -open import foundation.cartesian-product-types open import foundation.unit-type open import foundation.universe-levels open import foundation-core.booleans +open import foundation-core.cartesian-product-types open import foundation-core.identity-types open import primitives.machine-integers From 1fbc6035d227cf2294bad718236f5b3dcac08796 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 23:03:25 +0000 Subject: [PATCH 26/39] imports addition natural numbers --- .../addition-natural-numbers.lagda.md | 31 +++++-------------- 1 file changed, 8 insertions(+), 23 deletions(-) diff --git a/src/elementary-number-theory/addition-natural-numbers.lagda.md b/src/elementary-number-theory/addition-natural-numbers.lagda.md index 2bb395a863..cbb2406c1b 100644 --- a/src/elementary-number-theory/addition-natural-numbers.lagda.md +++ b/src/elementary-number-theory/addition-natural-numbers.lagda.md @@ -7,21 +7,19 @@ module elementary-number-theory.addition-natural-numbers where
Imports ```agda -open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps open import foundation.interchange-law -open import foundation.negated-equality -open import foundation.sets + +open import foundation-core.cartesian-product-types +open import foundation-core.empty-types +open import foundation-core.function-types +open import foundation-core.identity-types +open import foundation-core.injective-maps +open import foundation-core.negation ```
@@ -154,19 +152,6 @@ abstract ( commutative-add-ℕ x k ∙ (p ∙ commutative-add-ℕ k y)) ``` -### Addition by a fixed element on either side is an embedding - -```agda -abstract - is-emb-left-add-ℕ : (x : ℕ) → is-emb (x +ℕ_) - is-emb-left-add-ℕ x = - is-emb-is-injective is-set-ℕ (is-injective-left-add-ℕ x) - - is-emb-right-add-ℕ : (x : ℕ) → is-emb (_+ℕ x) - is-emb-right-add-ℕ x = - is-emb-is-injective is-set-ℕ (is-injective-right-add-ℕ x) -``` - ### `x + y ＝ 0` if and only if both `x` and `y` are `0` ```agda @@ -197,7 +182,7 @@ abstract ```agda abstract neq-add-ℕ : - (m n : ℕ) → m ≠ m +ℕ (succ-ℕ n) + (m n : ℕ) → ¬ (m ＝ m +ℕ (succ-ℕ n)) neq-add-ℕ (succ-ℕ m) n p = neq-add-ℕ m n ( ( is-injective-succ-ℕ p) ∙ From 3941908cb60a3ad80f0a453eabcadc2c1a2f9683 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 23:08:12 +0000 Subject: [PATCH 27/39] imports multiplication natural numbers --- .../divisibility-natural-numbers.lagda.md | 5 ++++- .../multiplication-natural-numbers.lagda.md | 21 ++++++------------- 2 files changed, 10 insertions(+), 16 deletions(-) diff --git a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md index 9bf81abc22..a7879e5365 100644 --- a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md +++ b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md @@ -9,6 +9,7 @@ module elementary-number-theory.divisibility-natural-numbers where ```agda open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers @@ -19,6 +20,7 @@ open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.empty-types open import foundation.identity-types +open import foundation.injective-maps open import foundation.logical-equivalences open import foundation.negated-equality open import foundation.negation @@ -114,7 +116,8 @@ eq-quotient-div-eq-div-ℕ x y z n e H I = ```agda is-prop-div-ℕ : (k x : ℕ) → is-nonzero-ℕ k → is-prop (div-ℕ k x) -is-prop-div-ℕ k x f = is-prop-map-is-emb (is-emb-right-mul-ℕ k f) x +is-prop-div-ℕ k x f = + is-prop-map-is-emb (is-emb-is-injective is-set-ℕ (is-injective-right-mul-ℕ k f)) x ``` ### The divisibility relation is a partial order on the natural numbers diff --git a/src/elementary-number-theory/multiplication-natural-numbers.lagda.md b/src/elementary-number-theory/multiplication-natural-numbers.lagda.md index b725a1a851..c6b37aa41d 100644 --- a/src/elementary-number-theory/multiplication-natural-numbers.lagda.md +++ b/src/elementary-number-theory/multiplication-natural-numbers.lagda.md @@ -8,18 +8,17 @@ module elementary-number-theory.multiplication-natural-numbers where ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types -open import foundation.injective-maps open import foundation.interchange-law -open import foundation.negated-equality + +open import foundation-core.coproduct-types +open import foundation-core.identity-types +open import foundation-core.injective-maps +open import foundation-core.negation ```
@@ -193,14 +192,6 @@ is-injective-left-mul-ℕ k H p with is-successor-is-nonzero-ℕ H ... | pair l refl = is-injective-left-mul-succ-ℕ l p -is-emb-left-mul-ℕ : (x : ℕ) → is-nonzero-ℕ x → is-emb (x *ℕ_) -is-emb-left-mul-ℕ x H = - is-emb-is-injective is-set-ℕ (is-injective-left-mul-ℕ x H) - -is-emb-right-mul-ℕ : (x : ℕ) → is-nonzero-ℕ x → is-emb (_*ℕ x) -is-emb-right-mul-ℕ x H = - is-emb-is-injective is-set-ℕ (is-injective-right-mul-ℕ x H) - is-nonzero-mul-ℕ : (x y : ℕ) → is-nonzero-ℕ x → is-nonzero-ℕ y → is-nonzero-ℕ (x *ℕ y) is-nonzero-mul-ℕ x y H K p = @@ -250,7 +241,7 @@ is-one-mul-ℕ : is-one-mul-ℕ .1 .1 refl refl = refl neq-mul-ℕ : - (m n : ℕ) → succ-ℕ m ≠ (succ-ℕ m *ℕ (succ-ℕ (succ-ℕ n))) + (m n : ℕ) → ¬ (succ-ℕ m ＝ succ-ℕ m *ℕ (succ-ℕ (succ-ℕ n))) neq-mul-ℕ m n p = neq-add-ℕ ( succ-ℕ m) From f402d8e7f598831a852d69072ec438a3dcdb1568 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Thu, 20 Mar 2025 23:19:55 +0000 Subject: [PATCH 28/39] depostulate funext --- scripts/add_funext_parameter.py | 17 +- src/category-theory.lagda.md | 325 +++---- .../adjunctions-large-categories.lagda.md | 23 +- .../adjunctions-large-precategories.lagda.md | 19 +- .../anafunctors-categories.lagda.md | 15 +- .../anafunctors-precategories.lagda.md | 19 +- .../augmented-simplex-category.lagda.md | 21 +- src/category-theory/categories.lagda.md | 39 +- ...rs-from-small-to-large-categories.lagda.md | 37 +- .../category-of-functors.lagda.md | 29 +- .../category-of-maps-categories.lagda.md | 43 +- ...ps-from-small-to-large-categories.lagda.md | 37 +- ...-morphisms-in-large-precategories.lagda.md | 11 +- ...res-of-morphisms-in-precategories.lagda.md | 11 +- ...ares-of-morphisms-in-set-magmoids.lagda.md | 11 +- ...les-of-morphisms-in-precategories.lagda.md | 13 +- ...gles-of-morphisms-in-set-magmoids.lagda.md | 11 +- .../complete-precategories.lagda.md | 17 +- ...ations-on-binary-families-of-sets.lagda.md | 24 +- .../cones-precategories.lagda.md | 64 +- ...nservative-functors-precategories.lagda.md | 17 +- .../constant-functors.lagda.md | 35 +- .../copresheaf-categories.lagda.md | 61 +- .../coproducts-in-precategories.lagda.md | 21 +- src/category-theory/cores-categories.lagda.md | 25 +- .../cores-precategories.lagda.md | 35 +- .../coslice-precategories.lagda.md | 15 +- ...ion-operations-over-precategories.lagda.md | 31 +- .../dependent-products-of-categories.lagda.md | 32 +- ...dent-products-of-large-categories.lagda.md | 30 +- ...t-products-of-large-precategories.lagda.md | 29 +- ...pendent-products-of-precategories.lagda.md | 31 +- .../discrete-categories.lagda.md | 15 +- .../displayed-precategories.lagda.md | 39 +- .../embedding-maps-precategories.lagda.md | 17 +- .../embeddings-precategories.lagda.md | 17 +- .../endomorphisms-in-categories.lagda.md | 19 +- .../endomorphisms-in-precategories.lagda.md | 17 +- ...imorphisms-in-large-precategories.lagda.md | 17 +- .../equivalences-of-categories.lagda.md | 13 +- ...uivalences-of-large-precategories.lagda.md | 13 +- .../equivalences-of-precategories.lagda.md | 15 +- ...-fibers-of-functors-precategories.lagda.md | 13 +- ...-injective-functors-precategories.lagda.md | 13 +- ...surjective-functors-precategories.lagda.md | 17 +- ...exponential-objects-precategories.lagda.md | 15 +- ...ensions-of-functors-precategories.lagda.md | 13 +- .../faithful-functors-precategories.lagda.md | 23 +- .../faithful-maps-precategories.lagda.md | 27 +- .../full-functors-precategories.lagda.md | 17 +- .../full-large-subcategories.lagda.md | 25 +- .../full-large-subprecategories.lagda.md | 29 +- .../full-maps-precategories.lagda.md | 19 +- .../full-subcategories.lagda.md | 35 +- .../full-subprecategories.lagda.md | 41 +- ...y-faithful-functors-precategories.lagda.md | 39 +- ...fully-faithful-maps-precategories.lagda.md | 25 +- .../function-categories.lagda.md | 27 +- .../function-precategories.lagda.md | 25 +- .../functors-categories.lagda.md | 27 +- ...rs-from-small-to-large-categories.lagda.md | 25 +- ...from-small-to-large-precategories.lagda.md | 25 +- .../functors-large-categories.lagda.md | 13 +- .../functors-large-precategories.lagda.md | 13 +- .../functors-nonunital-precategories.lagda.md | 21 +- .../functors-precategories.lagda.md | 31 +- .../functors-set-magmoids.lagda.md | 27 +- src/category-theory/gaunt-categories.lagda.md | 41 +- src/category-theory/groupoids.lagda.md | 41 +- ...ansformations-large-precategories.lagda.md | 17 +- .../indiscrete-precategories.lagda.md | 37 +- src/category-theory/initial-category.lagda.md | 31 +- .../initial-objects-large-categories.lagda.md | 11 +- ...itial-objects-large-precategories.lagda.md | 11 +- .../initial-objects-precategories.lagda.md | 15 +- .../isomorphism-induction-categories.lagda.md | 27 +- ...omorphism-induction-precategories.lagda.md | 21 +- .../isomorphisms-in-categories.lagda.md | 25 +- .../isomorphisms-in-large-categories.lagda.md | 29 +- ...omorphisms-in-large-precategories.lagda.md | 33 +- .../isomorphisms-in-precategories.lagda.md | 31 +- .../isomorphisms-in-subprecategories.lagda.md | 19 +- src/category-theory/large-categories.lagda.md | 25 +- .../large-function-categories.lagda.md | 23 +- .../large-function-precategories.lagda.md | 23 +- .../large-precategories.lagda.md | 19 +- .../large-subcategories.lagda.md | 11 +- .../large-subprecategories.lagda.md | 17 +- .../limits-precategories.lagda.md | 40 +- src/category-theory/maps-categories.lagda.md | 19 +- ...ps-from-small-to-large-categories.lagda.md | 19 +- ...from-small-to-large-precategories.lagda.md | 19 +- .../maps-precategories.lagda.md | 31 +- .../maps-set-magmoids.lagda.md | 13 +- .../monads-on-categories.lagda.md | 19 +- .../monads-on-precategories.lagda.md | 17 +- ...omorphisms-in-large-precategories.lagda.md | 17 +- ...-isomorphisms-functors-categories.lagda.md | 31 +- ...isms-functors-large-precategories.lagda.md | 17 +- ...omorphisms-functors-precategories.lagda.md | 31 +- ...ural-isomorphisms-maps-categories.lagda.md | 31 +- ...l-isomorphisms-maps-precategories.lagda.md | 31 +- ...ural-numbers-object-precategories.lagda.md | 17 +- ...ansformations-functors-categories.lagda.md | 27 +- ...rs-from-small-to-large-categories.lagda.md | 27 +- ...from-small-to-large-precategories.lagda.md | 29 +- ...mations-functors-large-categories.lagda.md | 13 +- ...ions-functors-large-precategories.lagda.md | 15 +- ...formations-functors-precategories.lagda.md | 29 +- ...l-transformations-maps-categories.lagda.md | 27 +- ...from-small-to-large-precategories.lagda.md | 36 +- ...ransformations-maps-precategories.lagda.md | 34 +- .../nonunital-precategories.lagda.md | 23 +- .../one-object-precategories.lagda.md | 21 +- .../opposite-categories.lagda.md | 27 +- .../opposite-large-precategories.lagda.md | 21 +- .../opposite-precategories.lagda.md | 23 +- .../opposite-preunivalent-categories.lagda.md | 29 +- 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...resentable-functors-precategories.lagda.md | 32 +- .../representing-arrow-category.lagda.md | 25 +- ...ions-functors-cores-precategories.lagda.md | 25 +- .../right-extensions-precategories.lagda.md | 52 +- ...ight-kan-extensions-precategories.lagda.md | 19 +- .../rigid-objects-categories.lagda.md | 13 +- .../rigid-objects-precategories.lagda.md | 15 +- src/category-theory/set-magmoids.lagda.md | 17 +- .../sieves-in-categories.lagda.md | 13 +- src/category-theory/simplex-category.lagda.md | 21 +- .../slice-precategories.lagda.md | 45 +- ...surjective-functors-precategories.lagda.md | 45 +- .../strict-categories.lagda.md | 33 +- .../strongly-preunivalent-categories.lagda.md | 35 +- ...ructure-equivalences-set-magmoids.lagda.md | 27 +- src/category-theory/subcategories.lagda.md | 49 +- src/category-theory/subprecategories.lagda.md | 31 +- .../subterminal-precategories.lagda.md | 39 +- .../terminal-category.lagda.md | 41 +- .../terminal-objects-precategories.lagda.md | 15 +- .../wide-subcategories.lagda.md | 49 +- .../wide-subprecategories.lagda.md | 35 +- .../yoneda-lemma-categories.lagda.md | 23 +- .../yoneda-lemma-precategories.lagda.md | 33 +- src/commutative-algebra.lagda.md | 117 +-- ...inomial-theorem-commutative-rings.lagda.md | 29 +- ...ial-theorem-commutative-semirings.lagda.md | 27 +- .../boolean-rings.lagda.md | 11 +- .../category-of-commutative-rings.lagda.md | 15 +- .../commutative-rings.lagda.md | 47 +- .../commutative-semirings.lagda.md | 21 +- ...endent-products-commutative-rings.lagda.md | 23 +- ...nt-products-commutative-semirings.lagda.md | 21 +- .../discrete-fields.lagda.md | 11 +- .../eisenstein-integers.lagda.md | 29 +- .../euclidean-domains.lagda.md | 55 +- .../full-ideals-commutative-rings.lagda.md | 27 +- .../function-commutative-rings.lagda.md | 21 +- .../function-commutative-semirings.lagda.md | 19 +- .../gaussian-integers.lagda.md | 31 +- ...groups-of-units-commutative-rings.lagda.md | 39 +- .../homomorphisms-commutative-rings.lagda.md | 31 +- ...momorphisms-commutative-semirings.lagda.md | 23 +- .../ideals-commutative-rings.lagda.md | 29 +- .../ideals-commutative-semirings.lagda.md | 17 +- ...ated-by-subsets-commutative-rings.lagda.md | 23 +- ...les-of-elements-commutative-rings.lagda.md | 23 +- .../integral-domains.lagda.md | 49 +- ...sections-ideals-commutative-rings.lagda.md | 23 +- ...-radical-ideals-commutative-rings.lagda.md | 39 +- ...rtible-elements-commutative-rings.lagda.md | 17 +- .../isomorphisms-commutative-rings.lagda.md | 33 +- .../joins-ideals-commutative-rings.lagda.md | 31 +- ...-radical-ideals-commutative-rings.lagda.md | 37 +- .../local-commutative-rings.lagda.md | 17 +- ...les-of-elements-commutative-rings.lagda.md | 13 +- .../nilradical-commutative-rings.lagda.md | 25 +- ...nilradicals-commutative-semirings.lagda.md | 17 +- ...poset-of-ideals-commutative-rings.lagda.md | 21 +- ...-radical-ideals-commutative-rings.lagda.md | 29 +- ...ers-of-elements-commutative-rings.lagda.md | 15 +- ...of-elements-commutative-semirings.lagda.md | 13 +- .../precategory-of-commutative-rings.lagda.md | 17 +- ...category-of-commutative-semirings.lagda.md | 17 +- .../prime-ideals-commutative-rings.lagda.md | 29 +- .../products-commutative-rings.lagda.md | 23 +- ...products-ideals-commutative-rings.lagda.md | 25 +- ...-radical-ideals-commutative-rings.lagda.md | 29 +- ...roducts-subsets-commutative-rings.lagda.md | 19 +- .../radical-ideals-commutative-rings.lagda.md | 23 +- ...ated-by-subsets-commutative-rings.lagda.md | 23 +- ...icals-of-ideals-commutative-rings.lagda.md | 41 +- .../subsets-commutative-rings.lagda.md | 23 +- .../subsets-commutative-semirings.lagda.md | 19 +- .../sums-commutative-rings.lagda.md | 27 +- .../sums-commutative-semirings.lagda.md | 25 +- ...cture-isomorphisms-abelian-groups.lagda.md | 27 +- .../trivial-commutative-rings.lagda.md | 27 +- .../zariski-locale.lagda.md | 19 +- .../zariski-topology.lagda.md | 19 +- src/domain-theory.lagda.md | 25 +- .../directed-complete-posets.lagda.md | 25 +- .../directed-families-posets.lagda.md | 33 +- ...int-theorem-omega-complete-posets.lagda.md | 53 +- ...leenes-fixed-point-theorem-posets.lagda.md | 45 +- .../omega-complete-posets.lagda.md | 31 +- ...inuous-maps-omega-complete-posets.lagda.md | 51 +- .../omega-continuous-maps-posets.lagda.md | 47 +- ...indexing-directed-families-posets.lagda.md | 35 +- .../scott-continuous-maps-posets.lagda.md | 45 +- src/elementary-number-theory.lagda.md | 329 +++---- .../absolute-value-integers.lagda.md | 23 +- .../addition-integer-fractions.lagda.md | 17 +- .../addition-integers.lagda.md | 29 +- ...on-positive-and-negative-integers.lagda.md | 27 +- .../addition-rational-numbers.lagda.md | 27 +- ...dditive-group-of-rational-numbers.lagda.md | 19 +- ...medean-property-integer-fractions.lagda.md | 29 +- .../archimedean-property-integers.lagda.md | 29 +- ...himedean-property-natural-numbers.lagda.md | 15 +- ...roperty-positive-rational-numbers.lagda.md | 25 +- ...imedean-property-rational-numbers.lagda.md | 27 +- .../arithmetic-functions.lagda.md | 11 +- .../based-induction-natural-numbers.lagda.md | 13 +- ...-strong-induction-natural-numbers.lagda.md | 29 +- .../bell-numbers.lagda.md | 15 +- .../bezouts-lemma-integers.lagda.md | 43 +- .../bezouts-lemma-natural-numbers.lagda.md | 61 +- .../binomial-coefficients.lagda.md | 25 +- .../binomial-theorem-integers.lagda.md | 27 +- .../binomial-theorem-natural-numbers.lagda.md | 23 +- ...bounded-sums-arithmetic-functions.lagda.md | 21 +- .../catalan-numbers.lagda.md | 19 +- .../cofibonacci.lagda.md | 29 +- .../collatz-bijection.lagda.md | 17 +- .../collatz-conjecture.lagda.md | 11 +- ...ative-semiring-of-natural-numbers.lagda.md | 13 +- .../conatural-numbers.lagda.md | 19 +- .../congruence-integers.lagda.md | 27 +- .../congruence-natural-numbers.lagda.md | 21 +- ...tion-difference-integer-fractions.lagda.md | 21 +- .../cubes-natural-numbers.lagda.md | 11 +- ...ecidable-dependent-function-types.lagda.md | 9 +- .../decidable-total-order-integers.lagda.md | 15 +- ...dable-total-order-natural-numbers.lagda.md | 25 +- ...able-total-order-rational-numbers.lagda.md | 15 +- ...total-order-standard-finite-types.lagda.md | 15 +- .../decidable-types.lagda.md | 23 +- .../difference-integers.lagda.md | 11 +- .../difference-rational-numbers.lagda.md | 13 +- .../dirichlet-convolution.lagda.md | 21 +- .../distance-integers.lagda.md | 23 +- .../distance-natural-numbers.lagda.md | 17 +- .../divisibility-integers.lagda.md | 47 +- .../divisibility-modular-arithmetic.lagda.md | 21 +- .../divisibility-natural-numbers.lagda.md | 35 +- ...ivisibility-standard-finite-types.lagda.md | 21 +- .../equality-conatural-numbers.lagda.md | 47 +- .../equality-integers.lagda.md | 37 +- .../equality-natural-numbers.lagda.md | 31 +- .../equality-rational-numbers.lagda.md | 25 +- .../euclid-mullin-sequence.lagda.md | 19 +- 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...lower-upper-dedekind-real-numbers.lagda.md | 41 +- .../negation-real-numbers.lagda.md | 31 +- ...sing-universe-levels-real-numbers.lagda.md | 45 +- ...ional-lower-dedekind-real-numbers.lagda.md | 21 +- .../rational-real-numbers.lagda.md | 41 +- ...ional-upper-dedekind-real-numbers.lagda.md | 21 +- .../similarity-real-numbers.lagda.md | 17 +- .../strict-inequality-real-numbers.lagda.md | 47 +- .../upper-dedekind-real-numbers.lagda.md | 37 +- src/reflection.lagda.md | 15 +- src/reflection/boolean-reflection.lagda.md | 9 +- src/reflection/fixity.lagda.md | 9 +- src/reflection/group-solver.lagda.md | 19 +- src/reflection/precategory-solver.lagda.md | 13 +- src/ring-theory.lagda.md | 157 ++-- ...additive-orders-of-elements-rings.lagda.md | 25 +- src/ring-theory/algebras-rings.lagda.md | 15 +- .../binomial-theorem-rings.lagda.md | 27 +- .../binomial-theorem-semirings.lagda.md | 29 +- .../category-of-cyclic-rings.lagda.md | 25 +- src/ring-theory/category-of-rings.lagda.md | 15 +- 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| 41 +- src/ring-theory/ideals-semirings.lagda.md | 19 +- .../idempotent-elements-rings.lagda.md | 15 +- src/ring-theory/initial-rings.lagda.md | 13 +- ...teger-multiples-of-elements-rings.lagda.md | 29 +- .../intersections-ideals-rings.lagda.md | 19 +- .../intersections-ideals-semirings.lagda.md | 15 +- .../invariant-basis-property-rings.lagda.md | 17 +- .../invertible-elements-rings.lagda.md | 27 +- src/ring-theory/isomorphisms-rings.lagda.md | 53 +- src/ring-theory/joins-ideals-rings.lagda.md | 27 +- .../joins-left-ideals-rings.lagda.md | 27 +- .../joins-right-ideals-rings.lagda.md | 27 +- .../kernels-of-ring-homomorphisms.lagda.md | 21 +- ...ideals-generated-by-subsets-rings.lagda.md | 49 +- src/ring-theory/left-ideals-rings.lagda.md | 23 +- src/ring-theory/local-rings.lagda.md | 17 +- src/ring-theory/localizations-rings.lagda.md | 31 +- src/ring-theory/modules-rings.lagda.md | 25 +- .../multiples-of-elements-rings.lagda.md | 15 +- src/ring-theory/nil-ideals-rings.lagda.md | 19 +- 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+- src/ring-theory/semirings.lagda.md | 23 +- src/ring-theory/subsets-rings.lagda.md | 21 +- src/ring-theory/subsets-semirings.lagda.md | 19 +- src/ring-theory/sums-rings.lagda.md | 25 +- src/ring-theory/sums-semirings.lagda.md | 25 +- ...along-isomorphisms-abelian-groups.lagda.md | 21 +- src/ring-theory/trivial-rings.lagda.md | 23 +- src/set-theory.lagda.md | 27 +- src/set-theory/baire-space.lagda.md | 25 +- src/set-theory/cantor-space.lagda.md | 33 +- .../cantors-diagonal-argument.lagda.md | 30 +- src/set-theory/cardinalities.lagda.md | 30 +- src/set-theory/countable-sets.lagda.md | 55 +- src/set-theory/cumulative-hierarchy.lagda.md | 45 +- src/set-theory/infinite-sets.lagda.md | 15 +- src/set-theory/russells-paradox.lagda.md | 31 +- src/set-theory/uncountable-sets.lagda.md | 15 +- src/species.lagda.md | 101 +- ...tesian-exponents-species-of-types.lagda.md | 9 +- ...rtesian-products-species-of-types.lagda.md | 21 +- ...-species-of-types-in-subuniverses.lagda.md | 49 +- 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.../precomposition-pointed-maps.lagda.md | 9 +- .../sets-equipped-with-automorphisms.lagda.md | 15 +- .../small-pointed-types.lagda.md | 21 +- ...mmetric-elements-involutive-types.lagda.md | 11 +- .../symmetric-h-spaces.lagda.md | 13 +- ...ansposition-pointed-span-diagrams.lagda.md | 11 +- ...types-equipped-with-automorphisms.lagda.md | 13 +- ...types-equipped-with-endomorphisms.lagda.md | 11 +- .../uniform-pointed-homotopies.lagda.md | 28 +- ...sal-property-pointed-equivalences.lagda.md | 13 +- ...ointed-2-homotopies-concatenation.lagda.md | 23 +- ...ng-pointed-homotopies-composition.lagda.md | 23 +- .../wild-category-of-pointed-types.lagda.md | 37 +- src/structured-types/wild-groups.lagda.md | 9 +- src/structured-types/wild-loops.lagda.md | 19 +- src/structured-types/wild-monoids.lagda.md | 11 +- .../wild-quasigroups.lagda.md | 13 +- src/structured-types/wild-semigroups.lagda.md | 11 +- src/synthetic-category-theory.lagda.md | 19 +- ...one-diagrams-synthetic-categories.lagda.md | 11 +- .../cospans-synthetic-categories.lagda.md | 11 +- ...equivalences-synthetic-categories.lagda.md | 9 +- ...ble-functors-synthetic-categories.lagda.md | 11 +- .../pullbacks-synthetic-categories.lagda.md | 15 +- src/synthetic-homotopy-theory.lagda.md | 269 +++--- .../0-acyclic-maps.lagda.md | 15 +- .../0-acyclic-types.lagda.md | 23 +- .../1-acyclic-types.lagda.md | 38 +- .../acyclic-maps.lagda.md | 79 +- .../acyclic-types.lagda.md | 19 +- ...y-of-connected-set-bundles-circle.lagda.md | 17 +- .../cavallos-trick.lagda.md | 21 +- src/synthetic-homotopy-theory/circle.lagda.md | 59 +- .../cocartesian-morphisms-arrows.lagda.md | 19 +- ...cones-under-pointed-span-diagrams.lagda.md | 17 +- ...cocones-under-sequential-diagrams.lagda.md | 31 +- .../cocones-under-spans.lagda.md | 20 +- .../codiagonals-of-maps.lagda.md | 29 +- .../coequalizers.lagda.md | 21 +- .../cofibers-of-maps.lagda.md | 25 +- .../cofibers-of-pointed-maps.lagda.md | 15 +- ...cocones-under-sequential-diagrams.lagda.md | 53 +- 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.../descent-circle-function-types.lagda.md | 40 +- .../descent-circle-subtypes.lagda.md | 31 +- .../descent-circle.lagda.md | 40 +- ...a-equivalence-types-over-pushouts.lagda.md | 49 +- ...data-function-types-over-pushouts.lagda.md | 51 +- ...data-identity-types-over-pushouts.lagda.md | 21 +- .../descent-data-pushouts.lagda.md | 15 +- .../descent-data-sequential-colimits.lagda.md | 21 +- .../descent-property-pushouts.lagda.md | 42 +- ...cent-property-sequential-colimits.lagda.md | 31 +- .../double-loop-spaces.lagda.md | 23 +- .../eckmann-hilton-argument.lagda.md | 31 +- .../equifibered-sequential-diagrams.lagda.md | 13 +- ...-equivalences-sequential-diagrams.lagda.md | 21 +- ...-under-equivalences-double-arrows.lagda.md | 23 +- ...ces-dependent-sequential-diagrams.lagda.md | 29 +- ...quivalences-descent-data-pushouts.lagda.md | 31 +- .../equivalences-sequential-diagrams.lagda.md | 31 +- .../families-descent-data-pushouts.lagda.md | 19 +- ...-descent-data-sequential-colimits.lagda.md | 19 +- .../flattening-lemma-coequalizers.lagda.md | 31 +- .../flattening-lemma-pushouts.lagda.md | 46 +- ...ttening-lemma-sequential-colimits.lagda.md | 39 +- .../free-loops.lagda.md | 19 +- .../functoriality-loop-spaces.lagda.md | 29 +- ...functoriality-sequential-colimits.lagda.md | 40 +- .../functoriality-suspensions.lagda.md | 31 +- .../groups-of-loops-in-1-types.lagda.md | 19 +- .../hatchers-acyclic-type.lagda.md | 45 +- .../homotopy-groups.lagda.md | 17 +- ...ity-systems-descent-data-pushouts.lagda.md | 57 +- .../induction-principle-pushouts.lagda.md | 15 +- ...infinite-complex-projective-space.lagda.md | 13 +- .../infinite-cyclic-types.lagda.md | 50 +- .../interval-type.lagda.md | 22 +- .../iterated-loop-spaces.lagda.md | 13 +- ...ated-suspensions-of-pointed-types.lagda.md | 11 +- .../join-powers-of-types.lagda.md | 13 +- .../joins-of-maps.lagda.md | 21 +- .../joins-of-types.lagda.md | 37 +- .../left-half-smash-products.lagda.md | 11 +- .../loop-homotopy-circle.lagda.md | 19 +- .../loop-spaces.lagda.md | 19 +- .../maps-of-prespectra.lagda.md | 23 +- .../mere-spheres.lagda.md | 13 +- ...der-morphisms-sequential-diagrams.lagda.md | 17 +- ...rks-under-morphisms-double-arrows.lagda.md | 17 +- ...sms-dependent-sequential-diagrams.lagda.md | 13 +- .../morphisms-descent-data-circle.lagda.md | 13 +- .../morphisms-descent-data-pushouts.lagda.md | 29 +- .../morphisms-sequential-diagrams.lagda.md | 31 +- .../multiplication-circle.lagda.md | 20 +- ...cones-under-pointed-span-diagrams.lagda.md | 27 +- .../plus-principle.lagda.md | 13 +- .../powers-of-loops.lagda.md | 23 +- .../premanifolds.lagda.md | 21 +- .../prespectra.lagda.md | 19 +- .../pullback-property-pushouts.lagda.md | 19 +- .../pushout-products.lagda.md | 23 +- .../pushouts-of-pointed-types.lagda.md | 15 +- .../pushouts.lagda.md | 43 +- .../recursion-principle-pushouts.lagda.md | 15 +- .../retracts-of-sequential-diagrams.lagda.md | 29 +- .../rewriting-pushouts.lagda.md | 17 +- .../sections-descent-circle.lagda.md | 39 +- .../sections-descent-data-pushouts.lagda.md | 47 +- .../sequential-colimits.lagda.md | 35 +- .../sequential-diagrams.lagda.md | 11 +- .../sequentially-compact-types.lagda.md | 15 +- .../shifts-sequential-diagrams.lagda.md | 39 +- .../smash-products-of-pointed-types.lagda.md | 33 +- .../spectra.lagda.md | 27 +- .../sphere-prespectrum.lagda.md | 13 +- .../spheres.lagda.md | 17 +- .../suspension-prespectra.lagda.md | 19 +- .../suspension-structures.lagda.md | 36 +- .../suspensions-of-pointed-types.lagda.md | 17 +- .../suspensions-of-propositions.lagda.md | 45 +- .../suspensions-of-types.lagda.md | 72 +- .../tangent-spheres.lagda.md | 19 +- ...ones-families-sequential-diagrams.lagda.md | 33 +- .../total-sequential-diagrams.lagda.md | 29 +- .../triple-loop-spaces.lagda.md | 17 +- .../truncated-acyclic-maps.lagda.md | 83 +- .../truncated-acyclic-types.lagda.md | 21 +- .../universal-cover-circle.lagda.md | 60 +- .../universal-property-circle.lagda.md | 34 +- .../universal-property-coequalizers.lagda.md | 37 +- .../universal-property-pushouts.lagda.md | 47 +- ...rsal-property-sequential-colimits.lagda.md | 50 +- ...erty-suspensions-of-pointed-types.lagda.md | 31 +- .../universal-property-suspensions.lagda.md | 23 +- .../wedges-of-pointed-types.lagda.md | 25 +- .../zigzags-sequential-diagrams.lagda.md | 35 +- src/trees.lagda.md | 111 +-- .../algebras-polynomial-endofunctors.lagda.md | 9 +- src/trees/bases-directed-trees.lagda.md | 35 +- .../bases-enriched-directed-trees.lagda.md | 29 +- src/trees/bounded-multisets.lagda.md | 19 +- .../coalgebra-of-directed-trees.lagda.md | 15 +- ...lgebra-of-enriched-directed-trees.lagda.md | 15 +- ...oalgebras-polynomial-endofunctors.lagda.md | 9 +- src/trees/combinator-directed-trees.lagda.md | 51 +- ...ombinator-enriched-directed-trees.lagda.md | 33 +- src/trees/directed-trees.lagda.md | 47 +- ...oalgebras-polynomial-endofunctors.lagda.md | 15 +- .../elementhood-relation-w-types.lagda.md | 15 +- src/trees/empty-multisets.lagda.md | 19 +- src/trees/enriched-directed-trees.lagda.md | 29 +- .../equivalences-directed-trees.lagda.md | 35 +- ...ivalences-enriched-directed-trees.lagda.md | 42 +- src/trees/extensional-w-types.lagda.md | 41 +- src/trees/fibers-directed-trees.lagda.md | 25 +- .../fibers-enriched-directed-trees.lagda.md | 25 +- src/trees/full-binary-trees.lagda.md | 11 +- ...riality-combinator-directed-trees.lagda.md | 25 +- ...functoriality-fiber-directed-tree.lagda.md | 23 +- src/trees/functoriality-w-types.lagda.md | 37 +- src/trees/hereditary-w-types.lagda.md | 20 +- src/trees/induction-w-types.lagda.md | 22 +- src/trees/inequality-w-types.lagda.md | 17 +- src/trees/lower-types-w-types.lagda.md | 13 +- ...-algebras-polynomial-endofunctors.lagda.md | 27 +- ...oalgebras-polynomial-endofunctors.lagda.md | 27 +- src/trees/morphisms-directed-trees.lagda.md | 33 +- ...morphisms-enriched-directed-trees.lagda.md | 21 +- ...dexed-dependent-products-of-types.lagda.md | 11 +- src/trees/multisets.lagda.md | 15 +- src/trees/planar-binary-trees.lagda.md | 15 +- src/trees/plane-trees.lagda.md | 25 +- src/trees/polynomial-endofunctors.lagda.md | 21 +- ...ng-universe-levels-directed-trees.lagda.md | 23 +- src/trees/ranks-of-elements-w-types.lagda.md | 27 +- .../rooted-morphisms-directed-trees.lagda.md | 29 +- ...morphisms-enriched-directed-trees.lagda.md | 21 +- src/trees/rooted-quasitrees.lagda.md | 13 +- src/trees/rooted-undirected-trees.lagda.md | 17 +- src/trees/small-multisets.lagda.md | 33 +- src/trees/submultisets.lagda.md | 13 +- src/trees/transitive-multisets.lagda.md | 11 +- ...oalgebras-polynomial-endofunctors.lagda.md | 59 +- ...ying-trees-of-elements-of-w-types.lagda.md | 57 +- src/trees/undirected-trees.lagda.md | 33 +- src/trees/universal-multiset.lagda.md | 25 +- src/trees/w-type-of-natural-numbers.lagda.md | 26 +- src/trees/w-type-of-propositions.lagda.md | 23 +- src/trees/w-types.lagda.md | 46 +- src/type-theories.lagda.md | 25 +- .../dependent-type-theories.lagda.md | 19 +- .../fibered-dependent-type-theories.lagda.md | 13 +- ...pes-precategories-with-attributes.lagda.md | 13 +- ...types-precategories-with-families.lagda.md | 13 +- .../precategories-with-attributes.lagda.md | 29 +- .../precategories-with-families.lagda.md | 19 +- .../sections-dependent-type-theories.lagda.md | 13 +- .../simple-type-theories.lagda.md | 17 +- .../unityped-type-theories.lagda.md | 15 +- src/univalent-combinatorics.lagda.md | 179 ++-- .../2-element-decidable-subtypes.lagda.md | 72 +- .../2-element-subtypes.lagda.md | 47 +- .../2-element-types.lagda.md | 77 +- .../binomial-types.lagda.md | 79 +- .../bracelets.lagda.md | 11 +- .../cartesian-product-types.lagda.md | 51 +- .../classical-finite-types.lagda.md | 17 +- .../complements-isolated-elements.lagda.md | 23 +- .../coproduct-types.lagda.md | 42 +- .../counting-decidable-subtypes.lagda.md | 51 +- .../counting-dependent-pair-types.lagda.md | 49 +- .../counting-maybe.lagda.md | 13 +- src/univalent-combinatorics/counting.lagda.md | 37 +- src/univalent-combinatorics/cubes.lagda.md | 11 +- .../cycle-partitions.lagda.md | 13 +- ...ime-decomposition-natural-numbers.lagda.md | 43 +- .../cyclic-finite-types.lagda.md | 59 +- .../de-morgans-law.lagda.md | 33 +- ...ecidable-dependent-function-types.lagda.md | 33 +- .../decidable-dependent-pair-types.lagda.md | 23 +- .../decidable-equivalence-relations.lagda.md | 51 +- .../decidable-propositions.lagda.md | 25 +- .../decidable-subtypes.lagda.md | 43 +- .../dedekind-finite-sets.lagda.md | 15 +- .../dependent-function-types.lagda.md | 39 +- .../dependent-pair-types.lagda.md | 53 +- .../discrete-sigma-decompositions.lagda.md | 23 +- ...t-truncation-over-finite-products.lagda.md | 62 +- .../double-counting.lagda.md | 15 +- .../embeddings-standard-finite-types.lagda.md | 27 +- .../embeddings.lagda.md | 33 +- .../equality-finite-types.lagda.md | 21 +- .../equality-standard-finite-types.lagda.md | 43 +- .../equivalences-cubes.lagda.md | 25 +- ...quivalences-standard-finite-types.lagda.md | 27 +- .../equivalences.lagda.md | 17 +- .../ferrers-diagrams.lagda.md | 27 +- .../fibers-of-maps.lagda.md | 49 +- .../finite-choice.lagda.md | 49 +- .../finite-types.lagda.md | 61 +- ...initely-many-connected-components.lagda.md | 43 +- .../finitely-presented-types.lagda.md | 31 +- .../function-types.lagda.md | 31 +- .../image-of-maps.lagda.md | 27 +- .../inequality-types-with-counting.lagda.md | 21 +- .../inhabited-finite-types.lagda.md | 29 +- .../injective-maps.lagda.md | 19 +- .../involution-standard-finite-types.lagda.md | 15 +- .../isotopies-latin-squares.lagda.md | 13 +- .../kuratowski-finite-sets.lagda.md | 27 +- .../latin-squares.lagda.md | 9 +- .../locally-finite-types.lagda.md | 51 +- .../main-classes-of-latin-hypercubes.lagda.md | 39 +- .../main-classes-of-latin-squares.lagda.md | 21 +- src/univalent-combinatorics/maybe.lagda.md | 11 +- .../necklaces.lagda.md | 26 +- ...tations-complete-undirected-graph.lagda.md | 91 +- .../orientations-cubes.lagda.md | 23 +- .../partitions.lagda.md | 35 +- .../petri-nets.lagda.md | 11 +- .../pi-finite-types.lagda.md | 21 +- .../pigeonhole-principle.lagda.md | 47 +- .../quotients-finite-types.lagda.md | 15 +- .../ramsey-theory.lagda.md | 17 +- .../repetitions-of-values.lagda.md | 37 +- .../retracts-of-finite-types.lagda.md | 35 +- .../riffle-shuffles.lagda.md | 23 +- .../sequences-finite-types.lagda.md | 41 +- .../set-quotients-of-index-two.lagda.md | 39 +- .../sigma-decompositions.lagda.md | 49 +- ...ing-element-standard-finite-types.lagda.md | 21 +- .../small-types.lagda.md | 15 +- .../standard-finite-pruned-trees.lagda.md | 9 +- .../standard-finite-trees.lagda.md | 19 +- .../standard-finite-types.lagda.md | 57 +- .../steiner-systems.lagda.md | 13 +- .../steiner-triple-systems.lagda.md | 9 +- .../sums-of-natural-numbers.lagda.md | 19 +- .../surjective-maps.lagda.md | 41 +- .../symmetric-difference.lagda.md | 27 +- .../trivial-sigma-decompositions.lagda.md | 25 +- .../type-duality.lagda.md | 39 +- .../unbounded-pi-finite-types.lagda.md | 47 +- .../unions-subtypes.lagda.md | 27 +- ...al-property-standard-finite-types.lagda.md | 36 +- .../untruncated-pi-finite-types.lagda.md | 92 +- src/universal-algebra.lagda.md | 29 +- ...bstract-equations-over-signatures.lagda.md | 13 +- .../algebraic-theories.lagda.md | 11 +- .../algebraic-theory-of-groups.lagda.md | 30 +- .../algebras-of-theories.lagda.md | 23 +- src/universal-algebra/congruences.lagda.md | 23 +- .../homomorphisms-of-algebras.lagda.md | 19 +- src/universal-algebra/kernels.lagda.md | 27 +- .../models-of-signatures.lagda.md | 13 +- .../quotient-algebras.lagda.md | 43 +- src/universal-algebra/signatures.lagda.md | 13 +- .../terms-over-signatures.lagda.md | 25 +- src/wild-category-theory.lagda.md | 23 +- ...oherent-large-omega-precategories.lagda.md | 11 +- ...n-noncoherent-omega-precategories.lagda.md | 9 +- ...oherent-large-omega-precategories.lagda.md | 31 +- ...s-noncoherent-omega-precategories.lagda.md | 23 +- ...oherent-large-omega-precategories.lagda.md | 21 +- ...s-noncoherent-omega-precategories.lagda.md | 15 +- ...oherent-large-omega-precategories.lagda.md | 29 +- .../noncoherent-omega-precategories.lagda.md | 25 +- 2097 files changed, 32398 insertions(+), 22015 deletions(-) diff --git a/scripts/add_funext_parameter.py b/scripts/add_funext_parameter.py index 078f9f42f3..c71172b522 100644 --- a/scripts/add_funext_parameter.py +++ b/scripts/add_funext_parameter.py @@ -68,13 +68,18 @@ def modify_file_content(file_path, module_name, dependent_modules): # Add funext parameter to module declaration if needed if not has_funext_param: - if "where" in line: - # If there's a 'where' clause, put parameters before it - updated_line = re.sub(r'(\s+where)', f" {FUNEXT_PARAM}\\1", line) + # Extract module name and any existing parameters/declarations + module_name_match = re.match(r'^module\s+([^\s\(]+)', line) + if module_name_match: + module_name = module_name_match.group(1) + # Create multi-line declaration with indentation + updated_lines.append("module") + updated_lines.append(" " + module_name) + updated_lines.append(" " + FUNEXT_PARAM) + updated_lines.append(" where") else: - # Otherwise, add at the end - updated_line = line.rstrip() + f" {FUNEXT_PARAM} where" - updated_lines.append(updated_line) + # Fallback if we can't parse the module name correctly + updated_lines.append(line) else: updated_lines.append(line) else: diff --git a/src/category-theory.lagda.md b/src/category-theory.lagda.md index 5d426bb25d..b8f906a0d5 100644 --- a/src/category-theory.lagda.md +++ b/src/category-theory.lagda.md @@ -11,165 +11,170 @@ ## Modules in the category theory namespace ```agda -module category-theory where +open import foundation.function-extensionality-axiom -open import category-theory.adjunctions-large-categories public -open import category-theory.adjunctions-large-precategories public -open import category-theory.anafunctors-categories public -open import category-theory.anafunctors-precategories public -open import category-theory.augmented-simplex-category public -open import category-theory.categories public -open import category-theory.category-of-functors public -open import category-theory.category-of-functors-from-small-to-large-categories public -open import category-theory.category-of-maps-categories public -open import category-theory.category-of-maps-from-small-to-large-categories public -open import category-theory.commuting-squares-of-morphisms-in-large-precategories public -open import category-theory.commuting-squares-of-morphisms-in-precategories public -open import category-theory.commuting-squares-of-morphisms-in-set-magmoids public -open import category-theory.commuting-triangles-of-morphisms-in-precategories public -open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids public -open import category-theory.complete-precategories public -open import category-theory.composition-operations-on-binary-families-of-sets public -open import category-theory.cones-precategories public -open import category-theory.conservative-functors-precategories public -open import category-theory.constant-functors public -open import category-theory.copresheaf-categories public -open import category-theory.coproducts-in-precategories public -open import category-theory.cores-categories public -open import category-theory.cores-precategories public -open import category-theory.coslice-precategories public -open import category-theory.dependent-composition-operations-over-precategories public -open import category-theory.dependent-products-of-categories public -open import category-theory.dependent-products-of-large-categories public -open import category-theory.dependent-products-of-large-precategories public -open import category-theory.dependent-products-of-precategories public -open import category-theory.discrete-categories public -open import category-theory.displayed-precategories public -open import category-theory.embedding-maps-precategories public -open import category-theory.embeddings-precategories public -open import category-theory.endomorphisms-in-categories public -open import category-theory.endomorphisms-in-precategories public -open import category-theory.epimorphisms-in-large-precategories public -open import category-theory.equivalences-of-categories public -open import category-theory.equivalences-of-large-precategories public -open import category-theory.equivalences-of-precategories public -open import category-theory.essential-fibers-of-functors-precategories public -open import category-theory.essentially-injective-functors-precategories public -open import category-theory.essentially-surjective-functors-precategories public -open import category-theory.exponential-objects-precategories public -open import category-theory.extensions-of-functors-precategories public -open import category-theory.faithful-functors-precategories public -open import category-theory.faithful-maps-precategories public -open import category-theory.full-functors-precategories public -open import category-theory.full-large-subcategories public -open import category-theory.full-large-subprecategories public -open import category-theory.full-maps-precategories public -open import category-theory.full-subcategories public -open import category-theory.full-subprecategories public -open import category-theory.fully-faithful-functors-precategories public -open import category-theory.fully-faithful-maps-precategories public -open import category-theory.function-categories public -open import category-theory.function-precategories public -open import category-theory.functors-categories public -open import category-theory.functors-from-small-to-large-categories public -open import category-theory.functors-from-small-to-large-precategories public -open import category-theory.functors-large-categories public -open import category-theory.functors-large-precategories public -open import category-theory.functors-nonunital-precategories public -open import category-theory.functors-precategories public -open import category-theory.functors-set-magmoids public -open import category-theory.gaunt-categories public -open import category-theory.groupoids public -open import category-theory.homotopies-natural-transformations-large-precategories public -open import category-theory.indiscrete-precategories public -open import category-theory.initial-category public -open import category-theory.initial-objects-large-categories public -open import category-theory.initial-objects-large-precategories public -open import category-theory.initial-objects-precategories public -open import category-theory.isomorphism-induction-categories public -open import category-theory.isomorphism-induction-precategories public -open import category-theory.isomorphisms-in-categories public -open import category-theory.isomorphisms-in-large-categories public -open import category-theory.isomorphisms-in-large-precategories public -open import category-theory.isomorphisms-in-precategories public -open import category-theory.isomorphisms-in-subprecategories public -open import category-theory.large-categories public -open import category-theory.large-function-categories public -open import category-theory.large-function-precategories public -open import category-theory.large-precategories public -open import category-theory.large-subcategories public -open import category-theory.large-subprecategories public -open import category-theory.limits-precategories public -open import category-theory.maps-categories public -open import category-theory.maps-from-small-to-large-categories public -open import category-theory.maps-from-small-to-large-precategories public -open import category-theory.maps-precategories public -open import category-theory.maps-set-magmoids public -open import category-theory.monads-on-categories public -open import category-theory.monads-on-precategories public -open import category-theory.monomorphisms-in-large-precategories public -open import category-theory.natural-isomorphisms-functors-categories public -open import category-theory.natural-isomorphisms-functors-large-precategories public -open import category-theory.natural-isomorphisms-functors-precategories public -open import category-theory.natural-isomorphisms-maps-categories public -open import category-theory.natural-isomorphisms-maps-precategories public -open import category-theory.natural-numbers-object-precategories public -open import category-theory.natural-transformations-functors-categories public -open import category-theory.natural-transformations-functors-from-small-to-large-categories public -open import category-theory.natural-transformations-functors-from-small-to-large-precategories public -open import category-theory.natural-transformations-functors-large-categories public -open import category-theory.natural-transformations-functors-large-precategories public -open import category-theory.natural-transformations-functors-precategories public -open import category-theory.natural-transformations-maps-categories public -open import category-theory.natural-transformations-maps-from-small-to-large-precategories public -open import category-theory.natural-transformations-maps-precategories public -open import category-theory.nonunital-precategories public -open import category-theory.one-object-precategories public -open import category-theory.opposite-categories public -open import category-theory.opposite-large-precategories public -open import category-theory.opposite-precategories public -open import category-theory.opposite-preunivalent-categories public -open import category-theory.opposite-strongly-preunivalent-categories public -open import category-theory.pointed-endofunctors-categories public -open import category-theory.pointed-endofunctors-precategories public -open import category-theory.precategories public -open import category-theory.precategory-of-elements-of-a-presheaf public -open import category-theory.precategory-of-functors public -open import category-theory.precategory-of-functors-from-small-to-large-precategories public -open import category-theory.precategory-of-maps-from-small-to-large-precategories public -open import category-theory.precategory-of-maps-precategories public -open import category-theory.pregroupoids public -open import category-theory.presheaf-categories public -open import category-theory.preunivalent-categories public -open import category-theory.products-in-precategories public -open import category-theory.products-of-precategories public -open import category-theory.pseudomonic-functors-precategories public -open import category-theory.pullbacks-in-precategories public -open import category-theory.replete-subprecategories public -open import category-theory.representable-functors-categories public -open import category-theory.representable-functors-large-precategories public -open import category-theory.representable-functors-precategories public -open import category-theory.representing-arrow-category public -open import category-theory.restrictions-functors-cores-precategories public -open import category-theory.right-extensions-precategories public -open import category-theory.right-kan-extensions-precategories public -open import category-theory.rigid-objects-categories public -open import category-theory.rigid-objects-precategories public -open import category-theory.set-magmoids public -open import category-theory.sieves-in-categories public -open import category-theory.simplex-category public -open import category-theory.slice-precategories public -open import category-theory.split-essentially-surjective-functors-precategories public -open import category-theory.strict-categories public -open import category-theory.strongly-preunivalent-categories public -open import category-theory.structure-equivalences-set-magmoids public -open import category-theory.subcategories public -open import category-theory.subprecategories public -open import category-theory.subterminal-precategories public -open import category-theory.terminal-category public -open import category-theory.terminal-objects-precategories public -open import category-theory.wide-subcategories public -open import category-theory.wide-subprecategories public -open import category-theory.yoneda-lemma-categories public -open import category-theory.yoneda-lemma-precategories public +module + category-theory + (funext : function-extensionality) + where + +open import category-theory.adjunctions-large-categories funext public +open import category-theory.adjunctions-large-precategories funext public +open import category-theory.anafunctors-categories funext public +open import category-theory.anafunctors-precategories funext public +open import category-theory.augmented-simplex-category funext public +open import category-theory.categories funext public +open import category-theory.category-of-functors funext public +open import category-theory.category-of-functors-from-small-to-large-categories funext public +open import category-theory.category-of-maps-categories funext public +open import category-theory.category-of-maps-from-small-to-large-categories funext public +open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext public +open import category-theory.commuting-squares-of-morphisms-in-precategories funext public +open import category-theory.commuting-squares-of-morphisms-in-set-magmoids funext public +open import category-theory.commuting-triangles-of-morphisms-in-precategories funext public +open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids funext public +open import category-theory.complete-precategories funext public +open import category-theory.composition-operations-on-binary-families-of-sets funext public +open import category-theory.cones-precategories funext public +open import category-theory.conservative-functors-precategories funext public +open import category-theory.constant-functors funext public +open import category-theory.copresheaf-categories funext public +open import category-theory.coproducts-in-precategories funext public +open import category-theory.cores-categories funext public +open import category-theory.cores-precategories funext public +open import category-theory.coslice-precategories funext public +open import category-theory.dependent-composition-operations-over-precategories funext public +open import category-theory.dependent-products-of-categories funext public +open import category-theory.dependent-products-of-large-categories funext public +open import category-theory.dependent-products-of-large-precategories funext public +open import category-theory.dependent-products-of-precategories funext public +open import category-theory.discrete-categories funext public +open import category-theory.displayed-precategories funext public +open import category-theory.embedding-maps-precategories funext public +open import category-theory.embeddings-precategories funext public +open import category-theory.endomorphisms-in-categories funext public +open import category-theory.endomorphisms-in-precategories funext public +open import category-theory.epimorphisms-in-large-precategories funext public +open import category-theory.equivalences-of-categories funext public +open import category-theory.equivalences-of-large-precategories funext public +open import category-theory.equivalences-of-precategories funext public +open import category-theory.essential-fibers-of-functors-precategories funext public +open import category-theory.essentially-injective-functors-precategories funext public +open import category-theory.essentially-surjective-functors-precategories funext public +open import category-theory.exponential-objects-precategories funext public +open import category-theory.extensions-of-functors-precategories funext public +open import category-theory.faithful-functors-precategories funext public +open import category-theory.faithful-maps-precategories funext public +open import category-theory.full-functors-precategories funext public +open import category-theory.full-large-subcategories funext public +open import category-theory.full-large-subprecategories funext public +open import category-theory.full-maps-precategories funext public +open import category-theory.full-subcategories funext public +open import category-theory.full-subprecategories funext public +open import category-theory.fully-faithful-functors-precategories funext public +open import category-theory.fully-faithful-maps-precategories funext public +open import category-theory.function-categories funext public +open import category-theory.function-precategories funext public +open import category-theory.functors-categories funext public +open import category-theory.functors-from-small-to-large-categories funext public +open import category-theory.functors-from-small-to-large-precategories funext public +open import category-theory.functors-large-categories funext public +open import category-theory.functors-large-precategories funext public +open import category-theory.functors-nonunital-precategories funext public +open import category-theory.functors-precategories funext public +open import category-theory.functors-set-magmoids funext public +open import category-theory.gaunt-categories funext public +open import category-theory.groupoids funext public +open import category-theory.homotopies-natural-transformations-large-precategories funext public +open import category-theory.indiscrete-precategories funext public +open import category-theory.initial-category funext public +open import category-theory.initial-objects-large-categories funext public +open import category-theory.initial-objects-large-precategories funext public +open import category-theory.initial-objects-precategories funext public +open import category-theory.isomorphism-induction-categories funext public +open import category-theory.isomorphism-induction-precategories funext public +open import category-theory.isomorphisms-in-categories funext public +open import category-theory.isomorphisms-in-large-categories funext public +open import category-theory.isomorphisms-in-large-precategories funext public +open import category-theory.isomorphisms-in-precategories funext public +open import category-theory.isomorphisms-in-subprecategories funext public +open import category-theory.large-categories funext public +open import category-theory.large-function-categories funext public +open import category-theory.large-function-precategories funext public +open import category-theory.large-precategories funext public +open import category-theory.large-subcategories funext public +open import category-theory.large-subprecategories funext public +open import category-theory.limits-precategories funext public +open import category-theory.maps-categories funext public +open import category-theory.maps-from-small-to-large-categories funext public +open import category-theory.maps-from-small-to-large-precategories funext public +open import category-theory.maps-precategories funext public +open import category-theory.maps-set-magmoids funext public +open import category-theory.monads-on-categories funext public +open import category-theory.monads-on-precategories funext public +open import category-theory.monomorphisms-in-large-precategories funext public +open import category-theory.natural-isomorphisms-functors-categories funext public +open import category-theory.natural-isomorphisms-functors-large-precategories funext public +open import category-theory.natural-isomorphisms-functors-precategories funext public +open import category-theory.natural-isomorphisms-maps-categories funext public +open import category-theory.natural-isomorphisms-maps-precategories funext public +open import category-theory.natural-numbers-object-precategories funext public +open import category-theory.natural-transformations-functors-categories funext public +open import category-theory.natural-transformations-functors-from-small-to-large-categories funext public +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext public +open import category-theory.natural-transformations-functors-large-categories funext public +open import category-theory.natural-transformations-functors-large-precategories funext public +open import category-theory.natural-transformations-functors-precategories funext public +open import category-theory.natural-transformations-maps-categories funext public +open import category-theory.natural-transformations-maps-from-small-to-large-precategories funext public +open import category-theory.natural-transformations-maps-precategories funext public +open import category-theory.nonunital-precategories funext public +open import category-theory.one-object-precategories funext public +open import category-theory.opposite-categories funext public +open import category-theory.opposite-large-precategories funext public +open import category-theory.opposite-precategories funext public +open import category-theory.opposite-preunivalent-categories funext public +open import category-theory.opposite-strongly-preunivalent-categories funext public +open import category-theory.pointed-endofunctors-categories funext public +open import category-theory.pointed-endofunctors-precategories funext public +open import category-theory.precategories funext public +open import category-theory.precategory-of-elements-of-a-presheaf funext public +open import category-theory.precategory-of-functors funext public +open import category-theory.precategory-of-functors-from-small-to-large-precategories funext public +open import category-theory.precategory-of-maps-from-small-to-large-precategories funext public +open import category-theory.precategory-of-maps-precategories funext public +open import category-theory.pregroupoids funext public +open import category-theory.presheaf-categories funext public +open import category-theory.preunivalent-categories funext public +open import category-theory.products-in-precategories funext public +open import category-theory.products-of-precategories funext public +open import category-theory.pseudomonic-functors-precategories funext public +open import category-theory.pullbacks-in-precategories funext public +open import category-theory.replete-subprecategories funext public +open import category-theory.representable-functors-categories funext public +open import category-theory.representable-functors-large-precategories funext public +open import category-theory.representable-functors-precategories funext public +open import category-theory.representing-arrow-category funext public +open import category-theory.restrictions-functors-cores-precategories funext public +open import category-theory.right-extensions-precategories funext public +open import category-theory.right-kan-extensions-precategories funext public +open import category-theory.rigid-objects-categories funext public +open import category-theory.rigid-objects-precategories funext public +open import category-theory.set-magmoids funext public +open import category-theory.sieves-in-categories funext public +open import category-theory.simplex-category funext public +open import category-theory.slice-precategories funext public +open import category-theory.split-essentially-surjective-functors-precategories funext public +open import category-theory.strict-categories funext public +open import category-theory.strongly-preunivalent-categories funext public +open import category-theory.structure-equivalences-set-magmoids funext public +open import category-theory.subcategories funext public +open import category-theory.subprecategories funext public +open import category-theory.subterminal-precategories funext public +open import category-theory.terminal-category funext public +open import category-theory.terminal-objects-precategories funext public +open import category-theory.wide-subcategories funext public +open import category-theory.wide-subprecategories funext public +open import category-theory.yoneda-lemma-categories funext public +open import category-theory.yoneda-lemma-precategories funext public ``` diff --git a/src/category-theory/adjunctions-large-categories.lagda.md b/src/category-theory/adjunctions-large-categories.lagda.md index a8adbd3bcd..68df714e49 100644 --- a/src/category-theory/adjunctions-large-categories.lagda.md +++ b/src/category-theory/adjunctions-large-categories.lagda.md @@ -1,20 +1,25 @@ # Adjunctions between large categories ```agda -module category-theory.adjunctions-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.adjunctions-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.adjunctions-large-precategories -open import category-theory.functors-large-categories -open import category-theory.large-categories -open import category-theory.natural-transformations-functors-large-categories - -open import foundation.commuting-squares-of-maps -open import foundation.equivalences -open import foundation.identity-types +open import category-theory.adjunctions-large-precategories funext +open import category-theory.functors-large-categories funext +open import category-theory.large-categories funext +open import category-theory.natural-transformations-functors-large-categories funext + +open import foundation.commuting-squares-of-maps funext +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/adjunctions-large-precategories.lagda.md b/src/category-theory/adjunctions-large-precategories.lagda.md index ac473c743e..56d22070c7 100644 --- a/src/category-theory/adjunctions-large-precategories.lagda.md +++ b/src/category-theory/adjunctions-large-precategories.lagda.md @@ -1,20 +1,25 @@ # Adjunctions between large precategories ```agda -module category-theory.adjunctions-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.adjunctions-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-large-precategories +open import category-theory.functors-large-precategories funext +open import category-theory.large-precategories funext +open import category-theory.natural-transformations-functors-large-precategories funext open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.equivalences -open import foundation.identity-types +open import foundation.commuting-squares-of-maps funext +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/anafunctors-categories.lagda.md b/src/category-theory/anafunctors-categories.lagda.md index 447086f3eb..eb7973d591 100644 --- a/src/category-theory/anafunctors-categories.lagda.md +++ b/src/category-theory/anafunctors-categories.lagda.md @@ -1,18 +1,23 @@ # Anafunctors between categories ```agda -module category-theory.anafunctors-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.anafunctors-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.anafunctors-precategories -open import category-theory.categories -open import category-theory.functors-categories +open import category-theory.anafunctors-precategories funext +open import category-theory.categories funext +open import category-theory.functors-categories funext open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext open import foundation.universe-levels ``` diff --git a/src/category-theory/anafunctors-precategories.lagda.md b/src/category-theory/anafunctors-precategories.lagda.md index 105714a8a5..5854692528 100644 --- a/src/category-theory/anafunctors-precategories.lagda.md +++ b/src/category-theory/anafunctors-precategories.lagda.md @@ -1,21 +1,26 @@ # Anafunctors between precategories ```agda -module category-theory.anafunctors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.anafunctors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels ``` diff --git a/src/category-theory/augmented-simplex-category.lagda.md b/src/category-theory/augmented-simplex-category.lagda.md index 9c59e0e7b2..696f77dfa2 100644 --- a/src/category-theory/augmented-simplex-category.lagda.md +++ b/src/category-theory/augmented-simplex-category.lagda.md @@ -1,25 +1,30 @@ # The augmented simplex category ```agda -module category-theory.augmented-simplex-category where +open import foundation.function-extensionality-axiom + +module + category-theory.augmented-simplex-category + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.precategories funext -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets +open import order-theory.order-preserving-maps-posets funext ```
diff --git a/src/category-theory/categories.lagda.md b/src/category-theory/categories.lagda.md index 42f12c7076..a2bf9538d5 100644 --- a/src/category-theory/categories.lagda.md +++ b/src/category-theory/categories.lagda.md @@ -1,30 +1,35 @@ # Categories ```agda -module category-theory.categories where +open import foundation.function-extensionality-axiom + +module + category-theory.categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.preunivalent-categories -open import category-theory.strongly-preunivalent-categories - -open import foundation.1-types -open import foundation.cartesian-product-types +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.nonunital-precategories funext +open import category-theory.precategories funext +open import category-theory.preunivalent-categories funext +open import category-theory.strongly-preunivalent-categories funext + +open import foundation.1-types funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.surjective-maps +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.surjective-maps funext open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md b/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md index a79a1fe316..179923ac1c 100644 --- a/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md @@ -1,27 +1,32 @@ # The category of functors and natural transformations from small to large categories ```agda -module category-theory.category-of-functors-from-small-to-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.category-of-functors-from-small-to-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.category-of-functors -open import category-theory.functors-from-small-to-large-categories -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.natural-isomorphisms-functors-categories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors-from-small-to-large-precategories - -open import foundation.equivalences -open import foundation.identity-types +open import category-theory.categories funext +open import category-theory.category-of-functors funext +open import category-theory.functors-from-small-to-large-categories funext +open import category-theory.functors-from-small-to-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.natural-isomorphisms-functors-categories funext +open import category-theory.natural-isomorphisms-functors-precategories funext +open import category-theory.precategories funext +open import category-theory.precategory-of-functors-from-small-to-large-precategories funext + +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-functors.lagda.md b/src/category-theory/category-of-functors.lagda.md index c2486d1ff0..fdcd59fb84 100644 --- a/src/category-theory/category-of-functors.lagda.md +++ b/src/category-theory/category-of-functors.lagda.md @@ -1,25 +1,30 @@ # The category of functors and natural transformations between two categories ```agda -module category-theory.category-of-functors where +open import foundation.function-extensionality-axiom + +module + category-theory.category-of-functors + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.category-of-maps-categories -open import category-theory.functors-categories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.natural-isomorphisms-functors-categories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors +open import category-theory.categories funext +open import category-theory.category-of-maps-categories funext +open import category-theory.functors-categories funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.natural-isomorphisms-functors-categories funext +open import category-theory.natural-isomorphisms-functors-precategories funext +open import category-theory.precategories funext +open import category-theory.precategory-of-functors funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-maps-categories.lagda.md b/src/category-theory/category-of-maps-categories.lagda.md index 1226b6f854..ba64359ccb 100644 --- a/src/category-theory/category-of-maps-categories.lagda.md +++ b/src/category-theory/category-of-maps-categories.lagda.md @@ -1,34 +1,39 @@ # The category of maps and natural transformations between two categories ```agda -module category-theory.category-of-maps-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.category-of-maps-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-categories -open import category-theory.maps-precategories -open import category-theory.natural-isomorphisms-maps-categories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.natural-transformations-maps-precategories -open import category-theory.precategories -open import category-theory.precategory-of-maps-precategories +open import category-theory.categories funext +open import category-theory.commuting-squares-of-morphisms-in-precategories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.maps-categories funext +open import category-theory.maps-precategories funext +open import category-theory.natural-isomorphisms-maps-categories funext +open import category-theory.natural-isomorphisms-maps-precategories funext +open import category-theory.natural-transformations-maps-precategories funext +open import category-theory.precategories funext +open import category-theory.precategory-of-maps-precategories funext open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.univalence +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.univalence funext open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md b/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md index bf67d50b0e..c05df315a2 100644 --- a/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md +++ b/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md @@ -1,27 +1,32 @@ # The category of maps and natural transformations from small to large categories ```agda -module category-theory.category-of-maps-from-small-to-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.category-of-maps-from-small-to-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.category-of-maps-categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.maps-from-small-to-large-categories -open import category-theory.maps-from-small-to-large-precategories -open import category-theory.natural-isomorphisms-maps-categories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.precategories -open import category-theory.precategory-of-maps-from-small-to-large-precategories - -open import foundation.equivalences -open import foundation.identity-types +open import category-theory.categories funext +open import category-theory.category-of-maps-categories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.maps-from-small-to-large-categories funext +open import category-theory.maps-from-small-to-large-precategories funext +open import category-theory.natural-isomorphisms-maps-categories funext +open import category-theory.natural-isomorphisms-maps-precategories funext +open import category-theory.precategories funext +open import category-theory.precategory-of-maps-from-small-to-large-precategories funext + +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md b/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md index 3e6f636e0b..e5b09d42d1 100644 --- a/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md +++ b/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md @@ -1,15 +1,20 @@ # Commuting squares of morphisms in large precategories ```agda -module category-theory.commuting-squares-of-morphisms-in-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.commuting-squares-of-morphisms-in-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md b/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md index 9fce14c311..2e66fd64eb 100644 --- a/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md +++ b/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md @@ -1,14 +1,19 @@ # Commuting squares of morphisms in precategories ```agda -module category-theory.commuting-squares-of-morphisms-in-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.commuting-squares-of-morphisms-in-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-set-magmoids -open import category-theory.precategories +open import category-theory.commuting-squares-of-morphisms-in-set-magmoids funext +open import category-theory.precategories funext open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md b/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md index 9bcce6ed57..99bd887dfd 100644 --- a/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md +++ b/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md @@ -1,15 +1,20 @@ # Commuting squares of morphisms in set-magmoids ```agda -module category-theory.commuting-squares-of-morphisms-in-set-magmoids where +open import foundation.function-extensionality-axiom + +module + category-theory.commuting-squares-of-morphisms-in-set-magmoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.set-magmoids +open import category-theory.set-magmoids funext -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md b/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md index 7ba7f47e35..a765cfded2 100644 --- a/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md +++ b/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md @@ -1,16 +1,21 @@ # Commuting triangles of morphisms in precategories ```agda -module category-theory.commuting-triangles-of-morphisms-in-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.commuting-triangles-of-morphisms-in-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids -open import category-theory.precategories +open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids funext +open import category-theory.precategories funext -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md b/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md index 3e43a6c09f..68fef1e45c 100644 --- a/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md +++ b/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md @@ -1,15 +1,20 @@ # Commuting triangles of morphisms in set-magmoids ```agda -module category-theory.commuting-triangles-of-morphisms-in-set-magmoids where +open import foundation.function-extensionality-axiom + +module + category-theory.commuting-triangles-of-morphisms-in-set-magmoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.set-magmoids +open import category-theory.set-magmoids funext -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/complete-precategories.lagda.md b/src/category-theory/complete-precategories.lagda.md index aed7151ba7..b54d1c7eaf 100644 --- a/src/category-theory/complete-precategories.lagda.md +++ b/src/category-theory/complete-precategories.lagda.md @@ -1,17 +1,22 @@ # Complete precategories ```agda -module category-theory.complete-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.complete-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.cones-precategories -open import category-theory.functors-precategories -open import category-theory.limits-precategories -open import category-theory.precategories -open import category-theory.terminal-objects-precategories +open import category-theory.cones-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.limits-precategories funext +open import category-theory.precategories funext +open import category-theory.terminal-objects-precategories funext open import foundation.universe-levels ``` diff --git a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md index 49fbe79018..87c06e6b9b 100644 --- a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md +++ b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md @@ -1,21 +1,27 @@ # Composition operations on binary families of sets ```agda -module category-theory.composition-operations-on-binary-families-of-sets where +open import foundation.function-extensionality-axiom + +module + category-theory.composition-operations-on-binary-families-of-sets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/cones-precategories.lagda.md b/src/category-theory/cones-precategories.lagda.md index 12df81dc10..d011e081f3 100644 --- a/src/category-theory/cones-precategories.lagda.md +++ b/src/category-theory/cones-precategories.lagda.md @@ -1,45 +1,51 @@ # Cones in precategories ```agda -module category-theory.cones-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.cones-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.commuting-triangles-of-morphisms-in-precategories -open import category-theory.constant-functors -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors -open import category-theory.right-extensions-precategories -open import category-theory.terminal-category +open import category-theory.commuting-squares-of-morphisms-in-precategories funext +open import category-theory.commuting-triangles-of-morphisms-in-precategories funext +open import category-theory.constant-functors funext +open import category-theory.functors-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext +open import category-theory.precategory-of-functors funext +open import category-theory.right-extensions-precategories funext +open import category-theory.terminal-category funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.contractible-types funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.multivariable-homotopies -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.multivariable-homotopies funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/conservative-functors-precategories.lagda.md b/src/category-theory/conservative-functors-precategories.lagda.md index e3b24903e9..394a60d3f4 100644 --- a/src/category-theory/conservative-functors-precategories.lagda.md +++ b/src/category-theory/conservative-functors-precategories.lagda.md @@ -1,19 +1,24 @@ # Conservative functors between precategories ```agda -module category-theory.conservative-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.conservative-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/constant-functors.lagda.md b/src/category-theory/constant-functors.lagda.md index a07c37b14b..18678afffa 100644 --- a/src/category-theory/constant-functors.lagda.md +++ b/src/category-theory/constant-functors.lagda.md @@ -1,28 +1,33 @@ # Constant functors ```agda -module category-theory.constant-functors where +open import foundation.function-extensionality-axiom + +module + category-theory.constant-functors + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.functors-large-categories -open import category-theory.functors-large-precategories -open import category-theory.functors-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors +open import category-theory.categories funext +open import category-theory.functors-categories funext +open import category-theory.functors-large-categories funext +open import category-theory.functors-large-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext +open import category-theory.precategory-of-functors funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.equality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/copresheaf-categories.lagda.md b/src/category-theory/copresheaf-categories.lagda.md index 71e72eff00..d19c4d335e 100644 --- a/src/category-theory/copresheaf-categories.lagda.md +++ b/src/category-theory/copresheaf-categories.lagda.md @@ -1,41 +1,46 @@ # Copresheaf categories ```agda -module category-theory.copresheaf-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.copresheaf-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.category-of-functors-from-small-to-large-categories -open import category-theory.constant-functors -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.functors-precategories -open import category-theory.initial-objects-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-functors-from-small-to-large-precategories -open import category-theory.terminal-objects-precategories - -open import foundation.category-of-sets -open import foundation.commuting-squares-of-maps +open import category-theory.categories funext +open import category-theory.category-of-functors-from-small-to-large-categories funext +open import category-theory.constant-functors funext +open import category-theory.functors-from-small-to-large-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.initial-objects-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext +open import category-theory.precategory-of-functors-from-small-to-large-precategories funext +open import category-theory.terminal-objects-precategories funext + +open import foundation.category-of-sets funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.empty-types funext open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/coproducts-in-precategories.lagda.md b/src/category-theory/coproducts-in-precategories.lagda.md index 89a697bd01..618ec80bb4 100644 --- a/src/category-theory/coproducts-in-precategories.lagda.md +++ b/src/category-theory/coproducts-in-precategories.lagda.md @@ -1,23 +1,28 @@ # Coproducts in precategories ```agda -module category-theory.coproducts-in-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.coproducts-in-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext open import foundation.telescopes -open import foundation.uniqueness-quantification +open import foundation.uniqueness-quantification funext open import foundation.universe-levels ``` diff --git a/src/category-theory/cores-categories.lagda.md b/src/category-theory/cores-categories.lagda.md index d8577944ab..0736e55876 100644 --- a/src/category-theory/cores-categories.lagda.md +++ b/src/category-theory/cores-categories.lagda.md @@ -1,23 +1,28 @@ # Cores of categories ```agda -module category-theory.cores-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.cores-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.cores-precategories -open import category-theory.groupoids -open import category-theory.isomorphisms-in-categories -open import category-theory.precategories -open import category-theory.pregroupoids -open import category-theory.subcategories -open import category-theory.wide-subcategories +open import category-theory.categories funext +open import category-theory.cores-precategories funext +open import category-theory.groupoids funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.precategories funext +open import category-theory.pregroupoids funext +open import category-theory.subcategories funext +open import category-theory.wide-subcategories funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels ``` diff --git a/src/category-theory/cores-precategories.lagda.md b/src/category-theory/cores-precategories.lagda.md index 210c08f99c..5d2bb04329 100644 --- a/src/category-theory/cores-precategories.lagda.md +++ b/src/category-theory/cores-precategories.lagda.md @@ -1,28 +1,33 @@ # Cores of precategories ```agda -module category-theory.cores-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.cores-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pregroupoids -open import category-theory.replete-subprecategories -open import category-theory.subprecategories -open import category-theory.wide-subprecategories - -open import foundation.contractible-types +open import category-theory.categories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext +open import category-theory.pregroupoids funext +open import category-theory.replete-subprecategories funext +open import category-theory.subprecategories funext +open import category-theory.wide-subprecategories funext + +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/coslice-precategories.lagda.md b/src/category-theory/coslice-precategories.lagda.md index b47a0de89f..d782a63d8b 100644 --- a/src/category-theory/coslice-precategories.lagda.md +++ b/src/category-theory/coslice-precategories.lagda.md @@ -1,16 +1,21 @@ # Coslice precategories ```agda -module category-theory.coslice-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.coslice-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.slice-precategories +open import category-theory.functors-precategories funext +open import category-theory.opposite-precategories funext +open import category-theory.precategories funext +open import category-theory.slice-precategories funext open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md index cd698e7403..1b9dc2998c 100644 --- a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md +++ b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md @@ -1,28 +1,33 @@ # Dependent composition operations over precategories ```agda -module category-theory.dependent-composition-operations-over-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.dependent-composition-operations-over-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.set-magmoids +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.nonunital-precategories funext +open import category-theory.precategories funext +open import category-theory.set-magmoids funext -open import foundation.cartesian-product-types -open import foundation.dependent-identifications +open import foundation.cartesian-product-types funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-categories.lagda.md b/src/category-theory/dependent-products-of-categories.lagda.md index 64742bf6c0..337fd902f2 100644 --- a/src/category-theory/dependent-products-of-categories.lagda.md +++ b/src/category-theory/dependent-products-of-categories.lagda.md @@ -1,26 +1,32 @@ # Dependent products of categories ```agda -module category-theory.dependent-products-of-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.dependent-products-of-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.dependent-products-of-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.dependent-products-of-precategories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-large-categories.lagda.md b/src/category-theory/dependent-products-of-large-categories.lagda.md index d674d884ab..b2c8aaa9e4 100644 --- a/src/category-theory/dependent-products-of-large-categories.lagda.md +++ b/src/category-theory/dependent-products-of-large-categories.lagda.md @@ -1,23 +1,29 @@ # Dependent products of large categories ```agda -module category-theory.dependent-products-of-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.dependent-products-of-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.dependent-products-of-large-precategories -open import category-theory.isomorphisms-in-large-categories -open import category-theory.large-categories -open import category-theory.large-precategories - -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.dependent-products-of-large-precategories funext +open import category-theory.isomorphisms-in-large-categories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext + +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-dependent-function-types funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-large-precategories.lagda.md b/src/category-theory/dependent-products-of-large-precategories.lagda.md index 4eacbea052..4b9c0f9a9c 100644 --- a/src/category-theory/dependent-products-of-large-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-large-precategories.lagda.md @@ -1,25 +1,30 @@ # Dependent products of large precategories ```agda -module category-theory.dependent-products-of-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.dependent-products-of-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-precategories.lagda.md b/src/category-theory/dependent-products-of-precategories.lagda.md index e4f7e693fb..bd1380b147 100644 --- a/src/category-theory/dependent-products-of-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-precategories.lagda.md @@ -1,26 +1,31 @@ # Dependent products of precategories ```agda -module category-theory.dependent-products-of-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.dependent-products-of-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/discrete-categories.lagda.md b/src/category-theory/discrete-categories.lagda.md index f4a10cea33..936de3d80c 100644 --- a/src/category-theory/discrete-categories.lagda.md +++ b/src/category-theory/discrete-categories.lagda.md @@ -1,18 +1,23 @@ # Discrete categories ```agda -module category-theory.discrete-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.discrete-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/displayed-precategories.lagda.md b/src/category-theory/displayed-precategories.lagda.md index 959ce0871a..ac5e3a734c 100644 --- a/src/category-theory/displayed-precategories.lagda.md +++ b/src/category-theory/displayed-precategories.lagda.md @@ -1,31 +1,36 @@ # Displayed precategories ```agda -module category-theory.displayed-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.displayed-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.dependent-composition-operations-over-precategories -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.set-magmoids - -open import foundation.cartesian-product-types -open import foundation.dependent-identifications +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.dependent-composition-operations-over-precategories funext +open import category-theory.nonunital-precategories funext +open import category-theory.precategories funext +open import category-theory.set-magmoids funext + +open import foundation.cartesian-product-types funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subsingleton-induction open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/embedding-maps-precategories.lagda.md b/src/category-theory/embedding-maps-precategories.lagda.md index 469ee2913d..604e51de46 100644 --- a/src/category-theory/embedding-maps-precategories.lagda.md +++ b/src/category-theory/embedding-maps-precategories.lagda.md @@ -1,19 +1,24 @@ # Embedding maps between precategories ```agda -module category-theory.embedding-maps-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.embedding-maps-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.fully-faithful-maps-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.fully-faithful-maps-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/embeddings-precategories.lagda.md b/src/category-theory/embeddings-precategories.lagda.md index 39ffe2e71f..fd576ef7f2 100644 --- a/src/category-theory/embeddings-precategories.lagda.md +++ b/src/category-theory/embeddings-precategories.lagda.md @@ -1,19 +1,24 @@ # Embeddings between precategories ```agda -module category-theory.embeddings-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.embeddings-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.embedding-maps-precategories -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.embedding-maps-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/endomorphisms-in-categories.lagda.md b/src/category-theory/endomorphisms-in-categories.lagda.md index 91a32f4441..2ac8aafdfe 100644 --- a/src/category-theory/endomorphisms-in-categories.lagda.md +++ b/src/category-theory/endomorphisms-in-categories.lagda.md @@ -1,21 +1,26 @@ # Endomorphisms in categories ```agda -module category-theory.endomorphisms-in-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.endomorphisms-in-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.endomorphisms-in-precategories +open import category-theory.categories funext +open import category-theory.endomorphisms-in-precategories funext -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/category-theory/endomorphisms-in-precategories.lagda.md b/src/category-theory/endomorphisms-in-precategories.lagda.md index 75cac02bde..46949de770 100644 --- a/src/category-theory/endomorphisms-in-precategories.lagda.md +++ b/src/category-theory/endomorphisms-in-precategories.lagda.md @@ -1,21 +1,26 @@ # Endomorphisms in precategories ```agda -module category-theory.endomorphisms-in-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.endomorphisms-in-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/category-theory/epimorphisms-in-large-precategories.lagda.md b/src/category-theory/epimorphisms-in-large-precategories.lagda.md index d03cd93b4a..d773b7e7af 100644 --- a/src/category-theory/epimorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/epimorphisms-in-large-precategories.lagda.md @@ -1,18 +1,23 @@ # Epimorphism in large precategories ```agda -module category-theory.epimorphisms-in-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.epimorphisms-in-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-precategories funext -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/equivalences-of-categories.lagda.md b/src/category-theory/equivalences-of-categories.lagda.md index 3f49dba3f0..52959660f3 100644 --- a/src/category-theory/equivalences-of-categories.lagda.md +++ b/src/category-theory/equivalences-of-categories.lagda.md @@ -1,15 +1,20 @@ # Equivalences between categories ```agda -module category-theory.equivalences-of-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.equivalences-of-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.equivalences-of-precategories -open import category-theory.functors-categories +open import category-theory.categories funext +open import category-theory.equivalences-of-precategories funext +open import category-theory.functors-categories funext open import foundation.universe-levels ``` diff --git a/src/category-theory/equivalences-of-large-precategories.lagda.md b/src/category-theory/equivalences-of-large-precategories.lagda.md index c6dd8e5fb5..f10b1cd6c6 100644 --- a/src/category-theory/equivalences-of-large-precategories.lagda.md +++ b/src/category-theory/equivalences-of-large-precategories.lagda.md @@ -1,15 +1,20 @@ # Equivalences between large precategories ```agda -module category-theory.equivalences-of-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.equivalences-of-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-isomorphisms-functors-large-precategories +open import category-theory.functors-large-precategories funext +open import category-theory.large-precategories funext +open import category-theory.natural-isomorphisms-functors-large-precategories funext open import foundation.universe-levels ``` diff --git a/src/category-theory/equivalences-of-precategories.lagda.md b/src/category-theory/equivalences-of-precategories.lagda.md index 5478d066df..e85229fdcd 100644 --- a/src/category-theory/equivalences-of-precategories.lagda.md +++ b/src/category-theory/equivalences-of-precategories.lagda.md @@ -1,17 +1,22 @@ # Equivalences between precategories ```agda -module category-theory.equivalences-of-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.equivalences-of-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.natural-isomorphisms-functors-precategories funext +open import category-theory.precategories funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/essential-fibers-of-functors-precategories.lagda.md b/src/category-theory/essential-fibers-of-functors-precategories.lagda.md index f0bdaf07fc..9874faeef6 100644 --- a/src/category-theory/essential-fibers-of-functors-precategories.lagda.md +++ b/src/category-theory/essential-fibers-of-functors-precategories.lagda.md @@ -1,15 +1,20 @@ # Essential fibers of functors between precategories ```agda -module category-theory.essential-fibers-of-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.essential-fibers-of-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/essentially-injective-functors-precategories.lagda.md b/src/category-theory/essentially-injective-functors-precategories.lagda.md index db632862bb..f8610a8048 100644 --- a/src/category-theory/essentially-injective-functors-precategories.lagda.md +++ b/src/category-theory/essentially-injective-functors-precategories.lagda.md @@ -1,15 +1,20 @@ # Essentially injective functors between precategories ```agda -module category-theory.essentially-injective-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.essentially-injective-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/essentially-surjective-functors-precategories.lagda.md b/src/category-theory/essentially-surjective-functors-precategories.lagda.md index da79c73d46..8618911aa0 100644 --- a/src/category-theory/essentially-surjective-functors-precategories.lagda.md +++ b/src/category-theory/essentially-surjective-functors-precategories.lagda.md @@ -1,19 +1,24 @@ # Essentially surjective functors between precategories ```agda -module category-theory.essentially-surjective-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.essentially-surjective-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.propositions +open import foundation.existential-quantification funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/exponential-objects-precategories.lagda.md b/src/category-theory/exponential-objects-precategories.lagda.md index e2fad05451..c921eebd63 100644 --- a/src/category-theory/exponential-objects-precategories.lagda.md +++ b/src/category-theory/exponential-objects-precategories.lagda.md @@ -1,19 +1,24 @@ # Exponential objects in precategories ```agda -module category-theory.exponential-objects-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.exponential-objects-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories -open import category-theory.products-in-precategories +open import category-theory.precategories funext +open import category-theory.products-in-precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.uniqueness-quantification +open import foundation.identity-types funext +open import foundation.uniqueness-quantification funext open import foundation.universe-levels ``` diff --git a/src/category-theory/extensions-of-functors-precategories.lagda.md b/src/category-theory/extensions-of-functors-precategories.lagda.md index bf91bbfdb8..96951fec22 100644 --- a/src/category-theory/extensions-of-functors-precategories.lagda.md +++ b/src/category-theory/extensions-of-functors-precategories.lagda.md @@ -1,17 +1,22 @@ # Extensions of functors between precategories ```agda -module category-theory.extensions-of-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.extensions-of-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/faithful-functors-precategories.lagda.md b/src/category-theory/faithful-functors-precategories.lagda.md index 8c6ea55099..7ba9a01752 100644 --- a/src/category-theory/faithful-functors-precategories.lagda.md +++ b/src/category-theory/faithful-functors-precategories.lagda.md @@ -1,22 +1,27 @@ # Faithful functors between precategories ```agda -module category-theory.faithful-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.faithful-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.faithful-maps-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.faithful-maps-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/faithful-maps-precategories.lagda.md b/src/category-theory/faithful-maps-precategories.lagda.md index 092f8cb396..ed9eda0477 100644 --- a/src/category-theory/faithful-maps-precategories.lagda.md +++ b/src/category-theory/faithful-maps-precategories.lagda.md @@ -1,24 +1,29 @@ # Faithful maps between precategories ```agda -module category-theory.faithful-maps-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.faithful-maps-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.maps-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.injective-maps -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.injective-maps funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/full-functors-precategories.lagda.md b/src/category-theory/full-functors-precategories.lagda.md index 6fcd4a2690..38af28bd71 100644 --- a/src/category-theory/full-functors-precategories.lagda.md +++ b/src/category-theory/full-functors-precategories.lagda.md @@ -1,19 +1,24 @@ # Full functors between precategories ```agda -module category-theory.full-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.full-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-maps-precategories -open import category-theory.functors-precategories -open import category-theory.precategories +open import category-theory.full-maps-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/full-large-subcategories.lagda.md b/src/category-theory/full-large-subcategories.lagda.md index 4b96c679d6..829d410f66 100644 --- a/src/category-theory/full-large-subcategories.lagda.md +++ b/src/category-theory/full-large-subcategories.lagda.md @@ -1,21 +1,26 @@ # Full large subcategories ```agda -module category-theory.full-large-subcategories where +open import foundation.function-extensionality-axiom + +module + category-theory.full-large-subcategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.functors-large-categories -open import category-theory.large-categories -open import category-theory.large-precategories - -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.full-large-subprecategories funext +open import category-theory.functors-large-categories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext + +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/full-large-subprecategories.lagda.md b/src/category-theory/full-large-subprecategories.lagda.md index a3789dd83e..3b5a435a5f 100644 --- a/src/category-theory/full-large-subprecategories.lagda.md +++ b/src/category-theory/full-large-subprecategories.lagda.md @@ -1,26 +1,31 @@ # Full large subprecategories ```agda -module category-theory.full-large-subprecategories where +open import foundation.function-extensionality-axiom + +module + category-theory.full-large-subprecategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.isomorphisms-in-large-categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories +open import category-theory.functors-large-precategories funext +open import category-theory.isomorphisms-in-large-categories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext -open import foundation.function-types +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/full-maps-precategories.lagda.md b/src/category-theory/full-maps-precategories.lagda.md index 0e88643319..8de930dcbe 100644 --- a/src/category-theory/full-maps-precategories.lagda.md +++ b/src/category-theory/full-maps-precategories.lagda.md @@ -1,20 +1,25 @@ # Full maps between precategories ```agda -module category-theory.full-maps-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.full-maps-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.maps-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.function-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.surjective-maps funext open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/full-subcategories.lagda.md b/src/category-theory/full-subcategories.lagda.md index a1921d9182..e84e529f1e 100644 --- a/src/category-theory/full-subcategories.lagda.md +++ b/src/category-theory/full-subcategories.lagda.md @@ -1,28 +1,33 @@ # Full subcategories ```agda -module category-theory.full-subcategories where +open import foundation.function-extensionality-axiom + +module + category-theory.full-subcategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.embeddings-precategories -open import category-theory.full-subprecategories -open import category-theory.fully-faithful-functors-precategories -open import category-theory.functors-categories -open import category-theory.maps-categories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.embeddings-precategories funext +open import category-theory.full-subprecategories funext +open import category-theory.fully-faithful-functors-precategories funext +open import category-theory.functors-categories funext +open import category-theory.maps-categories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/full-subprecategories.lagda.md b/src/category-theory/full-subprecategories.lagda.md index 7d2faeebad..f2e0014c57 100644 --- a/src/category-theory/full-subprecategories.lagda.md +++ b/src/category-theory/full-subprecategories.lagda.md @@ -1,33 +1,38 @@ # Full subprecategories ```agda -module category-theory.full-subprecategories where +open import foundation.function-extensionality-axiom + +module + category-theory.full-subprecategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.embeddings-precategories -open import category-theory.fully-faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.embeddings-precategories funext +open import category-theory.fully-faithful-functors-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/fully-faithful-functors-precategories.lagda.md b/src/category-theory/fully-faithful-functors-precategories.lagda.md index a0de4952c0..11f167d8bc 100644 --- a/src/category-theory/fully-faithful-functors-precategories.lagda.md +++ b/src/category-theory/fully-faithful-functors-precategories.lagda.md @@ -1,32 +1,37 @@ # Fully faithful functors between precategories ```agda -module category-theory.fully-faithful-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.fully-faithful-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.conservative-functors-precategories -open import category-theory.essentially-injective-functors-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.full-functors-precategories -open import category-theory.fully-faithful-maps-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pseudomonic-functors-precategories +open import category-theory.conservative-functors-precategories funext +open import category-theory.essentially-injective-functors-precategories funext +open import category-theory.faithful-functors-precategories funext +open import category-theory.full-functors-precategories funext +open import category-theory.fully-faithful-maps-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext +open import category-theory.pseudomonic-functors-precategories funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.universe-levels ``` diff --git a/src/category-theory/fully-faithful-maps-precategories.lagda.md b/src/category-theory/fully-faithful-maps-precategories.lagda.md index 2317e1536a..92ee592d08 100644 --- a/src/category-theory/fully-faithful-maps-precategories.lagda.md +++ b/src/category-theory/fully-faithful-maps-precategories.lagda.md @@ -1,23 +1,28 @@ # Fully faithful maps between precategories ```agda -module category-theory.fully-faithful-maps-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.fully-faithful-maps-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.faithful-maps-precategories -open import category-theory.full-maps-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.faithful-maps-precategories funext +open import category-theory.full-maps-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.surjective-maps funext open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/function-categories.lagda.md b/src/category-theory/function-categories.lagda.md index 2e86a66718..218e640473 100644 --- a/src/category-theory/function-categories.lagda.md +++ b/src/category-theory/function-categories.lagda.md @@ -1,22 +1,27 @@ # Function categories ```agda -module category-theory.function-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.function-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.dependent-products-of-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.precategories - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.categories funext +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.dependent-products-of-categories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.precategories funext + +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/function-precategories.lagda.md b/src/category-theory/function-precategories.lagda.md index 64506a827d..6b641f53b1 100644 --- a/src/category-theory/function-precategories.lagda.md +++ b/src/category-theory/function-precategories.lagda.md @@ -1,21 +1,26 @@ # Function precategories ```agda -module category-theory.function-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.function-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.dependent-products-of-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.dependent-products-of-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext + +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-categories.lagda.md b/src/category-theory/functors-categories.lagda.md index 8b751210a5..2cd5b37963 100644 --- a/src/category-theory/functors-categories.lagda.md +++ b/src/category-theory/functors-categories.lagda.md @@ -1,22 +1,27 @@ # Functors between categories ```agda -module category-theory.functors-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.functors-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.maps-categories - -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import category-theory.categories funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.maps-categories funext + +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-from-small-to-large-categories.lagda.md b/src/category-theory/functors-from-small-to-large-categories.lagda.md index 0194f3b8dd..78186e0cab 100644 --- a/src/category-theory/functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/functors-from-small-to-large-categories.lagda.md @@ -1,21 +1,26 @@ # Functors from small to large categories ```agda -module category-theory.functors-from-small-to-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.functors-from-small-to-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.large-categories -open import category-theory.maps-from-small-to-large-categories - -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import category-theory.categories funext +open import category-theory.functors-from-small-to-large-precategories funext +open import category-theory.large-categories funext +open import category-theory.maps-from-small-to-large-categories funext + +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-from-small-to-large-precategories.lagda.md b/src/category-theory/functors-from-small-to-large-precategories.lagda.md index 0565ce0d40..1b3550e637 100644 --- a/src/category-theory/functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/functors-from-small-to-large-precategories.lagda.md @@ -1,23 +1,28 @@ # Functors from small to large precategories ```agda -module category-theory.functors-from-small-to-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.functors-from-small-to-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.large-precategories -open import category-theory.maps-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.large-precategories funext +open import category-theory.maps-from-small-to-large-precategories funext +open import category-theory.precategories funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-large-categories.lagda.md b/src/category-theory/functors-large-categories.lagda.md index 450779039d..913247188b 100644 --- a/src/category-theory/functors-large-categories.lagda.md +++ b/src/category-theory/functors-large-categories.lagda.md @@ -1,16 +1,21 @@ # Functors between large categories ```agda -module category-theory.functors-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.functors-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-categories +open import category-theory.functors-large-precategories funext +open import category-theory.large-categories funext -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-large-precategories.lagda.md b/src/category-theory/functors-large-precategories.lagda.md index 0c4d15795a..0df8ba1c61 100644 --- a/src/category-theory/functors-large-precategories.lagda.md +++ b/src/category-theory/functors-large-precategories.lagda.md @@ -1,17 +1,22 @@ # Functors between large precategories ```agda -module category-theory.functors-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.functors-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-nonunital-precategories.lagda.md b/src/category-theory/functors-nonunital-precategories.lagda.md index a0a49b2b51..d88e97598c 100644 --- a/src/category-theory/functors-nonunital-precategories.lagda.md +++ b/src/category-theory/functors-nonunital-precategories.lagda.md @@ -1,21 +1,26 @@ # Functors between nonunital precategories ```agda -module category-theory.functors-nonunital-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.functors-nonunital-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-set-magmoids -open import category-theory.maps-set-magmoids -open import category-theory.nonunital-precategories +open import category-theory.functors-set-magmoids funext +open import category-theory.maps-set-magmoids funext +open import category-theory.nonunital-precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-precategories.lagda.md b/src/category-theory/functors-precategories.lagda.md index 0a9c7a225e..2b2728683e 100644 --- a/src/category-theory/functors-precategories.lagda.md +++ b/src/category-theory/functors-precategories.lagda.md @@ -1,27 +1,32 @@ # Functors between precategories ```agda -module category-theory.functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-set-magmoids -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories +open import category-theory.functors-set-magmoids funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.opposite-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-set-magmoids.lagda.md b/src/category-theory/functors-set-magmoids.lagda.md index 340252ac73..97029a1f12 100644 --- a/src/category-theory/functors-set-magmoids.lagda.md +++ b/src/category-theory/functors-set-magmoids.lagda.md @@ -1,25 +1,30 @@ # Functors between set-magmoids ```agda -module category-theory.functors-set-magmoids where +open import foundation.function-extensionality-axiom + +module + category-theory.functors-set-magmoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.maps-set-magmoids -open import category-theory.set-magmoids +open import category-theory.maps-set-magmoids funext +open import category-theory.set-magmoids funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/gaunt-categories.lagda.md b/src/category-theory/gaunt-categories.lagda.md index 01853cf160..6c789ddccc 100644 --- a/src/category-theory/gaunt-categories.lagda.md +++ b/src/category-theory/gaunt-categories.lagda.md @@ -1,30 +1,35 @@ # Gaunt categories ```agda -module category-theory.gaunt-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.gaunt-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphism-induction-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.rigid-objects-categories -open import category-theory.strict-categories -open import category-theory.strongly-preunivalent-categories - -open import foundation.cartesian-product-types +open import category-theory.categories funext +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.isomorphism-induction-categories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.nonunital-precategories funext +open import category-theory.precategories funext +open import category-theory.rigid-objects-categories funext +open import category-theory.strict-categories funext +open import category-theory.strongly-preunivalent-categories funext + +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.surjective-maps +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.surjective-maps funext open import foundation.universe-levels ``` diff --git a/src/category-theory/groupoids.lagda.md b/src/category-theory/groupoids.lagda.md index b137946933..1925e1a593 100644 --- a/src/category-theory/groupoids.lagda.md +++ b/src/category-theory/groupoids.lagda.md @@ -1,33 +1,38 @@ # Groupoids ```agda -module category-theory.groupoids where +open import foundation.function-extensionality-axiom + +module + category-theory.groupoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pregroupoids - -open import foundation.1-types -open import foundation.contractible-types +open import category-theory.categories funext +open import category-theory.functors-categories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext +open import category-theory.pregroupoids funext + +open import foundation.1-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.iterated-dependent-pair-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.telescopes -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md b/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md index 1359d2abd4..960d9ef36d 100644 --- a/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md +++ b/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md @@ -1,18 +1,23 @@ # Homotopies of natural transformations in large precategories ```agda -module category-theory.homotopies-natural-transformations-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.homotopies-natural-transformations-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-large-precategories +open import category-theory.functors-large-precategories funext +open import category-theory.large-precategories funext +open import category-theory.natural-transformations-functors-large-precategories funext -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/indiscrete-precategories.lagda.md b/src/category-theory/indiscrete-precategories.lagda.md index 7692b84a17..7fa6bbe805 100644 --- a/src/category-theory/indiscrete-precategories.lagda.md +++ b/src/category-theory/indiscrete-precategories.lagda.md @@ -1,28 +1,33 @@ # Indiscrete precategories ```agda -module category-theory.indiscrete-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.indiscrete-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pregroupoids -open import category-theory.preunivalent-categories -open import category-theory.strict-categories -open import category-theory.subterminal-precategories - -open import foundation.contractible-types +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext +open import category-theory.pregroupoids funext +open import category-theory.preunivalent-categories funext +open import category-theory.strict-categories funext +open import category-theory.subterminal-precategories funext + +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/initial-category.lagda.md b/src/category-theory/initial-category.lagda.md index c24a71c44d..3f22a06c30 100644 --- a/src/category-theory/initial-category.lagda.md +++ b/src/category-theory/initial-category.lagda.md @@ -1,25 +1,30 @@ # The initial category ```agda -module category-theory.initial-category where +open import foundation.function-extensionality-axiom + +module + category-theory.initial-category + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-precategories -open import category-theory.gaunt-categories -open import category-theory.indiscrete-precategories -open import category-theory.precategories -open import category-theory.strict-categories -open import category-theory.strongly-preunivalent-categories - -open import foundation.contractible-types +open import category-theory.categories funext +open import category-theory.functors-precategories funext +open import category-theory.gaunt-categories funext +open import category-theory.indiscrete-precategories funext +open import category-theory.precategories funext +open import category-theory.strict-categories funext +open import category-theory.strongly-preunivalent-categories funext + +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.sets +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-large-categories.lagda.md b/src/category-theory/initial-objects-large-categories.lagda.md index 8dce8c764a..83cf196a6b 100644 --- a/src/category-theory/initial-objects-large-categories.lagda.md +++ b/src/category-theory/initial-objects-large-categories.lagda.md @@ -1,14 +1,19 @@ # Initial objects of large categories ```agda -module category-theory.initial-objects-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.initial-objects-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.initial-objects-large-precategories -open import category-theory.large-categories +open import category-theory.initial-objects-large-precategories funext +open import category-theory.large-categories funext open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-large-precategories.lagda.md b/src/category-theory/initial-objects-large-precategories.lagda.md index c49900291d..ecdb68c72c 100644 --- a/src/category-theory/initial-objects-large-precategories.lagda.md +++ b/src/category-theory/initial-objects-large-precategories.lagda.md @@ -1,15 +1,20 @@ # Initial objects of large precategories ```agda -module category-theory.initial-objects-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.initial-objects-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-precategories.lagda.md b/src/category-theory/initial-objects-precategories.lagda.md index dac1af8fa9..fa087769b5 100644 --- a/src/category-theory/initial-objects-precategories.lagda.md +++ b/src/category-theory/initial-objects-precategories.lagda.md @@ -1,18 +1,23 @@ # Initial objects in a precategory ```agda -module category-theory.initial-objects-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.initial-objects-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.propositions funext open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/category-theory/isomorphism-induction-categories.lagda.md b/src/category-theory/isomorphism-induction-categories.lagda.md index a23461c24d..1544c21f60 100644 --- a/src/category-theory/isomorphism-induction-categories.lagda.md +++ b/src/category-theory/isomorphism-induction-categories.lagda.md @@ -1,24 +1,29 @@ # Isomorphism induction in categories ```agda -module category-theory.isomorphism-induction-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.isomorphism-induction-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphism-induction-precategories -open import category-theory.isomorphisms-in-categories +open import category-theory.categories funext +open import category-theory.isomorphism-induction-precategories funext +open import category-theory.isomorphisms-in-categories funext -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.sections -open import foundation.universal-property-identity-systems +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sections funext +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphism-induction-precategories.lagda.md b/src/category-theory/isomorphism-induction-precategories.lagda.md index 60acd05355..8271e97e37 100644 --- a/src/category-theory/isomorphism-induction-precategories.lagda.md +++ b/src/category-theory/isomorphism-induction-precategories.lagda.md @@ -1,22 +1,27 @@ # Isomorphism induction in precategories ```agda -module category-theory.isomorphism-induction-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.isomorphism-induction-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.identity-systems -open import foundation.identity-types -open import foundation.sections -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.sections funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-categories.lagda.md b/src/category-theory/isomorphisms-in-categories.lagda.md index a0f12490f9..c4aa6b8119 100644 --- a/src/category-theory/isomorphisms-in-categories.lagda.md +++ b/src/category-theory/isomorphisms-in-categories.lagda.md @@ -1,25 +1,30 @@ # Isomorphisms in categories ```agda -module category-theory.isomorphisms-in-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.isomorphisms-in-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories +open import category-theory.categories funext +open import category-theory.isomorphisms-in-precategories funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-large-categories.lagda.md b/src/category-theory/isomorphisms-in-large-categories.lagda.md index e6f13cb68a..2616747086 100644 --- a/src/category-theory/isomorphisms-in-large-categories.lagda.md +++ b/src/category-theory/isomorphisms-in-large-categories.lagda.md @@ -1,25 +1,30 @@ # Isomorphisms in large categories ```agda -module category-theory.isomorphisms-in-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.isomorphisms-in-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-categories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-large-precategories.lagda.md b/src/category-theory/isomorphisms-in-large-precategories.lagda.md index 065f4abe1e..4a7d4fe8b4 100644 --- a/src/category-theory/isomorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/isomorphisms-in-large-precategories.lagda.md @@ -1,28 +1,33 @@ # Isomorphisms in large precategories ```agda -module category-theory.isomorphisms-in-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.isomorphisms-in-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.large-precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-precategories.lagda.md b/src/category-theory/isomorphisms-in-precategories.lagda.md index 31a63e5d4f..e689424c05 100644 --- a/src/category-theory/isomorphisms-in-precategories.lagda.md +++ b/src/category-theory/isomorphisms-in-precategories.lagda.md @@ -1,27 +1,32 @@ # Isomorphisms in precategories ```agda -module category-theory.isomorphisms-in-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.isomorphisms-in-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-subprecategories.lagda.md b/src/category-theory/isomorphisms-in-subprecategories.lagda.md index e0d8560de0..65ebc536f6 100644 --- a/src/category-theory/isomorphisms-in-subprecategories.lagda.md +++ b/src/category-theory/isomorphisms-in-subprecategories.lagda.md @@ -1,21 +1,26 @@ # Isomorphisms in subprecategories ```agda -module category-theory.isomorphisms-in-subprecategories where +open import foundation.function-extensionality-axiom + +module + category-theory.isomorphisms-in-subprecategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.subprecategories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext +open import category-theory.subprecategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/large-categories.lagda.md b/src/category-theory/large-categories.lagda.md index b798eee311..8c97282fc8 100644 --- a/src/category-theory/large-categories.lagda.md +++ b/src/category-theory/large-categories.lagda.md @@ -1,24 +1,29 @@ # Large categories ```agda -module category-theory.large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/large-function-categories.lagda.md b/src/category-theory/large-function-categories.lagda.md index dedadafc7f..311b63bd30 100644 --- a/src/category-theory/large-function-categories.lagda.md +++ b/src/category-theory/large-function-categories.lagda.md @@ -1,20 +1,25 @@ # Large function categories ```agda -module category-theory.large-function-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.large-function-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.dependent-products-of-large-categories -open import category-theory.isomorphisms-in-large-categories -open import category-theory.large-categories - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.dependent-products-of-large-categories funext +open import category-theory.isomorphisms-in-large-categories funext +open import category-theory.large-categories funext + +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/large-function-precategories.lagda.md b/src/category-theory/large-function-precategories.lagda.md index e7b592b608..d0abcda17c 100644 --- a/src/category-theory/large-function-precategories.lagda.md +++ b/src/category-theory/large-function-precategories.lagda.md @@ -1,20 +1,25 @@ # Large function precategories ```agda -module category-theory.large-function-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.large-function-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.dependent-products-of-large-precategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.dependent-products-of-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-precategories funext + +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/large-precategories.lagda.md b/src/category-theory/large-precategories.lagda.md index 4220dda23e..2fd1c17181 100644 --- a/src/category-theory/large-precategories.lagda.md +++ b/src/category-theory/large-precategories.lagda.md @@ -1,21 +1,26 @@ # Large precategories ```agda -module category-theory.large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/large-subcategories.lagda.md b/src/category-theory/large-subcategories.lagda.md index 375f57780d..1ef32e660a 100644 --- a/src/category-theory/large-subcategories.lagda.md +++ b/src/category-theory/large-subcategories.lagda.md @@ -1,14 +1,19 @@ # Large subcategories ```agda -module category-theory.large-subcategories where +open import foundation.function-extensionality-axiom + +module + category-theory.large-subcategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-categories -open import category-theory.large-subprecategories +open import category-theory.large-categories funext +open import category-theory.large-subprecategories funext open import foundation.universe-levels ``` diff --git a/src/category-theory/large-subprecategories.lagda.md b/src/category-theory/large-subprecategories.lagda.md index 935a5ad81c..8999179f6b 100644 --- a/src/category-theory/large-subprecategories.lagda.md +++ b/src/category-theory/large-subprecategories.lagda.md @@ -1,19 +1,24 @@ # Large subprecategories ```agda -module category-theory.large-subprecategories where +open import foundation.function-extensionality-axiom + +module + category-theory.large-subprecategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/limits-precategories.lagda.md b/src/category-theory/limits-precategories.lagda.md index 60015d9a58..28b6294ba7 100644 --- a/src/category-theory/limits-precategories.lagda.md +++ b/src/category-theory/limits-precategories.lagda.md @@ -1,30 +1,36 @@ # Limits in precategories ```agda -module category-theory.limits-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.limits-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.cones-precategories -open import category-theory.constant-functors -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.right-extensions-precategories -open import category-theory.right-kan-extensions-precategories -open import category-theory.terminal-category +open import category-theory.cones-precategories funext +open import category-theory.constant-functors funext +open import category-theory.functors-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext +open import category-theory.right-extensions-precategories funext +open import category-theory.right-kan-extensions-precategories funext +open import category-theory.terminal-category funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/maps-categories.lagda.md b/src/category-theory/maps-categories.lagda.md index ac264b5160..b1aa76cca9 100644 --- a/src/category-theory/maps-categories.lagda.md +++ b/src/category-theory/maps-categories.lagda.md @@ -1,19 +1,24 @@ # Maps between categories ```agda -module category-theory.maps-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.maps-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.maps-precategories +open import category-theory.categories funext +open import category-theory.maps-precategories funext -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-from-small-to-large-categories.lagda.md b/src/category-theory/maps-from-small-to-large-categories.lagda.md index 9f96fbd611..f3f7d35642 100644 --- a/src/category-theory/maps-from-small-to-large-categories.lagda.md +++ b/src/category-theory/maps-from-small-to-large-categories.lagda.md @@ -1,19 +1,24 @@ # Maps from small to large categories ```agda -module category-theory.maps-from-small-to-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.maps-from-small-to-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories -open import category-theory.maps-from-small-to-large-precategories +open import category-theory.categories funext +open import category-theory.large-categories funext +open import category-theory.maps-from-small-to-large-precategories funext -open import foundation.equivalences -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-from-small-to-large-precategories.lagda.md b/src/category-theory/maps-from-small-to-large-precategories.lagda.md index e577f98972..a5b9b49af3 100644 --- a/src/category-theory/maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/maps-from-small-to-large-precategories.lagda.md @@ -1,19 +1,24 @@ # Maps from small to large precategories ```agda -module category-theory.maps-from-small-to-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.maps-from-small-to-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext -open import foundation.equivalences -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-precategories.lagda.md b/src/category-theory/maps-precategories.lagda.md index ba08c41d5c..3f3f8945f8 100644 --- a/src/category-theory/maps-precategories.lagda.md +++ b/src/category-theory/maps-precategories.lagda.md @@ -1,29 +1,34 @@ # Maps between precategories ```agda -module category-theory.maps-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.maps-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.maps-set-magmoids -open import category-theory.precategories +open import category-theory.commuting-squares-of-morphisms-in-precategories funext +open import category-theory.maps-set-magmoids funext +open import category-theory.precategories funext open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-set-magmoids.lagda.md b/src/category-theory/maps-set-magmoids.lagda.md index 33d9842d6b..6ac02f5ba3 100644 --- a/src/category-theory/maps-set-magmoids.lagda.md +++ b/src/category-theory/maps-set-magmoids.lagda.md @@ -1,19 +1,24 @@ # Maps between set-magmoids ```agda -module category-theory.maps-set-magmoids where +open import foundation.function-extensionality-axiom + +module + category-theory.maps-set-magmoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.set-magmoids +open import category-theory.set-magmoids funext open import foundation.action-on-identifications-functions open import foundation.commuting-pentagons-of-identifications open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/monads-on-categories.lagda.md b/src/category-theory/monads-on-categories.lagda.md index c09db9468b..36446e0cd1 100644 --- a/src/category-theory/monads-on-categories.lagda.md +++ b/src/category-theory/monads-on-categories.lagda.md @@ -1,20 +1,25 @@ # Monads on categories ```agda -module category-theory.monads-on-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.monads-on-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.monads-on-precategories -open import category-theory.natural-transformations-functors-categories -open import category-theory.pointed-endofunctors-categories +open import category-theory.categories funext +open import category-theory.functors-categories funext +open import category-theory.monads-on-precategories funext +open import category-theory.natural-transformations-functors-categories funext +open import category-theory.pointed-endofunctors-categories funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/category-theory/monads-on-precategories.lagda.md b/src/category-theory/monads-on-precategories.lagda.md index 63225d5d66..b573ed161a 100644 --- a/src/category-theory/monads-on-precategories.lagda.md +++ b/src/category-theory/monads-on-precategories.lagda.md @@ -1,19 +1,24 @@ # Monads on precategories ```agda -module category-theory.monads-on-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.monads-on-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.pointed-endofunctors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.pointed-endofunctors-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/category-theory/monomorphisms-in-large-precategories.lagda.md b/src/category-theory/monomorphisms-in-large-precategories.lagda.md index 73ce9e3886..1a37bacbeb 100644 --- a/src/category-theory/monomorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/monomorphisms-in-large-precategories.lagda.md @@ -1,18 +1,23 @@ # Monomorphisms in large precategories ```agda -module category-theory.monomorphisms-in-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.monomorphisms-in-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-precategories funext -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-functors-categories.lagda.md b/src/category-theory/natural-isomorphisms-functors-categories.lagda.md index f8f8894aea..e6d9ac88b2 100644 --- a/src/category-theory/natural-isomorphisms-functors-categories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-categories.lagda.md @@ -1,26 +1,31 @@ # Natural isomorphisms between functors between categories ```agda -module category-theory.natural-isomorphisms-functors-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-isomorphisms-functors-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.natural-transformations-functors-categories +open import category-theory.categories funext +open import category-theory.functors-categories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.natural-isomorphisms-functors-precategories funext +open import category-theory.natural-transformations-functors-categories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md b/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md index edaf9fc991..43804b0b8a 100644 --- a/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md @@ -1,17 +1,22 @@ # Natural isomorphisms between functors between large precategories ```agda -module category-theory.natural-isomorphisms-functors-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-isomorphisms-functors-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-large-precategories -open import category-theory.functors-large-precategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-large-precategories +open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext +open import category-theory.functors-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-precategories funext +open import category-theory.natural-transformations-functors-large-precategories funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md b/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md index 35a1b71552..d592d9efc9 100644 --- a/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md @@ -1,26 +1,31 @@ # Natural isomorphisms between functors between precategories ```agda -module category-theory.natural-isomorphisms-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-isomorphisms-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.natural-isomorphisms-maps-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-maps-categories.lagda.md b/src/category-theory/natural-isomorphisms-maps-categories.lagda.md index 571c2723dc..96c80943dc 100644 --- a/src/category-theory/natural-isomorphisms-maps-categories.lagda.md +++ b/src/category-theory/natural-isomorphisms-maps-categories.lagda.md @@ -1,26 +1,31 @@ # Natural isomorphisms between maps between categories ```agda -module category-theory.natural-isomorphisms-maps-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-isomorphisms-maps-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-categories -open import category-theory.maps-categories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.natural-transformations-maps-categories +open import category-theory.categories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.maps-categories funext +open import category-theory.natural-isomorphisms-maps-precategories funext +open import category-theory.natural-transformations-maps-categories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md b/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md index 1e2ff1ccc6..9e37fc5cec 100644 --- a/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md @@ -1,27 +1,32 @@ # Natural isomorphisms between maps between precategories ```agda -module category-theory.natural-isomorphisms-maps-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-isomorphisms-maps-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.natural-transformations-maps-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.natural-transformations-maps-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-numbers-object-precategories.lagda.md b/src/category-theory/natural-numbers-object-precategories.lagda.md index 33cad6e351..099b1d7c40 100644 --- a/src/category-theory/natural-numbers-object-precategories.lagda.md +++ b/src/category-theory/natural-numbers-object-precategories.lagda.md @@ -1,20 +1,25 @@ # Natural numbers object in a precategory ```agda -module category-theory.natural-numbers-object-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-numbers-object-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories -open import category-theory.terminal-objects-precategories +open import category-theory.precategories funext +open import category-theory.terminal-objects-precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.uniqueness-quantification +open import foundation.identity-types funext +open import foundation.uniqueness-quantification funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-categories.lagda.md b/src/category-theory/natural-transformations-functors-categories.lagda.md index 31ddf1de0b..dd8224542e 100644 --- a/src/category-theory/natural-transformations-functors-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-categories.lagda.md @@ -1,22 +1,27 @@ # Natural transformations between functors between categories ```agda -module category-theory.natural-transformations-functors-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-transformations-functors-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.natural-transformations-functors-precategories - -open import foundation.embeddings -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import category-theory.categories funext +open import category-theory.functors-categories funext +open import category-theory.natural-transformations-functors-precategories funext + +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md b/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md index 229103a8d2..3803c379d3 100644 --- a/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md @@ -1,24 +1,29 @@ # Natural transformations between functors from small to large categories ```agda -module category-theory.natural-transformations-functors-from-small-to-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-transformations-functors-from-small-to-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-from-small-to-large-categories -open import category-theory.large-categories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories +open import category-theory.categories funext +open import category-theory.functors-from-small-to-large-categories funext +open import category-theory.large-categories funext +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md b/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md index bde1b382d5..3a098e3a76 100644 --- a/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md @@ -1,25 +1,30 @@ # Natural transformations between functors from small to large precategories ```agda -module category-theory.natural-transformations-functors-from-small-to-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-transformations-functors-from-small-to-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-maps-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.functors-from-small-to-large-precategories funext +open import category-theory.large-precategories funext +open import category-theory.natural-transformations-maps-from-small-to-large-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-large-categories.lagda.md b/src/category-theory/natural-transformations-functors-large-categories.lagda.md index 756ae5d8b1..bef3e409ff 100644 --- a/src/category-theory/natural-transformations-functors-large-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-large-categories.lagda.md @@ -1,15 +1,20 @@ # Natural transformations between functors between large categories ```agda -module category-theory.natural-transformations-functors-large-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-transformations-functors-large-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-categories -open import category-theory.large-categories -open import category-theory.natural-transformations-functors-large-precategories +open import category-theory.functors-large-categories funext +open import category-theory.large-categories funext +open import category-theory.natural-transformations-functors-large-precategories funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-large-precategories.lagda.md b/src/category-theory/natural-transformations-functors-large-precategories.lagda.md index 40e89cd14c..7fe4223bf3 100644 --- a/src/category-theory/natural-transformations-functors-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-large-precategories.lagda.md @@ -1,18 +1,23 @@ # Natural transformations between functors between large precategories ```agda -module category-theory.natural-transformations-functors-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-transformations-functors-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-large-precategories -open import category-theory.functors-large-precategories -open import category-theory.large-precategories +open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext +open import category-theory.functors-large-precategories funext +open import category-theory.large-precategories funext open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-precategories.lagda.md b/src/category-theory/natural-transformations-functors-precategories.lagda.md index 7076ad1387..ad3c27d02d 100644 --- a/src/category-theory/natural-transformations-functors-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-precategories.lagda.md @@ -1,26 +1,31 @@ # Natural transformations between functors between precategories ```agda -module category-theory.natural-transformations-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-transformations-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-maps-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.natural-transformations-maps-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-maps-categories.lagda.md b/src/category-theory/natural-transformations-maps-categories.lagda.md index 04e78aa05e..2555c2a17e 100644 --- a/src/category-theory/natural-transformations-maps-categories.lagda.md +++ b/src/category-theory/natural-transformations-maps-categories.lagda.md @@ -1,22 +1,27 @@ # Natural transformations between maps between categories ```agda -module category-theory.natural-transformations-maps-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-transformations-maps-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.maps-categories -open import category-theory.natural-transformations-maps-precategories - -open import foundation.embeddings -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import category-theory.categories funext +open import category-theory.maps-categories funext +open import category-theory.natural-transformations-maps-precategories funext + +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md b/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md index 3158288d63..6414fa06b0 100644 --- a/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md @@ -1,29 +1,35 @@ # Natural transformations between maps from small to large precategories ```agda -module category-theory.natural-transformations-maps-from-small-to-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-transformations-maps-from-small-to-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-large-precategories -open import category-theory.large-precategories -open import category-theory.maps-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext +open import category-theory.large-precategories funext +open import category-theory.maps-from-small-to-large-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-maps-precategories.lagda.md b/src/category-theory/natural-transformations-maps-precategories.lagda.md index 57b61936ce..daa31f9058 100644 --- a/src/category-theory/natural-transformations-maps-precategories.lagda.md +++ b/src/category-theory/natural-transformations-maps-precategories.lagda.md @@ -1,28 +1,34 @@ # Natural transformations between maps between precategories ```agda -module category-theory.natural-transformations-maps-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.natural-transformations-maps-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.commuting-squares-of-morphisms-in-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/nonunital-precategories.lagda.md b/src/category-theory/nonunital-precategories.lagda.md index 32f4782eab..3815b716ee 100644 --- a/src/category-theory/nonunital-precategories.lagda.md +++ b/src/category-theory/nonunital-precategories.lagda.md @@ -1,22 +1,27 @@ # Nonunital precategories ```agda -module category-theory.nonunital-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.nonunital-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.set-magmoids +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.set-magmoids funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.truncated-types +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/one-object-precategories.lagda.md b/src/category-theory/one-object-precategories.lagda.md index 76dbd98741..0b720fecf7 100644 --- a/src/category-theory/one-object-precategories.lagda.md +++ b/src/category-theory/one-object-precategories.lagda.md @@ -1,24 +1,29 @@ # One object precategories ```agda -module category-theory.one-object-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.one-object-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.endomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.endomorphisms-in-precategories funext +open import category-theory.precategories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext ```
diff --git a/src/category-theory/opposite-categories.lagda.md b/src/category-theory/opposite-categories.lagda.md index 8eefb6735c..8282520eaf 100644 --- a/src/category-theory/opposite-categories.lagda.md +++ b/src/category-theory/opposite-categories.lagda.md @@ -1,24 +1,29 @@ # Opposite categories ```agda -module category-theory.opposite-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.opposite-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.opposite-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.involutions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.involutions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-large-precategories.lagda.md b/src/category-theory/opposite-large-precategories.lagda.md index 99647dd2de..67a2047114 100644 --- a/src/category-theory/opposite-large-precategories.lagda.md +++ b/src/category-theory/opposite-large-precategories.lagda.md @@ -1,22 +1,27 @@ # Opposite large precategories ```agda -module category-theory.opposite-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.opposite-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-precategories +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.large-identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-precategories.lagda.md b/src/category-theory/opposite-precategories.lagda.md index d349bfe93e..287c9cb8ea 100644 --- a/src/category-theory/opposite-precategories.lagda.md +++ b/src/category-theory/opposite-precategories.lagda.md @@ -1,22 +1,27 @@ # Opposite precategories ```agda -module category-theory.opposite-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.opposite-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.involutions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.involutions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-preunivalent-categories.lagda.md b/src/category-theory/opposite-preunivalent-categories.lagda.md index 4ea17ae265..834a7bb0ee 100644 --- a/src/category-theory/opposite-preunivalent-categories.lagda.md +++ b/src/category-theory/opposite-preunivalent-categories.lagda.md @@ -1,25 +1,30 @@ # Opposite preunivalent categories ```agda -module category-theory.opposite-preunivalent-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.opposite-preunivalent-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.preunivalent-categories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.opposite-precategories funext +open import category-theory.precategories funext +open import category-theory.preunivalent-categories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.involutions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.involutions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md b/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md index 131c39a411..6bd809ff2d 100644 --- a/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md +++ b/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md @@ -1,26 +1,31 @@ # Opposite strongly preunivalent categories ```agda -module category-theory.opposite-strongly-preunivalent-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.opposite-strongly-preunivalent-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.strongly-preunivalent-categories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.opposite-precategories funext +open import category-theory.precategories funext +open import category-theory.strongly-preunivalent-categories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.involutions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.involutions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/pointed-endofunctors-categories.lagda.md b/src/category-theory/pointed-endofunctors-categories.lagda.md index f5d7468bb0..53871fb02c 100644 --- a/src/category-theory/pointed-endofunctors-categories.lagda.md +++ b/src/category-theory/pointed-endofunctors-categories.lagda.md @@ -1,19 +1,24 @@ # Pointed endofunctors on categories ```agda -module category-theory.pointed-endofunctors-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.pointed-endofunctors-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.natural-transformations-functors-categories -open import category-theory.pointed-endofunctors-precategories +open import category-theory.categories funext +open import category-theory.functors-categories funext +open import category-theory.natural-transformations-functors-categories funext +open import category-theory.pointed-endofunctors-precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/pointed-endofunctors-precategories.lagda.md b/src/category-theory/pointed-endofunctors-precategories.lagda.md index 2472a4dab6..142b06c157 100644 --- a/src/category-theory/pointed-endofunctors-precategories.lagda.md +++ b/src/category-theory/pointed-endofunctors-precategories.lagda.md @@ -1,18 +1,23 @@ # Pointed endofunctors ```agda -module category-theory.pointed-endofunctors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.pointed-endofunctors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/precategories.lagda.md b/src/category-theory/precategories.lagda.md index 1eb71cad75..8e570f19be 100644 --- a/src/category-theory/precategories.lagda.md +++ b/src/category-theory/precategories.lagda.md @@ -1,25 +1,30 @@ # Precategories ```agda -module category-theory.precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.nonunital-precategories -open import category-theory.set-magmoids +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.nonunital-precategories funext +open import category-theory.set-magmoids funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.truncated-types +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md b/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md index 2e36074e3f..2bf8efad92 100644 --- a/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md +++ b/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md @@ -1,23 +1,28 @@ # Precategory of elements of a presheaf ```agda -module category-theory.precategory-of-elements-of-a-presheaf where +open import foundation.function-extensionality-axiom + +module + category-theory.precategory-of-elements-of-a-presheaf + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories -open import category-theory.presheaf-categories +open import category-theory.functors-precategories funext +open import category-theory.opposite-precategories funext +open import category-theory.precategories funext +open import category-theory.presheaf-categories funext open import foundation.action-on-identifications-functions -open import foundation.category-of-sets +open import foundation.category-of-sets funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md b/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md index 6494609f6b..5b44085f1c 100644 --- a/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md @@ -1,19 +1,24 @@ # The precategory of functors and natural transformations from small to large precategories ```agda -module category-theory.precategory-of-functors-from-small-to-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.precategory-of-functors-from-small-to-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.functors-from-small-to-large-precategories funext +open import category-theory.large-precategories funext +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext +open import category-theory.precategories funext -open import foundation.identity-types -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-functors.lagda.md b/src/category-theory/precategory-of-functors.lagda.md index 17626c170b..6bf104119d 100644 --- a/src/category-theory/precategory-of-functors.lagda.md +++ b/src/category-theory/precategory-of-functors.lagda.md @@ -1,27 +1,31 @@ # The precategory of functors and natural transformations between two precategories ```agda -module category-theory.precategory-of-functors where +open import foundation.function-extensionality-axiom + +module + category-theory.precategory-of-functors + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.natural-isomorphisms-functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.natural-isomorphisms-functors-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md b/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md index 7c755df183..61c129fc2c 100644 --- a/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md @@ -1,19 +1,24 @@ # The precategory of maps and natural transformations from a small to a large precategory ```agda -module category-theory.precategory-of-maps-from-small-to-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.precategory-of-maps-from-small-to-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.maps-from-small-to-large-precategories -open import category-theory.natural-transformations-maps-from-small-to-large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext +open import category-theory.maps-from-small-to-large-precategories funext +open import category-theory.natural-transformations-maps-from-small-to-large-precategories funext +open import category-theory.precategories funext -open import foundation.identity-types -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-maps-precategories.lagda.md b/src/category-theory/precategory-of-maps-precategories.lagda.md index cc303bf840..2205fd36a1 100644 --- a/src/category-theory/precategory-of-maps-precategories.lagda.md +++ b/src/category-theory/precategory-of-maps-precategories.lagda.md @@ -1,27 +1,31 @@ # The precategory of maps and natural transformations between two precategories ```agda -module category-theory.precategory-of-maps-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.precategory-of-maps-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.natural-isomorphisms-maps-precategories -open import category-theory.natural-transformations-maps-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.natural-isomorphisms-maps-precategories funext +open import category-theory.natural-transformations-maps-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/pregroupoids.lagda.md b/src/category-theory/pregroupoids.lagda.md index 6acee12a3c..7c814fc725 100644 --- a/src/category-theory/pregroupoids.lagda.md +++ b/src/category-theory/pregroupoids.lagda.md @@ -1,22 +1,27 @@ # Pregroupoids ```agda -module category-theory.pregroupoids where +open import foundation.function-extensionality-axiom + +module + category-theory.pregroupoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/presheaf-categories.lagda.md b/src/category-theory/presheaf-categories.lagda.md index 40467e0a41..c9a5810d45 100644 --- a/src/category-theory/presheaf-categories.lagda.md +++ b/src/category-theory/presheaf-categories.lagda.md @@ -1,29 +1,33 @@ # Presheaf categories ```agda -module category-theory.presheaf-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.presheaf-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.copresheaf-categories -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories - -open import foundation.category-of-sets -open import foundation.commuting-squares-of-maps -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import category-theory.categories funext +open import category-theory.copresheaf-categories funext +open import category-theory.functors-from-small-to-large-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext +open import category-theory.opposite-precategories funext +open import category-theory.precategories funext + +open import foundation.category-of-sets funext +open import foundation.commuting-squares-of-maps funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/preunivalent-categories.lagda.md b/src/category-theory/preunivalent-categories.lagda.md index 15f683b862..898eba8f06 100644 --- a/src/category-theory/preunivalent-categories.lagda.md +++ b/src/category-theory/preunivalent-categories.lagda.md @@ -1,24 +1,29 @@ # Preunivalent categories ```agda -module category-theory.preunivalent-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.preunivalent-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext -open import foundation.1-types -open import foundation.cartesian-product-types +open import foundation.1-types funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.embeddings funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/products-in-precategories.lagda.md b/src/category-theory/products-in-precategories.lagda.md index 69fc1f4b93..aa4f2d3e53 100644 --- a/src/category-theory/products-in-precategories.lagda.md +++ b/src/category-theory/products-in-precategories.lagda.md @@ -1,23 +1,28 @@ # Products in precategories ```agda -module category-theory.products-in-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.products-in-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext open import foundation.telescopes -open import foundation.uniqueness-quantification +open import foundation.uniqueness-quantification funext open import foundation.universe-levels ``` diff --git a/src/category-theory/products-of-precategories.lagda.md b/src/category-theory/products-of-precategories.lagda.md index cb52fdd0e6..4e3142f3b7 100644 --- a/src/category-theory/products-of-precategories.lagda.md +++ b/src/category-theory/products-of-precategories.lagda.md @@ -1,19 +1,24 @@ # Products of precategories ```agda -module category-theory.products-of-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.products-of-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/category-theory/pseudomonic-functors-precategories.lagda.md b/src/category-theory/pseudomonic-functors-precategories.lagda.md index f5127417ad..0e5844dfc0 100644 --- a/src/category-theory/pseudomonic-functors-precategories.lagda.md +++ b/src/category-theory/pseudomonic-functors-precategories.lagda.md @@ -1,27 +1,32 @@ # Pseudomonic functors between precategories ```agda -module category-theory.pseudomonic-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.pseudomonic-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.conservative-functors-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.conservative-functors-precategories funext +open import category-theory.faithful-functors-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.iterated-dependent-product-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.surjective-maps funext open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/pullbacks-in-precategories.lagda.md b/src/category-theory/pullbacks-in-precategories.lagda.md index 2ade1aec32..e76c9ee00e 100644 --- a/src/category-theory/pullbacks-in-precategories.lagda.md +++ b/src/category-theory/pullbacks-in-precategories.lagda.md @@ -1,23 +1,28 @@ # Pullbacks in precategories ```agda -module category-theory.pullbacks-in-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.pullbacks-in-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext open import foundation.telescopes -open import foundation.uniqueness-quantification +open import foundation.uniqueness-quantification funext open import foundation.universe-levels ``` diff --git a/src/category-theory/replete-subprecategories.lagda.md b/src/category-theory/replete-subprecategories.lagda.md index 4f15777ab4..3aa5392461 100644 --- a/src/category-theory/replete-subprecategories.lagda.md +++ b/src/category-theory/replete-subprecategories.lagda.md @@ -1,27 +1,32 @@ # Replete subprecategories ```agda -module category-theory.replete-subprecategories where +open import foundation.function-extensionality-axiom + +module + category-theory.replete-subprecategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphism-induction-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.isomorphisms-in-subprecategories -open import category-theory.precategories -open import category-theory.subprecategories +open import category-theory.categories funext +open import category-theory.isomorphism-induction-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.isomorphisms-in-subprecategories funext +open import category-theory.precategories funext +open import category-theory.subprecategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.subsingleton-induction -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.telescopes open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/category-theory/representable-functors-categories.lagda.md b/src/category-theory/representable-functors-categories.lagda.md index 22014d5f9d..4ee0500283 100644 --- a/src/category-theory/representable-functors-categories.lagda.md +++ b/src/category-theory/representable-functors-categories.lagda.md @@ -1,18 +1,23 @@ # Representable functors between categories ```agda -module category-theory.representable-functors-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.representable-functors-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.functors-categories -open import category-theory.natural-transformations-functors-categories -open import category-theory.representable-functors-precategories +open import category-theory.categories funext +open import category-theory.functors-categories funext +open import category-theory.natural-transformations-functors-categories funext +open import category-theory.representable-functors-precategories funext -open import foundation.category-of-sets +open import foundation.category-of-sets funext open import foundation.universe-levels ``` diff --git a/src/category-theory/representable-functors-large-precategories.lagda.md b/src/category-theory/representable-functors-large-precategories.lagda.md index 6a88be63e6..c97b3fcd49 100644 --- a/src/category-theory/representable-functors-large-precategories.lagda.md +++ b/src/category-theory/representable-functors-large-precategories.lagda.md @@ -1,21 +1,27 @@ # Representable functors between large precategories ```agda -module category-theory.representable-functors-large-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.representable-functors-large-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories -open import category-theory.large-precategories -open import category-theory.natural-transformations-functors-large-precategories - -open import foundation.category-of-sets -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets +open import category-theory.functors-large-precategories funext +open import category-theory.large-precategories funext +open import category-theory.natural-transformations-functors-large-precategories funext + +open import foundation.category-of-sets funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/category-theory/representable-functors-precategories.lagda.md b/src/category-theory/representable-functors-precategories.lagda.md index 64efc53409..c3d76c7d8c 100644 --- a/src/category-theory/representable-functors-precategories.lagda.md +++ b/src/category-theory/representable-functors-precategories.lagda.md @@ -1,25 +1,31 @@ # Representable functors between precategories ```agda -module category-theory.representable-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.representable-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.copresheaf-categories -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.opposite-precategories -open import category-theory.precategories - -open import foundation.category-of-sets +open import category-theory.copresheaf-categories funext +open import category-theory.functors-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.opposite-precategories funext +open import category-theory.precategories funext + +open import foundation.category-of-sets funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/category-theory/representing-arrow-category.lagda.md b/src/category-theory/representing-arrow-category.lagda.md index a4259a4611..537b9433a1 100644 --- a/src/category-theory/representing-arrow-category.lagda.md +++ b/src/category-theory/representing-arrow-category.lagda.md @@ -1,23 +1,28 @@ # The representing arrow category ```agda -module category-theory.representing-arrow-category where +open import foundation.function-extensionality-axiom + +module + category-theory.representing-arrow-category + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/restrictions-functors-cores-precategories.lagda.md b/src/category-theory/restrictions-functors-cores-precategories.lagda.md index 1463265b07..b72a053e50 100644 --- a/src/category-theory/restrictions-functors-cores-precategories.lagda.md +++ b/src/category-theory/restrictions-functors-cores-precategories.lagda.md @@ -1,23 +1,28 @@ # Restrictions of functors to cores of precategories ```agda -module category-theory.restrictions-functors-cores-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.restrictions-functors-cores-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.cores-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.fully-faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-precategories -open import category-theory.precategories -open import category-theory.pseudomonic-functors-precategories +open import category-theory.cores-precategories funext +open import category-theory.faithful-functors-precategories funext +open import category-theory.fully-faithful-functors-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext +open import category-theory.pseudomonic-functors-precategories funext open import foundation.dependent-pair-types -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/right-extensions-precategories.lagda.md b/src/category-theory/right-extensions-precategories.lagda.md index 4c3828347f..75abfbc96c 100644 --- a/src/category-theory/right-extensions-precategories.lagda.md +++ b/src/category-theory/right-extensions-precategories.lagda.md @@ -1,42 +1,48 @@ # Right extensions in precategories ```agda -module category-theory.right-extensions-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.right-extensions-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories +open import category-theory.functors-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext -open import foundation.action-on-equivalences-functions +open import foundation.action-on-equivalences-functions funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.contractible-types funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.multivariable-homotopies -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.multivariable-homotopies funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext ```
diff --git a/src/category-theory/right-kan-extensions-precategories.lagda.md b/src/category-theory/right-kan-extensions-precategories.lagda.md index 1af7fd92a1..a65d47a0e0 100644 --- a/src/category-theory/right-kan-extensions-precategories.lagda.md +++ b/src/category-theory/right-kan-extensions-precategories.lagda.md @@ -1,20 +1,25 @@ # Right Kan extensions in precategories ```agda -module category-theory.right-kan-extensions-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.right-kan-extensions-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.right-extensions-precategories +open import category-theory.functors-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext +open import category-theory.right-extensions-precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/rigid-objects-categories.lagda.md b/src/category-theory/rigid-objects-categories.lagda.md index ed69843f56..2e46ffd311 100644 --- a/src/category-theory/rigid-objects-categories.lagda.md +++ b/src/category-theory/rigid-objects-categories.lagda.md @@ -1,16 +1,21 @@ # Rigid objects in a category ```agda -module category-theory.rigid-objects-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.rigid-objects-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.rigid-objects-precategories +open import category-theory.categories funext +open import category-theory.rigid-objects-precategories funext -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/rigid-objects-precategories.lagda.md b/src/category-theory/rigid-objects-precategories.lagda.md index 356a7f517a..ec3f5c6779 100644 --- a/src/category-theory/rigid-objects-precategories.lagda.md +++ b/src/category-theory/rigid-objects-precategories.lagda.md @@ -1,18 +1,23 @@ # Rigid objects in a precategory ```agda -module category-theory.rigid-objects-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.rigid-objects-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/category-theory/set-magmoids.lagda.md b/src/category-theory/set-magmoids.lagda.md index ec501dc223..1a02bc7788 100644 --- a/src/category-theory/set-magmoids.lagda.md +++ b/src/category-theory/set-magmoids.lagda.md @@ -1,19 +1,24 @@ # Set-magmoids ```agda -module category-theory.set-magmoids where +open import foundation.function-extensionality-axiom + +module + category-theory.set-magmoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.composition-operations-on-binary-families-of-sets funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/sieves-in-categories.lagda.md b/src/category-theory/sieves-in-categories.lagda.md index 1bab198afa..753490b423 100644 --- a/src/category-theory/sieves-in-categories.lagda.md +++ b/src/category-theory/sieves-in-categories.lagda.md @@ -1,16 +1,21 @@ # Sieves in categories ```agda -module category-theory.sieves-in-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.sieves-in-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories +open import category-theory.categories funext -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/simplex-category.lagda.md b/src/category-theory/simplex-category.lagda.md index aa311fa6b6..b6b19eb689 100644 --- a/src/category-theory/simplex-category.lagda.md +++ b/src/category-theory/simplex-category.lagda.md @@ -1,25 +1,30 @@ # The simplex category ```agda -module category-theory.simplex-category where +open import foundation.function-extensionality-axiom + +module + category-theory.simplex-category + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.precategories funext -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets +open import order-theory.order-preserving-maps-posets funext ```
diff --git a/src/category-theory/slice-precategories.lagda.md b/src/category-theory/slice-precategories.lagda.md index 9443a721e1..e5f3489be9 100644 --- a/src/category-theory/slice-precategories.lagda.md +++ b/src/category-theory/slice-precategories.lagda.md @@ -1,34 +1,39 @@ # Slice precategories ```agda -module category-theory.slice-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.slice-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.precategories -open import category-theory.products-in-precategories -open import category-theory.pullbacks-in-precategories -open import category-theory.terminal-objects-precategories +open import category-theory.functors-precategories funext +open import category-theory.precategories funext +open import category-theory.products-in-precategories funext +open import category-theory.pullbacks-in-precategories funext +open import category-theory.terminal-objects-precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md b/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md index d62ed8e8fe..4d946c0b1c 100644 --- a/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md +++ b/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md @@ -1,32 +1,37 @@ # Split essentially surjective functors between precategories ```agda -module category-theory.split-essentially-surjective-functors-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.split-essentially-surjective-functors-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.cores-precategories -open import category-theory.essential-fibers-of-functors-precategories -open import category-theory.essentially-surjective-functors-precategories -open import category-theory.fully-faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pseudomonic-functors-precategories - -open import foundation.contractible-types +open import category-theory.categories funext +open import category-theory.cores-precategories funext +open import category-theory.essential-fibers-of-functors-precategories funext +open import category-theory.essentially-surjective-functors-precategories funext +open import category-theory.fully-faithful-functors-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext +open import category-theory.pseudomonic-functors-precategories funext + +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.retracts-of-types funext +open import foundation.sections funext open import foundation.universe-levels ``` diff --git a/src/category-theory/strict-categories.lagda.md b/src/category-theory/strict-categories.lagda.md index 549eed68e0..0d6e92e185 100644 --- a/src/category-theory/strict-categories.lagda.md +++ b/src/category-theory/strict-categories.lagda.md @@ -1,26 +1,31 @@ # Strict categories ```agda -module category-theory.strict-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.strict-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.nonunital-precategories -open import category-theory.precategories -open import category-theory.strongly-preunivalent-categories - -open import foundation.cartesian-product-types +open import category-theory.categories funext +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.nonunital-precategories funext +open import category-theory.precategories funext +open import category-theory.strongly-preunivalent-categories funext + +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/strongly-preunivalent-categories.lagda.md b/src/category-theory/strongly-preunivalent-categories.lagda.md index 8ba02ef3ba..565c7dd197 100644 --- a/src/category-theory/strongly-preunivalent-categories.lagda.md +++ b/src/category-theory/strongly-preunivalent-categories.lagda.md @@ -1,28 +1,33 @@ # Strongly preunivalent categories ```agda -module category-theory.strongly-preunivalent-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.strongly-preunivalent-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.preunivalent-categories +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext +open import category-theory.preunivalent-categories funext -open import foundation.1-types -open import foundation.cartesian-product-types +open import foundation.1-types funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.structured-equality-duality +open import foundation.embeddings funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.structured-equality-duality funext open import foundation.universe-levels ``` diff --git a/src/category-theory/structure-equivalences-set-magmoids.lagda.md b/src/category-theory/structure-equivalences-set-magmoids.lagda.md index 38be07d265..f95ae67773 100644 --- a/src/category-theory/structure-equivalences-set-magmoids.lagda.md +++ b/src/category-theory/structure-equivalences-set-magmoids.lagda.md @@ -1,26 +1,31 @@ # Structure equivalences between set-magmoids ```agda -module category-theory.structure-equivalences-set-magmoids where +open import foundation.function-extensionality-axiom + +module + category-theory.structure-equivalences-set-magmoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-set-magmoids -open import category-theory.set-magmoids +open import category-theory.functors-set-magmoids funext +open import category-theory.set-magmoids funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels ``` diff --git a/src/category-theory/subcategories.lagda.md b/src/category-theory/subcategories.lagda.md index cb8cf062cf..76c0a91b65 100644 --- a/src/category-theory/subcategories.lagda.md +++ b/src/category-theory/subcategories.lagda.md @@ -1,36 +1,41 @@ # Subcategories ```agda -module category-theory.subcategories where +open import foundation.function-extensionality-axiom + +module + category-theory.subcategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.isomorphisms-in-subprecategories -open import category-theory.maps-precategories -open import category-theory.precategories -open import category-theory.replete-subprecategories -open import category-theory.subprecategories - -open import foundation.contractible-types +open import category-theory.categories funext +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.faithful-functors-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.isomorphisms-in-subprecategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext +open import category-theory.replete-subprecategories funext +open import category-theory.subprecategories funext + +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/category-theory/subprecategories.lagda.md b/src/category-theory/subprecategories.lagda.md index 9d2ff28504..1950bce6fe 100644 --- a/src/category-theory/subprecategories.lagda.md +++ b/src/category-theory/subprecategories.lagda.md @@ -1,26 +1,31 @@ # Subprecategories ```agda -module category-theory.subprecategories where +open import foundation.function-extensionality-axiom + +module + category-theory.subprecategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.precategories +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.faithful-functors-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/subterminal-precategories.lagda.md b/src/category-theory/subterminal-precategories.lagda.md index a85c94a746..2f3b16a735 100644 --- a/src/category-theory/subterminal-precategories.lagda.md +++ b/src/category-theory/subterminal-precategories.lagda.md @@ -1,32 +1,37 @@ # Subterminal precategories ```agda -module category-theory.subterminal-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.subterminal-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.fully-faithful-functors-precategories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories -open import category-theory.pregroupoids -open import category-theory.strict-categories -open import category-theory.terminal-category +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.fully-faithful-functors-precategories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext +open import category-theory.pregroupoids funext +open import category-theory.strict-categories funext +open import category-theory.terminal-category funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/terminal-category.lagda.md b/src/category-theory/terminal-category.lagda.md index a8a8284077..2991a64e6b 100644 --- a/src/category-theory/terminal-category.lagda.md +++ b/src/category-theory/terminal-category.lagda.md @@ -1,32 +1,37 @@ # The terminal category ```agda -module category-theory.terminal-category where +open import foundation.function-extensionality-axiom + +module + category-theory.terminal-category + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.constant-functors -open import category-theory.functors-categories -open import category-theory.functors-precategories -open import category-theory.gaunt-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.strict-categories -open import category-theory.strongly-preunivalent-categories +open import category-theory.categories funext +open import category-theory.constant-functors funext +open import category-theory.functors-categories funext +open import category-theory.functors-precategories funext +open import category-theory.gaunt-categories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext +open import category-theory.strict-categories funext +open import category-theory.strongly-preunivalent-categories funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/terminal-objects-precategories.lagda.md b/src/category-theory/terminal-objects-precategories.lagda.md index 5a1fcb7d9c..7e38ccc0e6 100644 --- a/src/category-theory/terminal-objects-precategories.lagda.md +++ b/src/category-theory/terminal-objects-precategories.lagda.md @@ -1,18 +1,23 @@ # Terminal objects in a precategory ```agda -module category-theory.terminal-objects-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.terminal-objects-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/category-theory/wide-subcategories.lagda.md b/src/category-theory/wide-subcategories.lagda.md index 7c10b8b282..3da939955a 100644 --- a/src/category-theory/wide-subcategories.lagda.md +++ b/src/category-theory/wide-subcategories.lagda.md @@ -1,35 +1,40 @@ # Wide subcategories ```agda -module category-theory.wide-subcategories where +open import foundation.function-extensionality-axiom + +module + category-theory.wide-subcategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.faithful-functors-precategories -open import category-theory.functors-categories -open import category-theory.isomorphisms-in-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.maps-categories -open import category-theory.precategories -open import category-theory.subcategories -open import category-theory.wide-subprecategories - -open import foundation.contractible-types +open import category-theory.categories funext +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.faithful-functors-precategories funext +open import category-theory.functors-categories funext +open import category-theory.isomorphisms-in-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.maps-categories funext +open import category-theory.precategories funext +open import category-theory.subcategories funext +open import category-theory.wide-subprecategories funext + +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/wide-subprecategories.lagda.md b/src/category-theory/wide-subprecategories.lagda.md index 9c22aab29a..3b207a863e 100644 --- a/src/category-theory/wide-subprecategories.lagda.md +++ b/src/category-theory/wide-subprecategories.lagda.md @@ -1,28 +1,33 @@ # Wide subprecategories ```agda -module category-theory.wide-subprecategories where +open import foundation.function-extensionality-axiom + +module + category-theory.wide-subprecategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories -open import category-theory.maps-precategories -open import category-theory.precategories -open import category-theory.subprecategories +open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.faithful-functors-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.maps-precategories funext +open import category-theory.precategories funext +open import category-theory.subprecategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/yoneda-lemma-categories.lagda.md b/src/category-theory/yoneda-lemma-categories.lagda.md index 3548e0a58d..28206236ba 100644 --- a/src/category-theory/yoneda-lemma-categories.lagda.md +++ b/src/category-theory/yoneda-lemma-categories.lagda.md @@ -1,20 +1,25 @@ # The Yoneda lemma for categories ```agda -module category-theory.yoneda-lemma-categories where +open import foundation.function-extensionality-axiom + +module + category-theory.yoneda-lemma-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.copresheaf-categories -open import category-theory.natural-transformations-functors-from-small-to-large-categories -open import category-theory.representable-functors-categories -open import category-theory.yoneda-lemma-precategories - -open import foundation.category-of-sets -open import foundation.equivalences +open import category-theory.categories funext +open import category-theory.copresheaf-categories funext +open import category-theory.natural-transformations-functors-from-small-to-large-categories funext +open import category-theory.representable-functors-categories funext +open import category-theory.yoneda-lemma-precategories funext + +open import foundation.category-of-sets funext +open import foundation.equivalences funext open import foundation.universe-levels ``` diff --git a/src/category-theory/yoneda-lemma-precategories.lagda.md b/src/category-theory/yoneda-lemma-precategories.lagda.md index 1181e89b5f..0185ca898e 100644 --- a/src/category-theory/yoneda-lemma-precategories.lagda.md +++ b/src/category-theory/yoneda-lemma-precategories.lagda.md @@ -1,28 +1,33 @@ # The Yoneda lemma for precategories ```agda -module category-theory.yoneda-lemma-precategories where +open import foundation.function-extensionality-axiom + +module + category-theory.yoneda-lemma-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.copresheaf-categories -open import category-theory.functors-from-small-to-large-precategories -open import category-theory.natural-transformations-functors-from-small-to-large-precategories -open import category-theory.precategories -open import category-theory.representable-functors-precategories +open import category-theory.copresheaf-categories funext +open import category-theory.functors-from-small-to-large-precategories funext +open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext +open import category-theory.precategories funext +open import category-theory.representable-functors-precategories funext open import foundation.action-on-identifications-functions -open import foundation.category-of-sets +open import foundation.category-of-sets funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/commutative-algebra.lagda.md b/src/commutative-algebra.lagda.md index 7719d0d4d2..39c7e4aa6d 100644 --- a/src/commutative-algebra.lagda.md +++ b/src/commutative-algebra.lagda.md @@ -3,62 +3,67 @@ ## Modules in the commutative algebra namespace ```agda -module commutative-algebra where +open import foundation.function-extensionality-axiom -open import commutative-algebra.binomial-theorem-commutative-rings public -open import commutative-algebra.binomial-theorem-commutative-semirings public -open import commutative-algebra.boolean-rings public -open import commutative-algebra.category-of-commutative-rings public -open import commutative-algebra.commutative-rings public -open import commutative-algebra.commutative-semirings public -open import commutative-algebra.dependent-products-commutative-rings public -open import commutative-algebra.dependent-products-commutative-semirings public -open import commutative-algebra.discrete-fields public -open import commutative-algebra.eisenstein-integers public -open import commutative-algebra.euclidean-domains public -open import commutative-algebra.full-ideals-commutative-rings public -open import commutative-algebra.function-commutative-rings public -open import commutative-algebra.function-commutative-semirings public -open import commutative-algebra.gaussian-integers public -open import commutative-algebra.groups-of-units-commutative-rings public -open import commutative-algebra.homomorphisms-commutative-rings public -open import commutative-algebra.homomorphisms-commutative-semirings public -open import commutative-algebra.ideals-commutative-rings public -open import commutative-algebra.ideals-commutative-semirings public -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings public -open import commutative-algebra.integer-multiples-of-elements-commutative-rings public -open import commutative-algebra.integral-domains public -open import commutative-algebra.intersections-ideals-commutative-rings public -open import commutative-algebra.intersections-radical-ideals-commutative-rings public -open import commutative-algebra.invertible-elements-commutative-rings public -open import commutative-algebra.isomorphisms-commutative-rings public -open import commutative-algebra.joins-ideals-commutative-rings public -open import commutative-algebra.joins-radical-ideals-commutative-rings public -open import commutative-algebra.local-commutative-rings public +module + commutative-algebra + (funext : function-extensionality) + where + +open import commutative-algebra.binomial-theorem-commutative-rings funext public +open import commutative-algebra.binomial-theorem-commutative-semirings funext public +open import commutative-algebra.boolean-rings funext public +open import commutative-algebra.category-of-commutative-rings funext public +open import commutative-algebra.commutative-rings funext public +open import commutative-algebra.commutative-semirings funext public +open import commutative-algebra.dependent-products-commutative-rings funext public +open import commutative-algebra.dependent-products-commutative-semirings funext public +open import commutative-algebra.discrete-fields funext public +open import commutative-algebra.eisenstein-integers funext public +open import commutative-algebra.euclidean-domains funext public +open import commutative-algebra.full-ideals-commutative-rings funext public +open import commutative-algebra.function-commutative-rings funext public +open import commutative-algebra.function-commutative-semirings funext public +open import commutative-algebra.gaussian-integers funext public +open import commutative-algebra.groups-of-units-commutative-rings funext public +open import commutative-algebra.homomorphisms-commutative-rings funext public +open import commutative-algebra.homomorphisms-commutative-semirings funext public +open import commutative-algebra.ideals-commutative-rings funext public +open import commutative-algebra.ideals-commutative-semirings funext public +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext public +open import commutative-algebra.integer-multiples-of-elements-commutative-rings funext public +open import commutative-algebra.integral-domains funext public +open import commutative-algebra.intersections-ideals-commutative-rings funext public +open import commutative-algebra.intersections-radical-ideals-commutative-rings funext public +open import commutative-algebra.invertible-elements-commutative-rings funext public +open import commutative-algebra.isomorphisms-commutative-rings funext public +open import commutative-algebra.joins-ideals-commutative-rings funext public +open import commutative-algebra.joins-radical-ideals-commutative-rings funext public +open import commutative-algebra.local-commutative-rings funext public open import commutative-algebra.maximal-ideals-commutative-rings public -open import commutative-algebra.multiples-of-elements-commutative-rings public -open import commutative-algebra.nilradical-commutative-rings public -open import commutative-algebra.nilradicals-commutative-semirings public -open import commutative-algebra.poset-of-ideals-commutative-rings public -open import commutative-algebra.poset-of-radical-ideals-commutative-rings public -open import commutative-algebra.powers-of-elements-commutative-rings public -open import commutative-algebra.powers-of-elements-commutative-semirings public -open import commutative-algebra.precategory-of-commutative-rings public -open import commutative-algebra.precategory-of-commutative-semirings public -open import commutative-algebra.prime-ideals-commutative-rings public -open import commutative-algebra.products-commutative-rings public -open import commutative-algebra.products-ideals-commutative-rings public -open import commutative-algebra.products-radical-ideals-commutative-rings public -open import commutative-algebra.products-subsets-commutative-rings public -open import commutative-algebra.radical-ideals-commutative-rings public -open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings public -open import commutative-algebra.radicals-of-ideals-commutative-rings public -open import commutative-algebra.subsets-commutative-rings public -open import commutative-algebra.subsets-commutative-semirings public -open import commutative-algebra.sums-commutative-rings public -open import commutative-algebra.sums-commutative-semirings public -open import commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups public -open import commutative-algebra.trivial-commutative-rings public -open import commutative-algebra.zariski-locale public -open import commutative-algebra.zariski-topology public +open import commutative-algebra.multiples-of-elements-commutative-rings funext public +open import commutative-algebra.nilradical-commutative-rings funext public +open import commutative-algebra.nilradicals-commutative-semirings funext public +open import commutative-algebra.poset-of-ideals-commutative-rings funext public +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext public +open import commutative-algebra.powers-of-elements-commutative-rings funext public +open import commutative-algebra.powers-of-elements-commutative-semirings funext public +open import commutative-algebra.precategory-of-commutative-rings funext public +open import commutative-algebra.precategory-of-commutative-semirings funext public +open import commutative-algebra.prime-ideals-commutative-rings funext public +open import commutative-algebra.products-commutative-rings funext public +open import commutative-algebra.products-ideals-commutative-rings funext public +open import commutative-algebra.products-radical-ideals-commutative-rings funext public +open import commutative-algebra.products-subsets-commutative-rings funext public +open import commutative-algebra.radical-ideals-commutative-rings funext public +open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings funext public +open import commutative-algebra.radicals-of-ideals-commutative-rings funext public +open import commutative-algebra.subsets-commutative-rings funext public +open import commutative-algebra.subsets-commutative-semirings funext public +open import commutative-algebra.sums-commutative-rings funext public +open import commutative-algebra.sums-commutative-semirings funext public +open import commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups funext public +open import commutative-algebra.trivial-commutative-rings funext public +open import commutative-algebra.zariski-locale funext public +open import commutative-algebra.zariski-topology funext public ``` diff --git a/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md b/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md index 2e3e0a4f5e..66ed617765 100644 --- a/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md +++ b/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md @@ -1,31 +1,36 @@ # The binomial theorem in commutative rings ```agda -module commutative-algebra.binomial-theorem-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.binomial-theorem-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-semirings -open import commutative-algebra.commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.sums-commutative-rings +open import commutative-algebra.binomial-theorem-commutative-semirings funext +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.powers-of-elements-commutative-rings funext +open import commutative-algebra.sums-commutative-rings funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.binomial-coefficients funext +open import elementary-number-theory.distance-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors-on-commutative-rings +open import linear-algebra.vectors-on-commutative-rings funext -open import ring-theory.binomial-theorem-rings +open import ring-theory.binomial-theorem-rings funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md b/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md index 3bbda32f19..f5de2dcc09 100644 --- a/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md +++ b/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md @@ -1,30 +1,35 @@ # The binomial theorem in commutative semirings ```agda -module commutative-algebra.binomial-theorem-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.binomial-theorem-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings -open import commutative-algebra.powers-of-elements-commutative-semirings -open import commutative-algebra.sums-commutative-semirings +open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.powers-of-elements-commutative-semirings funext +open import commutative-algebra.sums-commutative-semirings funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.binomial-coefficients funext +open import elementary-number-theory.distance-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors-on-commutative-semirings +open import linear-algebra.vectors-on-commutative-semirings funext -open import ring-theory.binomial-theorem-semirings +open import ring-theory.binomial-theorem-semirings funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/commutative-algebra/boolean-rings.lagda.md b/src/commutative-algebra/boolean-rings.lagda.md index 6ae1075b5d..0d0a00364b 100644 --- a/src/commutative-algebra/boolean-rings.lagda.md +++ b/src/commutative-algebra/boolean-rings.lagda.md @@ -1,18 +1,23 @@ # Boolean rings ```agda -module commutative-algebra.boolean-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.boolean-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import ring-theory.idempotent-elements-rings +open import ring-theory.idempotent-elements-rings funext ```
diff --git a/src/commutative-algebra/category-of-commutative-rings.lagda.md b/src/commutative-algebra/category-of-commutative-rings.lagda.md index c3fd89fa48..a4cb09a777 100644 --- a/src/commutative-algebra/category-of-commutative-rings.lagda.md +++ b/src/commutative-algebra/category-of-commutative-rings.lagda.md @@ -1,17 +1,22 @@ # The category of commutative rings ```agda -module commutative-algebra.category-of-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.category-of-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories +open import category-theory.categories funext +open import category-theory.large-categories funext -open import commutative-algebra.isomorphisms-commutative-rings -open import commutative-algebra.precategory-of-commutative-rings +open import commutative-algebra.isomorphisms-commutative-rings funext +open import commutative-algebra.precategory-of-commutative-rings funext open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/commutative-rings.lagda.md b/src/commutative-algebra/commutative-rings.lagda.md index 06b3e5d600..0d09b9357c 100644 --- a/src/commutative-algebra/commutative-rings.lagda.md +++ b/src/commutative-algebra/commutative-rings.lagda.md @@ -1,47 +1,52 @@ # Commutative rings ```agda -module commutative-algebra.commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.involutions -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.involutions funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext +open import ring-theory.semirings funext ```
diff --git a/src/commutative-algebra/commutative-semirings.lagda.md b/src/commutative-algebra/commutative-semirings.lagda.md index 9f261db26a..f08205268f 100644 --- a/src/commutative-algebra/commutative-semirings.lagda.md +++ b/src/commutative-algebra/commutative-semirings.lagda.md @@ -1,7 +1,12 @@ # Commutative semirings ```agda -module commutative-algebra.commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.commutative-semirings + (funext : function-extensionality) + where ```
Imports @@ -11,17 +16,17 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.telescopes open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/commutative-algebra/dependent-products-commutative-rings.lagda.md b/src/commutative-algebra/dependent-products-commutative-rings.lagda.md index 45881aecf1..ce74483af8 100644 --- a/src/commutative-algebra/dependent-products-commutative-rings.lagda.md +++ b/src/commutative-algebra/dependent-products-commutative-rings.lagda.md @@ -1,25 +1,30 @@ # Dependent products of commutative rings ```agda -module commutative-algebra.dependent-products-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.dependent-products-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.dependent-products-commutative-monoids +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.dependent-products-commutative-monoids funext -open import ring-theory.dependent-products-rings -open import ring-theory.rings +open import ring-theory.dependent-products-rings funext +open import ring-theory.rings funext ```
diff --git a/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md b/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md index abcf6a837e..1bd7ed4d4d 100644 --- a/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md +++ b/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md @@ -1,24 +1,29 @@ # Dependent products of commutative semirings ```agda -module commutative-algebra.dependent-products-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.dependent-products-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.dependent-products-commutative-monoids +open import group-theory.commutative-monoids funext +open import group-theory.dependent-products-commutative-monoids funext -open import ring-theory.dependent-products-semirings -open import ring-theory.semirings +open import ring-theory.dependent-products-semirings funext +open import ring-theory.semirings funext ```
diff --git a/src/commutative-algebra/discrete-fields.lagda.md b/src/commutative-algebra/discrete-fields.lagda.md index 6943d29b4b..674e77107c 100644 --- a/src/commutative-algebra/discrete-fields.lagda.md +++ b/src/commutative-algebra/discrete-fields.lagda.md @@ -1,17 +1,22 @@ # Discrete fields ```agda -module commutative-algebra.discrete-fields where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.discrete-fields + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import foundation.universe-levels -open import ring-theory.division-rings +open import ring-theory.division-rings funext ```
diff --git a/src/commutative-algebra/eisenstein-integers.lagda.md b/src/commutative-algebra/eisenstein-integers.lagda.md index d0120575cd..44c469260e 100644 --- a/src/commutative-algebra/eisenstein-integers.lagda.md +++ b/src/commutative-algebra/eisenstein-integers.lagda.md @@ -1,32 +1,37 @@ # The Eisenstein integers ```agda -module commutative-algebra.eisenstein-integers where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.eisenstein-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext -open import elementary-number-theory.addition-integers -open import elementary-number-theory.equality-integers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.semigroups funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/commutative-algebra/euclidean-domains.lagda.md b/src/commutative-algebra/euclidean-domains.lagda.md index abd586d5ef..178d7dad95 100644 --- a/src/commutative-algebra/euclidean-domains.lagda.md +++ b/src/commutative-algebra/euclidean-domains.lagda.md @@ -1,51 +1,56 @@ # Euclidean domains ```agda -module commutative-algebra.euclidean-domains where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.euclidean-domains + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.commutative-semirings -open import commutative-algebra.integral-domains -open import commutative-algebra.trivial-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.integral-domains funext +open import commutative-algebra.trivial-commutative-rings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.involutions -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.involutions funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext +open import ring-theory.semirings funext ```
diff --git a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md index 762bbd4709..4df1509d28 100644 --- a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md @@ -1,28 +1,33 @@ # Full ideals of commutative rings ```agda -module commutative-algebra.full-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.full-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.poset-of-ideals-commutative-rings funext +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext +open import commutative-algebra.radical-ideals-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import order-theory.top-elements-large-posets +open import order-theory.top-elements-large-posets funext -open import ring-theory.full-ideals-rings +open import ring-theory.full-ideals-rings funext ```
diff --git a/src/commutative-algebra/function-commutative-rings.lagda.md b/src/commutative-algebra/function-commutative-rings.lagda.md index fb7920277a..a740285c39 100644 --- a/src/commutative-algebra/function-commutative-rings.lagda.md +++ b/src/commutative-algebra/function-commutative-rings.lagda.md @@ -1,23 +1,28 @@ # Function commutative rings ```agda -module commutative-algebra.function-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.function-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.dependent-products-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.dependent-products-commutative-rings funext -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/commutative-algebra/function-commutative-semirings.lagda.md b/src/commutative-algebra/function-commutative-semirings.lagda.md index 186bc1dbc1..005e2833de 100644 --- a/src/commutative-algebra/function-commutative-semirings.lagda.md +++ b/src/commutative-algebra/function-commutative-semirings.lagda.md @@ -1,22 +1,27 @@ # Function commutative semirings ```agda -module commutative-algebra.function-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.function-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings -open import commutative-algebra.dependent-products-commutative-semirings +open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.dependent-products-commutative-semirings funext -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.commutative-monoids +open import group-theory.commutative-monoids funext -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/commutative-algebra/gaussian-integers.lagda.md b/src/commutative-algebra/gaussian-integers.lagda.md index 2cbe987830..6529b2c3b0 100644 --- a/src/commutative-algebra/gaussian-integers.lagda.md +++ b/src/commutative-algebra/gaussian-integers.lagda.md @@ -1,33 +1,38 @@ # The Gaussian integers ```agda -module commutative-algebra.gaussian-integers where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.gaussian-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext -open import elementary-number-theory.addition-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.equality-integers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.semigroups funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md b/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md index f3fcd5aac1..f9e0b103be 100644 --- a/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md +++ b/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md @@ -1,34 +1,39 @@ # The group of multiplicative units of a commutative ring ```agda -module commutative-algebra.groups-of-units-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.groups-of-units-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories +open import category-theory.functors-large-precategories funext -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.precategory-of-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.homomorphisms-commutative-rings funext +open import commutative-algebra.precategory-of-commutative-rings funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.category-of-abelian-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.submonoids +open import group-theory.abelian-groups funext +open import group-theory.category-of-abelian-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext +open import group-theory.submonoids funext -open import ring-theory.groups-of-units-rings +open import ring-theory.groups-of-units-rings funext ```
diff --git a/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md b/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md index 284d752ce5..0bf8ee831f 100644 --- a/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md +++ b/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md @@ -1,27 +1,32 @@ # Homomorphisms of commutative rings ```agda -module commutative-algebra.homomorphisms-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.homomorphisms-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-semirings -open import commutative-algebra.invertible-elements-commutative-rings - -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.homomorphisms-commutative-semirings funext +open import commutative-algebra.invertible-elements-commutative-rings funext + +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.homomorphisms-monoids funext -open import ring-theory.homomorphisms-rings +open import ring-theory.homomorphisms-rings funext ```
diff --git a/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md b/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md index c5ee3254af..b7e95ceecd 100644 --- a/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md +++ b/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md @@ -1,24 +1,29 @@ # Homomorphisms of commutative semirings ```agda -module commutative-algebra.homomorphisms-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.homomorphisms-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-commutative-monoids funext +open import group-theory.homomorphisms-monoids funext -open import ring-theory.homomorphisms-semirings +open import ring-theory.homomorphisms-semirings funext ```
diff --git a/src/commutative-algebra/ideals-commutative-rings.lagda.md b/src/commutative-algebra/ideals-commutative-rings.lagda.md index 90f082cc86..ad2e40878a 100644 --- a/src/commutative-algebra/ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/ideals-commutative-rings.lagda.md @@ -1,29 +1,34 @@ # Ideals of commutative rings ```agda -module commutative-algebra.ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.powers-of-elements-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import ring-theory.ideals-rings -open import ring-theory.left-ideals-rings -open import ring-theory.right-ideals-rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-rings funext +open import ring-theory.left-ideals-rings funext +open import ring-theory.right-ideals-rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/commutative-algebra/ideals-commutative-semirings.lagda.md b/src/commutative-algebra/ideals-commutative-semirings.lagda.md index 8fb7d4a127..44111aa66d 100644 --- a/src/commutative-algebra/ideals-commutative-semirings.lagda.md +++ b/src/commutative-algebra/ideals-commutative-semirings.lagda.md @@ -1,21 +1,26 @@ # Ideals of commutative semirings ```agda -module commutative-algebra.ideals-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.ideals-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings -open import commutative-algebra.subsets-commutative-semirings +open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.subsets-commutative-semirings funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import ring-theory.ideals-semirings +open import ring-theory.ideals-semirings funext ```
diff --git a/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md b/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md index c057c98271..6705ffb22d 100644 --- a/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md @@ -1,24 +1,29 @@ # Ideals generated by subsets of commutative rings ```agda -module commutative-algebra.ideals-generated-by-subsets-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.ideals-generated-by-subsets-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.poset-of-ideals-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext -open import foundation.identity-types -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels -open import lists.concatenation-lists +open import lists.concatenation-lists funext -open import ring-theory.ideals-generated-by-subsets-rings +open import ring-theory.ideals-generated-by-subsets-rings funext ```
diff --git a/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md b/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md index ea8f228c18..9f26a8c364 100644 --- a/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md @@ -1,27 +1,32 @@ # Integer multiples of elements of commutative rings ```agda -module commutative-algebra.integer-multiples-of-elements-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.integer-multiples-of-elements-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.multiples-of-elements-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.homomorphisms-commutative-rings funext +open import commutative-algebra.multiples-of-elements-commutative-rings funext -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups +open import group-theory.homomorphisms-abelian-groups funext -open import ring-theory.integer-multiples-of-elements-rings +open import ring-theory.integer-multiples-of-elements-rings funext ```
diff --git a/src/commutative-algebra/integral-domains.lagda.md b/src/commutative-algebra/integral-domains.lagda.md index d960d94053..f74ed26a29 100644 --- a/src/commutative-algebra/integral-domains.lagda.md +++ b/src/commutative-algebra/integral-domains.lagda.md @@ -1,48 +1,53 @@ # Integral domains ```agda -module commutative-algebra.integral-domains where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.integral-domains + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.commutative-semirings -open import commutative-algebra.trivial-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.trivial-commutative-rings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.involutions -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.involutions funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext +open import ring-theory.semirings funext ```
diff --git a/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md b/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md index 6846baf280..7c65b17989 100644 --- a/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md @@ -1,25 +1,30 @@ # Intersections of ideals of commutative rings ```agda -module commutative-algebra.intersections-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.intersections-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.poset-of-ideals-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import foundation.dependent-pair-types -open import foundation.intersections-subtypes -open import foundation.subtypes +open import foundation.intersections-subtypes funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext -open import ring-theory.intersections-ideals-rings +open import ring-theory.intersections-ideals-rings funext ```
diff --git a/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md index 1bf031cb1c..657fd20b20 100644 --- a/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md @@ -1,34 +1,39 @@ # Intersections of radical ideals of commutative rings ```agda -module commutative-algebra.intersections-radical-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.intersections-radical-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.full-ideals-commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.intersections-ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.products-ideals-commutative-rings -open import commutative-algebra.products-radical-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.radicals-of-ideals-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.full-ideals-commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.intersections-ideals-commutative-rings funext +open import commutative-algebra.poset-of-ideals-commutative-rings funext +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext +open import commutative-algebra.powers-of-elements-commutative-rings funext +open import commutative-algebra.products-ideals-commutative-rings funext +open import commutative-algebra.products-radical-ideals-commutative-rings funext +open import commutative-algebra.radical-ideals-commutative-rings funext +open import commutative-algebra.radicals-of-ideals-commutative-rings funext open import elementary-number-theory.addition-natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-meet-semilattices funext ```
diff --git a/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md b/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md index ebc4116027..832a92a546 100644 --- a/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md @@ -1,21 +1,26 @@ # Invertible elements in commutative rings ```agda -module commutative-algebra.invertible-elements-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.invertible-elements-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import ring-theory.invertible-elements-rings +open import ring-theory.invertible-elements-rings funext ```
diff --git a/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md b/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md index 663583921f..97956b6146 100644 --- a/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md +++ b/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md @@ -1,33 +1,38 @@ # Isomorphisms of commutative rings ```agda -module commutative-algebra.isomorphisms-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.isomorphisms-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.invertible-elements-commutative-rings -open import commutative-algebra.precategory-of-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.homomorphisms-commutative-rings funext +open import commutative-algebra.invertible-elements-commutative-rings funext +open import commutative-algebra.precategory-of-commutative-rings funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.isomorphisms-abelian-groups +open import group-theory.isomorphisms-abelian-groups funext -open import ring-theory.isomorphisms-rings +open import ring-theory.isomorphisms-rings funext ```
diff --git a/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md b/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md index 52deaa9ff9..1378574e66 100644 --- a/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md @@ -1,28 +1,33 @@ # Joins of ideals of commutative rings ```agda -module commutative-algebra.joins-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.joins-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.products-ideals-commutative-rings -open import commutative-algebra.products-subsets-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext +open import commutative-algebra.poset-of-ideals-commutative-rings funext +open import commutative-algebra.products-ideals-commutative-rings funext +open import commutative-algebra.products-subsets-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.subtypes funext +open import foundation.unions-subtypes funext open import foundation.universe-levels -open import ring-theory.joins-ideals-rings +open import ring-theory.joins-ideals-rings funext ```
diff --git a/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md index 3cd6e927ed..cd8406084f 100644 --- a/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md @@ -1,31 +1,36 @@ # Joins of radical ideals of commutative rings ```agda -module commutative-algebra.joins-radical-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.joins-radical-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.intersections-radical-ideals-commutative-rings -open import commutative-algebra.joins-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.products-ideals-commutative-rings -open import commutative-algebra.products-radical-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings -open import commutative-algebra.radicals-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.intersections-radical-ideals-commutative-rings funext +open import commutative-algebra.joins-ideals-commutative-rings funext +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext +open import commutative-algebra.products-ideals-commutative-rings funext +open import commutative-algebra.products-radical-ideals-commutative-rings funext +open import commutative-algebra.radical-ideals-commutative-rings funext +open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings funext +open import commutative-algebra.radicals-of-ideals-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext ```
diff --git a/src/commutative-algebra/local-commutative-rings.lagda.md b/src/commutative-algebra/local-commutative-rings.lagda.md index 9de71b60fc..741dffe391 100644 --- a/src/commutative-algebra/local-commutative-rings.lagda.md +++ b/src/commutative-algebra/local-commutative-rings.lagda.md @@ -1,21 +1,26 @@ # Local commutative rings ```agda -module commutative-algebra.local-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.local-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import ring-theory.local-rings -open import ring-theory.rings +open import ring-theory.local-rings funext +open import ring-theory.rings funext ```
diff --git a/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md b/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md index 9121d62200..580c5524d9 100644 --- a/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md @@ -1,22 +1,27 @@ # Multiples of elements in commutative rings ```agda -module commutative-algebra.multiples-of-elements-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.multiples-of-elements-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.multiples-of-elements-rings +open import ring-theory.multiples-of-elements-rings funext ```
diff --git a/src/commutative-algebra/nilradical-commutative-rings.lagda.md b/src/commutative-algebra/nilradical-commutative-rings.lagda.md index e8cae03fe9..fbfe8ca6fe 100644 --- a/src/commutative-algebra/nilradical-commutative-rings.lagda.md +++ b/src/commutative-algebra/nilradical-commutative-rings.lagda.md @@ -1,25 +1,30 @@ # Nilradical of a commutative ring ```agda -module commutative-algebra.nilradical-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.nilradical-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.prime-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.prime-ideals-commutative-rings funext +open import commutative-algebra.radical-ideals-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import ring-theory.nilpotent-elements-rings +open import ring-theory.nilpotent-elements-rings funext ```
diff --git a/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md b/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md index 994c83bc29..a56e881c9c 100644 --- a/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md +++ b/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md @@ -1,20 +1,25 @@ # The nilradical of a commutative semiring ```agda -module commutative-algebra.nilradicals-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.nilradicals-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings -open import commutative-algebra.subsets-commutative-semirings +open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.subsets-commutative-semirings funext -open import foundation.existential-quantification -open import foundation.identity-types +open import foundation.existential-quantification funext +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.nilpotent-elements-semirings +open import ring-theory.nilpotent-elements-semirings funext ```
diff --git a/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md b/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md index 4b5b4c589f..de63dc2a43 100644 --- a/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md @@ -1,23 +1,28 @@ # The poset of ideals of a commutative ring ```agda -module commutative-algebra.poset-of-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.poset-of-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders +open import order-theory.large-posets funext +open import order-theory.large-preorders funext -open import ring-theory.poset-of-ideals-rings +open import ring-theory.poset-of-ideals-rings funext ```
diff --git a/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md index 79e6803732..4c2e24e6f6 100644 --- a/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md @@ -1,26 +1,31 @@ # The poset of radical ideals of a commutative ring ```agda -module commutative-algebra.poset-of-radical-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.poset-of-radical-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.poset-of-ideals-commutative-rings funext +open import commutative-algebra.radical-ideals-commutative-rings funext -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.similarity-of-elements-large-posets funext ```
diff --git a/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md b/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md index 9cd508163f..0e44f2a90a 100644 --- a/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md @@ -1,23 +1,28 @@ # Powers of elements in commutative rings ```agda -module commutative-algebra.powers-of-elements-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.powers-of-elements-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.powers-of-elements-rings +open import ring-theory.powers-of-elements-rings funext ```
diff --git a/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md b/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md index 0bda772d1a..e551a299b3 100644 --- a/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md +++ b/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md @@ -1,21 +1,26 @@ # Powers of elements in commutative semirings ```agda -module commutative-algebra.powers-of-elements-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.powers-of-elements-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.powers-of-elements-semirings +open import ring-theory.powers-of-elements-semirings funext ```
diff --git a/src/commutative-algebra/precategory-of-commutative-rings.lagda.md b/src/commutative-algebra/precategory-of-commutative-rings.lagda.md index 51c54f1c3f..ef537ea59d 100644 --- a/src/commutative-algebra/precategory-of-commutative-rings.lagda.md +++ b/src/commutative-algebra/precategory-of-commutative-rings.lagda.md @@ -1,21 +1,26 @@ # The precategory of commutative rings ```agda -module commutative-algebra.precategory-of-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.precategory-of-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import foundation.universe-levels -open import ring-theory.precategory-of-rings +open import ring-theory.precategory-of-rings funext ```
diff --git a/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md b/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md index e0239a074f..a7a4a16402 100644 --- a/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md +++ b/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md @@ -1,21 +1,26 @@ # The precategory of commutative semirings ```agda -module commutative-algebra.precategory-of-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.precategory-of-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext open import foundation.universe-levels -open import ring-theory.precategory-of-semirings +open import ring-theory.precategory-of-semirings funext ```
diff --git a/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md b/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md index de9a327c13..09636d11ab 100644 --- a/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md @@ -1,29 +1,34 @@ # Prime ideals of commutative rings ```agda -module commutative-algebra.prime-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.prime-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.full-ideals-commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.full-ideals-commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.powers-of-elements-commutative-rings funext +open import commutative-algebra.radical-ideals-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.disjunction funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import ring-theory.subsets-rings +open import ring-theory.subsets-rings funext ```
diff --git a/src/commutative-algebra/products-commutative-rings.lagda.md b/src/commutative-algebra/products-commutative-rings.lagda.md index dee1a7ee38..4518d26d3c 100644 --- a/src/commutative-algebra/products-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-commutative-rings.lagda.md @@ -1,26 +1,31 @@ # Products of commutative rings ```agda -module commutative-algebra.products-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.products-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.semigroups funext -open import ring-theory.products-rings -open import ring-theory.rings +open import ring-theory.products-rings funext +open import ring-theory.rings funext ```
diff --git a/src/commutative-algebra/products-ideals-commutative-rings.lagda.md b/src/commutative-algebra/products-ideals-commutative-rings.lagda.md index 9e1a2d1173..91245efc37 100644 --- a/src/commutative-algebra/products-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-ideals-commutative-rings.lagda.md @@ -1,28 +1,33 @@ # Products of ideals of commutative rings ```agda -module commutative-algebra.products-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.products-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.products-subsets-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext +open import commutative-algebra.poset-of-ideals-commutative-rings funext +open import commutative-algebra.products-subsets-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import lists.lists -open import ring-theory.products-ideals-rings +open import ring-theory.products-ideals-rings funext ```
diff --git a/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md index f112058f6d..e88c46f9ba 100644 --- a/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md @@ -1,27 +1,32 @@ # Products of radical ideals of a commutative ring ```agda -module commutative-algebra.products-radical-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.products-radical-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.products-ideals-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.radicals-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext +open import commutative-algebra.powers-of-elements-commutative-rings funext +open import commutative-algebra.products-ideals-commutative-rings funext +open import commutative-algebra.radical-ideals-commutative-rings funext +open import commutative-algebra.radicals-of-ideals-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/products-subsets-commutative-rings.lagda.md b/src/commutative-algebra/products-subsets-commutative-rings.lagda.md index 9bad16cb22..1615bcdbce 100644 --- a/src/commutative-algebra/products-subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-subsets-commutative-rings.lagda.md @@ -1,21 +1,26 @@ # Products of subsets of commutative rings ```agda -module commutative-algebra.products-subsets-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.products-subsets-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext -open import foundation.identity-types -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.subtypes funext +open import foundation.unions-subtypes funext open import foundation.universe-levels -open import ring-theory.products-subsets-rings +open import ring-theory.products-subsets-rings funext ```
diff --git a/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md index f087226bc9..a8662f9e6b 100644 --- a/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md @@ -1,26 +1,31 @@ # Radical ideals of commutative rings ```agda -module commutative-algebra.radical-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.radical-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.powers-of-elements-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md b/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md index 9c09b474bf..d01ca8f870 100644 --- a/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md @@ -9,14 +9,14 @@ module
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.radicals-of-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings - -open import foundation.subtypes +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext +open import commutative-algebra.radical-ideals-commutative-rings funext +open import commutative-algebra.radicals-of-ideals-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext + +open import foundation.subtypes funext open import foundation.universe-levels ``` @@ -34,7 +34,12 @@ containing `S`. ### The universal property of the radical ideal generated by a subset ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {l1 l2 l3 : Level} (A : Commutative-Ring l1) (S : subset-Commutative-Ring l2 A) (I : radical-ideal-Commutative-Ring l3 A) diff --git a/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md b/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md index 13a2f12ae2..283714df24 100644 --- a/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md @@ -1,37 +1,42 @@ # Radicals of ideals of commutative rings ```agda -module commutative-algebra.radicals-of-ideals-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.radicals-of-ideals-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-rings -open import commutative-algebra.commutative-rings -open import commutative-algebra.ideals-commutative-rings -open import commutative-algebra.poset-of-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings -open import commutative-algebra.powers-of-elements-commutative-rings -open import commutative-algebra.radical-ideals-commutative-rings -open import commutative-algebra.subsets-commutative-rings +open import commutative-algebra.binomial-theorem-commutative-rings funext +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.poset-of-ideals-commutative-rings funext +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext +open import commutative-algebra.powers-of-elements-commutative-rings funext +open import commutative-algebra.radical-ideals-commutative-rings funext +open import commutative-algebra.subsets-commutative-rings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.reflective-galois-connections-large-posets +open import order-theory.galois-connections-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.reflective-galois-connections-large-posets funext ```
diff --git a/src/commutative-algebra/subsets-commutative-rings.lagda.md b/src/commutative-algebra/subsets-commutative-rings.lagda.md index fd7c2d204e..0197c79c0b 100644 --- a/src/commutative-algebra/subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/subsets-commutative-rings.lagda.md @@ -1,24 +1,29 @@ # Subsets of commutative rings ```agda -module commutative-algebra.subsets-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.subsets-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext -open import foundation.identity-types -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositional-extensionality funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.subgroups-abelian-groups +open import group-theory.subgroups-abelian-groups funext -open import ring-theory.subsets-rings +open import ring-theory.subsets-rings funext ```
diff --git a/src/commutative-algebra/subsets-commutative-semirings.lagda.md b/src/commutative-algebra/subsets-commutative-semirings.lagda.md index 73f9932341..993233e06b 100644 --- a/src/commutative-algebra/subsets-commutative-semirings.lagda.md +++ b/src/commutative-algebra/subsets-commutative-semirings.lagda.md @@ -1,21 +1,26 @@ # Subsets of commutative semirings ```agda -module commutative-algebra.subsets-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.subsets-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import ring-theory.subsets-semirings +open import ring-theory.subsets-semirings funext ```
diff --git a/src/commutative-algebra/sums-commutative-rings.lagda.md b/src/commutative-algebra/sums-commutative-rings.lagda.md index f26a86e6db..e320adfe0e 100644 --- a/src/commutative-algebra/sums-commutative-rings.lagda.md +++ b/src/commutative-algebra/sums-commutative-rings.lagda.md @@ -1,32 +1,37 @@ # Sums in commutative rings ```agda -module commutative-algebra.sums-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.sums-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.coproduct-types funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors -open import linear-algebra.vectors-on-commutative-rings +open import linear-algebra.vectors funext +open import linear-algebra.vectors funext-on-commutative-rings -open import ring-theory.sums-rings +open import ring-theory.sums-rings funext -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/commutative-algebra/sums-commutative-semirings.lagda.md b/src/commutative-algebra/sums-commutative-semirings.lagda.md index 16eaf02de8..7b3da31ad7 100644 --- a/src/commutative-algebra/sums-commutative-semirings.lagda.md +++ b/src/commutative-algebra/sums-commutative-semirings.lagda.md @@ -1,29 +1,34 @@ # Sums in commutative semirings ```agda -module commutative-algebra.sums-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.sums-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors -open import linear-algebra.vectors-on-commutative-semirings +open import linear-algebra.vectors funext +open import linear-algebra.vectors funext-on-commutative-semirings -open import ring-theory.sums-semirings +open import ring-theory.sums-semirings funext -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md b/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md index d504ae3dbc..bdbc75dc63 100644 --- a/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md +++ b/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md @@ -9,23 +9,23 @@ module
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.isomorphisms-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.homomorphisms-commutative-rings funext +open import commutative-algebra.isomorphisms-commutative-rings funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.isomorphisms-abelian-groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.isomorphisms-abelian-groups funext +open import group-theory.semigroups funext -open import ring-theory.homomorphisms-rings -open import ring-theory.rings -open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups +open import ring-theory.homomorphisms-rings funext +open import ring-theory.rings funext +open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups funext ```
@@ -48,7 +48,12 @@ transported ring structure. ### Transporting the multiplicative structure of a commutative ring along an isomorphism of abelian groups ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {l1 l2 : Level} (A : Commutative-Ring l1) (B : Ab l2) (f : iso-Ab (ab-Commutative-Ring A) B) where diff --git a/src/commutative-algebra/trivial-commutative-rings.lagda.md b/src/commutative-algebra/trivial-commutative-rings.lagda.md index 8aa4781e63..2f4cf74b79 100644 --- a/src/commutative-algebra/trivial-commutative-rings.lagda.md +++ b/src/commutative-algebra/trivial-commutative-rings.lagda.md @@ -1,31 +1,36 @@ # Trivial commutative rings ```agda -module commutative-algebra.trivial-commutative-rings where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.trivial-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.isomorphisms-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.isomorphisms-commutative-rings funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.structure-identity-principle open import foundation.unit-type open import foundation.universe-levels open import foundation-core.identity-types -open import group-theory.abelian-groups -open import group-theory.trivial-groups +open import group-theory.abelian-groups funext +open import group-theory.trivial-groups funext -open import ring-theory.rings -open import ring-theory.trivial-rings +open import ring-theory.rings funext +open import ring-theory.trivial-rings funext ```
diff --git a/src/commutative-algebra/zariski-locale.lagda.md b/src/commutative-algebra/zariski-locale.lagda.md index 512b67f821..0a7fa646a8 100644 --- a/src/commutative-algebra/zariski-locale.lagda.md +++ b/src/commutative-algebra/zariski-locale.lagda.md @@ -1,21 +1,26 @@ # The Zariski locale ```agda -module commutative-algebra.zariski-locale where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.zariski-locale + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.intersections-radical-ideals-commutative-rings -open import commutative-algebra.joins-radical-ideals-commutative-rings -open import commutative-algebra.poset-of-radical-ideals-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.intersections-radical-ideals-commutative-rings funext +open import commutative-algebra.joins-radical-ideals-commutative-rings funext +open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext open import foundation.universe-levels -open import order-theory.large-frames -open import order-theory.large-locales +open import order-theory.large-frames funext +open import order-theory.large-locales funext ```
diff --git a/src/commutative-algebra/zariski-topology.lagda.md b/src/commutative-algebra/zariski-topology.lagda.md index b3bbbec25c..3f5f0dd52c 100644 --- a/src/commutative-algebra/zariski-topology.lagda.md +++ b/src/commutative-algebra/zariski-topology.lagda.md @@ -1,19 +1,24 @@ # The Zariski topology on the set of prime ideals of a commutative ring ```agda -module commutative-algebra.zariski-topology where +open import foundation.function-extensionality-axiom + +module + commutative-algebra.zariski-topology + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.prime-ideals-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.prime-ideals-commutative-rings funext -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/domain-theory.lagda.md b/src/domain-theory.lagda.md index 5e1cb84b7f..a2853d3ac7 100644 --- a/src/domain-theory.lagda.md +++ b/src/domain-theory.lagda.md @@ -3,15 +3,20 @@ ## Modules in the domain theory namespace ```agda -module domain-theory where +open import foundation.function-extensionality-axiom -open import domain-theory.directed-complete-posets public -open import domain-theory.directed-families-posets public -open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets public -open import domain-theory.kleenes-fixed-point-theorem-posets public -open import domain-theory.omega-complete-posets public -open import domain-theory.omega-continuous-maps-omega-complete-posets public -open import domain-theory.omega-continuous-maps-posets public -open import domain-theory.reindexing-directed-families-posets public -open import domain-theory.scott-continuous-maps-posets public +module + domain-theory + (funext : function-extensionality) + where + +open import domain-theory.directed-complete-posets funext public +open import domain-theory.directed-families-posets funext public +open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets funext public +open import domain-theory.kleenes-fixed-point-theorem-posets funext public +open import domain-theory.omega-complete-posets funext public +open import domain-theory.omega-continuous-maps-omega-complete-posets funext public +open import domain-theory.omega-continuous-maps-posets funext public +open import domain-theory.reindexing-directed-families-posets funext public +open import domain-theory.scott-continuous-maps-posets funext public ``` diff --git a/src/domain-theory/directed-complete-posets.lagda.md b/src/domain-theory/directed-complete-posets.lagda.md index 2225aeff51..fb840536f4 100644 --- a/src/domain-theory/directed-complete-posets.lagda.md +++ b/src/domain-theory/directed-complete-posets.lagda.md @@ -1,25 +1,30 @@ # Directed complete posets ```agda -module domain-theory.directed-complete-posets where +open import foundation.function-extensionality-axiom + +module + domain-theory.directed-complete-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import domain-theory.directed-families-posets +open import domain-theory.directed-families-posets funext -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.posets +open import order-theory.least-upper-bounds-posets funext +open import order-theory.posets funext ```
diff --git a/src/domain-theory/directed-families-posets.lagda.md b/src/domain-theory/directed-families-posets.lagda.md index 0b192c1b84..dd3523c946 100644 --- a/src/domain-theory/directed-families-posets.lagda.md +++ b/src/domain-theory/directed-families-posets.lagda.md @@ -1,29 +1,34 @@ # Directed families in posets ```agda -module domain-theory.directed-families-posets where +open import foundation.function-extensionality-axiom + +module + domain-theory.directed-families-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.surjective-maps -open import foundation.universal-quantification +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.surjective-maps funext +open import foundation.universal-quantification funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md b/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md index 0e760554ec..de4056d860 100644 --- a/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md +++ b/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md @@ -1,41 +1,46 @@ # Kleene's fixed point theorem for ω-complete posets ```agda -module domain-theory.kleenes-fixed-point-theorem-omega-complete-posets where +open import foundation.function-extensionality-axiom + +module + domain-theory.kleenes-fixed-point-theorem-omega-complete-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import domain-theory.directed-families-posets -open import domain-theory.kleenes-fixed-point-theorem-posets -open import domain-theory.omega-complete-posets -open import domain-theory.omega-continuous-maps-omega-complete-posets -open import domain-theory.omega-continuous-maps-posets - -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import domain-theory.directed-families-posets funext +open import domain-theory.kleenes-fixed-point-theorem-posets funext +open import domain-theory.omega-complete-posets funext +open import domain-theory.omega-continuous-maps-omega-complete-posets funext +open import domain-theory.omega-continuous-maps-posets funext + +open import elementary-number-theory.decidable-total-order-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.iterating-functions -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.iterating-functions funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import order-theory.bottom-elements-posets -open import order-theory.chains-posets -open import order-theory.inflattices -open import order-theory.inhabited-chains-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.suplattices -open import order-theory.upper-bounds-posets +open import order-theory.bottom-elements-posets funext +open import order-theory.chains-posets funext +open import order-theory.inflattices funext +open import order-theory.inhabited-chains-posets funext +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext +open import order-theory.suplattices funext +open import order-theory.upper-bounds-posets funext ```
diff --git a/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md b/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md index 8a3518c188..34cbc88b25 100644 --- a/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md +++ b/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md @@ -1,38 +1,43 @@ # Kleene's fixed point theorem for posets ```agda -module domain-theory.kleenes-fixed-point-theorem-posets where +open import foundation.function-extensionality-axiom + +module + domain-theory.kleenes-fixed-point-theorem-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import domain-theory.directed-families-posets -open import domain-theory.omega-continuous-maps-posets +open import domain-theory.directed-families-posets funext +open import domain-theory.omega-continuous-maps-posets funext -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.iterating-functions -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.iterating-functions funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import order-theory.bottom-elements-posets -open import order-theory.chains-posets -open import order-theory.inflattices -open import order-theory.inhabited-chains-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.suplattices -open import order-theory.upper-bounds-posets +open import order-theory.bottom-elements-posets funext +open import order-theory.chains-posets funext +open import order-theory.inflattices funext +open import order-theory.inhabited-chains-posets funext +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext +open import order-theory.suplattices funext +open import order-theory.upper-bounds-posets funext ```
diff --git a/src/domain-theory/omega-complete-posets.lagda.md b/src/domain-theory/omega-complete-posets.lagda.md index 612e60affb..cbae88df54 100644 --- a/src/domain-theory/omega-complete-posets.lagda.md +++ b/src/domain-theory/omega-complete-posets.lagda.md @@ -1,29 +1,34 @@ # ω-Complete posets ```agda -module domain-theory.omega-complete-posets where +open import foundation.function-extensionality-axiom + +module + domain-theory.omega-complete-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext +open import order-theory.upper-bounds-posets funext ```
diff --git a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md index 60ce16827f..36d6a284bf 100644 --- a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md @@ -1,43 +1,48 @@ # ω-Continuous maps between ω-complete posets ```agda -module domain-theory.omega-continuous-maps-omega-complete-posets where +open import foundation.function-extensionality-axiom + +module + domain-theory.omega-continuous-maps-omega-complete-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import domain-theory.directed-families-posets -open import domain-theory.omega-complete-posets -open import domain-theory.omega-continuous-maps-posets +open import domain-theory.directed-families-posets funext +open import domain-theory.omega-complete-posets funext +open import domain-theory.omega-continuous-maps-posets funext -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.booleans +open import foundation.booleans funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.existential-quantification -open import foundation.function-types +open import foundation.existential-quantification funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.surjective-maps funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import order-theory.join-preserving-maps-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.join-preserving-maps-posets funext +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/domain-theory/omega-continuous-maps-posets.lagda.md b/src/domain-theory/omega-continuous-maps-posets.lagda.md index 3781ac426b..179bdc67fd 100644 --- a/src/domain-theory/omega-continuous-maps-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-posets.lagda.md @@ -1,41 +1,46 @@ # ω-Continuous maps between posets ```agda -module domain-theory.omega-continuous-maps-posets where +open import foundation.function-extensionality-axiom + +module + domain-theory.omega-continuous-maps-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import domain-theory.directed-families-posets +open import domain-theory.directed-families-posets funext -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.booleans +open import foundation.booleans funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.existential-quantification -open import foundation.function-types +open import foundation.existential-quantification funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.surjective-maps funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import order-theory.join-preserving-maps-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.join-preserving-maps-posets funext +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/domain-theory/reindexing-directed-families-posets.lagda.md b/src/domain-theory/reindexing-directed-families-posets.lagda.md index 28396bf30a..6484b0d608 100644 --- a/src/domain-theory/reindexing-directed-families-posets.lagda.md +++ b/src/domain-theory/reindexing-directed-families-posets.lagda.md @@ -1,31 +1,36 @@ # Reindexing directed families in posets ```agda -module domain-theory.reindexing-directed-families-posets where +open import foundation.function-extensionality-axiom + +module + domain-theory.reindexing-directed-families-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import domain-theory.directed-families-posets +open import domain-theory.directed-families-posets funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.surjective-maps -open import foundation.universal-quantification +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.surjective-maps funext +open import foundation.universal-quantification funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/domain-theory/scott-continuous-maps-posets.lagda.md b/src/domain-theory/scott-continuous-maps-posets.lagda.md index bd50ff479e..bc2908bab3 100644 --- a/src/domain-theory/scott-continuous-maps-posets.lagda.md +++ b/src/domain-theory/scott-continuous-maps-posets.lagda.md @@ -1,38 +1,43 @@ # Scott-continuous maps between posets ```agda -module domain-theory.scott-continuous-maps-posets where +open import foundation.function-extensionality-axiom + +module + domain-theory.scott-continuous-maps-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import domain-theory.directed-families-posets -open import domain-theory.reindexing-directed-families-posets +open import domain-theory.directed-families-posets funext +open import domain-theory.reindexing-directed-families-posets funext -open import foundation.booleans +open import foundation.booleans funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.existential-quantification -open import foundation.function-types +open import foundation.existential-quantification funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.small-types funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.surjective-maps funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/elementary-number-theory.lagda.md b/src/elementary-number-theory.lagda.md index 11611b1a6a..a7cd00c920 100644 --- a/src/elementary-number-theory.lagda.md +++ b/src/elementary-number-theory.lagda.md @@ -7,180 +7,185 @@ ## Modules in the elementary number theory namespace ```agda -module elementary-number-theory where +open import foundation.function-extensionality-axiom -open import elementary-number-theory.absolute-value-integers public +module + elementary-number-theory + (funext : function-extensionality) + where + +open import elementary-number-theory.absolute-value-integers funext public open import elementary-number-theory.ackermann-function public -open import elementary-number-theory.addition-integer-fractions public -open import elementary-number-theory.addition-integers public +open import elementary-number-theory.addition-integer-fractions funext public +open import elementary-number-theory.addition-integers funext public open import elementary-number-theory.addition-natural-numbers public -open import elementary-number-theory.addition-positive-and-negative-integers public -open import elementary-number-theory.addition-rational-numbers public -open import elementary-number-theory.additive-group-of-rational-numbers public -open import elementary-number-theory.archimedean-property-integer-fractions public -open import elementary-number-theory.archimedean-property-integers public -open import elementary-number-theory.archimedean-property-natural-numbers public -open import elementary-number-theory.archimedean-property-positive-rational-numbers public -open import elementary-number-theory.archimedean-property-rational-numbers public -open import elementary-number-theory.arithmetic-functions public -open import elementary-number-theory.based-induction-natural-numbers public -open import elementary-number-theory.based-strong-induction-natural-numbers public -open import elementary-number-theory.bell-numbers public -open import elementary-number-theory.bezouts-lemma-integers public -open import elementary-number-theory.bezouts-lemma-natural-numbers public -open import elementary-number-theory.binomial-coefficients public -open import elementary-number-theory.binomial-theorem-integers public -open import elementary-number-theory.binomial-theorem-natural-numbers public -open import elementary-number-theory.bounded-sums-arithmetic-functions public -open import elementary-number-theory.catalan-numbers public -open import elementary-number-theory.cofibonacci public -open import elementary-number-theory.collatz-bijection public -open import elementary-number-theory.collatz-conjecture public -open import elementary-number-theory.commutative-semiring-of-natural-numbers public -open import elementary-number-theory.conatural-numbers public -open import elementary-number-theory.congruence-integers public -open import elementary-number-theory.congruence-natural-numbers public -open import elementary-number-theory.cross-multiplication-difference-integer-fractions public -open import elementary-number-theory.cubes-natural-numbers public -open import elementary-number-theory.decidable-dependent-function-types public -open import elementary-number-theory.decidable-total-order-integers public -open import elementary-number-theory.decidable-total-order-natural-numbers public -open import elementary-number-theory.decidable-total-order-rational-numbers public -open import elementary-number-theory.decidable-total-order-standard-finite-types public -open import elementary-number-theory.decidable-types public -open import elementary-number-theory.difference-integers public -open import elementary-number-theory.difference-rational-numbers public -open import elementary-number-theory.dirichlet-convolution public -open import elementary-number-theory.distance-integers public -open import elementary-number-theory.distance-natural-numbers public -open import elementary-number-theory.divisibility-integers public -open import elementary-number-theory.divisibility-modular-arithmetic public -open import elementary-number-theory.divisibility-natural-numbers public -open import elementary-number-theory.divisibility-standard-finite-types public -open import elementary-number-theory.equality-conatural-numbers public -open import elementary-number-theory.equality-integers public -open import elementary-number-theory.equality-natural-numbers public -open import elementary-number-theory.equality-rational-numbers public -open import elementary-number-theory.euclid-mullin-sequence public -open import elementary-number-theory.euclidean-division-natural-numbers public -open import elementary-number-theory.eulers-totient-function public -open import elementary-number-theory.exponentiation-natural-numbers public -open import elementary-number-theory.factorials public +open import elementary-number-theory.addition-positive-and-negative-integers funext public +open import elementary-number-theory.addition-rational-numbers funext public +open import elementary-number-theory.additive-group-of-rational-numbers funext public +open import elementary-number-theory.archimedean-property-integer-fractions funext public +open import elementary-number-theory.archimedean-property-integers funext public +open import elementary-number-theory.archimedean-property-natural-numbers funext public +open import elementary-number-theory.archimedean-property-positive-rational-numbers funext public +open import elementary-number-theory.archimedean-property-rational-numbers funext public +open import elementary-number-theory.arithmetic-functions funext public +open import elementary-number-theory.based-induction-natural-numbers funext public +open import elementary-number-theory.based-strong-induction-natural-numbers funext public +open import elementary-number-theory.bell-numbers funext public +open import elementary-number-theory.bezouts-lemma-integers funext public +open import elementary-number-theory.bezouts-lemma-natural-numbers funext public +open import elementary-number-theory.binomial-coefficients funext public +open import elementary-number-theory.binomial-theorem-integers funext public +open import elementary-number-theory.binomial-theorem-natural-numbers funext public +open import elementary-number-theory.bounded-sums-arithmetic-functions funext public +open import elementary-number-theory.catalan-numbers funext public +open import elementary-number-theory.cofibonacci funext public +open import elementary-number-theory.collatz-bijection funext public +open import elementary-number-theory.collatz-conjecture funext public +open import elementary-number-theory.commutative-semiring-of-natural-numbers funext public +open import elementary-number-theory.conatural-numbers funext public +open import elementary-number-theory.congruence-integers funext public +open import elementary-number-theory.congruence-natural-numbers funext public +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext public +open import elementary-number-theory.cubes-natural-numbers funext public +open import elementary-number-theory.decidable-dependent-function-types funext public +open import elementary-number-theory.decidable-total-order-integers funext public +open import elementary-number-theory.decidable-total-order-natural-numbers funext public +open import elementary-number-theory.decidable-total-order-rational-numbers funext public +open import elementary-number-theory.decidable-total-order-standard-finite-types funext public +open import elementary-number-theory.decidable-types funext public +open import elementary-number-theory.difference-integers funext public +open import elementary-number-theory.difference-rational-numbers funext public +open import elementary-number-theory.dirichlet-convolution funext public +open import elementary-number-theory.distance-integers funext public +open import elementary-number-theory.distance-natural-numbers funext public +open import elementary-number-theory.divisibility-integers funext public +open import elementary-number-theory.divisibility-modular-arithmetic funext public +open import elementary-number-theory.divisibility-natural-numbers funext public +open import elementary-number-theory.divisibility-standard-finite-types funext public +open import elementary-number-theory.equality-conatural-numbers funext public +open import elementary-number-theory.equality-integers funext public +open import elementary-number-theory.equality-natural-numbers funext public +open import elementary-number-theory.equality-rational-numbers funext public +open import elementary-number-theory.euclid-mullin-sequence funext public +open import elementary-number-theory.euclidean-division-natural-numbers funext public +open import elementary-number-theory.eulers-totient-function funext public +open import elementary-number-theory.exponentiation-natural-numbers funext public +open import elementary-number-theory.factorials funext public open import elementary-number-theory.falling-factorials public -open import elementary-number-theory.fermat-numbers public -open import elementary-number-theory.fibonacci-sequence public -open import elementary-number-theory.field-of-rational-numbers public -open import elementary-number-theory.finitary-natural-numbers public -open import elementary-number-theory.finitely-cyclic-maps public -open import elementary-number-theory.fundamental-theorem-of-arithmetic public -open import elementary-number-theory.goldbach-conjecture public -open import elementary-number-theory.greatest-common-divisor-integers public -open import elementary-number-theory.greatest-common-divisor-natural-numbers public -open import elementary-number-theory.group-of-integers public -open import elementary-number-theory.half-integers public -open import elementary-number-theory.hardy-ramanujan-number public -open import elementary-number-theory.inclusion-natural-numbers-conatural-numbers public -open import elementary-number-theory.inequality-conatural-numbers public -open import elementary-number-theory.inequality-integer-fractions public -open import elementary-number-theory.inequality-integers public -open import elementary-number-theory.inequality-natural-numbers public -open import elementary-number-theory.inequality-rational-numbers public -open import elementary-number-theory.inequality-standard-finite-types public -open import elementary-number-theory.infinite-conatural-numbers public -open import elementary-number-theory.infinitude-of-primes public -open import elementary-number-theory.initial-segments-natural-numbers public -open import elementary-number-theory.integer-fractions public +open import elementary-number-theory.fermat-numbers funext public +open import elementary-number-theory.fibonacci-sequence funext public +open import elementary-number-theory.field-of-rational-numbers funext public +open import elementary-number-theory.finitary-natural-numbers funext public +open import elementary-number-theory.finitely-cyclic-maps funext public +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext public +open import elementary-number-theory.goldbach-conjecture funext public +open import elementary-number-theory.greatest-common-divisor-integers funext public +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext public +open import elementary-number-theory.group-of-integers funext public +open import elementary-number-theory.half-integers funext public +open import elementary-number-theory.hardy-ramanujan-number funext public +open import elementary-number-theory.inclusion-natural-numbers-conatural-numbers funext public +open import elementary-number-theory.inequality-conatural-numbers funext public +open import elementary-number-theory.inequality-integer-fractions funext public +open import elementary-number-theory.inequality-integers funext public +open import elementary-number-theory.inequality-natural-numbers funext public +open import elementary-number-theory.inequality-rational-numbers funext public +open import elementary-number-theory.inequality-standard-finite-types funext public +open import elementary-number-theory.infinite-conatural-numbers funext public +open import elementary-number-theory.infinitude-of-primes funext public +open import elementary-number-theory.initial-segments-natural-numbers funext public +open import elementary-number-theory.integer-fractions funext public open import elementary-number-theory.integer-partitions public open import elementary-number-theory.integers public -open import elementary-number-theory.jacobi-symbol public -open import elementary-number-theory.kolakoski-sequence public -open import elementary-number-theory.legendre-symbol public -open import elementary-number-theory.lower-bounds-natural-numbers public -open import elementary-number-theory.maximum-natural-numbers public -open import elementary-number-theory.maximum-standard-finite-types public -open import elementary-number-theory.mediant-integer-fractions public -open import elementary-number-theory.mersenne-primes public -open import elementary-number-theory.minimum-natural-numbers public -open import elementary-number-theory.minimum-standard-finite-types public -open import elementary-number-theory.modular-arithmetic public -open import elementary-number-theory.modular-arithmetic-standard-finite-types public -open import elementary-number-theory.monoid-of-natural-numbers-with-addition public -open import elementary-number-theory.monoid-of-natural-numbers-with-maximum public -open import elementary-number-theory.multiplication-integer-fractions public -open import elementary-number-theory.multiplication-integers public -open import elementary-number-theory.multiplication-lists-of-natural-numbers public +open import elementary-number-theory.jacobi-symbol funext public +open import elementary-number-theory.kolakoski-sequence funext public +open import elementary-number-theory.legendre-symbol funext public +open import elementary-number-theory.lower-bounds-natural-numbers funext public +open import elementary-number-theory.maximum-natural-numbers funext public +open import elementary-number-theory.maximum-standard-finite-types funext public +open import elementary-number-theory.mediant-integer-fractions funext public +open import elementary-number-theory.mersenne-primes funext public +open import elementary-number-theory.minimum-natural-numbers funext public +open import elementary-number-theory.minimum-standard-finite-types funext public +open import elementary-number-theory.modular-arithmetic funext public +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext public +open import elementary-number-theory.monoid-of-natural-numbers-with-addition funext public +open import elementary-number-theory.monoid-of-natural-numbers-with-maximum funext public +open import elementary-number-theory.multiplication-integer-fractions funext public +open import elementary-number-theory.multiplication-integers funext public +open import elementary-number-theory.multiplication-lists-of-natural-numbers funext public open import elementary-number-theory.multiplication-natural-numbers public -open import elementary-number-theory.multiplication-positive-and-negative-integers public -open import elementary-number-theory.multiplication-rational-numbers public -open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers public -open import elementary-number-theory.multiplicative-group-of-rational-numbers public -open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions public -open import elementary-number-theory.multiplicative-monoid-of-natural-numbers public -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers public +open import elementary-number-theory.multiplication-positive-and-negative-integers funext public +open import elementary-number-theory.multiplication-rational-numbers funext public +open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers funext public +open import elementary-number-theory.multiplicative-group-of-rational-numbers funext public +open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions funext public +open import elementary-number-theory.multiplicative-monoid-of-natural-numbers funext public +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext public open import elementary-number-theory.multiplicative-units-integers public open import elementary-number-theory.multiplicative-units-standard-cyclic-rings public open import elementary-number-theory.multiset-coefficients public open import elementary-number-theory.natural-numbers public -open import elementary-number-theory.negative-integers public -open import elementary-number-theory.nonnegative-integers public -open import elementary-number-theory.nonpositive-integers public -open import elementary-number-theory.nonzero-integers public -open import elementary-number-theory.nonzero-natural-numbers public -open import elementary-number-theory.nonzero-rational-numbers public -open import elementary-number-theory.ordinal-induction-natural-numbers public -open import elementary-number-theory.parity-natural-numbers public -open import elementary-number-theory.peano-arithmetic public -open import elementary-number-theory.pisano-periods public -open import elementary-number-theory.poset-of-natural-numbers-ordered-by-divisibility public -open import elementary-number-theory.positive-and-negative-integers public -open import elementary-number-theory.positive-conatural-numbers public -open import elementary-number-theory.positive-integer-fractions public -open import elementary-number-theory.positive-integers public -open import elementary-number-theory.positive-rational-numbers public -open import elementary-number-theory.powers-integers public -open import elementary-number-theory.powers-of-two public -open import elementary-number-theory.prime-numbers public -open import elementary-number-theory.products-of-natural-numbers public -open import elementary-number-theory.proper-divisors-natural-numbers public -open import elementary-number-theory.pythagorean-triples public -open import elementary-number-theory.rational-numbers public -open import elementary-number-theory.reduced-integer-fractions public -open import elementary-number-theory.relatively-prime-integers public -open import elementary-number-theory.relatively-prime-natural-numbers public -open import elementary-number-theory.repeating-element-standard-finite-type public -open import elementary-number-theory.retracts-of-natural-numbers public -open import elementary-number-theory.ring-of-integers public -open import elementary-number-theory.ring-of-rational-numbers public -open import elementary-number-theory.sieve-of-eratosthenes public -open import elementary-number-theory.square-free-natural-numbers public -open import elementary-number-theory.squares-integers public -open import elementary-number-theory.squares-modular-arithmetic public -open import elementary-number-theory.squares-natural-numbers public -open import elementary-number-theory.standard-cyclic-groups public -open import elementary-number-theory.standard-cyclic-rings public +open import elementary-number-theory.negative-integers funext public +open import elementary-number-theory.nonnegative-integers funext public +open import elementary-number-theory.nonpositive-integers funext public +open import elementary-number-theory.nonzero-integers funext public +open import elementary-number-theory.nonzero-natural-numbers funext public +open import elementary-number-theory.nonzero-rational-numbers funext public +open import elementary-number-theory.ordinal-induction-natural-numbers funext public +open import elementary-number-theory.parity-natural-numbers funext public +open import elementary-number-theory.peano-arithmetic funext public +open import elementary-number-theory.pisano-periods funext public +open import elementary-number-theory.poset-of-natural-numbers-ordered-by-divisibility funext public +open import elementary-number-theory.positive-and-negative-integers funext public +open import elementary-number-theory.positive-conatural-numbers funext public +open import elementary-number-theory.positive-integer-fractions funext public +open import elementary-number-theory.positive-integers funext public +open import elementary-number-theory.positive-rational-numbers funext public +open import elementary-number-theory.powers-integers funext public +open import elementary-number-theory.powers-of-two funext public +open import elementary-number-theory.prime-numbers funext public +open import elementary-number-theory.products-of-natural-numbers funext public +open import elementary-number-theory.proper-divisors-natural-numbers funext public +open import elementary-number-theory.pythagorean-triples funext public +open import elementary-number-theory.rational-numbers funext public +open import elementary-number-theory.reduced-integer-fractions funext public +open import elementary-number-theory.relatively-prime-integers funext public +open import elementary-number-theory.relatively-prime-natural-numbers funext public +open import elementary-number-theory.repeating-element-standard-finite-type funext public +open import elementary-number-theory.retracts-of-natural-numbers funext public +open import elementary-number-theory.ring-of-integers funext public +open import elementary-number-theory.ring-of-rational-numbers funext public +open import elementary-number-theory.sieve-of-eratosthenes funext public +open import elementary-number-theory.square-free-natural-numbers funext public +open import elementary-number-theory.squares-integers funext public +open import elementary-number-theory.squares-modular-arithmetic funext public +open import elementary-number-theory.squares-natural-numbers funext public +open import elementary-number-theory.standard-cyclic-groups funext public +open import elementary-number-theory.standard-cyclic-rings funext public open import elementary-number-theory.stirling-numbers-of-the-second-kind public -open import elementary-number-theory.strict-inequality-integer-fractions public -open import elementary-number-theory.strict-inequality-integers public -open import elementary-number-theory.strict-inequality-natural-numbers public -open import elementary-number-theory.strict-inequality-rational-numbers public -open import elementary-number-theory.strict-inequality-standard-finite-types public -open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers public -open import elementary-number-theory.strong-induction-natural-numbers public -open import elementary-number-theory.sums-of-natural-numbers public -open import elementary-number-theory.sylvesters-sequence public -open import elementary-number-theory.taxicab-numbers public +open import elementary-number-theory.strict-inequality-integer-fractions funext public +open import elementary-number-theory.strict-inequality-integers funext public +open import elementary-number-theory.strict-inequality-natural-numbers funext public +open import elementary-number-theory.strict-inequality-rational-numbers funext public +open import elementary-number-theory.strict-inequality-standard-finite-types funext public +open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers funext public +open import elementary-number-theory.strong-induction-natural-numbers funext public +open import elementary-number-theory.sums-of-natural-numbers funext public +open import elementary-number-theory.sylvesters-sequence funext public +open import elementary-number-theory.taxicab-numbers funext public open import elementary-number-theory.telephone-numbers public open import elementary-number-theory.triangular-numbers public -open import elementary-number-theory.twin-prime-conjecture public -open import elementary-number-theory.type-arithmetic-natural-numbers public -open import elementary-number-theory.unit-elements-standard-finite-types public -open import elementary-number-theory.unit-fractions-rational-numbers public -open import elementary-number-theory.unit-similarity-standard-finite-types public -open import elementary-number-theory.universal-property-conatural-numbers public -open import elementary-number-theory.universal-property-integers public -open import elementary-number-theory.universal-property-natural-numbers public -open import elementary-number-theory.upper-bounds-natural-numbers public -open import elementary-number-theory.well-ordering-principle-natural-numbers public -open import elementary-number-theory.well-ordering-principle-standard-finite-types public -open import elementary-number-theory.zero-conatural-numbers public +open import elementary-number-theory.twin-prime-conjecture funext public +open import elementary-number-theory.type-arithmetic-natural-numbers funext public +open import elementary-number-theory.unit-elements-standard-finite-types funext public +open import elementary-number-theory.unit-fractions-rational-numbers funext public +open import elementary-number-theory.unit-similarity-standard-finite-types funext public +open import elementary-number-theory.universal-property-conatural-numbers funext public +open import elementary-number-theory.universal-property-integers funext public +open import elementary-number-theory.universal-property-natural-numbers funext public +open import elementary-number-theory.upper-bounds-natural-numbers funext public +open import elementary-number-theory.well-ordering-principle-natural-numbers funext public +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext public +open import elementary-number-theory.zero-conatural-numbers funext public ``` diff --git a/src/elementary-number-theory/absolute-value-integers.lagda.md b/src/elementary-number-theory/absolute-value-integers.lagda.md index 59455c73a5..d179466116 100644 --- a/src/elementary-number-theory/absolute-value-integers.lagda.md +++ b/src/elementary-number-theory/absolute-value-integers.lagda.md @@ -1,26 +1,31 @@ # The absolute value function on the integers ```agda -module elementary-number-theory.absolute-value-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.absolute-value-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.positive-integers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.coproduct-types funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/addition-integer-fractions.lagda.md b/src/elementary-number-theory/addition-integer-fractions.lagda.md index 2ae01f48aa..0facabd85a 100644 --- a/src/elementary-number-theory/addition-integer-fractions.lagda.md +++ b/src/elementary-number-theory/addition-integer-fractions.lagda.md @@ -1,22 +1,27 @@ # Addition on integer fractions ```agda -module elementary-number-theory.addition-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.addition-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/addition-integers.lagda.md b/src/elementary-number-theory/addition-integers.lagda.md index 0074401613..65ecc00ed3 100644 --- a/src/elementary-number-theory/addition-integers.lagda.md +++ b/src/elementary-number-theory/addition-integers.lagda.md @@ -1,7 +1,12 @@ # Addition on the integers ```agda -module elementary-number-theory.addition-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.addition-integers + (funext : function-extensionality) + where ```
Imports @@ -10,23 +15,23 @@ module elementary-number-theory.addition-integers where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.sets +open import foundation.sets funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md b/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md index cc38778380..70506f226a 100644 --- a/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md +++ b/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md @@ -1,26 +1,31 @@ # Addition of positive, negative, nonnegative and nonpositive integers ```agda -module elementary-number-theory.addition-positive-and-negative-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.addition-positive-and-negative-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.negative-integers funext +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonpositive-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/addition-rational-numbers.lagda.md b/src/elementary-number-theory/addition-rational-numbers.lagda.md index 4bd4afc3d5..622b9859c3 100644 --- a/src/elementary-number-theory/addition-rational-numbers.lagda.md +++ b/src/elementary-number-theory/addition-rational-numbers.lagda.md @@ -3,28 +3,33 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.addition-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.addition-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.reduced-integer-fractions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.retractions -open import foundation.sections +open import foundation.retractions funext +open import foundation.sections funext ```
diff --git a/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md b/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md index 60aeaf1fb9..12d33ba91a 100644 --- a/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md @@ -3,23 +3,28 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.additive-group-of-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.additive-group-of-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.rational-numbers funext open import foundation.dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md b/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md index c28ab250d1..c531f3ceaf 100644 --- a/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md +++ b/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md @@ -3,27 +3,32 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.archimedean-property-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.archimedean-property-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.archimedean-property-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integer-fractions funext +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.positive-integer-fractions -open import elementary-number-theory.strict-inequality-integer-fractions -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.positive-integer-fractions funext +open import elementary-number-theory.strict-inequality-integer-fractions funext +open import elementary-number-theory.strict-inequality-integers funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/archimedean-property-integers.lagda.md b/src/elementary-number-theory/archimedean-property-integers.lagda.md index 21e49492ed..41b8505179 100644 --- a/src/elementary-number-theory/archimedean-property-integers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-integers.lagda.md @@ -1,30 +1,35 @@ # The Archimedean property of the integers ```agda -module elementary-number-theory.archimedean-property-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.archimedean-property-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-natural-numbers +open import elementary-number-theory.archimedean-property-natural-numbers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.strict-inequality-integers funext open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext ```
diff --git a/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md index a24fbc0a07..2659b1e7f2 100644 --- a/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md @@ -1,20 +1,25 @@ # The Archimedean property of the natural numbers ```agda -module elementary-number-theory.archimedean-property-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.archimedean-property-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.euclidean-division-natural-numbers +open import elementary-number-theory.euclidean-division-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.propositional-truncations funext open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md index 0a61a1bf8e..6749dad688 100644 --- a/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md @@ -3,26 +3,31 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.archimedean-property-positive-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.archimedean-property-positive-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-rational-numbers +open import elementary-number-theory.archimedean-property-rational-numbers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-rational-numbers +open import elementary-number-theory.multiplication-rational-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.nonzero-natural-numbers funext +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md index dc4fd7b441..131ed344b4 100644 --- a/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md @@ -3,28 +3,33 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.archimedean-property-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.archimedean-property-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-integer-fractions -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.archimedean-property-integer-fractions funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-rational-numbers +open import elementary-number-theory.multiplication-integer-fractions funext +open import elementary-number-theory.multiplication-rational-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.action-on-identifications-binary-functions open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext ```
diff --git a/src/elementary-number-theory/arithmetic-functions.lagda.md b/src/elementary-number-theory/arithmetic-functions.lagda.md index 291d7d48e5..58c0a70549 100644 --- a/src/elementary-number-theory/arithmetic-functions.lagda.md +++ b/src/elementary-number-theory/arithmetic-functions.lagda.md @@ -1,17 +1,22 @@ # Arithmetic functions ```agda -module elementary-number-theory.arithmetic-functions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.arithmetic-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-natural-numbers funext open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/elementary-number-theory/based-induction-natural-numbers.lagda.md b/src/elementary-number-theory/based-induction-natural-numbers.lagda.md index 04b3c569a4..72ed796b19 100644 --- a/src/elementary-number-theory/based-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/based-induction-natural-numbers.lagda.md @@ -1,17 +1,22 @@ # The based induction principle of the natural numbers ```agda -module elementary-number-theory.based-induction-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.based-induction-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md index d355c01418..0aa8cdeb28 100644 --- a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md @@ -1,27 +1,32 @@ # Based strong induction for the natural numbers ```agda -module elementary-number-theory.based-strong-induction-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.based-strong-induction-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.based-induction-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.based-induction-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.empty-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.universal-property-contractible-types +open import foundation.coproduct-types funext +open import foundation.empty-types funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.universal-property-contractible-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/bell-numbers.lagda.md b/src/elementary-number-theory/bell-numbers.lagda.md index d824cdd82b..116971dd11 100644 --- a/src/elementary-number-theory/bell-numbers.lagda.md +++ b/src/elementary-number-theory/bell-numbers.lagda.md @@ -1,18 +1,23 @@ # The Bell numbers ```agda -module elementary-number-theory.bell-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.bell-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.binomial-coefficients +open import elementary-number-theory.binomial-coefficients funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strong-induction-natural-numbers funext +open import elementary-number-theory.sums-of-natural-numbers funext ```
diff --git a/src/elementary-number-theory/bezouts-lemma-integers.lagda.md b/src/elementary-number-theory/bezouts-lemma-integers.lagda.md index 1b169fb860..ee8aba77b9 100644 --- a/src/elementary-number-theory/bezouts-lemma-integers.lagda.md +++ b/src/elementary-number-theory/bezouts-lemma-integers.lagda.md @@ -1,37 +1,42 @@ # Bezout's lemma in the integers ```agda -module elementary-number-theory.bezouts-lemma-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.bezouts-lemma-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers +open import elementary-number-theory.absolute-value-integers funext +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.bezouts-lemma-natural-numbers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.distance-integers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.greatest-common-divisor-natural-numbers +open import elementary-number-theory.bezouts-lemma-natural-numbers funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.distance-integers funext +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.divisibility-integers funext +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.greatest-common-divisor-integers funext +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md b/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md index 681142d4bb..a72e10aea8 100755 --- a/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md +++ b/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md @@ -1,49 +1,54 @@ # Bezout's lemma on the natural numbers ```agda -module elementary-number-theory.bezouts-lemma-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.bezouts-lemma-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers +open import elementary-number-theory.absolute-value-integers funext +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-integers -open import elementary-number-theory.distance-integers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-modular-arithmetic -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.euclidean-division-natural-numbers -open import elementary-number-theory.greatest-common-divisor-natural-numbers -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.congruence-integers funext +open import elementary-number-theory.distance-integers funext +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.divisibility-modular-arithmetic funext +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.euclidean-division-natural-numbers funext +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext +open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.integers -open import elementary-number-theory.lower-bounds-natural-numbers -open import elementary-number-theory.modular-arithmetic -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.lower-bounds-natural-numbers funext +open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.well-ordering-principle-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.negation +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/binomial-coefficients.lagda.md b/src/elementary-number-theory/binomial-coefficients.lagda.md index 655ad9e203..9170cca111 100644 --- a/src/elementary-number-theory/binomial-coefficients.lagda.md +++ b/src/elementary-number-theory/binomial-coefficients.lagda.md @@ -1,30 +1,35 @@ # The binomial coefficients ```agda -module elementary-number-theory.binomial-coefficients where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.binomial-coefficients + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.commutative-semiring-of-natural-numbers -open import elementary-number-theory.factorials -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.commutative-semiring-of-natural-numbers funext +open import elementary-number-theory.factorials funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.identity-types funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/binomial-theorem-integers.lagda.md b/src/elementary-number-theory/binomial-theorem-integers.lagda.md index ec01e91220..ca4be4bd7b 100644 --- a/src/elementary-number-theory/binomial-theorem-integers.lagda.md +++ b/src/elementary-number-theory/binomial-theorem-integers.lagda.md @@ -1,28 +1,33 @@ # The binomial theorem for the integers ```agda -module elementary-number-theory.binomial-theorem-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.binomial-theorem-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-rings +open import commutative-algebra.binomial-theorem-commutative-rings funext -open import elementary-number-theory.addition-integers -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.distance-natural-numbers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.powers-integers -open import elementary-number-theory.ring-of-integers +open import elementary-number-theory.powers-integers funext +open import elementary-number-theory.ring-of-integers funext -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md b/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md index 08f650294f..f1d115118f 100644 --- a/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md +++ b/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md @@ -1,27 +1,32 @@ # The binomial theorem for the natural numbers ```agda -module elementary-number-theory.binomial-theorem-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.binomial-theorem-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-semirings +open import commutative-algebra.binomial-theorem-commutative-semirings funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.commutative-semiring-of-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.commutative-semiring-of-natural-numbers funext +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.exponentiation-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md b/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md index 7e513fd97a..9ddaf4ed0b 100644 --- a/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md +++ b/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md @@ -1,23 +1,28 @@ # Bounded sums of arithmetic functions ```agda -module elementary-number-theory.bounded-sums-arithmetic-functions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.bounded-sums-arithmetic-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.arithmetic-functions +open import elementary-number-theory.arithmetic-functions funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-natural-numbers funext -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types -open import foundation.function-types +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext +open import foundation.function-types funext open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/elementary-number-theory/catalan-numbers.lagda.md b/src/elementary-number-theory/catalan-numbers.lagda.md index 55257b4c79..43cbaf36ac 100644 --- a/src/elementary-number-theory/catalan-numbers.lagda.md +++ b/src/elementary-number-theory/catalan-numbers.lagda.md @@ -1,21 +1,26 @@ # Catalan numbers ```agda -module elementary-number-theory.catalan-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.catalan-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.binomial-coefficients funext +open import elementary-number-theory.distance-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strong-induction-natural-numbers funext +open import elementary-number-theory.sums-of-natural-numbers funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/cofibonacci.lagda.md b/src/elementary-number-theory/cofibonacci.lagda.md index e2a6f001ba..18cc9c5dfc 100644 --- a/src/elementary-number-theory/cofibonacci.lagda.md +++ b/src/elementary-number-theory/cofibonacci.lagda.md @@ -1,27 +1,32 @@ # The cofibonacci sequence ```agda -module elementary-number-theory.cofibonacci where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.cofibonacci + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.fibonacci-sequence -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.fibonacci-sequence funext +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.pisano-periods -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.pisano-periods funext +open import elementary-number-theory.well-ordering-principle-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/collatz-bijection.lagda.md b/src/elementary-number-theory/collatz-bijection.lagda.md index 8e734174e5..0c1fd19602 100644 --- a/src/elementary-number-theory/collatz-bijection.lagda.md +++ b/src/elementary-number-theory/collatz-bijection.lagda.md @@ -1,20 +1,25 @@ # The Collatz bijection ```agda -module elementary-number-theory.collatz-bijection where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.collatz-bijection + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.euclidean-division-natural-numbers -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.euclidean-division-natural-numbers funext +open import elementary-number-theory.modular-arithmetic funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.identity-types +open import foundation.coproduct-types funext +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/collatz-conjecture.lagda.md b/src/elementary-number-theory/collatz-conjecture.lagda.md index 9c44a48d71..dbc5791c1c 100644 --- a/src/elementary-number-theory/collatz-conjecture.lagda.md +++ b/src/elementary-number-theory/collatz-conjecture.lagda.md @@ -1,17 +1,22 @@ # The Collatz conjecture ```agda -module elementary-number-theory.collatz-conjecture where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.collatz-conjecture + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md b/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md index 45f3324d10..20b714eb16 100644 --- a/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md @@ -1,21 +1,26 @@ # The commutative semiring of natural numbers ```agda -module elementary-number-theory.commutative-semiring-of-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.commutative-semiring-of-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext -open import elementary-number-theory.monoid-of-natural-numbers-with-addition +open import elementary-number-theory.monoid-of-natural-numbers-with-addition funext open import elementary-number-theory.multiplication-natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/elementary-number-theory/conatural-numbers.lagda.md b/src/elementary-number-theory/conatural-numbers.lagda.md index 54310d096a..9eeb51c23d 100644 --- a/src/elementary-number-theory/conatural-numbers.lagda.md +++ b/src/elementary-number-theory/conatural-numbers.lagda.md @@ -3,20 +3,25 @@ ```agda {-# OPTIONS --guardedness #-} -module elementary-number-theory.conatural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.conatural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.retractions -open import foundation.sections +open import foundation.homotopies funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/congruence-integers.lagda.md b/src/elementary-number-theory/congruence-integers.lagda.md index 9844348d01..d35036bd44 100644 --- a/src/elementary-number-theory/congruence-integers.lagda.md +++ b/src/elementary-number-theory/congruence-integers.lagda.md @@ -1,27 +1,32 @@ # The congruence relations on the integers ```agda -module elementary-number-theory.congruence-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.congruence-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.distance-integers -open import elementary-number-theory.divisibility-integers +open import elementary-number-theory.absolute-value-integers funext +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.distance-integers funext +open import elementary-number-theory.divisibility-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/congruence-natural-numbers.lagda.md b/src/elementary-number-theory/congruence-natural-numbers.lagda.md index d4c0ff60a4..97d78b729b 100644 --- a/src/elementary-number-theory/congruence-natural-numbers.lagda.md +++ b/src/elementary-number-theory/congruence-natural-numbers.lagda.md @@ -1,28 +1,33 @@ # The congruence relations on the natural numbers ```agda -module elementary-number-theory.congruence-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.congruence-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.coproduct-types +open import foundation.binary-relations funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md b/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md index 38bca51942..736039a2bc 100644 --- a/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md +++ b/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md @@ -1,23 +1,28 @@ # The cross-multiplication difference of two integer fractions ```agda -module elementary-number-theory.cross-multiplication-difference-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.cross-multiplication-difference-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext ```
diff --git a/src/elementary-number-theory/cubes-natural-numbers.lagda.md b/src/elementary-number-theory/cubes-natural-numbers.lagda.md index 491369a597..027f4b150b 100644 --- a/src/elementary-number-theory/cubes-natural-numbers.lagda.md +++ b/src/elementary-number-theory/cubes-natural-numbers.lagda.md @@ -1,7 +1,12 @@ # Cubes of natural numbers ```agda -module elementary-number-theory.cubes-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.cubes-natural-numbers + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module elementary-number-theory.cubes-natural-numbers where ```agda open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.squares-natural-numbers funext open import foundation.dependent-pair-types -open import foundation.fibers-of-maps +open import foundation.fibers-of-maps funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/decidable-dependent-function-types.lagda.md b/src/elementary-number-theory/decidable-dependent-function-types.lagda.md index ca2d7fd780..93da615aa3 100644 --- a/src/elementary-number-theory/decidable-dependent-function-types.lagda.md +++ b/src/elementary-number-theory/decidable-dependent-function-types.lagda.md @@ -1,9 +1,14 @@ # Decidable dependent function types ```agda -module elementary-number-theory.decidable-dependent-function-types where +open import foundation.function-extensionality-axiom -open import foundation.decidable-dependent-function-types public +module + elementary-number-theory.decidable-dependent-function-types + (funext : function-extensionality) + where + +open import foundation.decidable-dependent-function-types funext public ```
Imports diff --git a/src/elementary-number-theory/decidable-total-order-integers.lagda.md b/src/elementary-number-theory/decidable-total-order-integers.lagda.md index f4e2772ec7..fcc2241128 100644 --- a/src/elementary-number-theory/decidable-total-order-integers.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-integers.lagda.md @@ -1,20 +1,25 @@ # The decidable total order of integers ```agda -module elementary-number-theory.decidable-total-order-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.decidable-total-order-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-integers +open import elementary-number-theory.inequality-integers funext open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.total-orders +open import order-theory.decidable-total-orders funext +open import order-theory.total-orders funext ```
diff --git a/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md b/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md index ba6c9d2db7..8517b2c81b 100644 --- a/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md @@ -1,27 +1,32 @@ # The decidable total order of natural numbers ```agda -module elementary-number-theory.decidable-total-order-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.decidable-total-order-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositional-truncations +open import foundation.function-types funext +open import foundation.propositional-truncations funext open import foundation.unit-type open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.order-preserving-maps-posets -open import order-theory.order-preserving-maps-preorders -open import order-theory.posets -open import order-theory.preorders -open import order-theory.total-orders +open import order-theory.decidable-total-orders funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.order-preserving-maps-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.total-orders funext ```
diff --git a/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md b/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md index 3a1b901c63..a0658424a8 100644 --- a/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md @@ -1,20 +1,25 @@ # The decidable total order of rational numbers ```agda -module elementary-number-theory.decidable-total-order-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.decidable-total-order-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.total-orders +open import order-theory.decidable-total-orders funext +open import order-theory.total-orders funext ```
diff --git a/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md b/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md index a33da4e7bb..528ee3ac94 100644 --- a/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md @@ -1,21 +1,26 @@ # The decidable total order of a standard finite type ```agda -module elementary-number-theory.decidable-total-order-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.decidable-total-order-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.total-orders +open import order-theory.decidable-total-orders funext +open import order-theory.total-orders funext ```
diff --git a/src/elementary-number-theory/decidable-types.lagda.md b/src/elementary-number-theory/decidable-types.lagda.md index 047ada9a91..5857bfabd5 100644 --- a/src/elementary-number-theory/decidable-types.lagda.md +++ b/src/elementary-number-theory/decidable-types.lagda.md @@ -1,23 +1,28 @@ # Decidable types in elementary number theory ```agda -module elementary-number-theory.decidable-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.decidable-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.upper-bounds-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.upper-bounds-natural-numbers funext -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types +open import foundation.empty-types funext +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/difference-integers.lagda.md b/src/elementary-number-theory/difference-integers.lagda.md index 6cd796526c..e5ade4877e 100644 --- a/src/elementary-number-theory/difference-integers.lagda.md +++ b/src/elementary-number-theory/difference-integers.lagda.md @@ -1,18 +1,23 @@ # The difference between integers ```agda -module elementary-number-theory.difference-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.difference-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.interchange-law ``` diff --git a/src/elementary-number-theory/difference-rational-numbers.lagda.md b/src/elementary-number-theory/difference-rational-numbers.lagda.md index 7dbe0779c1..d330660e57 100644 --- a/src/elementary-number-theory/difference-rational-numbers.lagda.md +++ b/src/elementary-number-theory/difference-rational-numbers.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.difference-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.difference-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.rational-numbers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.interchange-law ``` diff --git a/src/elementary-number-theory/dirichlet-convolution.lagda.md b/src/elementary-number-theory/dirichlet-convolution.lagda.md index 0745ebdfe9..fd8fb7aa53 100644 --- a/src/elementary-number-theory/dirichlet-convolution.lagda.md +++ b/src/elementary-number-theory/dirichlet-convolution.lagda.md @@ -1,24 +1,29 @@ # Dirichlet convolution ```agda -module elementary-number-theory.dirichlet-convolution where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.dirichlet-convolution + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.arithmetic-functions -open import elementary-number-theory.bounded-sums-arithmetic-functions -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.arithmetic-functions funext +open import elementary-number-theory.bounded-sums-arithmetic-functions funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-natural-numbers funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/elementary-number-theory/distance-integers.lagda.md b/src/elementary-number-theory/distance-integers.lagda.md index ee659aed25..f220847ab9 100644 --- a/src/elementary-number-theory/distance-integers.lagda.md +++ b/src/elementary-number-theory/distance-integers.lagda.md @@ -1,25 +1,30 @@ # The distance between integers ```agda -module elementary-number-theory.distance-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.distance-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.absolute-value-integers funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.distance-natural-numbers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.identity-types +open import foundation.coproduct-types funext +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/distance-natural-numbers.lagda.md b/src/elementary-number-theory/distance-natural-numbers.lagda.md index 6026c735da..c492ecfd41 100644 --- a/src/elementary-number-theory/distance-natural-numbers.lagda.md +++ b/src/elementary-number-theory/distance-natural-numbers.lagda.md @@ -1,24 +1,29 @@ # The distance between natural numbers ```agda -module elementary-number-theory.distance-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.distance-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/divisibility-integers.lagda.md b/src/elementary-number-theory/divisibility-integers.lagda.md index bed59408c3..95f5d21d39 100644 --- a/src/elementary-number-theory/divisibility-integers.lagda.md +++ b/src/elementary-number-theory/divisibility-integers.lagda.md @@ -1,37 +1,42 @@ # Divisibility of integers ```agda -module elementary-number-theory.divisibility-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.divisibility-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-integers +open import elementary-number-theory.absolute-value-integers funext +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonpositive-integers funext +open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.positive-and-negative-integers funext open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-maps -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-maps funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md b/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md index 6d2a85ab6f..880efaa503 100644 --- a/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md +++ b/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md @@ -1,24 +1,29 @@ # Divisibility in modular arithmetic ```agda -module elementary-number-theory.divisibility-modular-arithmetic where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.divisibility-modular-arithmetic + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.divisibility-standard-finite-types -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.divisibility-integers funext +open import elementary-number-theory.divisibility-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic funext open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.fibers-of-maps +open import univalent-combinatorics.fibers-of-maps funext ```
diff --git a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md index a7879e5365..1058b4042a 100644 --- a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md +++ b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md @@ -1,33 +1,38 @@ # Divisibility of natural numbers ```agda -module elementary-number-theory.divisibility-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.divisibility-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-maps -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-maps funext +open import foundation.propositions funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md b/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md index 0e659d21ac..f39a9c36f2 100644 --- a/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md @@ -1,25 +1,30 @@ # The divisibility relation on the standard finite types ```agda -module elementary-number-theory.divisibility-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.divisibility-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.decidable-dependent-pair-types funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/equality-conatural-numbers.lagda.md b/src/elementary-number-theory/equality-conatural-numbers.lagda.md index eb8d842c46..453259bc0a 100644 --- a/src/elementary-number-theory/equality-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/equality-conatural-numbers.lagda.md @@ -3,41 +3,46 @@ ```agda {-# OPTIONS --guardedness #-} -module elementary-number-theory.equality-conatural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.equality-conatural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers +open import elementary-number-theory.conatural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.coherently-invertible-maps -open import foundation.coproduct-types +open import foundation.coherently-invertible-maps funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.double-negation-stable-equality -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types +open import foundation.double-negation funext +open import foundation.double-negation funext-stable-equality +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negation -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections -open import foundation.sets -open import foundation.tight-apartness-relations -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negation funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext +open import foundation.sections funext +open import foundation.sets funext +open import foundation.tight-apartness-relations funext +open import foundation.torsorial-type-families funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.maybe -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext ```
diff --git a/src/elementary-number-theory/equality-integers.lagda.md b/src/elementary-number-theory/equality-integers.lagda.md index 0ff7538a18..27a164ffea 100644 --- a/src/elementary-number-theory/equality-integers.lagda.md +++ b/src/elementary-number-theory/equality-integers.lagda.md @@ -1,32 +1,37 @@ # Equality of integers ```agda -module elementary-number-theory.equality-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.equality-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.integers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.discrete-types funext +open import foundation.empty-types funext +open import foundation.equality-coproduct-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.set-truncations funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/equality-natural-numbers.lagda.md b/src/elementary-number-theory/equality-natural-numbers.lagda.md index bb335e5e58..7403562b0e 100644 --- a/src/elementary-number-theory/equality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/equality-natural-numbers.lagda.md @@ -1,7 +1,12 @@ # Equality of natural numbers ```agda -module elementary-number-theory.equality-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.equality-natural-numbers + (funext : function-extensionality) + where ```
Imports @@ -10,23 +15,23 @@ module elementary-number-theory.equality-natural-numbers where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.decidable-propositions -open import foundation-core.discrete-types +open import foundation-core.decidable-propositions funext +open import foundation-core.discrete-types funext open import foundation-core.torsorial-type-families ``` diff --git a/src/elementary-number-theory/equality-rational-numbers.lagda.md b/src/elementary-number-theory/equality-rational-numbers.lagda.md index aaf8ae64f0..01f92ec7a6 100644 --- a/src/elementary-number-theory/equality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/equality-rational-numbers.lagda.md @@ -1,24 +1,29 @@ # Equality of rational numbers ```agda -module elementary-number-theory.equality-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.equality-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.integer-fractions -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.reduced-integer-fractions funext -open import foundation.decidable-equality +open import foundation.decidable-equality funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/euclid-mullin-sequence.lagda.md b/src/elementary-number-theory/euclid-mullin-sequence.lagda.md index be53df7a65..3c4f9bbf82 100644 --- a/src/elementary-number-theory/euclid-mullin-sequence.lagda.md +++ b/src/elementary-number-theory/euclid-mullin-sequence.lagda.md @@ -1,23 +1,28 @@ # The Euclid–Mullin sequence ```agda -module elementary-number-theory.euclid-mullin-sequence where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.euclid-mullin-sequence + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.products-of-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strong-induction-natural-numbers funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md b/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md index 1ef17f8247..18d51a3a30 100644 --- a/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md +++ b/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md @@ -1,27 +1,32 @@ # Euclidean division on the natural numbers ```agda -module elementary-number-theory.euclidean-division-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.euclidean-division-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.identity-types funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/eulers-totient-function.lagda.md b/src/elementary-number-theory/eulers-totient-function.lagda.md index 83f8c0970d..8870278296 100644 --- a/src/elementary-number-theory/eulers-totient-function.lagda.md +++ b/src/elementary-number-theory/eulers-totient-function.lagda.md @@ -1,18 +1,23 @@ # Euler's totient function ```agda -module elementary-number-theory.eulers-totient-function where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.eulers-totient-function + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.relatively-prime-natural-numbers +open import elementary-number-theory.relatively-prime-natural-numbers funext -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.decidable-subtypes funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md b/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md index abbf1734ae..cbfbc7dc50 100644 --- a/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md +++ b/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md @@ -1,22 +1,27 @@ # Exponentiation of natural numbers ```agda -module elementary-number-theory.exponentiation-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.exponentiation-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.powers-of-elements-commutative-semirings +open import commutative-algebra.powers-of-elements-commutative-semirings funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.commutative-semiring-of-natural-numbers +open import elementary-number-theory.commutative-semiring-of-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers +open import elementary-number-theory.products-of-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/factorials.lagda.md b/src/elementary-number-theory/factorials.lagda.md index 05851e426e..2a07db5520 100644 --- a/src/elementary-number-theory/factorials.lagda.md +++ b/src/elementary-number-theory/factorials.lagda.md @@ -1,22 +1,27 @@ # Factorials of natural numbers ```agda -module elementary-number-theory.factorials where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.factorials + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/fermat-numbers.lagda.md b/src/elementary-number-theory/fermat-numbers.lagda.md index 8a76e9fc21..e79ab6519b 100644 --- a/src/elementary-number-theory/fermat-numbers.lagda.md +++ b/src/elementary-number-theory/fermat-numbers.lagda.md @@ -1,19 +1,24 @@ # Fermat numbers ```agda -module elementary-number-theory.fermat-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.fermat-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.products-of-natural-numbers funext +open import elementary-number-theory.strong-induction-natural-numbers funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/fibonacci-sequence.lagda.md b/src/elementary-number-theory/fibonacci-sequence.lagda.md index 89af95e039..03d39b2446 100644 --- a/src/elementary-number-theory/fibonacci-sequence.lagda.md +++ b/src/elementary-number-theory/fibonacci-sequence.lagda.md @@ -1,22 +1,27 @@ # The Fibonacci sequence ```agda -module elementary-number-theory.fibonacci-sequence where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.fibonacci-sequence + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.greatest-common-divisor-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.relatively-prime-natural-numbers +open import elementary-number-theory.relatively-prime-natural-numbers funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/field-of-rational-numbers.lagda.md b/src/elementary-number-theory/field-of-rational-numbers.lagda.md index 88e4a88422..5ed5d9b6be 100644 --- a/src/elementary-number-theory/field-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/field-of-rational-numbers.lagda.md @@ -1,23 +1,28 @@ # The field of rational numbers ```agda -module elementary-number-theory.field-of-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.field-of-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.discrete-fields +open import commutative-algebra.discrete-fields funext -open import elementary-number-theory.multiplicative-group-of-rational-numbers -open import elementary-number-theory.nonzero-rational-numbers -open import elementary-number-theory.ring-of-rational-numbers +open import elementary-number-theory.multiplicative-group-of-rational-numbers funext +open import elementary-number-theory.nonzero-rational-numbers funext +open import elementary-number-theory.ring-of-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext -open import ring-theory.division-rings +open import ring-theory.division-rings funext ```
diff --git a/src/elementary-number-theory/finitary-natural-numbers.lagda.md b/src/elementary-number-theory/finitary-natural-numbers.lagda.md index 57acf9d9c0..85a00da121 100644 --- a/src/elementary-number-theory/finitary-natural-numbers.lagda.md +++ b/src/elementary-number-theory/finitary-natural-numbers.lagda.md @@ -1,30 +1,35 @@ # The natural numbers base `k` ```agda -module elementary-number-theory.finitary-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.finitary-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.sets funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/finitely-cyclic-maps.lagda.md b/src/elementary-number-theory/finitely-cyclic-maps.lagda.md index d70daec324..9e0597c7b4 100644 --- a/src/elementary-number-theory/finitely-cyclic-maps.lagda.md +++ b/src/elementary-number-theory/finitely-cyclic-maps.lagda.md @@ -1,25 +1,30 @@ # Finitely cyclic maps ```agda -module elementary-number-theory.finitely-cyclic-maps where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.finitely-cyclic-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterating-functions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterating-functions funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md index 770e230cd9..3b2797a025 100644 --- a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md +++ b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md @@ -1,54 +1,59 @@ # The fundamental theorem of arithmetic ```agda -module elementary-number-theory.fundamental-theorem-of-arithmetic where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.fundamental-theorem-of-arithmetic + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.based-strong-induction-natural-numbers -open import elementary-number-theory.bezouts-lemma-integers -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types -open import elementary-number-theory.multiplication-lists-of-natural-numbers +open import elementary-number-theory.based-strong-induction-natural-numbers funext +open import elementary-number-theory.bezouts-lemma-integers funext +open import elementary-number-theory.decidable-total-order-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.lower-bounds-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.multiplication-lists-of-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers -open import elementary-number-theory.relatively-prime-natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.prime-numbers funext +open import elementary-number-theory.relatively-prime-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.well-ordering-principle-natural-numbers funext -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.equality-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext +open import lists.equality-lists funext +open import lists.functoriality-lists funext open import lists.lists -open import lists.permutation-lists -open import lists.predicates-on-lists -open import lists.sort-by-insertion-lists -open import lists.sorted-lists +open import lists.permutation-lists funext +open import lists.predicates-on-lists funext +open import lists.sort-by-insertion-lists funext +open import lists.sorted-lists funext ```
diff --git a/src/elementary-number-theory/goldbach-conjecture.lagda.md b/src/elementary-number-theory/goldbach-conjecture.lagda.md index ab096dfab1..1642006127 100644 --- a/src/elementary-number-theory/goldbach-conjecture.lagda.md +++ b/src/elementary-number-theory/goldbach-conjecture.lagda.md @@ -1,7 +1,12 @@ # The Goldbach conjecture ```agda -module elementary-number-theory.goldbach-conjecture where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.goldbach-conjecture + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module elementary-number-theory.goldbach-conjecture where ```agda open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers -open import elementary-number-theory.prime-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext +open import elementary-number-theory.prime-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md b/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md index fc8abf413d..914755108d 100644 --- a/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md +++ b/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md @@ -1,32 +1,37 @@ # The greatest common divisor of integers ```agda -module elementary-number-theory.greatest-common-divisor-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.greatest-common-divisor-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.absolute-value-integers funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.equality-integers -open import elementary-number-theory.greatest-common-divisor-natural-numbers +open import elementary-number-theory.divisibility-integers funext +open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md b/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md index 13347d69ac..14a8b300b5 100644 --- a/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md +++ b/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md @@ -1,35 +1,40 @@ # The greatest common divisor of natural numbers ```agda -module elementary-number-theory.greatest-common-divisor-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.greatest-common-divisor-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.decidable-types -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.euclidean-division-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.decidable-types funext +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.euclidean-division-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.lower-bounds-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.well-ordering-principle-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.empty-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/group-of-integers.lagda.md b/src/elementary-number-theory/group-of-integers.lagda.md index e1c12a108d..711c0db1c8 100644 --- a/src/elementary-number-theory/group-of-integers.lagda.md +++ b/src/elementary-number-theory/group-of-integers.lagda.md @@ -1,24 +1,29 @@ # The group of integers ```agda -module elementary-number-theory.group-of-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.group-of-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.equality-integers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.semigroups funext -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext ```
diff --git a/src/elementary-number-theory/half-integers.lagda.md b/src/elementary-number-theory/half-integers.lagda.md index b62b4ae496..4b18b64680 100644 --- a/src/elementary-number-theory/half-integers.lagda.md +++ b/src/elementary-number-theory/half-integers.lagda.md @@ -1,16 +1,21 @@ # The half-integers ```agda -module elementary-number-theory.half-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.half-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/hardy-ramanujan-number.lagda.md b/src/elementary-number-theory/hardy-ramanujan-number.lagda.md index 9ecffa68bf..1371f97fa7 100644 --- a/src/elementary-number-theory/hardy-ramanujan-number.lagda.md +++ b/src/elementary-number-theory/hardy-ramanujan-number.lagda.md @@ -1,17 +1,22 @@ # The Hardy-Ramanujan number ```agda -module elementary-number-theory.hardy-ramanujan-number where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.hardy-ramanujan-number + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.taxicab-numbers +open import elementary-number-theory.taxicab-numbers funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md b/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md index ea3f148c51..71d6884566 100644 --- a/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md @@ -3,22 +3,27 @@ ```agda {-# OPTIONS --guardedness #-} -module elementary-number-theory.inclusion-natural-numbers-conatural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.inclusion-natural-numbers-conatural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers -open import elementary-number-theory.infinite-conatural-numbers +open import elementary-number-theory.conatural-numbers funext +open import elementary-number-theory.infinite-conatural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.existential-quantification -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.surjective-maps +open import foundation.existential-quantification funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.surjective-maps funext open import foundation-core.empty-types open import foundation-core.identity-types diff --git a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md index 5a90091ea9..7db168ea47 100644 --- a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md @@ -3,33 +3,38 @@ ```agda {-# OPTIONS --guardedness #-} -module elementary-number-theory.inequality-conatural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.inequality-conatural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers +open import elementary-number-theory.conatural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.maybe -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/elementary-number-theory/inequality-integer-fractions.lagda.md b/src/elementary-number-theory/inequality-integer-fractions.lagda.md index e87b85c1c3..b0e5112365 100644 --- a/src/elementary-number-theory/inequality-integer-fractions.lagda.md +++ b/src/elementary-number-theory/inequality-integer-fractions.lagda.md @@ -1,37 +1,42 @@ # Inequality on integer fractions ```agda -module elementary-number-theory.inequality-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.inequality-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-positive-and-negative-integers funext +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonpositive-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.strict-inequality-integers funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/inequality-integers.lagda.md b/src/elementary-number-theory/inequality-integers.lagda.md index 1e9c9063f6..4b1972f799 100644 --- a/src/elementary-number-theory/inequality-integers.lagda.md +++ b/src/elementary-number-theory/inequality-integers.lagda.md @@ -1,40 +1,45 @@ # Inequality on the integers ```agda -module elementary-number-theory.inequality-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.inequality-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-positive-and-negative-integers funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.negative-integers funext +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonpositive-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/elementary-number-theory/inequality-natural-numbers.lagda.md b/src/elementary-number-theory/inequality-natural-numbers.lagda.md index a31c50691d..13c1510b2d 100644 --- a/src/elementary-number-theory/inequality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-natural-numbers.lagda.md @@ -1,35 +1,40 @@ # Inequality of natural numbers ```agda -module elementary-number-theory.inequality-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.inequality-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/elementary-number-theory/inequality-rational-numbers.lagda.md b/src/elementary-number-theory/inequality-rational-numbers.lagda.md index c8956f0ff1..9fa7192e16 100644 --- a/src/elementary-number-theory/inequality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-rational-numbers.lagda.md @@ -1,41 +1,46 @@ # Inequality on the rational numbers ```agda -module elementary-number-theory.inequality-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.inequality-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-integer-fractions -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.addition-integer-fractions funext +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.difference-rational-numbers funext +open import elementary-number-theory.inequality-integer-fractions funext +open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.reduced-integer-fractions funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositions +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/elementary-number-theory/inequality-standard-finite-types.lagda.md b/src/elementary-number-theory/inequality-standard-finite-types.lagda.md index d21985ad6f..c8f1d75439 100644 --- a/src/elementary-number-theory/inequality-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/inequality-standard-finite-types.lagda.md @@ -1,32 +1,37 @@ # Inequality on the standard finite types ```agda -module elementary-number-theory.inequality-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.inequality-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext +open import order-theory.preorders funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/infinite-conatural-numbers.lagda.md b/src/elementary-number-theory/infinite-conatural-numbers.lagda.md index 4b5d718a19..fb0d750414 100644 --- a/src/elementary-number-theory/infinite-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/infinite-conatural-numbers.lagda.md @@ -3,17 +3,22 @@ ```agda {-# OPTIONS --guardedness #-} -module elementary-number-theory.infinite-conatural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.infinite-conatural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers -open import elementary-number-theory.equality-conatural-numbers +open import elementary-number-theory.conatural-numbers funext +open import elementary-number-theory.equality-conatural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/elementary-number-theory/infinitude-of-primes.lagda.md b/src/elementary-number-theory/infinitude-of-primes.lagda.md index 2da5b37a90..9924f6d426 100644 --- a/src/elementary-number-theory/infinitude-of-primes.lagda.md +++ b/src/elementary-number-theory/infinitude-of-primes.lagda.md @@ -1,32 +1,37 @@ # The infinitude of primes ```agda -module elementary-number-theory.infinitude-of-primes where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.infinitude-of-primes + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.factorials -open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.factorials funext +open import elementary-number-theory.lower-bounds-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers -open import elementary-number-theory.proper-divisors-natural-numbers -open import elementary-number-theory.sieve-of-eratosthenes -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers - -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import elementary-number-theory.prime-numbers funext +open import elementary-number-theory.proper-divisors-natural-numbers funext +open import elementary-number-theory.sieve-of-eratosthenes funext +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.well-ordering-principle-natural-numbers funext + +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.iterating-functions -open import foundation.negation -open import foundation.type-arithmetic-empty-type +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.iterating-functions funext +open import foundation.negation funext +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md b/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md index 9823b2c9a1..48663e56ac 100644 --- a/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md +++ b/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md @@ -1,20 +1,25 @@ # Initial segments of the natural numbers ```agda -module elementary-number-theory.initial-segments-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.initial-segments-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.maximum-natural-numbers +open import elementary-number-theory.maximum-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/integer-fractions.lagda.md b/src/elementary-number-theory/integer-fractions.lagda.md index c2bc0db1a8..b1f2e054a0 100644 --- a/src/elementary-number-theory/integer-fractions.lagda.md +++ b/src/elementary-number-theory/integer-fractions.lagda.md @@ -1,32 +1,37 @@ # Integer fractions ```agda -module elementary-number-theory.integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers -open import elementary-number-theory.greatest-common-divisor-integers +open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.greatest-common-divisor-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.positive-integers +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.positive-integers funext open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.decidable-equality +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext +open import foundation.decidable-equality funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.equivalence-relations funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import set-theory.countable-sets +open import set-theory.countable-sets funext ```
diff --git a/src/elementary-number-theory/jacobi-symbol.lagda.md b/src/elementary-number-theory/jacobi-symbol.lagda.md index b7c291a319..077d3a8ba9 100644 --- a/src/elementary-number-theory/jacobi-symbol.lagda.md +++ b/src/elementary-number-theory/jacobi-symbol.lagda.md @@ -1,22 +1,27 @@ # The Jacobi symbol ```agda -module elementary-number-theory.jacobi-symbol where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.jacobi-symbol + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext open import elementary-number-theory.integers -open import elementary-number-theory.legendre-symbol -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.legendre-symbol funext +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers -open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-arithmetic-dependent-function-types funext open import foundation.unit-type -open import lists.functoriality-lists +open import lists.functoriality-lists funext open import lists.lists ``` diff --git a/src/elementary-number-theory/kolakoski-sequence.lagda.md b/src/elementary-number-theory/kolakoski-sequence.lagda.md index 602bc2597a..a6d3b8b601 100644 --- a/src/elementary-number-theory/kolakoski-sequence.lagda.md +++ b/src/elementary-number-theory/kolakoski-sequence.lagda.md @@ -1,18 +1,23 @@ # The Kolakoski sequence ```agda -module elementary-number-theory.kolakoski-sequence where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.kolakoski-sequence + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.strong-induction-natural-numbers funext -open import foundation.booleans -open import foundation.cartesian-product-types +open import foundation.booleans funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types ``` diff --git a/src/elementary-number-theory/legendre-symbol.lagda.md b/src/elementary-number-theory/legendre-symbol.lagda.md index 57f91cb937..363d1ba015 100644 --- a/src/elementary-number-theory/legendre-symbol.lagda.md +++ b/src/elementary-number-theory/legendre-symbol.lagda.md @@ -1,23 +1,28 @@ # The Legendre symbol ```agda -module elementary-number-theory.legendre-symbol where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.legendre-symbol + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers -open import elementary-number-theory.squares-modular-arithmetic +open import elementary-number-theory.prime-numbers funext +open import elementary-number-theory.squares-modular-arithmetic funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md b/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md index 1a84c70750..1a69bb4a4b 100644 --- a/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md +++ b/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md @@ -1,17 +1,22 @@ # Lower bounds of type families over the natural numbers ```agda -module elementary-number-theory.lower-bounds-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.lower-bounds-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/maximum-natural-numbers.lagda.md b/src/elementary-number-theory/maximum-natural-numbers.lagda.md index 97038be80f..f463ad2859 100644 --- a/src/elementary-number-theory/maximum-natural-numbers.lagda.md +++ b/src/elementary-number-theory/maximum-natural-numbers.lagda.md @@ -1,26 +1,31 @@ # Maximum on the natural numbers ```agda -module elementary-number-theory.maximum-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.maximum-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type -open import order-theory.least-upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/maximum-standard-finite-types.lagda.md b/src/elementary-number-theory/maximum-standard-finite-types.lagda.md index 160a0de610..825fc31e8b 100644 --- a/src/elementary-number-theory/maximum-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/maximum-standard-finite-types.lagda.md @@ -1,22 +1,27 @@ # Maximum on the standard finite types ```agda -module elementary-number-theory.maximum-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.maximum-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.unit-type -open import order-theory.least-upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/mediant-integer-fractions.lagda.md b/src/elementary-number-theory/mediant-integer-fractions.lagda.md index 96adcb2df1..cd4715e9fb 100644 --- a/src/elementary-number-theory/mediant-integer-fractions.lagda.md +++ b/src/elementary-number-theory/mediant-integer-fractions.lagda.md @@ -1,21 +1,26 @@ # The mediant fraction of two integer fractions ```agda -module elementary-number-theory.mediant-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.mediant-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.integer-fractions -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-positive-and-negative-integers funext +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.multiplication-integers funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/mersenne-primes.lagda.md b/src/elementary-number-theory/mersenne-primes.lagda.md index 072edc42fe..b3e6ce9262 100644 --- a/src/elementary-number-theory/mersenne-primes.lagda.md +++ b/src/elementary-number-theory/mersenne-primes.lagda.md @@ -1,20 +1,25 @@ # Mersenne primes ```agda -module elementary-number-theory.mersenne-primes where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.mersenne-primes + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.exponentiation-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers +open import elementary-number-theory.prime-numbers funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/minimum-natural-numbers.lagda.md b/src/elementary-number-theory/minimum-natural-numbers.lagda.md index 71d9c60530..e7e1d4e6be 100644 --- a/src/elementary-number-theory/minimum-natural-numbers.lagda.md +++ b/src/elementary-number-theory/minimum-natural-numbers.lagda.md @@ -1,26 +1,31 @@ # Minimum on the natural numbers ```agda -module elementary-number-theory.minimum-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.minimum-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type -open import order-theory.greatest-lower-bounds-posets +open import order-theory.greatest-lower-bounds-posets funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/minimum-standard-finite-types.lagda.md b/src/elementary-number-theory/minimum-standard-finite-types.lagda.md index d2eef65a72..b2f09690d3 100644 --- a/src/elementary-number-theory/minimum-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/minimum-standard-finite-types.lagda.md @@ -1,22 +1,27 @@ # Minimum on the standard finite types ```agda -module elementary-number-theory.minimum-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.minimum-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.unit-type -open import order-theory.greatest-lower-bounds-posets +open import order-theory.greatest-lower-bounds-posets funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md b/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md index 302d0c9537..6f50697afc 100644 --- a/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md @@ -1,37 +1,42 @@ # Modular arithmetic on the standard finite types ```agda -module elementary-number-theory.modular-arithmetic-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.modular-arithmetic-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.split-surjective-maps -open import foundation.surjective-maps +open import foundation.surjective-maps funext open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/modular-arithmetic.lagda.md b/src/elementary-number-theory/modular-arithmetic.lagda.md index b75b74c017..d58bab9f81 100644 --- a/src/elementary-number-theory/modular-arithmetic.lagda.md +++ b/src/elementary-number-theory/modular-arithmetic.lagda.md @@ -1,50 +1,55 @@ # Modular arithmetic ```agda -module elementary-number-theory.modular-arithmetic where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.modular-arithmetic + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.addition-integers -open import elementary-number-theory.congruence-integers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.equality-integers -open import elementary-number-theory.inequality-integers +open import elementary-number-theory.absolute-value-integers funext +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.congruence-integers funext +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.divisibility-integers funext +open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.inequality-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic-standard-finite-types -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonnegative-integers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.sets -open import foundation.surjective-maps +open import foundation.discrete-types funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.sets funext +open import foundation.surjective-maps funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md b/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md index da4c41ed15..4835841780 100644 --- a/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md +++ b/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md @@ -1,21 +1,26 @@ # The monoid of natural numbers with addition ```agda -module elementary-number-theory.monoid-of-natural-numbers-with-addition where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.monoid-of-natural-numbers-with-addition + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md b/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md index ae0b8fe991..5aa7f55c55 100644 --- a/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md +++ b/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md @@ -1,25 +1,30 @@ # The monoid of the natural numbers with maximum ```agda -module elementary-number-theory.monoid-of-natural-numbers-with-maximum where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.monoid-of-natural-numbers-with-maximum + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.initial-segments-natural-numbers -open import elementary-number-theory.maximum-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.initial-segments-natural-numbers funext +open import elementary-number-theory.maximum-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.normal-submonoids-commutative-monoids -open import group-theory.semigroups -open import group-theory.submonoids-commutative-monoids +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.normal-submonoids-commutative-monoids funext +open import group-theory.semigroups funext +open import group-theory.submonoids-commutative-monoids funext ```
diff --git a/src/elementary-number-theory/multiplication-integer-fractions.lagda.md b/src/elementary-number-theory/multiplication-integer-fractions.lagda.md index 33ca87b0b6..0463457a12 100644 --- a/src/elementary-number-theory/multiplication-integer-fractions.lagda.md +++ b/src/elementary-number-theory/multiplication-integer-fractions.lagda.md @@ -1,23 +1,28 @@ # Multiplication on integer fractions ```agda -module elementary-number-theory.multiplication-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplication-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/multiplication-integers.lagda.md b/src/elementary-number-theory/multiplication-integers.lagda.md index 41d4dfcc1b..473818289d 100644 --- a/src/elementary-number-theory/multiplication-integers.lagda.md +++ b/src/elementary-number-theory/multiplication-integers.lagda.md @@ -1,31 +1,36 @@ # Multiplication of integers ```agda -module elementary-number-theory.multiplication-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplication-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.equality-integers +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.nonzero-integers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.coproduct-types funext +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md b/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md index 85b452a28c..afe65c6a0b 100644 --- a/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md @@ -1,7 +1,12 @@ # Multiplication of the elements of a list of natural numbers ```agda -module elementary-number-theory.multiplication-lists-of-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplication-lists-of-natural-numbers + (funext : function-extensionality) + where ```
Imports @@ -11,14 +16,14 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import lists.permutation-lists +open import lists.permutation-lists funext ```
diff --git a/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md b/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md index a8c0e801c0..9101352d75 100644 --- a/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md +++ b/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md @@ -1,28 +1,33 @@ # Multiplication of positive, negative, nonnegative and nonpositive integers ```agda -module elementary-number-theory.multiplication-positive-and-negative-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplication-positive-and-negative-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.inequality-integers +open import elementary-number-theory.addition-positive-and-negative-integers funext +open import elementary-number-theory.inequality-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-integers - -open import foundation.coproduct-types +open import elementary-number-theory.negative-integers funext +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonpositive-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.strict-inequality-integers funext + +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.identity-types funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/multiplication-rational-numbers.lagda.md b/src/elementary-number-theory/multiplication-rational-numbers.lagda.md index 367d83d9a5..95e2c69b2b 100644 --- a/src/elementary-number-theory/multiplication-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplication-rational-numbers.lagda.md @@ -3,28 +3,33 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.multiplication-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplication-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.difference-rational-numbers funext +open import elementary-number-theory.greatest-common-divisor-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.multiplication-integer-fractions funext +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.reduced-integer-fractions funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.interchange-law ``` diff --git a/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md b/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md index 5c6d0553be..15e4a6df69 100644 --- a/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md @@ -3,26 +3,31 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.multiplicative-group-of-positive-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplicative-group-of-positive-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.multiplication-rational-numbers funext +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.rational-numbers funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.submonoids +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.submonoids funext ```
diff --git a/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md b/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md index 9fd3c96f59..70ddff8542 100644 --- a/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md @@ -3,33 +3,38 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.multiplicative-group-of-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplicative-group-of-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers -open import elementary-number-theory.nonzero-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.ring-of-rational-numbers +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext +open import elementary-number-theory.nonzero-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.ring-of-rational-numbers funext -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.cores-monoids -open import group-theory.groups -open import group-theory.submonoids-commutative-monoids +open import group-theory.abelian-groups funext +open import group-theory.cores-monoids funext +open import group-theory.groups funext +open import group-theory.submonoids-commutative-monoids funext -open import ring-theory.groups-of-units-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.trivial-rings +open import ring-theory.groups-of-units-rings funext +open import ring-theory.invertible-elements-rings funext +open import ring-theory.trivial-rings funext ```
diff --git a/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md b/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md index 8f8e78a309..9fb781b8ec 100644 --- a/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md +++ b/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md @@ -1,22 +1,27 @@ # Multiplicative inverses of positive integer fractions ```agda -module elementary-number-theory.multiplicative-inverses-positive-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplicative-inverses-positive-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.greatest-common-divisor-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.positive-integer-fractions -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.multiplication-integer-fractions funext +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.positive-integer-fractions funext +open import elementary-number-theory.reduced-integer-fractions funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md b/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md index 691a9935fd..3c2c649a3d 100644 --- a/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md @@ -1,20 +1,25 @@ # The multiplicative monoid of natural numbers ```agda -module elementary-number-theory.multiplicative-monoid-of-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplicative-monoid-of-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md b/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md index 781ac3df4c..91159ebfe1 100644 --- a/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md @@ -3,22 +3,27 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.multiplicative-monoid-of-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.multiplicative-monoid-of-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.multiplication-rational-numbers funext +open import elementary-number-theory.rational-numbers funext open import foundation.dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/elementary-number-theory/negative-integers.lagda.md b/src/elementary-number-theory/negative-integers.lagda.md index 86dd90ed11..212fc9a23d 100644 --- a/src/elementary-number-theory/negative-integers.lagda.md +++ b/src/elementary-number-theory/negative-integers.lagda.md @@ -1,31 +1,36 @@ # The negative integers ```agda -module elementary-number-theory.negative-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.negative-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.nonzero-integers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/nonnegative-integers.lagda.md b/src/elementary-number-theory/nonnegative-integers.lagda.md index d9c2b50561..85d7c32dc1 100644 --- a/src/elementary-number-theory/nonnegative-integers.lagda.md +++ b/src/elementary-number-theory/nonnegative-integers.lagda.md @@ -1,30 +1,35 @@ # The nonnegative integers ```agda -module elementary-number-theory.nonnegative-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.nonnegative-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/nonpositive-integers.lagda.md b/src/elementary-number-theory/nonpositive-integers.lagda.md index e5a31ad753..21055aa06b 100644 --- a/src/elementary-number-theory/nonpositive-integers.lagda.md +++ b/src/elementary-number-theory/nonpositive-integers.lagda.md @@ -1,30 +1,35 @@ # The nonpositive integers ```agda -module elementary-number-theory.nonpositive-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.nonpositive-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/nonzero-integers.lagda.md b/src/elementary-number-theory/nonzero-integers.lagda.md index 2d7dd2e4a9..354a8bfd41 100644 --- a/src/elementary-number-theory/nonzero-integers.lagda.md +++ b/src/elementary-number-theory/nonzero-integers.lagda.md @@ -1,7 +1,12 @@ # Nonzero integers ```agda -module elementary-number-theory.nonzero-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.nonzero-integers + (funext : function-extensionality) + where ```
Imports @@ -10,12 +15,12 @@ module elementary-number-theory.nonzero-integers where open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/nonzero-natural-numbers.lagda.md b/src/elementary-number-theory/nonzero-natural-numbers.lagda.md index 4661f74095..45af8dfd26 100644 --- a/src/elementary-number-theory/nonzero-natural-numbers.lagda.md +++ b/src/elementary-number-theory/nonzero-natural-numbers.lagda.md @@ -1,23 +1,28 @@ # Nonzero natural numbers ```agda -module elementary-number-theory.nonzero-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.nonzero-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/nonzero-rational-numbers.lagda.md b/src/elementary-number-theory/nonzero-rational-numbers.lagda.md index 29defc2276..3c3635b449 100644 --- a/src/elementary-number-theory/nonzero-rational-numbers.lagda.md +++ b/src/elementary-number-theory/nonzero-rational-numbers.lagda.md @@ -3,34 +3,39 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.nonzero-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.nonzero-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-rational-numbers funext +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext +open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.reduced-integer-fractions funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.submonoids +open import group-theory.submonoids funext ```
diff --git a/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md b/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md index 80761f26c3..ad8cf3ad71 100644 --- a/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md @@ -1,16 +1,21 @@ # The ordinal induction principle for the natural numbers ```agda -module elementary-number-theory.ordinal-induction-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.ordinal-induction-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext -open import foundation.empty-types +open import foundation.empty-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/parity-natural-numbers.lagda.md b/src/elementary-number-theory/parity-natural-numbers.lagda.md index 78da36cfb4..cd59ccb495 100644 --- a/src/elementary-number-theory/parity-natural-numbers.lagda.md +++ b/src/elementary-number-theory/parity-natural-numbers.lagda.md @@ -1,25 +1,30 @@ # Parity of the natural numbers ```agda -module elementary-number-theory.parity-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.parity-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.negation +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/peano-arithmetic.lagda.md b/src/elementary-number-theory/peano-arithmetic.lagda.md index 97139b2a63..5e16b29e79 100644 --- a/src/elementary-number-theory/peano-arithmetic.lagda.md +++ b/src/elementary-number-theory/peano-arithmetic.lagda.md @@ -1,7 +1,12 @@ # Peano arithmetic ```agda -module elementary-number-theory.peano-arithmetic where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.peano-arithmetic + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module elementary-number-theory.peano-arithmetic where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.propositions +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/pisano-periods.lagda.md b/src/elementary-number-theory/pisano-periods.lagda.md index f765a59fb3..085b071d38 100644 --- a/src/elementary-number-theory/pisano-periods.lagda.md +++ b/src/elementary-number-theory/pisano-periods.lagda.md @@ -1,37 +1,42 @@ # Pisano periods ```agda -module elementary-number-theory.pisano-periods where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.pisano-periods + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.fibonacci-sequence -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.fibonacci-sequence funext +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.lower-bounds-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.well-ordering-principle-natural-numbers funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.repetitions-sequences -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.repetitions-sequences funext +open import foundation.sets funext open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.sequences-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.sequences-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md b/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md index 4977a5e18b..b131a7258a 100644 --- a/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md +++ b/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md @@ -9,21 +9,21 @@ module
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/elementary-number-theory/positive-and-negative-integers.lagda.md b/src/elementary-number-theory/positive-and-negative-integers.lagda.md index 844b95a8b8..dceafdf324 100644 --- a/src/elementary-number-theory/positive-and-negative-integers.lagda.md +++ b/src/elementary-number-theory/positive-and-negative-integers.lagda.md @@ -1,7 +1,12 @@ # The positive, negative, nonnegative and nonpositive integers ```agda -module elementary-number-theory.positive-and-negative-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.positive-and-negative-integers + (funext : function-extensionality) + where ```
Imports @@ -9,20 +14,20 @@ module elementary-number-theory.positive-and-negative-integers where ```agda open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.positive-integers - -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import elementary-number-theory.negative-integers funext +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonpositive-integers funext +open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.positive-integers funext + +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/positive-conatural-numbers.lagda.md b/src/elementary-number-theory/positive-conatural-numbers.lagda.md index 4d2dd9340a..6f20822ef4 100644 --- a/src/elementary-number-theory/positive-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/positive-conatural-numbers.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module elementary-number-theory.positive-conatural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.positive-conatural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers -open import elementary-number-theory.zero-conatural-numbers +open import elementary-number-theory.conatural-numbers funext +open import elementary-number-theory.zero-conatural-numbers funext -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.negation +open import foundation.negation funext open import foundation.universe-levels open import foundation-core.empty-types diff --git a/src/elementary-number-theory/positive-integer-fractions.lagda.md b/src/elementary-number-theory/positive-integer-fractions.lagda.md index 7e92ff3e65..3137adcbdb 100644 --- a/src/elementary-number-theory/positive-integer-fractions.lagda.md +++ b/src/elementary-number-theory/positive-integer-fractions.lagda.md @@ -1,23 +1,28 @@ # Positive integer fractions ```agda -module elementary-number-theory.positive-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.positive-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext +open import elementary-number-theory.addition-positive-and-negative-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.multiplication-integer-fractions funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.reduced-integer-fractions funext -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/positive-integers.lagda.md b/src/elementary-number-theory/positive-integers.lagda.md index 9070e78e0c..eb52cf9a29 100644 --- a/src/elementary-number-theory/positive-integers.lagda.md +++ b/src/elementary-number-theory/positive-integers.lagda.md @@ -1,37 +1,42 @@ # The positive integers ```agda -module elementary-number-theory.positive-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.positive-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.nonzero-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import set-theory.countable-sets +open import set-theory.countable-sets funext ```
diff --git a/src/elementary-number-theory/positive-rational-numbers.lagda.md b/src/elementary-number-theory/positive-rational-numbers.lagda.md index 439940ac49..c6d938475a 100644 --- a/src/elementary-number-theory/positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/positive-rational-numbers.lagda.md @@ -3,61 +3,66 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.positive-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.positive-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.additive-group-of-rational-numbers funext +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext +open import elementary-number-theory.difference-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonzero-natural-numbers -open import elementary-number-theory.nonzero-rational-numbers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integer-fractions -open import elementary-number-theory.positive-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-integers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.multiplication-integer-fractions funext +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.multiplication-rational-numbers funext +open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions funext +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext +open import elementary-number-theory.negative-integers funext +open import elementary-number-theory.nonzero-natural-numbers funext +open import elementary-number-theory.nonzero-rational-numbers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integer-fractions funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-integers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.invertible-elements-monoids -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.submonoids -open import group-theory.submonoids-commutative-monoids -open import group-theory.subsemigroups +open import group-theory.commutative-monoids funext +open import group-theory.invertible-elements-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext +open import group-theory.submonoids funext +open import group-theory.submonoids funext-commutative-monoids +open import group-theory.subsemigroups funext ```
diff --git a/src/elementary-number-theory/powers-integers.lagda.md b/src/elementary-number-theory/powers-integers.lagda.md index 05ec3f9e69..42ad59684a 100644 --- a/src/elementary-number-theory/powers-integers.lagda.md +++ b/src/elementary-number-theory/powers-integers.lagda.md @@ -1,20 +1,25 @@ # Powers of integers ```agda -module elementary-number-theory.powers-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.powers-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.powers-of-elements-commutative-rings +open import commutative-algebra.powers-of-elements-commutative-rings funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.ring-of-integers +open import elementary-number-theory.ring-of-integers funext -open import foundation.identity-types +open import foundation.identity-types funext ```
diff --git a/src/elementary-number-theory/powers-of-two.lagda.md b/src/elementary-number-theory/powers-of-two.lagda.md index d856d60206..4e4237b21d 100644 --- a/src/elementary-number-theory/powers-of-two.lagda.md +++ b/src/elementary-number-theory/powers-of-two.lagda.md @@ -1,25 +1,30 @@ # Powers of two ```agda -module elementary-number-theory.powers-of-two where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.powers-of-two + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.exponentiation-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext +open import elementary-number-theory.strong-induction-natural-numbers funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.split-surjective-maps open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/elementary-number-theory/prime-numbers.lagda.md b/src/elementary-number-theory/prime-numbers.lagda.md index 930d240933..f94a341849 100644 --- a/src/elementary-number-theory/prime-numbers.lagda.md +++ b/src/elementary-number-theory/prime-numbers.lagda.md @@ -1,34 +1,39 @@ # Prime numbers ```agda -module elementary-number-theory.prime-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.prime-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.decidable-types -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-types funext +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.proper-divisors-natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.proper-divisors-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.empty-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/products-of-natural-numbers.lagda.md b/src/elementary-number-theory/products-of-natural-numbers.lagda.md index bf853f365e..c4009c3964 100644 --- a/src/elementary-number-theory/products-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/products-of-natural-numbers.lagda.md @@ -1,7 +1,12 @@ # Products of natural numbers ```agda -module elementary-number-theory.products-of-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.products-of-natural-numbers + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module elementary-number-theory.products-of-natural-numbers where ```agda open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext -open import foundation.coproduct-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.coproduct-types funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.unit-type open import lists.lists -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md b/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md index 0f35339378..7caf0fd235 100644 --- a/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md +++ b/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md @@ -1,29 +1,34 @@ # Proper divisors of natural numbers ```agda -module elementary-number-theory.proper-divisors-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.proper-divisors-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext -open import foundation.cartesian-product-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.type-arithmetic-empty-type +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.type-arithmetic-empty-type funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/pythagorean-triples.lagda.md b/src/elementary-number-theory/pythagorean-triples.lagda.md index bc76529522..6509312d59 100644 --- a/src/elementary-number-theory/pythagorean-triples.lagda.md +++ b/src/elementary-number-theory/pythagorean-triples.lagda.md @@ -1,7 +1,12 @@ # Pythagorean triples ```agda -module elementary-number-theory.pythagorean-triples where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.pythagorean-triples + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module elementary-number-theory.pythagorean-triples where ```agda open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.squares-natural-numbers funext -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/rational-numbers.lagda.md b/src/elementary-number-theory/rational-numbers.lagda.md index 732f9bb66f..c8290ccd3e 100644 --- a/src/elementary-number-theory/rational-numbers.lagda.md +++ b/src/elementary-number-theory/rational-numbers.lagda.md @@ -1,35 +1,40 @@ # The rational numbers ```agda -module elementary-number-theory.rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.divisibility-integers funext +open import elementary-number-theory.greatest-common-divisor-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.mediant-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.mediant-integer-fractions funext +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.reduced-integer-fractions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.retracts-of-types -open import foundation.sections -open import foundation.sets +open import foundation.equality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.retracts-of-types funext +open import foundation.sections funext +open import foundation.sets funext open import foundation.universe-levels -open import set-theory.countable-sets +open import set-theory.countable-sets funext ```
diff --git a/src/elementary-number-theory/reduced-integer-fractions.lagda.md b/src/elementary-number-theory/reduced-integer-fractions.lagda.md index b74d316dd3..7fb038bbd6 100644 --- a/src/elementary-number-theory/reduced-integer-fractions.lagda.md +++ b/src/elementary-number-theory/reduced-integer-fractions.lagda.md @@ -1,35 +1,40 @@ # Reduced integer fractions ```agda -module elementary-number-theory.reduced-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.reduced-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.bezouts-lemma-integers -open import elementary-number-theory.divisibility-integers -open import elementary-number-theory.equality-integers -open import elementary-number-theory.greatest-common-divisor-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.bezouts-lemma-integers funext +open import elementary-number-theory.divisibility-integers funext +open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.greatest-common-divisor-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.relatively-prime-integers +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.relatively-prime-integers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.empty-types funext open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes +open import foundation.equality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/relatively-prime-integers.lagda.md b/src/elementary-number-theory/relatively-prime-integers.lagda.md index a3719203ab..485b1c1a78 100644 --- a/src/elementary-number-theory/relatively-prime-integers.lagda.md +++ b/src/elementary-number-theory/relatively-prime-integers.lagda.md @@ -1,20 +1,25 @@ # Relatively prime integers ```agda -module elementary-number-theory.relatively-prime-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.relatively-prime-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers -open import elementary-number-theory.equality-integers -open import elementary-number-theory.greatest-common-divisor-integers +open import elementary-number-theory.absolute-value-integers funext +open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.greatest-common-divisor-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.relatively-prime-natural-numbers +open import elementary-number-theory.relatively-prime-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md b/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md index 01f59c2f4b..6f2f38b833 100644 --- a/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md +++ b/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md @@ -1,25 +1,30 @@ # Relatively prime natural numbers ```agda -module elementary-number-theory.relatively-prime-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.relatively-prime-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.greatest-common-divisor-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.greatest-common-divisor-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers +open import elementary-number-theory.prime-numbers funext -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md b/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md index d8a354ec93..a59209b752 100644 --- a/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md +++ b/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md @@ -1,7 +1,12 @@ # Repeating an element in a standard finite type ```agda -module elementary-number-theory.repeating-element-standard-finite-type where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.repeating-element-standard-finite-type + (funext : function-extensionality) + where ```
Imports @@ -10,14 +15,14 @@ module elementary-number-theory.repeating-element-standard-finite-type where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.negated-equality +open import foundation.coproduct-types funext +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext open import foundation.unit-type -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md b/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md index f6fc313258..ffa1a33e98 100644 --- a/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md @@ -1,17 +1,22 @@ # Retracts of the type of natural numbers ```agda -module elementary-number-theory.retracts-of-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.retracts-of-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.decidable-maps -open import foundation.retractions +open import foundation.decidable-maps funext +open import foundation.retractions funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/ring-of-integers.lagda.md b/src/elementary-number-theory/ring-of-integers.lagda.md index 1ef3b8fff6..4cc1f3d020 100644 --- a/src/elementary-number-theory/ring-of-integers.lagda.md +++ b/src/elementary-number-theory/ring-of-integers.lagda.md @@ -1,35 +1,40 @@ # The ring of integers ```agda -module elementary-number-theory.ring-of-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.ring-of-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext -open import elementary-number-theory.addition-integers -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.group-of-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.nonzero-integers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator -open import group-theory.homomorphisms-groups +open import group-theory.free-groups-with-one-generator funext +open import group-theory.homomorphisms-groups funext -open import ring-theory.homomorphisms-rings -open import ring-theory.initial-rings -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings -open import ring-theory.trivial-rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.initial-rings funext +open import ring-theory.integer-multiples-of-elements-rings funext +open import ring-theory.rings funext +open import ring-theory.trivial-rings funext ```
diff --git a/src/elementary-number-theory/ring-of-rational-numbers.lagda.md b/src/elementary-number-theory/ring-of-rational-numbers.lagda.md index d0e4e6f220..f806c74ec4 100644 --- a/src/elementary-number-theory/ring-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/ring-of-rational-numbers.lagda.md @@ -3,26 +3,31 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.ring-of-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.ring-of-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers +open import elementary-number-theory.additive-group-of-rational-numbers funext +open import elementary-number-theory.multiplication-rational-numbers funext +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md b/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md index 1727176161..9319b26661 100644 --- a/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md +++ b/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md @@ -1,29 +1,34 @@ # The sieve of Eratosthenes ```agda -module elementary-number-theory.sieve-of-eratosthenes where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.sieve-of-eratosthenes + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.decidable-types -open import elementary-number-theory.divisibility-natural-numbers -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.factorials -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.decidable-types funext +open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.factorials funext +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/square-free-natural-numbers.lagda.md b/src/elementary-number-theory/square-free-natural-numbers.lagda.md index c168fab9ea..5c8145c7eb 100644 --- a/src/elementary-number-theory/square-free-natural-numbers.lagda.md +++ b/src/elementary-number-theory/square-free-natural-numbers.lagda.md @@ -1,15 +1,20 @@ # Square-free natural numbers ```agda -module elementary-number-theory.square-free-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.square-free-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.squares-natural-numbers funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/squares-integers.lagda.md b/src/elementary-number-theory/squares-integers.lagda.md index 2497b17b33..a2e5d0a22b 100644 --- a/src/elementary-number-theory/squares-integers.lagda.md +++ b/src/elementary-number-theory/squares-integers.lagda.md @@ -1,29 +1,34 @@ # Squares in the integers ```agda -module elementary-number-theory.squares-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.squares-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.absolute-value-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.squares-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/elementary-number-theory/squares-modular-arithmetic.lagda.md b/src/elementary-number-theory/squares-modular-arithmetic.lagda.md index 7d77108c0c..5048114191 100644 --- a/src/elementary-number-theory/squares-modular-arithmetic.lagda.md +++ b/src/elementary-number-theory/squares-modular-arithmetic.lagda.md @@ -1,22 +1,27 @@ # Squares in ℤₚ ```agda -module elementary-number-theory.squares-modular-arithmetic where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.squares-modular-arithmetic + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-integers +open import elementary-number-theory.squares-integers funext -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.fibers-of-maps +open import univalent-combinatorics.fibers-of-maps funext ```
diff --git a/src/elementary-number-theory/squares-natural-numbers.lagda.md b/src/elementary-number-theory/squares-natural-numbers.lagda.md index f8afd7063e..380da85a51 100644 --- a/src/elementary-number-theory/squares-natural-numbers.lagda.md +++ b/src/elementary-number-theory/squares-natural-numbers.lagda.md @@ -1,24 +1,29 @@ # Squares in the natural numbers ```agda -module elementary-number-theory.squares-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.squares-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.decidable-types -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-types funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negation +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/standard-cyclic-groups.lagda.md b/src/elementary-number-theory/standard-cyclic-groups.lagda.md index dc65ddde36..dc733a625f 100644 --- a/src/elementary-number-theory/standard-cyclic-groups.lagda.md +++ b/src/elementary-number-theory/standard-cyclic-groups.lagda.md @@ -1,21 +1,26 @@ # The standard cyclic groups ```agda -module elementary-number-theory.standard-cyclic-groups where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.standard-cyclic-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.semigroups funext ```
diff --git a/src/elementary-number-theory/standard-cyclic-rings.lagda.md b/src/elementary-number-theory/standard-cyclic-rings.lagda.md index 60ffeb3ce6..4acaf2d692 100644 --- a/src/elementary-number-theory/standard-cyclic-rings.lagda.md +++ b/src/elementary-number-theory/standard-cyclic-rings.lagda.md @@ -1,37 +1,42 @@ # The standard cyclic rings ```agda -module elementary-number-theory.standard-cyclic-rings where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.standard-cyclic-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.modular-arithmetic funext-standard-finite-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.ring-of-integers -open import elementary-number-theory.standard-cyclic-groups +open import elementary-number-theory.ring-of-integers funext +open import elementary-number-theory.standard-cyclic-groups funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.homotopies -open import foundation.identity-types -open import foundation.surjective-maps +open import foundation.existential-quantification funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import group-theory.cyclic-groups -open import group-theory.generating-elements-groups +open import group-theory.cyclic-groups funext +open import group-theory.generating-elements-groups funext -open import ring-theory.cyclic-rings -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings +open import ring-theory.cyclic-rings funext +open import ring-theory.integer-multiples-of-elements-rings funext +open import ring-theory.rings funext ```
diff --git a/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md b/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md index d58fbf1f4c..3f653608c4 100644 --- a/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md +++ b/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md @@ -1,45 +1,50 @@ # Strict inequality on the integer fractions ```agda -module elementary-number-theory.strict-inequality-integer-fractions where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.strict-inequality-integer-fractions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.inequality-integer-fractions -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-positive-and-negative-integers funext +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.inequality-integer-fractions funext +open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.mediant-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-positive-and-negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.mediant-integer-fractions funext +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonpositive-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.strict-inequality-integers funext open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.disjunction funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/strict-inequality-integers.lagda.md b/src/elementary-number-theory/strict-inequality-integers.lagda.md index 107592ee5c..a734e29b5b 100644 --- a/src/elementary-number-theory/strict-inequality-integers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-integers.lagda.md @@ -1,44 +1,49 @@ # Strict inequality on the integers ```agda -module elementary-number-theory.strict-inequality-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.strict-inequality-integers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.addition-positive-and-negative-integers -open import elementary-number-theory.difference-integers -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-positive-and-negative-integers funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.negative-integers funext +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonpositive-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md b/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md index 623bc26c65..3a3a3a2668 100644 --- a/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md @@ -1,31 +1,36 @@ # Strict inequality on the natural numbers ```agda -module elementary-number-theory.strict-inequality-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.strict-inequality-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md b/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md index 99d4619055..dfeed4a537 100644 --- a/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md @@ -1,49 +1,54 @@ # Strict inequality on the rational numbers ```agda -module elementary-number-theory.strict-inequality-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.strict-inequality-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.cross-multiplication-difference-integer-fractions -open import elementary-number-theory.difference-integers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-integer-fractions -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.integer-fractions +open import elementary-number-theory.addition-integer-fractions funext +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext +open import elementary-number-theory.difference-integers funext +open import elementary-number-theory.difference-rational-numbers funext +open import elementary-number-theory.inequality-integer-fractions funext +open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.integer-fractions funext open import elementary-number-theory.integers -open import elementary-number-theory.mediant-integer-fractions -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.nonnegative-integers -open import elementary-number-theory.nonpositive-integers -open import elementary-number-theory.positive-and-negative-integers -open import elementary-number-theory.positive-integers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.reduced-integer-fractions -open import elementary-number-theory.strict-inequality-integer-fractions -open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.mediant-integer-fractions funext +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonpositive-integers funext +open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.reduced-integer-fractions funext +open import elementary-number-theory.strict-inequality-integer-fractions funext +open import elementary-number-theory.strict-inequality-integers funext open import foundation.action-on-identifications-functions -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.disjunction funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md b/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md index 5083034a1f..386ffb069a 100644 --- a/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md @@ -1,26 +1,31 @@ # Strict inequality on the standard finite types ```agda -module elementary-number-theory.strict-inequality-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.strict-inequality-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.coproduct-types funext +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md b/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md index faab496e28..4b4a3a7a42 100644 --- a/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md @@ -1,23 +1,28 @@ # Strictly ordered pairs of natural numbers ```agda -module elementary-number-theory.strictly-ordered-pairs-of-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.strictly-ordered-pairs-of-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.pairs-of-distinct-elements +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.pairs-of-distinct-elements funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md b/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md index 6a0bf777c5..8fe08da086 100644 --- a/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md @@ -1,25 +1,31 @@ # The strong induction principle for the natural numbers ```agda -module elementary-number-theory.strong-induction-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.strong-induction-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/sums-of-natural-numbers.lagda.md b/src/elementary-number-theory/sums-of-natural-numbers.lagda.md index a026d32a7c..a67b8c7c50 100644 --- a/src/elementary-number-theory/sums-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/sums-of-natural-numbers.lagda.md @@ -1,7 +1,12 @@ # Sums of natural numbers ```agda -module elementary-number-theory.sums-of-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.sums-of-natural-numbers + (funext : function-extensionality) + where ```
Imports @@ -10,24 +15,24 @@ module elementary-number-theory.sums-of-natural-numbers where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.constant-maps -open import foundation.coproduct-types +open import foundation.constant-maps funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import lists.lists -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/sylvesters-sequence.lagda.md b/src/elementary-number-theory/sylvesters-sequence.lagda.md index 5b7094c31d..4dab1c75b2 100644 --- a/src/elementary-number-theory/sylvesters-sequence.lagda.md +++ b/src/elementary-number-theory/sylvesters-sequence.lagda.md @@ -1,17 +1,22 @@ # Sylvester's sequence ```agda -module elementary-number-theory.sylvesters-sequence where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.sylvesters-sequence + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.ordinal-induction-natural-numbers -open import elementary-number-theory.products-of-natural-numbers +open import elementary-number-theory.ordinal-induction-natural-numbers funext +open import elementary-number-theory.products-of-natural-numbers funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/taxicab-numbers.lagda.md b/src/elementary-number-theory/taxicab-numbers.lagda.md index 6c89d1db21..3f4a986b63 100644 --- a/src/elementary-number-theory/taxicab-numbers.lagda.md +++ b/src/elementary-number-theory/taxicab-numbers.lagda.md @@ -1,25 +1,30 @@ # Taxicab numbers ```agda -module elementary-number-theory.taxicab-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.taxicab-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.cubes-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.cubes-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-natural-numbers funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/twin-prime-conjecture.lagda.md b/src/elementary-number-theory/twin-prime-conjecture.lagda.md index a3c6993cca..3af15730ba 100644 --- a/src/elementary-number-theory/twin-prime-conjecture.lagda.md +++ b/src/elementary-number-theory/twin-prime-conjecture.lagda.md @@ -1,17 +1,22 @@ # The Twin Prime conjecture ```agda -module elementary-number-theory.twin-prime-conjecture where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.twin-prime-conjecture + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers +open import elementary-number-theory.prime-numbers funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md b/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md index 9d3fa6833f..4870b16e9d 100644 --- a/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md +++ b/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md @@ -1,29 +1,34 @@ # Type arithmetic with natural numbers ```agda -module elementary-number-theory.type-arithmetic-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.type-arithmetic-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers funext open import elementary-number-theory.integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers -open import elementary-number-theory.powers-of-two +open import elementary-number-theory.parity-natural-numbers funext +open import elementary-number-theory.powers-of-two funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.iterating-functions +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.iterating-functions funext open import foundation.split-surjective-maps -open import foundation.type-arithmetic-coproduct-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-empty-type funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type @@ -36,7 +41,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.negation -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md b/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md index 4b6f36cc3b..50027169cd 100644 --- a/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md @@ -1,26 +1,31 @@ # Unit elements in the standard finite types ```agda -module elementary-number-theory.unit-elements-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.unit-elements-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.divisibility-standard-finite-types -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.divisibility-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers +open import elementary-number-theory.squares-natural-numbers funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md b/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md index 6740932fae..8b18c2c036 100644 --- a/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md +++ b/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md @@ -3,31 +3,36 @@ ```agda {-# OPTIONS --lossy-unification #-} -module elementary-number-theory.unit-fractions-rational-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.unit-fractions-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-positive-rational-numbers -open import elementary-number-theory.inequality-integers -open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.archimedean-property-positive-rational-numbers funext +open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.inequality-rational-numbers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.multiplication-rational-numbers -open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers -open import elementary-number-theory.nonzero-natural-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-integers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-rational-numbers funext +open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers funext +open import elementary-number-theory.nonzero-natural-numbers funext +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-integers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext -open import group-theory.groups +open import group-theory.groups funext ```
diff --git a/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md b/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md index 3830ea8381..0d12f7c2c0 100644 --- a/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md @@ -1,25 +1,30 @@ # Unit similarity on the standard finite types ```agda -module elementary-number-theory.unit-similarity-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.unit-similarity-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.unit-elements-standard-finite-types +open import elementary-number-theory.unit-elements-standard-finite-types funext open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md index 54e612e108..241312ac95 100644 --- a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md @@ -1,15 +1,20 @@ # The universal property of the conatural numbers ```agda -module elementary-number-theory.universal-property-conatural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.universal-property-conatural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coalgebras-maybe -open import foundation.contractible-types -open import foundation.morphisms-coalgebras-maybe +open import foundation.coalgebras-maybe funext +open import foundation.contractible-types funext +open import foundation.morphisms-coalgebras-maybe funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/universal-property-integers.lagda.md b/src/elementary-number-theory/universal-property-integers.lagda.md index 2d36403b4e..01b3fe13b1 100644 --- a/src/elementary-number-theory/universal-property-integers.lagda.md +++ b/src/elementary-number-theory/universal-property-integers.lagda.md @@ -1,7 +1,12 @@ # The universal property of the integers ```agda -module elementary-number-theory.universal-property-integers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.universal-property-integers + (funext : function-extensionality) + where ```
Imports @@ -10,20 +15,20 @@ module elementary-number-theory.universal-property-integers where open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/universal-property-natural-numbers.lagda.md b/src/elementary-number-theory/universal-property-natural-numbers.lagda.md index 69460d3015..1de318743b 100644 --- a/src/elementary-number-theory/universal-property-natural-numbers.lagda.md +++ b/src/elementary-number-theory/universal-property-natural-numbers.lagda.md @@ -1,7 +1,12 @@ # The universal property of the natural numbers ```agda -module elementary-number-theory.universal-property-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.universal-property-natural-numbers + (funext : function-extensionality) + where ```
Imports @@ -10,19 +15,19 @@ module elementary-number-theory.universal-property-natural-numbers where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext ```
diff --git a/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md b/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md index 2a0529164b..c667e4cbb4 100644 --- a/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md +++ b/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md @@ -1,15 +1,20 @@ # Upper bounds for type families over the natural numbers ```agda -module elementary-number-theory.upper-bounds-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.upper-bounds-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md b/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md index a72905645f..8155f22fee 100644 --- a/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md +++ b/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md @@ -1,28 +1,33 @@ # The well-ordering principle of the natural numbers ```agda -module elementary-number-theory.well-ordering-principle-natural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.well-ordering-principle-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.lower-bounds-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.functoriality-dependent-pair-types -open import foundation.hilberts-epsilon-operators -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.hilberts-epsilon-operators funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md index a422c722f0..68a7cf59ae 100644 --- a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md @@ -1,46 +1,51 @@ # The well-ordering principle of the standard finite types ```agda -module elementary-number-theory.well-ordering-principle-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.well-ordering-principle-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.well-ordering-principle-natural-numbers funext -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.hilberts-epsilon-operators -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.hilberts-epsilon-operators funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-empty-type funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.decidable-dependent-pair-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/elementary-number-theory/zero-conatural-numbers.lagda.md b/src/elementary-number-theory/zero-conatural-numbers.lagda.md index 0daa319c80..0dda5718df 100644 --- a/src/elementary-number-theory/zero-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/zero-conatural-numbers.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --guardedness #-} -module elementary-number-theory.zero-conatural-numbers where +open import foundation.function-extensionality-axiom + +module + elementary-number-theory.zero-conatural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers +open import elementary-number-theory.conatural-numbers funext -open import foundation.coproduct-types -open import foundation.decidable-types -open import foundation.function-types -open import foundation.negation +open import foundation.coproduct-types funext +open import foundation.decidable-types funext +open import foundation.function-types funext +open import foundation.negation funext open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/finite-algebra.lagda.md b/src/finite-algebra.lagda.md index 3e2d66d204..87674a38f5 100644 --- a/src/finite-algebra.lagda.md +++ b/src/finite-algebra.lagda.md @@ -3,16 +3,21 @@ ## Modules in the finite algebra namespace ```agda -module finite-algebra where +open import foundation.function-extensionality-axiom -open import finite-algebra.commutative-finite-rings public -open import finite-algebra.dependent-products-commutative-finite-rings public -open import finite-algebra.dependent-products-finite-rings public -open import finite-algebra.finite-fields public -open import finite-algebra.finite-rings public -open import finite-algebra.homomorphisms-commutative-finite-rings public -open import finite-algebra.homomorphisms-finite-rings public -open import finite-algebra.products-commutative-finite-rings public -open import finite-algebra.products-finite-rings public -open import finite-algebra.semisimple-commutative-finite-rings public +module + finite-algebra + (funext : function-extensionality) + where + +open import finite-algebra.commutative-finite-rings funext public +open import finite-algebra.dependent-products-commutative-finite-rings funext public +open import finite-algebra.dependent-products-finite-rings funext public +open import finite-algebra.finite-fields funext public +open import finite-algebra.finite-rings funext public +open import finite-algebra.homomorphisms-commutative-finite-rings funext public +open import finite-algebra.homomorphisms-finite-rings funext public +open import finite-algebra.products-commutative-finite-rings funext public +open import finite-algebra.products-finite-rings funext public +open import finite-algebra.semisimple-commutative-finite-rings funext public ``` diff --git a/src/finite-algebra/commutative-finite-rings.lagda.md b/src/finite-algebra/commutative-finite-rings.lagda.md index 035aeea3e7..05cece41f0 100644 --- a/src/finite-algebra/commutative-finite-rings.lagda.md +++ b/src/finite-algebra/commutative-finite-rings.lagda.md @@ -1,51 +1,56 @@ # Commutative finite rings ```agda -module finite-algebra.commutative-finite-rings where +open import foundation.function-extensionality-axiom + +module + finite-algebra.commutative-finite-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-semirings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-algebra.finite-rings +open import finite-algebra.finite-rings funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.involutions -open import foundation.propositions -open import foundation.sets +open import foundation.involutions funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext +open import ring-theory.semirings funext -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md b/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md index 82cdf56aa9..0806911183 100644 --- a/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md @@ -1,32 +1,37 @@ # Dependent products of commutative finit rings ```agda -module finite-algebra.dependent-products-commutative-finite-rings where +open import foundation.function-extensionality-axiom + +module + finite-algebra.dependent-products-commutative-finite-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.dependent-products-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.dependent-products-commutative-rings funext -open import finite-algebra.commutative-finite-rings -open import finite-algebra.dependent-products-finite-rings -open import finite-algebra.finite-rings +open import finite-algebra.commutative-finite-rings funext +open import finite-algebra.dependent-products-finite-rings funext +open import finite-algebra.finite-rings funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext -open import ring-theory.dependent-products-rings -open import ring-theory.rings +open import ring-theory.dependent-products-rings funext +open import ring-theory.rings funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-algebra/dependent-products-finite-rings.lagda.md b/src/finite-algebra/dependent-products-finite-rings.lagda.md index a1c2f98a52..493d1bccdf 100644 --- a/src/finite-algebra/dependent-products-finite-rings.lagda.md +++ b/src/finite-algebra/dependent-products-finite-rings.lagda.md @@ -1,31 +1,36 @@ # Dependent products of finite rings ```agda -module finite-algebra.dependent-products-finite-rings where +open import foundation.function-extensionality-axiom + +module + finite-algebra.dependent-products-finite-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import finite-algebra.finite-rings +open import finite-algebra.finite-rings funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import ring-theory.dependent-products-rings -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.dependent-products-rings funext +open import ring-theory.rings funext +open import ring-theory.semirings funext -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-algebra/finite-fields.lagda.md b/src/finite-algebra/finite-fields.lagda.md index 27425b25c9..56c2465cdd 100644 --- a/src/finite-algebra/finite-fields.lagda.md +++ b/src/finite-algebra/finite-fields.lagda.md @@ -1,47 +1,52 @@ # Finite fields ```agda -module finite-algebra.finite-fields where +open import foundation.function-extensionality-axiom + +module + finite-algebra.finite-fields + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-semirings funext open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-algebra.commutative-finite-rings -open import finite-algebra.finite-rings +open import finite-algebra.commutative-finite-rings funext +open import finite-algebra.finite-rings funext open import foundation.action-on-identifications-binary-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import ring-theory.division-rings -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.division-rings funext +open import ring-theory.rings funext +open import ring-theory.semirings funext ```
diff --git a/src/finite-algebra/finite-rings.lagda.md b/src/finite-algebra/finite-rings.lagda.md index e78ca56b4d..199d1dbc48 100644 --- a/src/finite-algebra/finite-rings.lagda.md +++ b/src/finite-algebra/finite-rings.lagda.md @@ -1,7 +1,12 @@ # Finite rings ```agda -module finite-algebra.finite-rings where +open import foundation.function-extensionality-axiom + +module + finite-algebra.finite-rings + (funext : function-extensionality) + where ```
Imports @@ -10,39 +15,39 @@ module finite-algebra.finite-rings where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-abelian-groups -open import finite-group-theory.finite-groups -open import finite-group-theory.finite-monoids +open import finite-group-theory.finite-abelian-groups funext +open import finite-group-theory.finite-groups funext +open import finite-group-theory.finite-monoids funext -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.rings funext +open import ring-theory.semirings funext -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md b/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md index 21ac9504c6..d0f57b14d8 100644 --- a/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md @@ -1,28 +1,33 @@ # Homomorphisms of commutative finite rings ```agda -module finite-algebra.homomorphisms-commutative-finite-rings where +open import foundation.function-extensionality-axiom + +module + finite-algebra.homomorphisms-commutative-finite-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.homomorphisms-commutative-rings -open import commutative-algebra.homomorphisms-commutative-semirings +open import commutative-algebra.homomorphisms-commutative-rings funext +open import commutative-algebra.homomorphisms-commutative-semirings funext -open import finite-algebra.commutative-finite-rings +open import finite-algebra.commutative-finite-rings funext -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.homomorphisms-monoids funext -open import ring-theory.homomorphisms-rings +open import ring-theory.homomorphisms-rings funext ```
diff --git a/src/finite-algebra/homomorphisms-finite-rings.lagda.md b/src/finite-algebra/homomorphisms-finite-rings.lagda.md index 9cc03a1249..e7b4be06cc 100644 --- a/src/finite-algebra/homomorphisms-finite-rings.lagda.md +++ b/src/finite-algebra/homomorphisms-finite-rings.lagda.md @@ -1,25 +1,30 @@ # Homomorphisms of finite rings ```agda -module finite-algebra.homomorphisms-finite-rings where +open import foundation.function-extensionality-axiom + +module + finite-algebra.homomorphisms-finite-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import finite-algebra.finite-rings +open import finite-algebra.finite-rings funext -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.homomorphisms-monoids funext -open import ring-theory.homomorphisms-rings +open import ring-theory.homomorphisms-rings funext ```
diff --git a/src/finite-algebra/products-commutative-finite-rings.lagda.md b/src/finite-algebra/products-commutative-finite-rings.lagda.md index 46ad564c75..c0c5f3654a 100644 --- a/src/finite-algebra/products-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/products-commutative-finite-rings.lagda.md @@ -1,28 +1,33 @@ # Products of commutative finite rings ```agda -module finite-algebra.products-commutative-finite-rings where +open import foundation.function-extensionality-axiom + +module + finite-algebra.products-commutative-finite-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings -open import commutative-algebra.products-commutative-rings +open import commutative-algebra.commutative-rings funext +open import commutative-algebra.products-commutative-rings funext -open import finite-algebra.commutative-finite-rings -open import finite-algebra.products-finite-rings +open import finite-algebra.commutative-finite-rings funext +open import finite-algebra.products-finite-rings funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.semigroups funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-algebra/products-finite-rings.lagda.md b/src/finite-algebra/products-finite-rings.lagda.md index 4555ad4b74..c97d3d8d74 100644 --- a/src/finite-algebra/products-finite-rings.lagda.md +++ b/src/finite-algebra/products-finite-rings.lagda.md @@ -1,28 +1,33 @@ # Products of finite rings ```agda -module finite-algebra.products-finite-rings where +open import foundation.function-extensionality-axiom + +module + finite-algebra.products-finite-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import finite-algebra.finite-rings +open import finite-algebra.finite-rings funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.semigroups funext -open import ring-theory.products-rings -open import ring-theory.rings +open import ring-theory.products-rings funext +open import ring-theory.rings funext -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md b/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md index 7c72cb1712..2e3029af1b 100644 --- a/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md @@ -1,7 +1,12 @@ # Semisimple commutative finite rings ```agda -module finite-algebra.semisimple-commutative-finite-rings where +open import foundation.function-extensionality-axiom + +module + finite-algebra.semisimple-commutative-finite-rings + (funext : function-extensionality) + where ```
Imports @@ -9,20 +14,20 @@ module finite-algebra.semisimple-commutative-finite-rings where ```agda open import elementary-number-theory.natural-numbers -open import finite-algebra.commutative-finite-rings -open import finite-algebra.dependent-products-commutative-finite-rings -open import finite-algebra.finite-fields -open import finite-algebra.homomorphisms-commutative-finite-rings +open import finite-algebra.commutative-finite-rings funext +open import finite-algebra.dependent-products-commutative-finite-rings funext +open import finite-algebra.finite-fields funext +open import finite-algebra.homomorphisms-commutative-finite-rings funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory.lagda.md b/src/finite-group-theory.lagda.md index 8c555ee159..82cd1a7004 100644 --- a/src/finite-group-theory.lagda.md +++ b/src/finite-group-theory.lagda.md @@ -3,28 +3,33 @@ ## Modules in the finite group theory namespace ```agda -module finite-group-theory where +open import foundation.function-extensionality-axiom -open import finite-group-theory.abstract-quaternion-group public -open import finite-group-theory.alternating-concrete-groups public -open import finite-group-theory.alternating-groups public -open import finite-group-theory.cartier-delooping-sign-homomorphism public -open import finite-group-theory.concrete-quaternion-group public -open import finite-group-theory.delooping-sign-homomorphism public -open import finite-group-theory.finite-abelian-groups public -open import finite-group-theory.finite-commutative-monoids public -open import finite-group-theory.finite-groups public -open import finite-group-theory.finite-monoids public -open import finite-group-theory.finite-semigroups public -open import finite-group-theory.finite-type-groups public -open import finite-group-theory.groups-of-order-2 public -open import finite-group-theory.orbits-permutations public -open import finite-group-theory.permutations public -open import finite-group-theory.permutations-standard-finite-types public -open import finite-group-theory.sign-homomorphism public -open import finite-group-theory.simpson-delooping-sign-homomorphism public -open import finite-group-theory.subgroups-finite-groups public -open import finite-group-theory.tetrahedra-in-3-space public -open import finite-group-theory.transpositions public -open import finite-group-theory.transpositions-standard-finite-types public +module + finite-group-theory + (funext : function-extensionality) + where + +open import finite-group-theory.abstract-quaternion-group funext public +open import finite-group-theory.alternating-concrete-groups funext public +open import finite-group-theory.alternating-groups funext public +open import finite-group-theory.cartier-delooping-sign-homomorphism funext public +open import finite-group-theory.concrete-quaternion-group funext public +open import finite-group-theory.delooping-sign-homomorphism funext public +open import finite-group-theory.finite-abelian-groups funext public +open import finite-group-theory.finite-commutative-monoids funext public +open import finite-group-theory.finite-groups funext public +open import finite-group-theory.finite-monoids funext public +open import finite-group-theory.finite-semigroups funext public +open import finite-group-theory.finite-type-groups funext public +open import finite-group-theory.groups-of-order-2 funext public +open import finite-group-theory.orbits-permutations funext public +open import finite-group-theory.permutations funext public +open import finite-group-theory.permutations-standard-finite-types funext public +open import finite-group-theory.sign-homomorphism funext public +open import finite-group-theory.simpson-delooping-sign-homomorphism funext public +open import finite-group-theory.subgroups-finite-groups funext public +open import finite-group-theory.tetrahedra-in-3-space funext public +open import finite-group-theory.transpositions funext public +open import finite-group-theory.transpositions-standard-finite-types funext public ``` diff --git a/src/finite-group-theory/abstract-quaternion-group.lagda.md b/src/finite-group-theory/abstract-quaternion-group.lagda.md index c8a8199ee7..2b947f4143 100644 --- a/src/finite-group-theory/abstract-quaternion-group.lagda.md +++ b/src/finite-group-theory/abstract-quaternion-group.lagda.md @@ -1,33 +1,38 @@ # The abstract quaternion group of order `8` ```agda -module finite-group-theory.abstract-quaternion-group where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.abstract-quaternion-group + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.groups funext +open import group-theory.semigroups funext -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/alternating-concrete-groups.lagda.md b/src/finite-group-theory/alternating-concrete-groups.lagda.md index 388be53b80..3a2447efff 100644 --- a/src/finite-group-theory/alternating-concrete-groups.lagda.md +++ b/src/finite-group-theory/alternating-concrete-groups.lagda.md @@ -1,7 +1,12 @@ # Alternating concrete groups ```agda -module finite-group-theory.alternating-concrete-groups where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.alternating-concrete-groups + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module finite-group-theory.alternating-concrete-groups where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.cartier-delooping-sign-homomorphism -open import finite-group-theory.finite-type-groups +open import finite-group-theory.cartier-delooping-sign-homomorphism funext +open import finite-group-theory.finite-type-groups funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.kernels-homomorphisms-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.kernels-homomorphisms-concrete-groups funext ```
diff --git a/src/finite-group-theory/alternating-groups.lagda.md b/src/finite-group-theory/alternating-groups.lagda.md index 975c699ac4..02a37d0493 100644 --- a/src/finite-group-theory/alternating-groups.lagda.md +++ b/src/finite-group-theory/alternating-groups.lagda.md @@ -1,7 +1,12 @@ # Alternating groups ```agda -module finite-group-theory.alternating-groups where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.alternating-groups + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module finite-group-theory.alternating-groups where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.sign-homomorphism +open import finite-group-theory.sign-homomorphism funext -open import group-theory.groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.symmetric-groups +open import group-theory.groups funext +open import group-theory.kernels-homomorphisms-groups funext +open import group-theory.symmetric-groups funext -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md index bf4f606cc2..d89db866d8 100644 --- a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module finite-group-theory.cartier-delooping-sign-homomorphism where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.cartier-delooping-sign-homomorphism + (funext : function-extensionality) + where ```
Imports @@ -12,36 +17,36 @@ module finite-group-theory.cartier-delooping-sign-homomorphism where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.delooping-sign-homomorphism -open import finite-group-theory.finite-type-groups -open import finite-group-theory.sign-homomorphism -open import finite-group-theory.transpositions +open import finite-group-theory.delooping-sign-homomorphism funext +open import finite-group-theory.finite-type-groups funext +open import finite-group-theory.sign-homomorphism funext +open import finite-group-theory.transpositions funext -open import foundation.action-on-equivalences-type-families-over-subuniverses +open import foundation.action-on-equivalences-type-families-over-subuniverses funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.raising-universe-levels +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.raising-universe-levels funext open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.homomorphisms-concrete-groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.loop-groups-sets -open import group-theory.symmetric-groups +open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.loop-groups-sets funext +open import group-theory.symmetric-groups funext -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.orientations-complete-undirected-graph -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.orientations-complete-undirected-graph funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/concrete-quaternion-group.lagda.md b/src/finite-group-theory/concrete-quaternion-group.lagda.md index d424d3600b..aa95200325 100644 --- a/src/finite-group-theory/concrete-quaternion-group.lagda.md +++ b/src/finite-group-theory/concrete-quaternion-group.lagda.md @@ -1,7 +1,12 @@ # The concrete quaternion group ```agda -module finite-group-theory.concrete-quaternion-group where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.concrete-quaternion-group + (funext : function-extensionality) + where ```
Imports @@ -10,16 +15,16 @@ module finite-group-theory.concrete-quaternion-group where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.isolated-elements +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.complements-isolated-elements -open import univalent-combinatorics.cubes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.equivalences-cubes +open import univalent-combinatorics.complements-isolated-elements funext +open import univalent-combinatorics.cubes funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.equivalences-cubes funext ```
diff --git a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md index 4cc333bf45..230155c4a4 100644 --- a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md @@ -3,80 +3,86 @@ ```agda {-# OPTIONS --lossy-unification #-} -module finite-group-theory.delooping-sign-homomorphism where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.delooping-sign-homomorphism + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-type-groups -open import finite-group-theory.permutations -open import finite-group-theory.sign-homomorphism -open import finite-group-theory.transpositions +open import finite-group-theory.finite-type-groups funext +open import finite-group-theory.permutations funext +open import finite-group-theory.sign-homomorphism funext +open import finite-group-theory.transpositions funext -open import foundation.action-on-equivalences-type-families-over-subuniverses +open import foundation.action-on-equivalences-type-families-over-subuniverses funext open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-extensionality -open import foundation.equivalence-induction -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-propositional-truncation -open import foundation.functoriality-set-quotients -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-classes funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-induction funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.functoriality-set-quotients funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.sets funext open import foundation.transport-along-identifications -open import foundation.truncated-types -open import foundation.uniqueness-set-quotients +open import foundation.truncated-types funext +open import foundation.uniqueness-set-quotients funext open import foundation.unit-type -open import foundation.univalence -open import foundation.universal-property-set-quotients +open import foundation.univalence funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import group-theory.generating-sets-groups -open import group-theory.groups -open import group-theory.homomorphisms-concrete-groups -open import group-theory.homomorphisms-generated-subgroups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-groups -open import group-theory.loop-groups-sets -open import group-theory.symmetric-groups +open import group-theory.generating-sets-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.homomorphisms-generated-subgroups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-semigroups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.loop-groups-sets funext +open import group-theory.symmetric-groups funext -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.set-quotients-of-index-two -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.set-quotients-of-index-two funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/finite-abelian-groups.lagda.md b/src/finite-group-theory/finite-abelian-groups.lagda.md index 51bc616d82..f4fb6e2263 100644 --- a/src/finite-group-theory/finite-abelian-groups.lagda.md +++ b/src/finite-group-theory/finite-abelian-groups.lagda.md @@ -1,31 +1,36 @@ # Abelian groups ```agda -module finite-group-theory.finite-abelian-groups where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.finite-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import finite-group-theory.finite-groups +open import finite-group-theory.finite-groups funext -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.interchange-law -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-group-theory/finite-commutative-monoids.lagda.md b/src/finite-group-theory/finite-commutative-monoids.lagda.md index d66dd10353..8003e1c6bb 100644 --- a/src/finite-group-theory/finite-commutative-monoids.lagda.md +++ b/src/finite-group-theory/finite-commutative-monoids.lagda.md @@ -1,27 +1,32 @@ # Finite Commutative monoids ```agda -module finite-group-theory.finite-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.finite-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import finite-group-theory.finite-monoids +open import finite-group-theory.finite-monoids funext -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-group-theory/finite-groups.lagda.md b/src/finite-group-theory/finite-groups.lagda.md index b52469f559..faf3070352 100644 --- a/src/finite-group-theory/finite-groups.lagda.md +++ b/src/finite-group-theory/finite-groups.lagda.md @@ -1,7 +1,12 @@ # Finite groups ```agda -module finite-group-theory.finite-groups where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.finite-groups + (funext : function-extensionality) + where ```
Imports @@ -9,51 +14,51 @@ module finite-group-theory.finite-groups where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-monoids -open import finite-group-theory.finite-semigroups +open import finite-group-theory.finite-monoids funext +open import finite-group-theory.finite-semigroups funext -open import foundation.1-types -open import foundation.binary-embeddings +open import foundation.1-types funext +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.decidable-equality -open import foundation.decidable-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets +open import foundation.decidable-equality funext +open import foundation.decidable-types funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.category-of-groups -open import group-theory.commuting-elements-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.category-of-groups funext +open import group-theory.commuting-elements-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext open import structured-types.pointed-types -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.function-types -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-dependent-pair-types +open import univalent-combinatorics.decidable-dependent-function-types funext +open import univalent-combinatorics.decidable-dependent-pair-types funext +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finitely-many-connected-components funext +open import univalent-combinatorics.function-types funext +open import univalent-combinatorics.pi-finite-types funext +open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.untruncated-pi-finite-types funext ```
diff --git a/src/finite-group-theory/finite-monoids.lagda.md b/src/finite-group-theory/finite-monoids.lagda.md index 36b3f1e29b..4215719fa4 100644 --- a/src/finite-group-theory/finite-monoids.lagda.md +++ b/src/finite-group-theory/finite-monoids.lagda.md @@ -1,7 +1,12 @@ # Finite monoids ```agda -module finite-group-theory.finite-monoids where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.finite-monoids + (funext : function-extensionality) + where ```
Imports @@ -9,38 +14,38 @@ module finite-group-theory.finite-monoids where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-semigroups +open import finite-group-theory.finite-semigroups funext -open import foundation.1-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.1-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups - -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import group-theory.monoids funext +open import group-theory.semigroups funext + +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.decidable-dependent-function-types funext +open import univalent-combinatorics.decidable-dependent-pair-types funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finitely-many-connected-components funext +open import univalent-combinatorics.pi-finite-types funext +open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.untruncated-pi-finite-types funext ```
diff --git a/src/finite-group-theory/finite-semigroups.lagda.md b/src/finite-group-theory/finite-semigroups.lagda.md index 40f90172d9..18769ff110 100644 --- a/src/finite-group-theory/finite-semigroups.lagda.md +++ b/src/finite-group-theory/finite-semigroups.lagda.md @@ -1,7 +1,12 @@ # Finite semigroups ```agda -module finite-group-theory.finite-semigroups where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.finite-semigroups + (funext : function-extensionality) + where ```
Imports @@ -9,31 +14,31 @@ module finite-group-theory.finite-semigroups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types -open import foundation.decidable-propositions -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets +open import foundation.1-types funext +open import foundation.decidable-propositions funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext +open import foundation.propositions funext +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.category-of-semigroups -open import group-theory.semigroups - -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.function-types -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import group-theory.category-of-semigroups funext +open import group-theory.semigroups funext + +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finitely-many-connected-components funext +open import univalent-combinatorics.function-types funext +open import univalent-combinatorics.pi-finite-types funext +open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.untruncated-pi-finite-types funext ```
diff --git a/src/finite-group-theory/finite-type-groups.lagda.md b/src/finite-group-theory/finite-type-groups.lagda.md index 4b7783f027..32862afa87 100644 --- a/src/finite-group-theory/finite-type-groups.lagda.md +++ b/src/finite-group-theory/finite-type-groups.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module finite-group-theory.finite-type-groups where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.finite-type-groups + (funext : function-extensionality) + where ```
Imports @@ -11,35 +16,36 @@ module finite-group-theory.finite-type-groups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.sets -open import foundation.truncated-types +open import foundation.equality-dependent-pair-types funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.sets funext +open import foundation.truncated-types funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-groups -open import group-theory.loop-groups-sets -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.concrete-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-semigroups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.loop-groups-sets funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/groups-of-order-2.lagda.md b/src/finite-group-theory/groups-of-order-2.lagda.md index 05de139f31..623f3cc98e 100644 --- a/src/finite-group-theory/groups-of-order-2.lagda.md +++ b/src/finite-group-theory/groups-of-order-2.lagda.md @@ -3,34 +3,39 @@ ```agda {-# OPTIONS --lossy-unification #-} -module finite-group-theory.groups-of-order-2 where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.groups-of-order-2 + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.standard-cyclic-groups +open import elementary-number-theory.standard-cyclic-groups funext -open import finite-group-theory.finite-groups +open import finite-group-theory.finite-groups funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.isomorphisms-groups -open import group-theory.symmetric-groups +open import group-theory.groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.symmetric-groups funext -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/orbits-permutations.lagda.md b/src/finite-group-theory/orbits-permutations.lagda.md index 06919a3b39..743761041a 100644 --- a/src/finite-group-theory/orbits-permutations.lagda.md +++ b/src/finite-group-theory/orbits-permutations.lagda.md @@ -3,66 +3,71 @@ ```agda {-# OPTIONS --lossy-unification #-} -module finite-group-theory.orbits-permutations where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.orbits-permutations + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.decidable-types -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.euclidean-division-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.decidable-types funext +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.euclidean-division-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.lower-bounds-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.well-ordering-principle-natural-numbers funext -open import finite-group-theory.transpositions +open import finite-group-theory.transpositions funext open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-equivalence-relations -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.automorphisms funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-equivalence-relations funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-extensionality -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.iterating-functions -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.repetitions-of-values -open import foundation.sets +open import foundation.double-negation funext +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-classes funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.iterating-functions funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.repetitions-of-values funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.image-of-maps -open import univalent-combinatorics.pigeonhole-principle -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.image-of-maps funext +open import univalent-combinatorics.pigeonhole-principle funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/permutations-standard-finite-types.lagda.md b/src/finite-group-theory/permutations-standard-finite-types.lagda.md index 0be0d3314d..7c89ca92cc 100644 --- a/src/finite-group-theory/permutations-standard-finite-types.lagda.md +++ b/src/finite-group-theory/permutations-standard-finite-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module finite-group-theory.permutations-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.permutations-standard-finite-types + (funext : function-extensionality) + where ```
Imports @@ -11,37 +16,37 @@ module finite-group-theory.permutations-standard-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.transpositions +open import finite-group-theory.transpositions funext open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.automorphisms funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.propositions -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.equivalences funext-maybe +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import lists.functoriality-lists +open import lists.functoriality-lists funext open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/permutations.lagda.md b/src/finite-group-theory/permutations.lagda.md index 02097ffebf..65e2f75e14 100644 --- a/src/finite-group-theory/permutations.lagda.md +++ b/src/finite-group-theory/permutations.lagda.md @@ -3,53 +3,58 @@ ```agda {-# OPTIONS --lossy-unification #-} -module finite-group-theory.permutations where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.permutations + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import finite-group-theory.orbits-permutations -open import finite-group-theory.permutations-standard-finite-types -open import finite-group-theory.transpositions +open import finite-group-theory.orbits-permutations funext +open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.transpositions funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterating-functions -open import foundation.iterating-involutions -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterating-functions funext +open import foundation.iterating-involutions funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.generating-sets-groups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.symmetric-groups +open import group-theory.generating-sets-groups funext +open import group-theory.subgroups-generated-by-subsets-groups funext +open import group-theory.symmetric-groups funext -open import lists.functoriality-lists +open import lists.functoriality-lists funext open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/sign-homomorphism.lagda.md b/src/finite-group-theory/sign-homomorphism.lagda.md index 877705c2d4..152ac57b17 100644 --- a/src/finite-group-theory/sign-homomorphism.lagda.md +++ b/src/finite-group-theory/sign-homomorphism.lagda.md @@ -1,45 +1,50 @@ # The sign homomorphism ```agda -module finite-group-theory.sign-homomorphism where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.sign-homomorphism + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations -open import finite-group-theory.transpositions +open import finite-group-theory.permutations funext +open import finite-group-theory.transpositions funext open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.automorphisms funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.symmetric-groups +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-semigroups funext +open import group-theory.symmetric-groups funext -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext +open import lists.functoriality-lists funext open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md index b416cd96b6..197facd71d 100644 --- a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md @@ -3,65 +3,70 @@ ```agda {-# OPTIONS --lossy-unification #-} -module finite-group-theory.simpson-delooping-sign-homomorphism where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.simpson-delooping-sign-homomorphism + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import finite-group-theory.delooping-sign-homomorphism -open import finite-group-theory.finite-type-groups -open import finite-group-theory.permutations -open import finite-group-theory.sign-homomorphism -open import finite-group-theory.transpositions +open import finite-group-theory.delooping-sign-homomorphism funext +open import finite-group-theory.finite-type-groups funext +open import finite-group-theory.permutations funext +open import finite-group-theory.sign-homomorphism funext +open import finite-group-theory.transpositions funext -open import foundation.action-on-equivalences-type-families-over-subuniverses +open import foundation.action-on-equivalences-type-families-over-subuniverses funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-equivalence-relations -open import foundation.decidable-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-equivalence-relations funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-classes -open import foundation.equivalence-extensionality -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.involutions -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.raising-universe-levels -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equivalence-classes funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.involutions funext +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.raising-universe-levels funext +open import foundation.sets funext open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-concrete-groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.loop-groups-sets -open import group-theory.symmetric-groups +open import group-theory.groups funext +open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.loop-groups-sets funext +open import group-theory.symmetric-groups funext open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/subgroups-finite-groups.lagda.md b/src/finite-group-theory/subgroups-finite-groups.lagda.md index e693dcaa67..613bc2c382 100644 --- a/src/finite-group-theory/subgroups-finite-groups.lagda.md +++ b/src/finite-group-theory/subgroups-finite-groups.lagda.md @@ -1,34 +1,39 @@ # Subgroups of finite groups ```agda -module finite-group-theory.subgroups-finite-groups where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.subgroups-finite-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import finite-group-theory.finite-groups -open import finite-group-theory.finite-semigroups +open import finite-group-theory.finite-groups funext +open import finite-group-theory.finite-semigroups funext -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.decidable-subgroups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.semigroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.decidable-subgroups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.semigroups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.decidable-subtypes funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-group-theory/tetrahedra-in-3-space.lagda.md b/src/finite-group-theory/tetrahedra-in-3-space.lagda.md index 6fac18a6da..c3b5fc5b66 100644 --- a/src/finite-group-theory/tetrahedra-in-3-space.lagda.md +++ b/src/finite-group-theory/tetrahedra-in-3-space.lagda.md @@ -1,19 +1,24 @@ # Tetrahedra in `3`-dimensional space ```agda -module finite-group-theory.tetrahedra-in-3-space where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.tetrahedra-in-3-space + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types +open import foundation.empty-types funext open import foundation.universe-levels -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.cyclic-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.cyclic-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/finite-group-theory/transpositions-standard-finite-types.lagda.md b/src/finite-group-theory/transpositions-standard-finite-types.lagda.md index bd345f2692..fc8a76b666 100644 --- a/src/finite-group-theory/transpositions-standard-finite-types.lagda.md +++ b/src/finite-group-theory/transpositions-standard-finite-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module finite-group-theory.transpositions-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.transpositions-standard-finite-types + (funext : function-extensionality) + where ```
Imports @@ -11,31 +16,31 @@ module finite-group-theory.transpositions-standard-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types -open import finite-group-theory.transpositions +open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.transpositions funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import lists.functoriality-lists +open import lists.functoriality-lists funext open import lists.lists -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/finite-group-theory/transpositions.lagda.md b/src/finite-group-theory/transpositions.lagda.md index ad26d6e6af..8a6de1d4bb 100644 --- a/src/finite-group-theory/transpositions.lagda.md +++ b/src/finite-group-theory/transpositions.lagda.md @@ -1,62 +1,67 @@ # Transpositions ```agda -module finite-group-theory.transpositions where +open import foundation.function-extensionality-axiom + +module + finite-group-theory.transpositions + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.automorphisms funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-propositions funext +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.equivalences funext-maybe +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.sets funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext +open import lists.functoriality-lists funext open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation-core.lagda.md b/src/foundation-core.lagda.md index 17d58ece65..071efcb72f 100644 --- a/src/foundation-core.lagda.md +++ b/src/foundation-core.lagda.md @@ -3,36 +3,41 @@ ## Modules in the foundation-core namespace ```agda -module foundation-core where +open import foundation.function-extensionality-axiom -open import foundation-core.1-types public +module + foundation-core + (funext : function-extensionality) + where + +open import foundation-core.1-types funext public open import foundation-core.booleans public open import foundation-core.cartesian-product-types public open import foundation-core.coherently-invertible-maps public -open import foundation-core.commuting-prisms-of-maps public +open import foundation-core.commuting-prisms-of-maps funext public open import foundation-core.commuting-squares-of-homotopies public open import foundation-core.commuting-squares-of-identifications public -open import foundation-core.commuting-squares-of-maps public +open import foundation-core.commuting-squares-of-maps funext public open import foundation-core.commuting-triangles-of-maps public open import foundation-core.constant-maps public open import foundation-core.contractible-maps public open import foundation-core.contractible-types public open import foundation-core.coproduct-types public -open import foundation-core.decidable-propositions public +open import foundation-core.decidable-propositions funext public open import foundation-core.dependent-identifications public open import foundation-core.diagonal-maps-cartesian-products-of-types public open import foundation-core.diagonal-maps-of-types public -open import foundation-core.discrete-types public +open import foundation-core.discrete-types funext public open import foundation-core.embeddings public open import foundation-core.empty-types public -open import foundation-core.endomorphisms public +open import foundation-core.endomorphisms funext public open import foundation-core.equality-dependent-pair-types public -open import foundation-core.equivalence-relations public +open import foundation-core.equivalence-relations funext public open import foundation-core.equivalences public open import foundation-core.families-of-equivalences public open import foundation-core.fibers-of-maps public open import foundation-core.function-types public -open import foundation-core.functoriality-dependent-function-types public +open import foundation-core.functoriality-dependent-function-types funext public open import foundation-core.functoriality-dependent-pair-types public open import foundation-core.homotopies public open import foundation-core.identity-types public @@ -41,8 +46,8 @@ open import foundation-core.invertible-maps public open import foundation-core.logical-equivalences public open import foundation-core.maybe public open import foundation-core.negation public -open import foundation-core.operations-span-diagrams public -open import foundation-core.operations-spans public +open import foundation-core.operations-span-diagrams funext public +open import foundation-core.operations-spans funext public open import foundation-core.path-split-maps public open import foundation-core.postcomposition-dependent-functions public open import foundation-core.postcomposition-functions public @@ -50,22 +55,22 @@ open import foundation-core.precomposition-dependent-functions public open import foundation-core.precomposition-functions public open import foundation-core.propositional-maps public open import foundation-core.propositions public -open import foundation-core.pullbacks public +open import foundation-core.pullbacks funext public open import foundation-core.retractions public open import foundation-core.retracts-of-types public open import foundation-core.sections public open import foundation-core.sets public -open import foundation-core.small-types public -open import foundation-core.subtypes public +open import foundation-core.small-types funext public +open import foundation-core.subtypes funext public open import foundation-core.torsorial-type-families public open import foundation-core.transport-along-identifications public -open import foundation-core.truncated-maps public +open import foundation-core.truncated-maps funext public open import foundation-core.truncated-types public open import foundation-core.truncation-levels public open import foundation-core.type-theoretic-principle-of-choice public open import foundation-core.univalence public -open import foundation-core.universal-property-pullbacks public -open import foundation-core.universal-property-truncation public +open import foundation-core.universal-property-pullbacks funext public +open import foundation-core.universal-property-truncation funext public open import foundation-core.whiskering-homotopies-concatenation public open import foundation-core.whiskering-identifications-concatenation public ``` diff --git a/src/foundation-core/1-types.lagda.md b/src/foundation-core/1-types.lagda.md index 79ac7bd491..6f313c023b 100644 --- a/src/foundation-core/1-types.lagda.md +++ b/src/foundation-core/1-types.lagda.md @@ -1,15 +1,20 @@ # `1`-Types ```agda -module foundation-core.1-types where +open import foundation.function-extensionality-axiom + +module + foundation-core.1-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation-core/commuting-prisms-of-maps.lagda.md b/src/foundation-core/commuting-prisms-of-maps.lagda.md index 40f37dea92..811b534295 100644 --- a/src/foundation-core/commuting-prisms-of-maps.lagda.md +++ b/src/foundation-core/commuting-prisms-of-maps.lagda.md @@ -1,7 +1,12 @@ # Commuting prisms of maps ```agda -module foundation-core.commuting-prisms-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation-core.commuting-prisms-of-maps + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ open import foundation.commuting-pentagons-of-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation-core/commuting-squares-of-maps.lagda.md b/src/foundation-core/commuting-squares-of-maps.lagda.md index 6cce4fb386..5112dbca55 100644 --- a/src/foundation-core/commuting-squares-of-maps.lagda.md +++ b/src/foundation-core/commuting-squares-of-maps.lagda.md @@ -1,14 +1,19 @@ # Commuting squares of maps ```agda -module foundation-core.commuting-squares-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation-core.commuting-squares-of-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.transposition-identifications-along-equivalences +open import foundation.transposition-identifications-along-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation-core/decidable-propositions.lagda.md b/src/foundation-core/decidable-propositions.lagda.md index 8337ddd8fa..a50983318c 100644 --- a/src/foundation-core/decidable-propositions.lagda.md +++ b/src/foundation-core/decidable-propositions.lagda.md @@ -1,19 +1,24 @@ # Decidable propositions ```agda -module foundation-core.decidable-propositions where +open import foundation.function-extensionality-axiom + +module + foundation-core.decidable-propositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.double-negation -open import foundation.negation -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext +open import foundation.negation funext +open import foundation.propositional-truncations funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels @@ -24,7 +29,7 @@ open import foundation-core.empty-types open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation-core/discrete-types.lagda.md b/src/foundation-core/discrete-types.lagda.md index 6ace450fc3..26de275f2f 100644 --- a/src/foundation-core/discrete-types.lagda.md +++ b/src/foundation-core/discrete-types.lagda.md @@ -1,13 +1,18 @@ # Discrete types ```agda -module foundation-core.discrete-types where +open import foundation.function-extensionality-axiom + +module + foundation-core.discrete-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-equality +open import foundation.decidable-equality funext open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation-core/endomorphisms.lagda.md b/src/foundation-core/endomorphisms.lagda.md index b374c58abd..531b90c65a 100644 --- a/src/foundation-core/endomorphisms.lagda.md +++ b/src/foundation-core/endomorphisms.lagda.md @@ -1,15 +1,20 @@ # Endomorphisms ```agda -module foundation-core.endomorphisms where +open import foundation.function-extensionality-axiom + +module + foundation-core.endomorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.sets +open import foundation.dependent-products-truncated-types funext +open import foundation.sets funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation-core/equivalence-relations.lagda.md b/src/foundation-core/equivalence-relations.lagda.md index cf970f3056..09493249f2 100644 --- a/src/foundation-core/equivalence-relations.lagda.md +++ b/src/foundation-core/equivalence-relations.lagda.md @@ -1,19 +1,24 @@ # Equivalence relations ```agda -module foundation-core.equivalence-relations where +open import foundation.function-extensionality-axiom + +module + foundation-core.equivalence-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.raising-universe-levels-unit-type +open import foundation.inhabited-subtypes funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.subtype-identity-principle open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation-core/functoriality-dependent-function-types.lagda.md b/src/foundation-core/functoriality-dependent-function-types.lagda.md index 6c17228aec..181bd0643a 100644 --- a/src/foundation-core/functoriality-dependent-function-types.lagda.md +++ b/src/foundation-core/functoriality-dependent-function-types.lagda.md @@ -1,15 +1,21 @@ # Functoriality of dependent function types ```agda -module foundation-core.functoriality-dependent-function-types where +open import foundation.function-extensionality-axiom + +module + foundation-core.functoriality-dependent-function-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext +open import foundation.function-extensionality funext + open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation-core/operations-span-diagrams.lagda.md b/src/foundation-core/operations-span-diagrams.lagda.md index 78b68e8722..b6900df2c2 100644 --- a/src/foundation-core/operations-span-diagrams.lagda.md +++ b/src/foundation-core/operations-span-diagrams.lagda.md @@ -1,16 +1,21 @@ # Operations on span diagrams ```agda -module foundation-core.operations-span-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation-core.operations-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.operations-spans -open import foundation.span-diagrams +open import foundation.morphisms-arrows funext +open import foundation.operations-spans funext +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation-core/operations-spans.lagda.md b/src/foundation-core/operations-spans.lagda.md index 47e60de4d7..7b4b9095c7 100644 --- a/src/foundation-core/operations-spans.lagda.md +++ b/src/foundation-core/operations-spans.lagda.md @@ -1,14 +1,19 @@ # Operations on spans ```agda -module foundation-core.operations-spans where +open import foundation.function-extensionality-axiom + +module + foundation-core.operations-spans + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation-core/pullbacks.lagda.md b/src/foundation-core/pullbacks.lagda.md index 332e6e96e2..8d22d3eff4 100644 --- a/src/foundation-core/pullbacks.lagda.md +++ b/src/foundation-core/pullbacks.lagda.md @@ -1,21 +1,26 @@ # Pullbacks ```agda -module foundation-core.pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation-core.pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-fibers-of-maps -open import foundation.identity-types -open import foundation.morphisms-arrows -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-standard-pullbacks +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext +open import foundation.standard-pullbacks funext +open import foundation.type-arithmetic-standard-pullbacks funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -27,7 +32,7 @@ open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation-core/small-types.lagda.md b/src/foundation-core/small-types.lagda.md index adb78b9475..13e556ba81 100644 --- a/src/foundation-core/small-types.lagda.md +++ b/src/foundation-core/small-types.lagda.md @@ -1,25 +1,30 @@ # Small types ```agda -module foundation-core.small-types where +open import foundation.function-extensionality-axiom + +module + foundation-core.small-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-function-types -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation-core/subtypes.lagda.md b/src/foundation-core/subtypes.lagda.md index c6a4afc4c4..4926f69e19 100644 --- a/src/foundation-core/subtypes.lagda.md +++ b/src/foundation-core/subtypes.lagda.md @@ -1,7 +1,12 @@ # Subtypes ```agda -module foundation-core.subtypes where +open import foundation.function-extensionality-axiom + +module + foundation-core.subtypes + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module foundation-core.subtypes where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.logical-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext open import foundation.subtype-identity-principle open import foundation.universe-levels @@ -24,7 +29,7 @@ open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets open import foundation-core.transport-along-identifications -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation-core/truncated-maps.lagda.md b/src/foundation-core/truncated-maps.lagda.md index 6c68755acc..c5d3c59d6f 100644 --- a/src/foundation-core/truncated-maps.lagda.md +++ b/src/foundation-core/truncated-maps.lagda.md @@ -1,7 +1,12 @@ # Truncated maps ```agda -module foundation-core.truncated-maps where +open import foundation.function-extensionality-axiom + +module + foundation-core.truncated-maps + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module foundation-core.truncated-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-fibers-of-maps +open import foundation.equality-fibers-of-maps funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation-core/universal-property-pullbacks.lagda.md b/src/foundation-core/universal-property-pullbacks.lagda.md index 8ec97f1f27..83f6e54f11 100644 --- a/src/foundation-core/universal-property-pullbacks.lagda.md +++ b/src/foundation-core/universal-property-pullbacks.lagda.md @@ -1,16 +1,21 @@ # The universal property of pullbacks ```agda -module foundation-core.universal-property-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation-core.universal-property-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.postcomposition-functions +open import foundation.postcomposition-functions funext open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation-core/universal-property-truncation.lagda.md b/src/foundation-core/universal-property-truncation.lagda.md index 875fd1d2ba..fa87fddef3 100644 --- a/src/foundation-core/universal-property-truncation.lagda.md +++ b/src/foundation-core/universal-property-truncation.lagda.md @@ -1,16 +1,22 @@ # The universal property of truncations ```agda -module foundation-core.universal-property-truncation where +open import foundation.function-extensionality-axiom + +module + foundation-core.universal-property-truncation + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.function-extensionality -open import foundation.universal-property-equivalences +open import foundation.dependent-products-truncated-types funext +open import foundation.function-extensionality funext + +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index ebab239526..5a67c7c2ae 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -7,508 +7,514 @@ ## Modules in the foundation namespace ```agda -module foundation where +open import foundation.function-extensionality-axiom -open import foundation.0-connected-types public -open import foundation.0-images-of-maps public -open import foundation.0-maps public -open import foundation.1-types public +module + foundation + (funext : function-extensionality) + where + +open import foundation.0-connected-types funext public +open import foundation.0-images-of-maps funext public +open import foundation.0-maps funext public +open import foundation.1-types funext public open import foundation.2-types public -open import foundation.action-on-equivalences-functions public -open import foundation.action-on-equivalences-functions-out-of-subuniverses public -open import foundation.action-on-equivalences-type-families public -open import foundation.action-on-equivalences-type-families-over-subuniverses public -open import foundation.action-on-higher-identifications-functions public -open import foundation.action-on-homotopies-functions public +open import foundation.action-on-equivalences-functions funext public +open import foundation.action-on-equivalences-functions-out-of-subuniverses funext public +open import foundation.action-on-equivalences-type-families funext public +open import foundation.action-on-equivalences-type-families-over-subuniverses funext public +open import foundation.action-on-higher-identifications-functions funext public +open import foundation.action-on-homotopies-functions funext public open import foundation.action-on-identifications-binary-dependent-functions public open import foundation.action-on-identifications-binary-functions public open import foundation.action-on-identifications-dependent-functions public open import foundation.action-on-identifications-functions public -open import foundation.apartness-relations public -open import foundation.arithmetic-law-coproduct-and-sigma-decompositions public -open import foundation.arithmetic-law-product-and-pi-decompositions public -open import foundation.automorphisms public -open import foundation.axiom-of-choice public -open import foundation.bands public -open import foundation.base-changes-span-diagrams public -open import foundation.bicomposition-functions public +open import foundation.apartness-relations funext public +open import foundation.arithmetic-law-coproduct-and-sigma-decompositions funext public +open import foundation.arithmetic-law-product-and-pi-decompositions funext public +open import foundation.automorphisms funext public +open import foundation.axiom-of-choice funext public +open import foundation.bands funext public +open import foundation.base-changes-span-diagrams funext public +open import foundation.bicomposition-functions funext public open import foundation.binary-dependent-identifications public -open import foundation.binary-embeddings public +open import foundation.binary-embeddings funext public open import foundation.binary-equivalences public -open import foundation.binary-equivalences-unordered-pairs-of-types public -open import foundation.binary-functoriality-set-quotients public -open import foundation.binary-homotopies public -open import foundation.binary-operations-unordered-pairs-of-types public -open import foundation.binary-reflecting-maps-equivalence-relations public -open import foundation.binary-relations public -open import foundation.binary-relations-with-extensions public -open import foundation.binary-relations-with-lifts public +open import foundation.binary-equivalences-unordered-pairs-of-types funext public +open import foundation.binary-functoriality-set-quotients funext public +open import foundation.binary-homotopies funext public +open import foundation.binary-operations-unordered-pairs-of-types funext public +open import foundation.binary-reflecting-maps-equivalence-relations funext public +open import foundation.binary-relations funext public +open import foundation.binary-relations-with-extensions funext public +open import foundation.binary-relations-with-lifts funext public open import foundation.binary-transport public -open import foundation.binary-type-duality public -open import foundation.booleans public -open import foundation.cantor-schroder-bernstein-escardo public -open import foundation.cantors-theorem public -open import foundation.cartesian-morphisms-arrows public -open import foundation.cartesian-morphisms-span-diagrams public -open import foundation.cartesian-product-types public -open import foundation.cartesian-products-set-quotients public -open import foundation.category-of-families-of-sets public -open import foundation.category-of-sets public -open import foundation.choice-of-representatives-equivalence-relation public -open import foundation.coalgebras-maybe public +open import foundation.binary-type-duality funext public +open import foundation.booleans funext public +open import foundation.cantor-schroder-bernstein-escardo funext public +open import foundation.cantors-theorem funext public +open import foundation.cartesian-morphisms-arrows funext public +open import foundation.cartesian-morphisms-span-diagrams funext public +open import foundation.cartesian-product-types funext public +open import foundation.cartesian-products-set-quotients funext public +open import foundation.category-of-families-of-sets funext public +open import foundation.category-of-sets funext public +open import foundation.choice-of-representatives-equivalence-relation funext public +open import foundation.coalgebras-maybe funext public open import foundation.codiagonal-maps-of-types public -open import foundation.coherently-idempotent-maps public -open import foundation.coherently-invertible-maps public -open import foundation.coinhabited-pairs-of-types public -open import foundation.commuting-cubes-of-maps public +open import foundation.coherently-idempotent-maps funext public +open import foundation.coherently-invertible-maps funext public +open import foundation.coinhabited-pairs-of-types funext public +open import foundation.commuting-cubes-of-maps funext public open import foundation.commuting-hexagons-of-identifications public open import foundation.commuting-pentagons-of-identifications public -open import foundation.commuting-prisms-of-maps public -open import foundation.commuting-squares-of-homotopies public -open import foundation.commuting-squares-of-identifications public -open import foundation.commuting-squares-of-maps public -open import foundation.commuting-tetrahedra-of-homotopies public +open import foundation.commuting-prisms-of-maps funext public +open import foundation.commuting-squares-of-homotopies funext public +open import foundation.commuting-squares-of-identifications funext public +open import foundation.commuting-squares-of-maps funext public +open import foundation.commuting-tetrahedra-of-homotopies funext public open import foundation.commuting-tetrahedra-of-maps public -open import foundation.commuting-triangles-of-homotopies public -open import foundation.commuting-triangles-of-identifications public -open import foundation.commuting-triangles-of-maps public -open import foundation.commuting-triangles-of-morphisms-arrows public +open import foundation.commuting-triangles-of-homotopies funext public +open import foundation.commuting-triangles-of-identifications funext public +open import foundation.commuting-triangles-of-maps funext public +open import foundation.commuting-triangles-of-morphisms-arrows funext public open import foundation.complements public -open import foundation.complements-subtypes public -open import foundation.composite-maps-in-inverse-sequential-diagrams public -open import foundation.composition-algebra public -open import foundation.composition-spans public -open import foundation.computational-identity-types public -open import foundation.cones-over-cospan-diagrams public -open import foundation.cones-over-inverse-sequential-diagrams public -open import foundation.conjunction public -open import foundation.connected-components public -open import foundation.connected-components-universes public -open import foundation.connected-maps public -open import foundation.connected-types public -open import foundation.constant-maps public -open import foundation.constant-span-diagrams public -open import foundation.constant-type-families public -open import foundation.continuations public -open import foundation.contractible-maps public -open import foundation.contractible-types public -open import foundation.copartial-elements public -open import foundation.copartial-functions public -open import foundation.coproduct-decompositions public -open import foundation.coproduct-decompositions-subuniverse public -open import foundation.coproduct-types public -open import foundation.coproducts-pullbacks public -open import foundation.coslice public +open import foundation.complements-subtypes funext public +open import foundation.composite-maps-in-inverse-sequential-diagrams funext public +open import foundation.composition-algebra funext public +open import foundation.composition-spans funext public +open import foundation.computational-identity-types funext public +open import foundation.cones-over-cospan-diagrams funext public +open import foundation.cones-over-inverse-sequential-diagrams funext public +open import foundation.conjunction funext public +open import foundation.connected-components funext public +open import foundation.connected-components-universes funext public +open import foundation.connected-maps funext public +open import foundation.connected-types funext public +open import foundation.constant-maps funext public +open import foundation.constant-span-diagrams funext public +open import foundation.constant-type-families funext public +open import foundation.continuations funext public +open import foundation.contractible-maps funext public +open import foundation.contractible-types funext public +open import foundation.copartial-elements funext public +open import foundation.copartial-functions funext public +open import foundation.coproduct-decompositions funext public +open import foundation.coproduct-decompositions-subuniverse funext public +open import foundation.coproduct-types funext public +open import foundation.coproducts-pullbacks funext public +open import foundation.coslice funext public open import foundation.cospan-diagrams public open import foundation.cospans public -open import foundation.decidable-dependent-function-types public -open import foundation.decidable-dependent-pair-types public -open import foundation.decidable-embeddings public -open import foundation.decidable-equality public -open import foundation.decidable-equivalence-relations public -open import foundation.decidable-maps public -open import foundation.decidable-propositions public -open import foundation.decidable-relations public -open import foundation.decidable-subtypes public -open import foundation.decidable-types public -open import foundation.dependent-binary-homotopies public -open import foundation.dependent-binomial-theorem public -open import foundation.dependent-epimorphisms public -open import foundation.dependent-epimorphisms-with-respect-to-truncated-types public -open import foundation.dependent-function-types public +open import foundation.decidable-dependent-function-types funext public +open import foundation.decidable-dependent-pair-types funext public +open import foundation.decidable-embeddings funext public +open import foundation.decidable-equality funext public +open import foundation.decidable-equivalence-relations funext public +open import foundation.decidable-maps funext public +open import foundation.decidable-propositions funext public +open import foundation.decidable-relations funext public +open import foundation.decidable-subtypes funext public +open import foundation.decidable-types funext public +open import foundation.dependent-binary-homotopies funext public +open import foundation.dependent-binomial-theorem funext public +open import foundation.dependent-epimorphisms funext public +open import foundation.dependent-epimorphisms-with-respect-to-truncated-types funext public +open import foundation.dependent-function-types funext public open import foundation.dependent-homotopies public -open import foundation.dependent-identifications public -open import foundation.dependent-inverse-sequential-diagrams public +open import foundation.dependent-identifications funext public +open import foundation.dependent-inverse-sequential-diagrams funext public open import foundation.dependent-pair-types public -open import foundation.dependent-products-contractible-types public -open import foundation.dependent-products-propositions public -open import foundation.dependent-products-pullbacks public -open import foundation.dependent-products-truncated-types public +open import foundation.dependent-products-contractible-types funext public +open import foundation.dependent-products-propositions funext public +open import foundation.dependent-products-pullbacks funext public +open import foundation.dependent-products-truncated-types funext public open import foundation.dependent-sequences public -open import foundation.dependent-sums-pullbacks public +open import foundation.dependent-sums-pullbacks funext public open import foundation.dependent-telescopes public -open import foundation.dependent-universal-property-equivalences public -open import foundation.descent-coproduct-types public -open import foundation.descent-dependent-pair-types public -open import foundation.descent-empty-types public -open import foundation.descent-equivalences public -open import foundation.diaconescus-theorem public -open import foundation.diagonal-maps-cartesian-products-of-types public -open import foundation.diagonal-maps-of-types public -open import foundation.diagonal-span-diagrams public -open import foundation.diagonals-of-maps public +open import foundation.dependent-universal-property-equivalences funext public +open import foundation.descent-coproduct-types funext public +open import foundation.descent-dependent-pair-types funext public +open import foundation.descent-empty-types funext public +open import foundation.descent-equivalences funext public +open import foundation.diaconescus-theorem funext public +open import foundation.diagonal-maps-cartesian-products-of-types funext public +open import foundation.diagonal-maps-of-types funext public +open import foundation.diagonal-span-diagrams funext public +open import foundation.diagonals-of-maps funext public open import foundation.diagonals-of-morphisms-arrows public -open import foundation.discrete-binary-relations public -open import foundation.discrete-reflexive-relations public -open import foundation.discrete-relaxed-sigma-decompositions public -open import foundation.discrete-sigma-decompositions public -open import foundation.discrete-types public -open import foundation.disjoint-subtypes public -open import foundation.disjunction public +open import foundation.discrete-binary-relations funext public +open import foundation.discrete-reflexive-relations funext public +open import foundation.discrete-relaxed-sigma-decompositions funext public +open import foundation.discrete-sigma-decompositions funext public +open import foundation.discrete-types funext public +open import foundation.disjoint-subtypes funext public +open import foundation.disjunction funext public open import foundation.double-arrows public -open import foundation.double-negation public -open import foundation.double-negation-modality public -open import foundation.double-negation-stable-equality public -open import foundation.double-negation-stable-propositions public -open import foundation.double-powersets public -open import foundation.dubuc-penon-compact-types public -open import foundation.effective-maps-equivalence-relations public -open import foundation.embeddings public -open import foundation.empty-types public -open import foundation.endomorphisms public -open import foundation.epimorphisms public -open import foundation.epimorphisms-with-respect-to-sets public -open import foundation.epimorphisms-with-respect-to-truncated-types public +open import foundation.double-negation funext public +open import foundation.double-negation-modality funext public +open import foundation.double-negation-stable-equality funext public +open import foundation.double-negation-stable-propositions funext public +open import foundation.double-powersets funext public +open import foundation.dubuc-penon-compact-types funext public +open import foundation.effective-maps-equivalence-relations funext public +open import foundation.embeddings funext public +open import foundation.empty-types funext public +open import foundation.endomorphisms funext public +open import foundation.epimorphisms funext public +open import foundation.epimorphisms-with-respect-to-sets funext public +open import foundation.epimorphisms-with-respect-to-truncated-types funext public open import foundation.equality-cartesian-product-types public -open import foundation.equality-coproduct-types public -open import foundation.equality-dependent-function-types public -open import foundation.equality-dependent-pair-types public -open import foundation.equality-fibers-of-maps public -open import foundation.equivalence-classes public -open import foundation.equivalence-extensionality public -open import foundation.equivalence-induction public -open import foundation.equivalence-injective-type-families public -open import foundation.equivalence-relations public -open import foundation.equivalences public -open import foundation.equivalences-arrows public -open import foundation.equivalences-cospans public -open import foundation.equivalences-double-arrows public -open import foundation.equivalences-inverse-sequential-diagrams public -open import foundation.equivalences-maybe public -open import foundation.equivalences-span-diagrams public -open import foundation.equivalences-span-diagrams-families-of-types public -open import foundation.equivalences-spans public -open import foundation.equivalences-spans-families-of-types public +open import foundation.equality-coproduct-types funext public +open import foundation.equality-dependent-function-types funext public +open import foundation.equality-dependent-pair-types funext public +open import foundation.equality-fibers-of-maps funext public +open import foundation.equivalence-classes funext public +open import foundation.equivalence-extensionality funext public +open import foundation.equivalence-induction funext public +open import foundation.equivalence-injective-type-families funext public +open import foundation.equivalence-relations funext public +open import foundation.equivalences funext public +open import foundation.equivalences-arrows funext public +open import foundation.equivalences-cospans funext public +open import foundation.equivalences-double-arrows funext public +open import foundation.equivalences-inverse-sequential-diagrams funext public +open import foundation.equivalences-maybe funext public +open import foundation.equivalences-span-diagrams funext public +open import foundation.equivalences-span-diagrams-families-of-types funext public +open import foundation.equivalences-spans funext public +open import foundation.equivalences-spans-families-of-types funext public open import foundation.evaluation-functions public -open import foundation.exclusive-disjunction public -open import foundation.exclusive-sum public -open import foundation.existential-quantification public -open import foundation.exponents-set-quotients public -open import foundation.extensions-types public -open import foundation.extensions-types-global-subuniverses public -open import foundation.extensions-types-subuniverses public -open import foundation.faithful-maps public -open import foundation.families-of-equivalences public -open import foundation.families-of-maps public -open import foundation.families-over-telescopes public -open import foundation.fiber-inclusions public -open import foundation.fibered-equivalences public -open import foundation.fibered-involutions public -open import foundation.fibered-maps public -open import foundation.fibers-of-maps public -open import foundation.finitely-coherent-equivalences public -open import foundation.finitely-coherently-invertible-maps public +open import foundation.exclusive-disjunction funext public +open import foundation.exclusive-sum funext public +open import foundation.existential-quantification funext public +open import foundation.exponents-set-quotients funext public +open import foundation.extensions-types funext public +open import foundation.extensions-types-global-subuniverses funext public +open import foundation.extensions-types-subuniverses funext public +open import foundation.faithful-maps funext public +open import foundation.families-of-equivalences funext public +open import foundation.families-of-maps funext public +open import foundation.families-over-telescopes funext public +open import foundation.fiber-inclusions funext public +open import foundation.fibered-equivalences funext public +open import foundation.fibered-involutions funext public +open import foundation.fibered-maps funext public +open import foundation.fibers-of-maps funext public +open import foundation.finitely-coherent-equivalences funext public +open import foundation.finitely-coherently-invertible-maps funext public open import foundation.fixed-points-endofunctions public -open import foundation.full-subtypes public -open import foundation.function-extensionality public +open import foundation.full-subtypes funext public +open import foundation.function-extensionality funext + public open import foundation.function-extensionality-axiom public -open import foundation.function-types public -open import foundation.functional-correspondences public -open import foundation.functoriality-action-on-identifications-functions public -open import foundation.functoriality-cartesian-product-types public -open import foundation.functoriality-coproduct-types public -open import foundation.functoriality-dependent-function-types public -open import foundation.functoriality-dependent-pair-types public -open import foundation.functoriality-fibers-of-maps public -open import foundation.functoriality-function-types public -open import foundation.functoriality-morphisms-arrows public -open import foundation.functoriality-propositional-truncation public -open import foundation.functoriality-pullbacks public -open import foundation.functoriality-sequential-limits public -open import foundation.functoriality-set-quotients public -open import foundation.functoriality-set-truncation public -open import foundation.functoriality-truncation public -open import foundation.fundamental-theorem-of-equivalence-relations public +open import foundation.function-types funext public +open import foundation.functional-correspondences funext public +open import foundation.functoriality-action-on-identifications-functions funext public +open import foundation.functoriality-cartesian-product-types funext public +open import foundation.functoriality-coproduct-types funext public +open import foundation.functoriality-dependent-function-types funext public +open import foundation.functoriality-dependent-pair-types funext public +open import foundation.functoriality-fibers-of-maps funext public +open import foundation.functoriality-function-types funext public +open import foundation.functoriality-morphisms-arrows funext public +open import foundation.functoriality-propositional-truncation funext public +open import foundation.functoriality-pullbacks funext public +open import foundation.functoriality-sequential-limits funext public +open import foundation.functoriality-set-quotients funext public +open import foundation.functoriality-set-truncation funext public +open import foundation.functoriality-truncation funext public +open import foundation.fundamental-theorem-of-equivalence-relations funext public open import foundation.fundamental-theorem-of-identity-types public -open import foundation.global-choice public -open import foundation.global-subuniverses public -open import foundation.globular-type-of-dependent-functions public -open import foundation.globular-type-of-functions public -open import foundation.higher-homotopies-morphisms-arrows public -open import foundation.hilberts-epsilon-operators public -open import foundation.homotopies public -open import foundation.homotopies-morphisms-arrows public -open import foundation.homotopies-morphisms-cospan-diagrams public +open import foundation.global-choice funext public +open import foundation.global-subuniverses funext public +open import foundation.globular-type-of-dependent-functions funext public +open import foundation.globular-type-of-functions funext public +open import foundation.higher-homotopies-morphisms-arrows funext public +open import foundation.hilberts-epsilon-operators funext public +open import foundation.homotopies funext public +open import foundation.homotopies-morphisms-arrows funext public +open import foundation.homotopies-morphisms-cospan-diagrams funext public open import foundation.homotopy-algebra public -open import foundation.homotopy-induction public -open import foundation.homotopy-preorder-of-types public -open import foundation.horizontal-composition-spans-of-spans public -open import foundation.idempotent-maps public +open import foundation.homotopy-induction funext public +open import foundation.homotopy-preorder-of-types funext public +open import foundation.horizontal-composition-spans-of-spans funext public +open import foundation.idempotent-maps funext public open import foundation.identity-systems public -open import foundation.identity-truncated-types public -open import foundation.identity-types public -open import foundation.images public -open import foundation.images-subtypes public +open import foundation.identity-truncated-types funext public +open import foundation.identity-types funext public +open import foundation.images funext public +open import foundation.images-subtypes funext public open import foundation.implicit-function-types public -open import foundation.impredicative-encodings public -open import foundation.impredicative-universes public +open import foundation.impredicative-encodings funext public +open import foundation.impredicative-universes funext public open import foundation.induction-principle-propositional-truncation public -open import foundation.infinitely-coherent-equivalences public -open import foundation.inhabited-subtypes public -open import foundation.inhabited-types public -open import foundation.injective-maps public +open import foundation.infinitely-coherent-equivalences funext public +open import foundation.inhabited-subtypes funext public +open import foundation.inhabited-types funext public +open import foundation.injective-maps funext public open import foundation.interchange-law public -open import foundation.intersections-subtypes public -open import foundation.inverse-sequential-diagrams public -open import foundation.invertible-maps public -open import foundation.involutions public -open import foundation.irrefutable-propositions public -open import foundation.isolated-elements public -open import foundation.isomorphisms-of-sets public -open import foundation.iterated-cartesian-product-types public +open import foundation.intersections-subtypes funext public +open import foundation.inverse-sequential-diagrams funext public +open import foundation.invertible-maps funext public +open import foundation.involutions funext public +open import foundation.irrefutable-propositions funext public +open import foundation.isolated-elements funext public +open import foundation.isomorphisms-of-sets funext public +open import foundation.iterated-cartesian-product-types funext public open import foundation.iterated-dependent-pair-types public -open import foundation.iterated-dependent-product-types public -open import foundation.iterating-automorphisms public -open import foundation.iterating-families-of-maps public -open import foundation.iterating-functions public -open import foundation.iterating-involutions public -open import foundation.kernel-span-diagrams-of-maps public -open import foundation.large-apartness-relations public -open import foundation.large-binary-relations public +open import foundation.iterated-dependent-product-types funext public +open import foundation.iterating-automorphisms funext public +open import foundation.iterating-families-of-maps funext public +open import foundation.iterating-functions funext public +open import foundation.iterating-involutions funext public +open import foundation.kernel-span-diagrams-of-maps funext public +open import foundation.large-apartness-relations funext public +open import foundation.large-binary-relations funext public open import foundation.large-dependent-pair-types public open import foundation.large-homotopies public open import foundation.large-identity-types public -open import foundation.large-locale-of-propositions public -open import foundation.large-locale-of-subtypes public -open import foundation.law-of-excluded-middle public -open import foundation.lawveres-fixed-point-theorem public -open import foundation.lesser-limited-principle-of-omniscience public +open import foundation.large-locale-of-propositions funext public +open import foundation.large-locale-of-subtypes funext public +open import foundation.law-of-excluded-middle funext public +open import foundation.lawveres-fixed-point-theorem funext public +open import foundation.lesser-limited-principle-of-omniscience funext public open import foundation.lifts-types public -open import foundation.limited-principle-of-omniscience public -open import foundation.locale-of-propositions public -open import foundation.locally-small-types public -open import foundation.logical-equivalences public -open import foundation.maps-in-global-subuniverses public -open import foundation.maps-in-subuniverses public -open import foundation.maybe public -open import foundation.mere-embeddings public -open import foundation.mere-equality public -open import foundation.mere-equivalences public -open import foundation.mere-functions public -open import foundation.mere-logical-equivalences public -open import foundation.mere-path-cosplit-maps public -open import foundation.monomorphisms public -open import foundation.morphisms-arrows public -open import foundation.morphisms-binary-relations public -open import foundation.morphisms-coalgebras-maybe public +open import foundation.limited-principle-of-omniscience funext public +open import foundation.locale-of-propositions funext public +open import foundation.locally-small-types funext public +open import foundation.logical-equivalences funext public +open import foundation.maps-in-global-subuniverses funext public +open import foundation.maps-in-subuniverses funext public +open import foundation.maybe funext public +open import foundation.mere-embeddings funext public +open import foundation.mere-equality funext public +open import foundation.mere-equivalences funext public +open import foundation.mere-functions funext public +open import foundation.mere-logical-equivalences funext public +open import foundation.mere-path-cosplit-maps funext public +open import foundation.monomorphisms funext public +open import foundation.morphisms-arrows funext public +open import foundation.morphisms-binary-relations funext public +open import foundation.morphisms-coalgebras-maybe funext public open import foundation.morphisms-cospan-diagrams public open import foundation.morphisms-cospans public -open import foundation.morphisms-double-arrows public -open import foundation.morphisms-inverse-sequential-diagrams public -open import foundation.morphisms-span-diagrams public +open import foundation.morphisms-double-arrows funext public +open import foundation.morphisms-inverse-sequential-diagrams funext public +open import foundation.morphisms-span-diagrams funext public open import foundation.morphisms-spans public -open import foundation.morphisms-spans-families-of-types public +open import foundation.morphisms-spans-families-of-types funext public open import foundation.morphisms-twisted-arrows public -open import foundation.multisubsets public -open import foundation.multivariable-correspondences public -open import foundation.multivariable-decidable-relations public -open import foundation.multivariable-functoriality-set-quotients public -open import foundation.multivariable-homotopies public -open import foundation.multivariable-operations public -open import foundation.multivariable-relations public -open import foundation.multivariable-sections public -open import foundation.negated-equality public -open import foundation.negation public -open import foundation.noncontractible-types public -open import foundation.null-homotopic-maps public -open import foundation.operations-span-diagrams public -open import foundation.operations-spans public +open import foundation.multisubsets funext public +open import foundation.multivariable-correspondences funext public +open import foundation.multivariable-decidable-relations funext public +open import foundation.multivariable-functoriality-set-quotients funext public +open import foundation.multivariable-homotopies funext public +open import foundation.multivariable-operations funext public +open import foundation.multivariable-relations funext public +open import foundation.multivariable-sections funext public +open import foundation.negated-equality funext public +open import foundation.negation funext public +open import foundation.noncontractible-types funext public +open import foundation.null-homotopic-maps funext public +open import foundation.operations-span-diagrams funext public +open import foundation.operations-spans funext public open import foundation.operations-spans-families-of-types public open import foundation.opposite-spans public -open import foundation.pairs-of-distinct-elements public +open import foundation.pairs-of-distinct-elements funext public open import foundation.partial-elements public open import foundation.partial-functions public open import foundation.partial-sequences public -open import foundation.partitions public -open import foundation.path-algebra public -open import foundation.path-cosplit-maps public -open import foundation.path-split-maps public -open import foundation.path-split-type-families public -open import foundation.perfect-images public +open import foundation.partitions funext public +open import foundation.path-algebra funext public +open import foundation.path-cosplit-maps funext public +open import foundation.path-split-maps funext public +open import foundation.path-split-type-families funext public +open import foundation.perfect-images funext public open import foundation.permutations-spans-families-of-types public -open import foundation.pi-decompositions public -open import foundation.pi-decompositions-subuniverse public -open import foundation.pointed-torsorial-type-families public -open import foundation.postcomposition-dependent-functions public -open import foundation.postcomposition-functions public -open import foundation.postcomposition-pullbacks public -open import foundation.powersets public -open import foundation.precomposition-dependent-functions public -open import foundation.precomposition-functions public -open import foundation.precomposition-functions-into-subuniverses public -open import foundation.precomposition-type-families public -open import foundation.preunivalence public -open import foundation.preunivalent-type-families public -open import foundation.principle-of-omniscience public +open import foundation.pi-decompositions funext public +open import foundation.pi-decompositions-subuniverse funext public +open import foundation.pointed-torsorial-type-families funext public +open import foundation.postcomposition-dependent-functions funext public +open import foundation.postcomposition-functions funext public +open import foundation.postcomposition-pullbacks funext public +open import foundation.powersets funext public +open import foundation.precomposition-dependent-functions funext public +open import foundation.precomposition-functions funext public +open import foundation.precomposition-functions-into-subuniverses funext public +open import foundation.precomposition-type-families funext public +open import foundation.preunivalence funext public +open import foundation.preunivalent-type-families funext public +open import foundation.principle-of-omniscience funext public open import foundation.product-decompositions public -open import foundation.product-decompositions-subuniverse public -open import foundation.products-binary-relations public -open import foundation.products-equivalence-relations public -open import foundation.products-of-tuples-of-types public -open import foundation.products-pullbacks public -open import foundation.products-unordered-pairs-of-types public -open import foundation.products-unordered-tuples-of-types public -open import foundation.projective-types public -open import foundation.proper-subtypes public -open import foundation.propositional-extensionality public -open import foundation.propositional-maps public -open import foundation.propositional-resizing public -open import foundation.propositional-truncations public -open import foundation.propositions public -open import foundation.pullback-cones public -open import foundation.pullbacks public -open import foundation.pullbacks-subtypes public -open import foundation.quasicoherently-idempotent-maps public -open import foundation.raising-universe-levels public -open import foundation.raising-universe-levels-booleans public -open import foundation.raising-universe-levels-unit-type public -open import foundation.reflecting-maps-equivalence-relations public -open import foundation.reflexive-relations public -open import foundation.regensburg-extension-fundamental-theorem-of-identity-types public -open import foundation.relaxed-sigma-decompositions public -open import foundation.repetitions-of-values public -open import foundation.repetitions-sequences public -open import foundation.replacement public -open import foundation.retractions public -open import foundation.retracts-of-maps public -open import foundation.retracts-of-types public -open import foundation.sections public -open import foundation.separated-types-subuniverses public +open import foundation.product-decompositions-subuniverse funext public +open import foundation.products-binary-relations funext public +open import foundation.products-equivalence-relations funext public +open import foundation.products-of-tuples-of-types funext public +open import foundation.products-pullbacks funext public +open import foundation.products-unordered-pairs-of-types funext public +open import foundation.products-unordered-tuples-of-types funext public +open import foundation.projective-types funext public +open import foundation.proper-subtypes funext public +open import foundation.propositional-extensionality funext public +open import foundation.propositional-maps funext public +open import foundation.propositional-resizing funext public +open import foundation.propositional-truncations funext public +open import foundation.propositions funext public +open import foundation.pullback-cones funext public +open import foundation.pullbacks funext public +open import foundation.pullbacks-subtypes funext public +open import foundation.quasicoherently-idempotent-maps funext public +open import foundation.raising-universe-levels funext public +open import foundation.raising-universe-levels-booleans funext public +open import foundation.raising-universe-levels-unit-type funext public +open import foundation.reflecting-maps-equivalence-relations funext public +open import foundation.reflexive-relations funext public +open import foundation.regensburg-extension-fundamental-theorem-of-identity-types funext public +open import foundation.relaxed-sigma-decompositions funext public +open import foundation.repetitions-of-values funext public +open import foundation.repetitions-sequences funext public +open import foundation.replacement funext public +open import foundation.retractions funext public +open import foundation.retracts-of-maps funext public +open import foundation.retracts-of-types funext public +open import foundation.sections funext public +open import foundation.separated-types-subuniverses funext public open import foundation.sequences public -open import foundation.sequential-limits public -open import foundation.set-presented-types public -open import foundation.set-quotients public -open import foundation.set-truncations public -open import foundation.sets public +open import foundation.sequential-limits funext public +open import foundation.set-presented-types funext public +open import foundation.set-quotients funext public +open import foundation.set-truncations funext public +open import foundation.sets funext public open import foundation.shifting-sequences public -open import foundation.sigma-closed-subuniverses public -open import foundation.sigma-decomposition-subuniverse public -open import foundation.sigma-decompositions public +open import foundation.sigma-closed-subuniverses funext public +open import foundation.sigma-decomposition-subuniverse funext public +open import foundation.sigma-decompositions funext public open import foundation.singleton-induction public -open import foundation.singleton-subtypes public -open import foundation.slice public -open import foundation.small-maps public -open import foundation.small-types public -open import foundation.small-universes public +open import foundation.singleton-subtypes funext public +open import foundation.slice funext public +open import foundation.small-maps funext public +open import foundation.small-types funext public +open import foundation.small-universes funext public open import foundation.sorial-type-families public -open import foundation.span-diagrams public +open import foundation.span-diagrams funext public open import foundation.span-diagrams-families-of-types public open import foundation.spans public open import foundation.spans-families-of-types public -open import foundation.spans-of-spans public -open import foundation.split-idempotent-maps public +open import foundation.spans-of-spans funext public +open import foundation.split-idempotent-maps funext public open import foundation.split-surjective-maps public -open import foundation.standard-apartness-relations public -open import foundation.standard-pullbacks public -open import foundation.standard-ternary-pullbacks public -open import foundation.strict-symmetrization-binary-relations public -open import foundation.strictly-involutive-identity-types public +open import foundation.standard-apartness-relations funext public +open import foundation.standard-pullbacks funext public +open import foundation.standard-ternary-pullbacks funext public +open import foundation.strict-symmetrization-binary-relations funext public +open import foundation.strictly-involutive-identity-types funext public open import foundation.strictly-right-unital-concatenation-identifications public -open import foundation.strong-preunivalence public -open import foundation.strongly-extensional-maps public -open import foundation.structure public +open import foundation.strong-preunivalence funext public +open import foundation.strongly-extensional-maps funext public +open import foundation.structure funext public open import foundation.structure-identity-principle public -open import foundation.structured-equality-duality public -open import foundation.structured-type-duality public +open import foundation.structured-equality-duality funext public +open import foundation.structured-type-duality funext public open import foundation.subsingleton-induction public open import foundation.subterminal-types public -open import foundation.subtype-duality public +open import foundation.subtype-duality funext public open import foundation.subtype-identity-principle public -open import foundation.subtypes public -open import foundation.subuniverses public -open import foundation.surjective-maps public -open import foundation.symmetric-binary-relations public -open import foundation.symmetric-cores-binary-relations public -open import foundation.symmetric-difference public -open import foundation.symmetric-identity-types public -open import foundation.symmetric-operations public +open import foundation.subtypes funext public +open import foundation.subuniverses funext public +open import foundation.surjective-maps funext public +open import foundation.symmetric-binary-relations funext public +open import foundation.symmetric-cores-binary-relations funext public +open import foundation.symmetric-difference funext public +open import foundation.symmetric-identity-types funext public +open import foundation.symmetric-operations funext public open import foundation.telescopes public -open import foundation.terminal-spans-families-of-types public -open import foundation.tight-apartness-relations public -open import foundation.torsorial-type-families public +open import foundation.terminal-spans-families-of-types funext public +open import foundation.tight-apartness-relations funext public +open import foundation.torsorial-type-families funext public open import foundation.total-partial-elements public -open import foundation.total-partial-functions public -open import foundation.transfinite-cocomposition-of-maps public -open import foundation.transport-along-equivalences public -open import foundation.transport-along-higher-identifications public -open import foundation.transport-along-homotopies public +open import foundation.total-partial-functions funext public +open import foundation.transfinite-cocomposition-of-maps funext public +open import foundation.transport-along-equivalences funext public +open import foundation.transport-along-higher-identifications funext public +open import foundation.transport-along-homotopies funext public open import foundation.transport-along-identifications public -open import foundation.transport-split-type-families public -open import foundation.transposition-identifications-along-equivalences public -open import foundation.transposition-identifications-along-retractions public -open import foundation.transposition-identifications-along-sections public -open import foundation.transposition-span-diagrams public -open import foundation.trivial-relaxed-sigma-decompositions public -open import foundation.trivial-sigma-decompositions public -open import foundation.truncated-equality public -open import foundation.truncated-maps public -open import foundation.truncated-types public -open import foundation.truncation-equivalences public -open import foundation.truncation-images-of-maps public +open import foundation.transport-split-type-families funext public +open import foundation.transposition-identifications-along-equivalences funext public +open import foundation.transposition-identifications-along-retractions funext public +open import foundation.transposition-identifications-along-sections funext public +open import foundation.transposition-span-diagrams funext public +open import foundation.trivial-relaxed-sigma-decompositions funext public +open import foundation.trivial-sigma-decompositions funext public +open import foundation.truncated-equality funext public +open import foundation.truncated-maps funext public +open import foundation.truncated-types funext public +open import foundation.truncation-equivalences funext public +open import foundation.truncation-images-of-maps funext public open import foundation.truncation-levels public -open import foundation.truncation-modalities public -open import foundation.truncations public -open import foundation.tuples-of-types public +open import foundation.truncation-modalities funext public +open import foundation.truncations funext public +open import foundation.tuples-of-types funext public open import foundation.type-arithmetic-booleans public open import foundation.type-arithmetic-cartesian-product-types public -open import foundation.type-arithmetic-coproduct-types public -open import foundation.type-arithmetic-dependent-function-types public +open import foundation.type-arithmetic-coproduct-types funext public +open import foundation.type-arithmetic-dependent-function-types funext public open import foundation.type-arithmetic-dependent-pair-types public -open import foundation.type-arithmetic-empty-type public -open import foundation.type-arithmetic-standard-pullbacks public +open import foundation.type-arithmetic-empty-type funext public +open import foundation.type-arithmetic-standard-pullbacks funext public open import foundation.type-arithmetic-unit-type public -open import foundation.type-duality public -open import foundation.type-theoretic-principle-of-choice public -open import foundation.uniformly-decidable-type-families public -open import foundation.unions-subtypes public -open import foundation.uniqueness-image public -open import foundation.uniqueness-quantification public -open import foundation.uniqueness-set-quotients public -open import foundation.uniqueness-set-truncations public -open import foundation.uniqueness-truncation public +open import foundation.type-duality funext public +open import foundation.type-theoretic-principle-of-choice funext public +open import foundation.uniformly-decidable-type-families funext public +open import foundation.unions-subtypes funext public +open import foundation.uniqueness-image funext public +open import foundation.uniqueness-quantification funext public +open import foundation.uniqueness-set-quotients funext public +open import foundation.uniqueness-set-truncations funext public +open import foundation.uniqueness-truncation funext public open import foundation.unit-type public open import foundation.unital-binary-operations public -open import foundation.univalence public -open import foundation.univalence-implies-function-extensionality public -open import foundation.univalent-type-families public -open import foundation.universal-property-booleans public -open import foundation.universal-property-cartesian-product-types public -open import foundation.universal-property-contractible-types public -open import foundation.universal-property-coproduct-types public -open import foundation.universal-property-dependent-function-types public -open import foundation.universal-property-dependent-pair-types public -open import foundation.universal-property-empty-type public -open import foundation.universal-property-equivalences public -open import foundation.universal-property-family-of-fibers-of-maps public -open import foundation.universal-property-fiber-products public -open import foundation.universal-property-identity-systems public -open import foundation.universal-property-identity-types public -open import foundation.universal-property-image public -open import foundation.universal-property-maybe public -open import foundation.universal-property-propositional-truncation public -open import foundation.universal-property-propositional-truncation-into-sets public -open import foundation.universal-property-pullbacks public -open import foundation.universal-property-sequential-limits public -open import foundation.universal-property-set-quotients public -open import foundation.universal-property-set-truncation public -open import foundation.universal-property-truncation public -open import foundation.universal-property-unit-type public -open import foundation.universal-quantification public +open import foundation.univalence funext public +open import foundation.univalence-implies-function-extensionality funext public +open import foundation.univalent-type-families funext public +open import foundation.universal-property-booleans funext public +open import foundation.universal-property-cartesian-product-types funext public +open import foundation.universal-property-contractible-types funext public +open import foundation.universal-property-coproduct-types funext public +open import foundation.universal-property-dependent-function-types funext public +open import foundation.universal-property-dependent-pair-types funext public +open import foundation.universal-property-empty-type funext public +open import foundation.universal-property-equivalences funext public +open import foundation.universal-property-family-of-fibers-of-maps funext public +open import foundation.universal-property-fiber-products funext public +open import foundation.universal-property-identity-systems funext public +open import foundation.universal-property-identity-types funext public +open import foundation.universal-property-image funext public +open import foundation.universal-property-maybe funext public +open import foundation.universal-property-propositional-truncation funext public +open import foundation.universal-property-propositional-truncation-into-sets funext public +open import foundation.universal-property-pullbacks funext public +open import foundation.universal-property-sequential-limits funext public +open import foundation.universal-property-set-quotients funext public +open import foundation.universal-property-set-truncation funext public +open import foundation.universal-property-truncation funext public +open import foundation.universal-property-unit-type funext public +open import foundation.universal-quantification funext public open import foundation.universe-levels public -open import foundation.unordered-pairs public -open import foundation.unordered-pairs-of-types public -open import foundation.unordered-tuples public -open import foundation.unordered-tuples-of-types public -open import foundation.vectors-set-quotients public -open import foundation.vertical-composition-spans-of-spans public -open import foundation.weak-function-extensionality public -open import foundation.weak-limited-principle-of-omniscience public -open import foundation.weakly-constant-maps public +open import foundation.unordered-pairs funext public +open import foundation.unordered-pairs-of-types funext public +open import foundation.unordered-tuples funext public +open import foundation.unordered-tuples-of-types funext public +open import foundation.vectors-set-quotients funext public +open import foundation.vertical-composition-spans-of-spans funext public +open import foundation.weak-function-extensionality funext public +open import foundation.weak-limited-principle-of-omniscience funext public +open import foundation.weakly-constant-maps funext public open import foundation.whiskering-higher-homotopies-composition public open import foundation.whiskering-homotopies-composition public -open import foundation.whiskering-homotopies-concatenation public -open import foundation.whiskering-identifications-concatenation public +open import foundation.whiskering-homotopies-concatenation funext public +open import foundation.whiskering-identifications-concatenation funext public open import foundation.whiskering-operations public -open import foundation.wild-category-of-types public -open import foundation.yoneda-identity-types public +open import foundation.wild-category-of-types funext public +open import foundation.yoneda-identity-types funext public ``` diff --git a/src/foundation/0-connected-types.lagda.md b/src/foundation/0-connected-types.lagda.md index d2bdc9203d..5e19217f13 100644 --- a/src/foundation/0-connected-types.lagda.md +++ b/src/foundation/0-connected-types.lagda.md @@ -1,28 +1,33 @@ # `0`-Connected types ```agda -module foundation.0-connected-types where +open import foundation.function-extensionality-axiom + +module + foundation.0-connected-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.constant-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.fiber-inclusions -open import foundation.functoriality-set-truncation -open import foundation.images -open import foundation.inhabited-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.set-truncations -open import foundation.sets -open import foundation.surjective-maps +open import foundation.fiber-inclusions funext +open import foundation.functoriality-set-truncation funext +open import foundation.images funext +open import foundation.inhabited-types funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.set-truncations funext +open import foundation.sets funext +open import foundation.surjective-maps funext open import foundation.unit-type -open import foundation.universal-property-contractible-types -open import foundation.universal-property-unit-type +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -32,7 +37,7 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.precomposition-functions open import foundation-core.propositions -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/0-images-of-maps.lagda.md b/src/foundation/0-images-of-maps.lagda.md index 26121635f8..839add5b7c 100644 --- a/src/foundation/0-images-of-maps.lagda.md +++ b/src/foundation/0-images-of-maps.lagda.md @@ -1,13 +1,18 @@ # `0`-Images of maps ```agda -module foundation.0-images-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.0-images-of-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.truncation-images-of-maps +open import foundation.truncation-images-of-maps funext open import foundation.universe-levels open import foundation-core.truncation-levels diff --git a/src/foundation/0-maps.lagda.md b/src/foundation/0-maps.lagda.md index 365e87053d..8b214200f4 100644 --- a/src/foundation/0-maps.lagda.md +++ b/src/foundation/0-maps.lagda.md @@ -1,21 +1,26 @@ # `0`-Maps ```agda -module foundation.0-maps where +open import foundation.function-extensionality-axiom + +module + foundation.0-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels ``` diff --git a/src/foundation/1-types.lagda.md b/src/foundation/1-types.lagda.md index 9a4b7da289..c4517552a1 100644 --- a/src/foundation/1-types.lagda.md +++ b/src/foundation/1-types.lagda.md @@ -1,25 +1,30 @@ # `1`-Types ```agda -module foundation.1-types where +open import foundation.function-extensionality-axiom -open import foundation-core.1-types public +module + foundation.1-types + (funext : function-extensionality) + where + +open import foundation-core.1-types funext public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.subuniverses -open import foundation.truncated-types +open import foundation.dependent-products-truncated-types funext +open import foundation.subuniverses funext +open import foundation.truncated-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.truncation-levels ``` diff --git a/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md b/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md index 77d4813bf5..90ef1a273a 100644 --- a/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md +++ b/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md @@ -1,17 +1,22 @@ # The action on equivalences of functions out of subuniverses ```agda -module foundation.action-on-equivalences-functions-out-of-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.action-on-equivalences-functions-out-of-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-induction -open import foundation.subuniverses +open import foundation.equivalence-induction funext +open import foundation.subuniverses funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/action-on-equivalences-functions.lagda.md b/src/foundation/action-on-equivalences-functions.lagda.md index 497a160778..3caf907230 100644 --- a/src/foundation/action-on-equivalences-functions.lagda.md +++ b/src/foundation/action-on-equivalences-functions.lagda.md @@ -1,17 +1,22 @@ # Action on equivalences of functions ```agda -module foundation.action-on-equivalences-functions where +open import foundation.function-extensionality-axiom + +module + foundation.action-on-equivalences-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-induction -open import foundation.univalence +open import foundation.equivalence-induction funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.constant-maps diff --git a/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md b/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md index 9285de702a..383e2cd014 100644 --- a/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md +++ b/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md @@ -1,7 +1,12 @@ # Action on equivalences in type families over subuniverses ```agda -module foundation.action-on-equivalences-type-families-over-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.action-on-equivalences-type-families-over-subuniverses + (funext : function-extensionality) + where ```
Imports @@ -9,11 +14,11 @@ module foundation.action-on-equivalences-type-families-over-subuniverses where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-induction -open import foundation.subuniverses +open import foundation.equivalence-induction funext +open import foundation.subuniverses funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation/action-on-equivalences-type-families.lagda.md b/src/foundation/action-on-equivalences-type-families.lagda.md index 909f4c4011..39601ce297 100644 --- a/src/foundation/action-on-equivalences-type-families.lagda.md +++ b/src/foundation/action-on-equivalences-type-families.lagda.md @@ -1,20 +1,25 @@ # Action on equivalences of type families ```agda -module foundation.action-on-equivalences-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.action-on-equivalences-type-families + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-equivalences-functions +open import foundation.action-on-equivalences-functions funext open import foundation.action-on-identifications-functions -open import foundation.equivalence-induction -open import foundation.univalence +open import foundation.equivalence-induction funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.constant-maps open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/action-on-higher-identifications-functions.lagda.md b/src/foundation/action-on-higher-identifications-functions.lagda.md index ad3c91bea7..784280cc66 100644 --- a/src/foundation/action-on-higher-identifications-functions.lagda.md +++ b/src/foundation/action-on-higher-identifications-functions.lagda.md @@ -1,14 +1,19 @@ # The action of functions on higher identifications ```agda -module foundation.action-on-higher-identifications-functions where +open import foundation.function-extensionality-axiom + +module + foundation.action-on-higher-identifications-functions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.path-algebra +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications diff --git a/src/foundation/action-on-homotopies-functions.lagda.md b/src/foundation/action-on-homotopies-functions.lagda.md index e8dbeeaaba..a19c63291c 100644 --- a/src/foundation/action-on-homotopies-functions.lagda.md +++ b/src/foundation/action-on-homotopies-functions.lagda.md @@ -1,17 +1,23 @@ # The action on homotopies of functions ```agda -module foundation.action-on-homotopies-functions where +open import foundation.function-extensionality-axiom + +module + foundation.action-on-homotopies-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopy-induction +open import foundation.function-extensionality funext + +open import foundation.homotopy-induction funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/apartness-relations.lagda.md b/src/foundation/apartness-relations.lagda.md index 605d8b5b43..a8cf30a73c 100644 --- a/src/foundation/apartness-relations.lagda.md +++ b/src/foundation/apartness-relations.lagda.md @@ -1,19 +1,24 @@ # Apartness relations ```agda -module foundation.apartness-relations where +open import foundation.function-extensionality-axiom + +module + foundation.apartness-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.propositional-truncations -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext +open import foundation.existential-quantification funext +open import foundation.propositional-truncations funext +open import foundation.universal-quantification funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md b/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md index c29be5ba4a..c6654596ca 100644 --- a/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md +++ b/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md @@ -1,21 +1,26 @@ # Arithmetic law for coproduct decomposition and Σ-decomposition ```agda -module foundation.arithmetic-law-coproduct-and-sigma-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.arithmetic-law-coproduct-and-sigma-decompositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-decompositions +open import foundation.coproduct-decompositions funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.relaxed-sigma-decompositions -open import foundation.type-arithmetic-coproduct-types +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext +open import foundation.relaxed-sigma-decompositions funext +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence -open import foundation.universal-property-coproduct-types +open import foundation.univalence funext +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md b/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md index 2f70b0a358..b965cbe4f0 100644 --- a/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md +++ b/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md @@ -1,21 +1,26 @@ # Arithmetic law for product decomposition and Π-decomposition ```agda -module foundation.arithmetic-law-product-and-pi-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.arithmetic-law-product-and-pi-decompositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-decompositions +open import foundation.coproduct-decompositions funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.pi-decompositions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.pi-decompositions funext open import foundation.product-decompositions open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence -open import foundation.universal-property-coproduct-types +open import foundation.univalence funext +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/automorphisms.lagda.md b/src/foundation/automorphisms.lagda.md index bc5d12d351..8170916f8c 100644 --- a/src/foundation/automorphisms.lagda.md +++ b/src/foundation/automorphisms.lagda.md @@ -1,14 +1,19 @@ # Automorphisms ```agda -module foundation.automorphisms where +open import foundation.function-extensionality-axiom + +module + foundation.automorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.sets +open import foundation.sets funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/axiom-of-choice.lagda.md b/src/foundation/axiom-of-choice.lagda.md index aa6b055a68..70ca2d3a27 100644 --- a/src/foundation/axiom-of-choice.lagda.md +++ b/src/foundation/axiom-of-choice.lagda.md @@ -1,21 +1,25 @@ # The axiom of choice ```agda -module foundation.axiom-of-choice where +open import foundation.function-extensionality-axiom + +module + foundation.axiom-of-choice + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality-axiom -open import foundation.functoriality-propositional-truncation -open import foundation.inhabited-types -open import foundation.postcomposition-functions -open import foundation.projective-types -open import foundation.sections +open import foundation.functoriality-propositional-truncation funext +open import foundation.inhabited-types funext +open import foundation.postcomposition-functions funext +open import foundation.projective-types funext +open import foundation.sections funext open import foundation.split-surjective-maps -open import foundation.surjective-maps +open import foundation.surjective-maps funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/bands.lagda.md b/src/foundation/bands.lagda.md index 9b846f6934..07ac2553b7 100644 --- a/src/foundation/bands.lagda.md +++ b/src/foundation/bands.lagda.md @@ -1,13 +1,18 @@ # Bands ```agda -module foundation.bands where +open import foundation.function-extensionality-axiom + +module + foundation.bands + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.set-truncations +open import foundation.set-truncations funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/base-changes-span-diagrams.lagda.md b/src/foundation/base-changes-span-diagrams.lagda.md index 10882ba5e2..caf7f650b7 100644 --- a/src/foundation/base-changes-span-diagrams.lagda.md +++ b/src/foundation/base-changes-span-diagrams.lagda.md @@ -1,19 +1,24 @@ # Base changes of span diagrams ```agda -module foundation.base-changes-span-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.base-changes-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows -open import foundation.cartesian-morphisms-span-diagrams -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-morphisms-arrows funext +open import foundation.cartesian-morphisms-span-diagrams funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.morphisms-span-diagrams -open import foundation.span-diagrams +open import foundation.morphisms-arrows funext +open import foundation.morphisms-span-diagrams funext +open import foundation.span-diagrams funext open import foundation.universe-levels ``` diff --git a/src/foundation/bicomposition-functions.lagda.md b/src/foundation/bicomposition-functions.lagda.md index fceca92642..824dd875ee 100644 --- a/src/foundation/bicomposition-functions.lagda.md +++ b/src/foundation/bicomposition-functions.lagda.md @@ -1,7 +1,12 @@ # Bicomposition of functions ```agda -module foundation.bicomposition-functions where +open import foundation.function-extensionality-axiom + +module + foundation.bicomposition-functions + (funext : function-extensionality) + where ```
Imports @@ -9,19 +14,20 @@ module foundation.bicomposition-functions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.postcomposition-dependent-functions +open import foundation.function-extensionality funext + +open import foundation.postcomposition-dependent-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/binary-embeddings.lagda.md b/src/foundation/binary-embeddings.lagda.md index fb822a3918..64e6d3adb3 100644 --- a/src/foundation/binary-embeddings.lagda.md +++ b/src/foundation/binary-embeddings.lagda.md @@ -1,7 +1,12 @@ # Binary embeddings ```agda -module foundation.binary-embeddings where +open import foundation.function-extensionality-axiom + +module + foundation.binary-embeddings + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md b/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md index 8f52b2aee3..d7802914d4 100644 --- a/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md +++ b/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md @@ -1,16 +1,21 @@ # Binary equivalences on unordered pairs of types ```agda -module foundation.binary-equivalences-unordered-pairs-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.binary-equivalences-unordered-pairs-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-operations-unordered-pairs-of-types -open import foundation.products-unordered-pairs-of-types +open import foundation.binary-operations-unordered-pairs-of-types funext +open import foundation.products-unordered-pairs-of-types funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/binary-functoriality-set-quotients.lagda.md b/src/foundation/binary-functoriality-set-quotients.lagda.md index 767805918d..b683cde907 100644 --- a/src/foundation/binary-functoriality-set-quotients.lagda.md +++ b/src/foundation/binary-functoriality-set-quotients.lagda.md @@ -3,38 +3,43 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.binary-functoriality-set-quotients where +open import foundation.function-extensionality-axiom + +module + foundation.binary-functoriality-set-quotients + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-homotopies +open import foundation.binary-homotopies funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.exponents-set-quotients -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.functoriality-set-quotients +open import foundation.dependent-products-propositions funext +open import foundation.exponents-set-quotients funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-set-quotients funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.set-quotients funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.universal-property-set-quotients +open import foundation.surjective-maps funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels open import foundation-core.contractible-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/binary-homotopies.lagda.md b/src/foundation/binary-homotopies.lagda.md index bbfde019b4..117d5781dd 100644 --- a/src/foundation/binary-homotopies.lagda.md +++ b/src/foundation/binary-homotopies.lagda.md @@ -1,17 +1,23 @@ # Homotopies of binary operations ```agda -module foundation.binary-homotopies where +open import foundation.function-extensionality-axiom + +module + foundation.binary-homotopies + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.function-extensionality +open import foundation.equality-dependent-function-types funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md b/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md index 2f5a31ac3c..ed8a02e9c9 100644 --- a/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md +++ b/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md @@ -1,15 +1,20 @@ # Binary operations on unordered pairs of types ```agda -module foundation.binary-operations-unordered-pairs-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.binary-operations-unordered-pairs-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.products-unordered-pairs-of-types +open import foundation.products-unordered-pairs-of-types funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext ```
diff --git a/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md b/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md index 954e06617b..feac4c0b4e 100644 --- a/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md +++ b/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md @@ -1,21 +1,26 @@ # Binary reflecting maps of equivalence relations ```agda -module foundation.binary-reflecting-maps-equivalence-relations where +open import foundation.function-extensionality-axiom + +module + foundation.binary-reflecting-maps-equivalence-relations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equality-dependent-function-types +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.subtype-identity-principle open import foundation.universe-levels -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/binary-relations-with-extensions.lagda.md b/src/foundation/binary-relations-with-extensions.lagda.md index 50543f32af..25ff3c4acf 100644 --- a/src/foundation/binary-relations-with-extensions.lagda.md +++ b/src/foundation/binary-relations-with-extensions.lagda.md @@ -1,15 +1,20 @@ # Binary relations with extensions ```agda -module foundation.binary-relations-with-extensions where +open import foundation.function-extensionality-axiom + +module + foundation.binary-relations-with-extensions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types +open import foundation.iterated-dependent-product-types funext open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/binary-relations-with-lifts.lagda.md b/src/foundation/binary-relations-with-lifts.lagda.md index f6ef244510..dd81c2f64f 100644 --- a/src/foundation/binary-relations-with-lifts.lagda.md +++ b/src/foundation/binary-relations-with-lifts.lagda.md @@ -1,15 +1,20 @@ # Binary relations with lifts ```agda -module foundation.binary-relations-with-lifts where +open import foundation.function-extensionality-axiom + +module + foundation.binary-relations-with-lifts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types +open import foundation.iterated-dependent-product-types funext open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/binary-relations.lagda.md b/src/foundation/binary-relations.lagda.md index d564eebeb0..862847ca22 100644 --- a/src/foundation/binary-relations.lagda.md +++ b/src/foundation/binary-relations.lagda.md @@ -1,20 +1,25 @@ # Binary relations ```agda -module foundation.binary-relations where +open import foundation.function-extensionality-axiom + +module + foundation.binary-relations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equality-dependent-function-types +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.iterated-dependent-product-types -open import foundation.subtypes +open import foundation.iterated-dependent-product-types funext +open import foundation.subtypes funext open import foundation.telescopes -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/binary-type-duality.lagda.md b/src/foundation/binary-type-duality.lagda.md index 5a4cfa15a6..0011b7a204 100644 --- a/src/foundation/binary-type-duality.lagda.md +++ b/src/foundation/binary-type-duality.lagda.md @@ -1,22 +1,27 @@ # Binary type duality ```agda -module foundation.binary-type-duality where +open import foundation.function-extensionality-axiom + +module + foundation.binary-type-duality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-spans -open import foundation.function-types -open import foundation.multivariable-homotopies -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.equivalences funext-spans +open import foundation.function-types funext +open import foundation.multivariable-homotopies funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.spans open import foundation.telescopes -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/booleans.lagda.md b/src/foundation/booleans.lagda.md index 3ac9ef298c..52841cd831 100644 --- a/src/foundation/booleans.lagda.md +++ b/src/foundation/booleans.lagda.md @@ -1,7 +1,12 @@ # The booleans ```agda -module foundation.booleans where +open import foundation.function-extensionality-axiom + +module + foundation.booleans + (funext : function-extensionality) + where open import foundation-core.booleans public ``` @@ -9,11 +14,11 @@ open import foundation-core.booleans public
Imports ```agda -open import foundation.decidable-equality +open import foundation.decidable-equality funext open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.involutions -open import foundation.negated-equality +open import foundation.discrete-types funext +open import foundation.involutions funext +open import foundation.negated-equality funext open import foundation.unit-type open import foundation.universe-levels @@ -29,8 +34,8 @@ open import foundation-core.propositions open import foundation-core.sections open import foundation-core.sets -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/cantor-schroder-bernstein-escardo.lagda.md b/src/foundation/cantor-schroder-bernstein-escardo.lagda.md index c48597b785..bc12428176 100644 --- a/src/foundation/cantor-schroder-bernstein-escardo.lagda.md +++ b/src/foundation/cantor-schroder-bernstein-escardo.lagda.md @@ -1,18 +1,23 @@ # The Cantor–Schröder–Bernstein–Escardó theorem ```agda -module foundation.cantor-schroder-bernstein-escardo where +open import foundation.function-extensionality-axiom + +module + foundation.cantor-schroder-bernstein-escardo + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.injective-maps -open import foundation.law-of-excluded-middle -open import foundation.perfect-images +open import foundation.injective-maps funext +open import foundation.law-of-excluded-middle funext +open import foundation.perfect-images funext open import foundation.split-surjective-maps open import foundation.universe-levels diff --git a/src/foundation/cantors-theorem.lagda.md b/src/foundation/cantors-theorem.lagda.md index f44e28067a..6b5a0e6fbd 100644 --- a/src/foundation/cantors-theorem.lagda.md +++ b/src/foundation/cantors-theorem.lagda.md @@ -1,31 +1,35 @@ # Cantor's theorem ```agda -module foundation.cantors-theorem where +open import foundation.function-extensionality-axiom + +module + foundation.cantors-theorem + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.decidable-propositions -open import foundation.decidable-subtypes +open import foundation.decidable-propositions funext +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions -open import foundation.function-extensionality-axiom -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.surjective-maps +open import foundation.double-negation-stable-propositions funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.surjective-maps funext open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.fibers-of-maps -open import logic.de-morgan-propositions -open import logic.de-morgan-subtypes -open import logic.double-negation-stable-subtypes +open import logic.de-morgan-propositions funext +open import logic.de-morgan-subtypes funext +open import logic.double-negation-stable-subtypes funext ```
diff --git a/src/foundation/cartesian-morphisms-arrows.lagda.md b/src/foundation/cartesian-morphisms-arrows.lagda.md index 58ea9ebfbb..dd0c0fe1d1 100644 --- a/src/foundation/cartesian-morphisms-arrows.lagda.md +++ b/src/foundation/cartesian-morphisms-arrows.lagda.md @@ -1,44 +1,49 @@ # Cartesian morphisms of arrows ```agda -module foundation.cartesian-morphisms-arrows where +open import foundation.function-extensionality-axiom + +module + foundation.cartesian-morphisms-arrows + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.commuting-triangles-of-morphisms-arrows -open import foundation.cones-over-cospan-diagrams -open import foundation.coproducts-pullbacks +open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-triangles-of-morphisms-arrows funext +open import foundation.cones-over-cospan-diagrams funext +open import foundation.coproducts-pullbacks funext open import foundation.dependent-pair-types -open import foundation.dependent-products-pullbacks -open import foundation.dependent-sums-pullbacks -open import foundation.diagonal-maps-cartesian-products-of-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies-morphisms-arrows -open import foundation.identity-types -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.postcomposition-pullbacks -open import foundation.products-pullbacks -open import foundation.pullbacks -open import foundation.standard-pullbacks +open import foundation.dependent-products-pullbacks funext +open import foundation.dependent-sums-pullbacks funext +open import foundation.diagonal-maps-cartesian-products-of-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies-morphisms-arrows funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.postcomposition-pullbacks funext +open import foundation.products-pullbacks funext +open import foundation.pullbacks funext +open import foundation.standard-pullbacks funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.homotopies open import foundation-core.propositions -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/cartesian-morphisms-span-diagrams.lagda.md b/src/foundation/cartesian-morphisms-span-diagrams.lagda.md index 0441d162f7..d338a43fa6 100644 --- a/src/foundation/cartesian-morphisms-span-diagrams.lagda.md +++ b/src/foundation/cartesian-morphisms-span-diagrams.lagda.md @@ -1,19 +1,24 @@ # Cartesian morphisms of span diagrams ```agda -module foundation.cartesian-morphisms-span-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.cartesian-morphisms-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-morphisms-arrows funext +open import foundation.cartesian-product-types funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.morphisms-span-diagrams -open import foundation.span-diagrams +open import foundation.morphisms-arrows funext +open import foundation.morphisms-span-diagrams funext +open import foundation.span-diagrams funext open import foundation.universe-levels ``` diff --git a/src/foundation/cartesian-product-types.lagda.md b/src/foundation/cartesian-product-types.lagda.md index 08740b0e83..5a117cd369 100644 --- a/src/foundation/cartesian-product-types.lagda.md +++ b/src/foundation/cartesian-product-types.lagda.md @@ -1,7 +1,12 @@ # Cartesian product types ```agda -module foundation.cartesian-product-types where +open import foundation.function-extensionality-axiom + +module + foundation.cartesian-product-types + (funext : function-extensionality) + where open import foundation-core.cartesian-product-types public ``` @@ -10,7 +15,7 @@ open import foundation-core.cartesian-product-types public ```agda open import foundation.dependent-pair-types -open import foundation.subuniverses +open import foundation.subuniverses funext open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/cartesian-products-set-quotients.lagda.md b/src/foundation/cartesian-products-set-quotients.lagda.md index f016d8c0f7..a11402b82f 100644 --- a/src/foundation/cartesian-products-set-quotients.lagda.md +++ b/src/foundation/cartesian-products-set-quotients.lagda.md @@ -1,7 +1,12 @@ # Cartesian products of set quotients ```agda -module foundation.cartesian-products-set-quotients where +open import foundation.function-extensionality-axiom + +module + foundation.cartesian-products-set-quotients + (funext : function-extensionality) + where ```
Imports @@ -10,19 +15,19 @@ module foundation.cartesian-products-set-quotients where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.products-equivalence-relations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-set-quotients +open import foundation.function-extensionality funext + +open import foundation.products-equivalence-relations funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.set-quotients funext +open import foundation.sets funext +open import foundation.uniqueness-set-quotients funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equality-dependent-pair-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies diff --git a/src/foundation/category-of-families-of-sets.lagda.md b/src/foundation/category-of-families-of-sets.lagda.md index a5d7dff0ff..ccf7350d8a 100644 --- a/src/foundation/category-of-families-of-sets.lagda.md +++ b/src/foundation/category-of-families-of-sets.lagda.md @@ -1,20 +1,25 @@ # The category of families of sets ```agda -module foundation.category-of-families-of-sets where +open import foundation.function-extensionality-axiom + +module + foundation.category-of-families-of-sets + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories -open import category-theory.large-function-categories -open import category-theory.large-function-precategories -open import category-theory.large-precategories -open import category-theory.precategories - -open import foundation.category-of-sets +open import category-theory.categories funext +open import category-theory.large-categories funext +open import category-theory.large-function-categories funext +open import category-theory.large-function-precategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext + +open import foundation.category-of-sets funext open import foundation.universe-levels ``` diff --git a/src/foundation/category-of-sets.lagda.md b/src/foundation/category-of-sets.lagda.md index 23f7b9be68..cbe5e451ba 100644 --- a/src/foundation/category-of-sets.lagda.md +++ b/src/foundation/category-of-sets.lagda.md @@ -1,38 +1,43 @@ # The category of sets ```agda -module foundation.category-of-sets where +open import foundation.function-extensionality-axiom + +module + foundation.category-of-sets + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.complete-precategories -open import category-theory.cones-precategories -open import category-theory.constant-functors -open import category-theory.functors-precategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.limits-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.complete-precategories funext +open import category-theory.cones-precategories funext +open import category-theory.constant-functors funext +open import category-theory.functors-precategories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.limits-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.isomorphisms-of-sets -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type -open import foundation.retractions -open import foundation.sections -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.isomorphisms-of-sets funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/choice-of-representatives-equivalence-relation.lagda.md b/src/foundation/choice-of-representatives-equivalence-relation.lagda.md index 6ba3e69b75..3f9fa8f6cc 100644 --- a/src/foundation/choice-of-representatives-equivalence-relation.lagda.md +++ b/src/foundation/choice-of-representatives-equivalence-relation.lagda.md @@ -1,7 +1,12 @@ # Choice of representatives for an equivalence relation ```agda -module foundation.choice-of-representatives-equivalence-relation where +open import foundation.function-extensionality-axiom + +module + foundation.choice-of-representatives-equivalence-relation + (funext : function-extensionality) + where ```
Imports @@ -9,18 +14,18 @@ module foundation.choice-of-representatives-equivalence-relation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-classes +open import foundation.equivalence-classes funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.surjective-maps +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.surjective-maps funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.contractible-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.functoriality-dependent-pair-types diff --git a/src/foundation/coalgebras-maybe.lagda.md b/src/foundation/coalgebras-maybe.lagda.md index afca8c6ef1..45627df61e 100644 --- a/src/foundation/coalgebras-maybe.lagda.md +++ b/src/foundation/coalgebras-maybe.lagda.md @@ -1,7 +1,12 @@ # Coalgebras of the maybe monad ```agda -module foundation.coalgebras-maybe where +open import foundation.function-extensionality-axiom + +module + foundation.coalgebras-maybe + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ open import foundation.universe-levels open import foundation-core.maybe -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext ```
diff --git a/src/foundation/coherently-idempotent-maps.lagda.md b/src/foundation/coherently-idempotent-maps.lagda.md index d746a1ec6a..3e9b54d0b6 100644 --- a/src/foundation/coherently-idempotent-maps.lagda.md +++ b/src/foundation/coherently-idempotent-maps.lagda.md @@ -1,7 +1,12 @@ # Coherently idempotent maps ```agda -module foundation.coherently-idempotent-maps where +open import foundation.function-extensionality-axiom + +module + foundation.coherently-idempotent-maps + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.homotopy-algebra -open import foundation.quasicoherently-idempotent-maps -open import foundation.split-idempotent-maps +open import foundation.quasicoherently-idempotent-maps funext +open import foundation.split-idempotent-maps funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/coherently-invertible-maps.lagda.md b/src/foundation/coherently-invertible-maps.lagda.md index d811bbad78..62415c3ea1 100644 --- a/src/foundation/coherently-invertible-maps.lagda.md +++ b/src/foundation/coherently-invertible-maps.lagda.md @@ -1,7 +1,12 @@ # Coherently invertible maps ```agda -module foundation.coherently-invertible-maps where +open import foundation.function-extensionality-axiom + +module + foundation.coherently-invertible-maps + (funext : function-extensionality) + where open import foundation-core.coherently-invertible-maps public ``` @@ -10,10 +15,10 @@ open import foundation-core.coherently-invertible-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.dependent-products-contractible-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/coinhabited-pairs-of-types.lagda.md b/src/foundation/coinhabited-pairs-of-types.lagda.md index bb9be37fb9..7a578be166 100644 --- a/src/foundation/coinhabited-pairs-of-types.lagda.md +++ b/src/foundation/coinhabited-pairs-of-types.lagda.md @@ -1,15 +1,20 @@ # Coinhabited pairs of types ```agda -module foundation.coinhabited-pairs-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.coinhabited-pairs-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.inhabited-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/commuting-cubes-of-maps.lagda.md b/src/foundation/commuting-cubes-of-maps.lagda.md index 0309bafe4b..8420b590d7 100644 --- a/src/foundation/commuting-cubes-of-maps.lagda.md +++ b/src/foundation/commuting-cubes-of-maps.lagda.md @@ -1,7 +1,12 @@ # Commuting cubes of maps ```agda -module foundation.commuting-cubes-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.commuting-cubes-of-maps + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,16 @@ module foundation.commuting-cubes-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.commuting-hexagons-of-identifications -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopies +open import foundation.function-extensionality funext + +open import foundation.homotopies funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation +open import foundation.whiskering-homotopies-concatenation funext open import foundation-core.function-types open import foundation-core.identity-types diff --git a/src/foundation/commuting-prisms-of-maps.lagda.md b/src/foundation/commuting-prisms-of-maps.lagda.md index 1abe1edc03..d08afb582c 100644 --- a/src/foundation/commuting-prisms-of-maps.lagda.md +++ b/src/foundation/commuting-prisms-of-maps.lagda.md @@ -1,29 +1,35 @@ # Commuting prisms of maps ```agda -module foundation.commuting-prisms-of-maps where +open import foundation.function-extensionality-axiom -open import foundation-core.commuting-prisms-of-maps public +module + foundation.commuting-prisms-of-maps + (funext : function-extensionality) + where + +open import foundation-core.commuting-prisms-of-maps funext public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.composition-algebra -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-functions +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.composition-algebra funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.homotopies ``` diff --git a/src/foundation/commuting-squares-of-homotopies.lagda.md b/src/foundation/commuting-squares-of-homotopies.lagda.md index 102c3cee57..bbbc0d1673 100644 --- a/src/foundation/commuting-squares-of-homotopies.lagda.md +++ b/src/foundation/commuting-squares-of-homotopies.lagda.md @@ -1,7 +1,12 @@ # Commuting squares of homotopies ```agda -module foundation.commuting-squares-of-homotopies where +open import foundation.function-extensionality-axiom + +module + foundation.commuting-squares-of-homotopies + (funext : function-extensionality) + where open import foundation-core.commuting-squares-of-homotopies public ``` @@ -9,13 +14,13 @@ open import foundation-core.commuting-squares-of-homotopies public
Imports ```agda -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.universe-levels open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext ```
diff --git a/src/foundation/commuting-squares-of-identifications.lagda.md b/src/foundation/commuting-squares-of-identifications.lagda.md index d0b7caf8b4..a755bd1fce 100644 --- a/src/foundation/commuting-squares-of-identifications.lagda.md +++ b/src/foundation/commuting-squares-of-identifications.lagda.md @@ -1,7 +1,12 @@ # Commuting squares of identifications ```agda -module foundation.commuting-squares-of-identifications where +open import foundation.function-extensionality-axiom + +module + foundation.commuting-squares-of-identifications + (funext : function-extensionality) + where open import foundation-core.commuting-squares-of-identifications public ``` @@ -10,7 +15,7 @@ open import foundation-core.commuting-squares-of-identifications public ```agda open import foundation.dependent-pair-types -open import foundation.path-algebra +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/commuting-squares-of-maps.lagda.md b/src/foundation/commuting-squares-of-maps.lagda.md index 347bb16120..2bd0ff7863 100644 --- a/src/foundation/commuting-squares-of-maps.lagda.md +++ b/src/foundation/commuting-squares-of-maps.lagda.md @@ -1,9 +1,14 @@ # Commuting squares of maps ```agda -module foundation.commuting-squares-of-maps where +open import foundation.function-extensionality-axiom -open import foundation-core.commuting-squares-of-maps public +module + foundation.commuting-squares-of-maps + (funext : function-extensionality) + where + +open import foundation-core.commuting-squares-of-maps funext public ```
Imports @@ -11,18 +16,19 @@ open import foundation-core.commuting-squares-of-maps public ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-homotopies -open import foundation.commuting-triangles-of-maps -open import foundation.function-extensionality +open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.function-extensionality funext + open import foundation.homotopy-algebra -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.transposition-identifications-along-equivalences +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-prisms-of-maps +open import foundation-core.commuting-prisms-of-maps funext open import foundation-core.commuting-squares-of-homotopies open import foundation-core.commuting-squares-of-identifications open import foundation-core.equivalences diff --git a/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md b/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md index 2aa6902f83..6c2e191aae 100644 --- a/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md +++ b/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md @@ -1,13 +1,18 @@ # Commuting tetrahedra of homotopies ```agda -module foundation.commuting-tetrahedra-of-homotopies where +open import foundation.function-extensionality-axiom + +module + foundation.commuting-tetrahedra-of-homotopies + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.universe-levels open import foundation-core.homotopies diff --git a/src/foundation/commuting-triangles-of-homotopies.lagda.md b/src/foundation/commuting-triangles-of-homotopies.lagda.md index a9a57c0d7e..6342b7ebc0 100644 --- a/src/foundation/commuting-triangles-of-homotopies.lagda.md +++ b/src/foundation/commuting-triangles-of-homotopies.lagda.md @@ -1,13 +1,18 @@ # Commuting triangles of homotopies ```agda -module foundation.commuting-triangles-of-homotopies where +open import foundation.function-extensionality-axiom + +module + foundation.commuting-triangles-of-homotopies + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-triangles-of-identifications funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/commuting-triangles-of-identifications.lagda.md b/src/foundation/commuting-triangles-of-identifications.lagda.md index ab6e12a82d..b3476511f3 100644 --- a/src/foundation/commuting-triangles-of-identifications.lagda.md +++ b/src/foundation/commuting-triangles-of-identifications.lagda.md @@ -1,7 +1,12 @@ # Commuting triangles of identifications ```agda -module foundation.commuting-triangles-of-identifications where +open import foundation.function-extensionality-axiom + +module + foundation.commuting-triangles-of-identifications + (funext : function-extensionality) + where ```
Imports @@ -10,9 +15,9 @@ module foundation.commuting-triangles-of-identifications where open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.commuting-squares-of-identifications open import foundation-core.equivalences diff --git a/src/foundation/commuting-triangles-of-maps.lagda.md b/src/foundation/commuting-triangles-of-maps.lagda.md index ef0e081b0a..9e90b435ba 100644 --- a/src/foundation/commuting-triangles-of-maps.lagda.md +++ b/src/foundation/commuting-triangles-of-maps.lagda.md @@ -1,7 +1,12 @@ # Commuting triangles of maps ```agda -module foundation.commuting-triangles-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.commuting-triangles-of-maps + (funext : function-extensionality) + where open import foundation-core.commuting-triangles-of-maps public ``` @@ -10,16 +15,16 @@ open import foundation-core.commuting-triangles-of-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.functoriality-dependent-function-types -open import foundation.homotopies +open import foundation.functoriality-dependent-function-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-functions +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.whiskering-identifications-concatenation diff --git a/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md b/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md index 2e375cefa7..1b958b4538 100644 --- a/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md +++ b/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md @@ -1,14 +1,19 @@ # Commuting triangles of morphisms of arrows ```agda -module foundation.commuting-triangles-of-morphisms-arrows where +open import foundation.function-extensionality-axiom + +module + foundation.commuting-triangles-of-morphisms-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.homotopies-morphisms-arrows -open import foundation.morphisms-arrows +open import foundation.homotopies-morphisms-arrows funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels ``` diff --git a/src/foundation/complements-subtypes.lagda.md b/src/foundation/complements-subtypes.lagda.md index 3331a3455c..73cc09728b 100644 --- a/src/foundation/complements-subtypes.lagda.md +++ b/src/foundation/complements-subtypes.lagda.md @@ -1,35 +1,40 @@ # Complements of subtypes ```agda -module foundation.complements-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.complements-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-propositions -open import foundation.decidable-subtypes -open import foundation.double-negation-stable-propositions -open import foundation.full-subtypes -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.unions-subtypes +open import foundation.decidable-propositions funext +open import foundation.decidable-subtypes funext +open import foundation.double-negation-stable-propositions funext +open import foundation.full-subtypes funext +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.unions-subtypes funext open import foundation.universe-levels open import foundation-core.function-types -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import logic.double-negation-stable-subtypes +open import logic.double-negation-stable-subtypes funext -open import order-theory.large-posets -open import order-theory.opposite-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.order-preserving-maps-preorders -open import order-theory.posets +open import order-theory.large-posets funext +open import order-theory.opposite-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.order-preserving-maps-preorders funext +open import order-theory.posets funext ```
diff --git a/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md b/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md index 78c23727e3..dde0f03941 100644 --- a/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Composite maps in inverse sequential diagrams ```agda -module foundation.composite-maps-in-inverse-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.composite-maps-in-inverse-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module foundation.composite-maps-in-inverse-sequential-diagrams where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.dependent-inverse-sequential-diagrams -open import foundation.inverse-sequential-diagrams +open import foundation.dependent-inverse-sequential-diagrams funext +open import foundation.inverse-sequential-diagrams funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/composition-algebra.lagda.md b/src/foundation/composition-algebra.lagda.md index d78d99cfee..6ab2802918 100644 --- a/src/foundation/composition-algebra.lagda.md +++ b/src/foundation/composition-algebra.lagda.md @@ -1,17 +1,23 @@ # Composition algebra ```agda -module foundation.composition-algebra where +open import foundation.function-extensionality-axiom + +module + foundation.composition-algebra + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-extensionality -open import foundation.homotopy-induction -open import foundation.postcomposition-functions -open import foundation.precomposition-functions +open import foundation.function-extensionality funext + +open import foundation.homotopy-induction funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/composition-spans.lagda.md b/src/foundation/composition-spans.lagda.md index 2611cdf5b1..2ffff15d37 100644 --- a/src/foundation/composition-spans.lagda.md +++ b/src/foundation/composition-spans.lagda.md @@ -1,25 +1,30 @@ # Composition of spans ```agda -module foundation.composition-spans where +open import foundation.function-extensionality-axiom + +module + foundation.composition-spans + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-spans -open import foundation.homotopies -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.equivalences-spans funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.morphisms-spans -open import foundation.pullbacks +open import foundation.pullbacks funext open import foundation.spans -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-standard-pullbacks +open import foundation.standard-pullbacks funext +open import foundation.type-arithmetic-standard-pullbacks funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/computational-identity-types.lagda.md b/src/foundation/computational-identity-types.lagda.md index 5c40b6da91..1d64404a7e 100644 --- a/src/foundation/computational-identity-types.lagda.md +++ b/src/foundation/computational-identity-types.lagda.md @@ -1,7 +1,12 @@ # Computational identity types ```agda -module foundation.computational-identity-types where +open import foundation.function-extensionality-axiom + +module + foundation.computational-identity-types + (funext : function-extensionality) + where ```
Imports @@ -11,14 +16,14 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.function-extensionality funext + open import foundation.strictly-right-unital-concatenation-identifications open import foundation.transport-along-identifications -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.univalence funext +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels -open import foundation.yoneda-identity-types +open import foundation.yoneda-identity-types funext open import foundation-core.cartesian-product-types open import foundation-core.contractible-types diff --git a/src/foundation/cones-over-cospan-diagrams.lagda.md b/src/foundation/cones-over-cospan-diagrams.lagda.md index 8bc7769426..072599a672 100644 --- a/src/foundation/cones-over-cospan-diagrams.lagda.md +++ b/src/foundation/cones-over-cospan-diagrams.lagda.md @@ -1,7 +1,12 @@ # Cones over cospan diagrams ```agda -module foundation.cones-over-cospan-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.cones-over-cospan-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,19 +14,20 @@ module foundation.cones-over-cospan-diagrams where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.function-extensionality +open import foundation.dependent-universal-property-equivalences funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.multivariable-homotopies +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.multivariable-homotopies funext open import foundation.structure-identity-principle open import foundation.telescopes open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md b/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md index a062c7b9d4..9ede8855b1 100644 --- a/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Cones over inverse sequential diagrams ```agda -module foundation.cones-over-inverse-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.cones-over-inverse-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,14 @@ module foundation.cones-over-inverse-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies +open import foundation.binary-homotopies funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.function-extensionality +open import foundation.equality-dependent-function-types funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.inverse-sequential-diagrams +open import foundation.homotopy-induction funext +open import foundation.inverse-sequential-diagrams funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/conjunction.lagda.md b/src/foundation/conjunction.lagda.md index 0ba08d98b8..5305e5f67d 100644 --- a/src/foundation/conjunction.lagda.md +++ b/src/foundation/conjunction.lagda.md @@ -1,22 +1,27 @@ # Conjunction ```agda -module foundation.conjunction where +open import foundation.function-extensionality-axiom + +module + foundation.conjunction + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.universal-property-cartesian-product-types +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.propositions diff --git a/src/foundation/connected-components-universes.lagda.md b/src/foundation/connected-components-universes.lagda.md index 6e4a87e413..0aaeb111cd 100644 --- a/src/foundation/connected-components-universes.lagda.md +++ b/src/foundation/connected-components-universes.lagda.md @@ -1,29 +1,34 @@ # Connected components of universes ```agda -module foundation.connected-components-universes where +open import foundation.function-extensionality-axiom + +module + foundation.connected-components-universes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.functoriality-propositional-truncation +open import foundation.empty-types funext +open import foundation.functoriality-propositional-truncation funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.raising-universe-levels +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.raising-universe-levels funext open import foundation.subtype-identity-principle -open import foundation.subuniverses -open import foundation.univalence +open import foundation.subuniverses funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.identity-types -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/connected-components.lagda.md b/src/foundation/connected-components.lagda.md index 9de3f80bbc..757f7433f6 100644 --- a/src/foundation/connected-components.lagda.md +++ b/src/foundation/connected-components.lagda.md @@ -1,27 +1,32 @@ # Connected components of types ```agda -module foundation.connected-components where +open import foundation.function-extensionality-axiom + +module + foundation.connected-components + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.logical-equivalences funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.universe-levels open import foundation-core.equality-dependent-pair-types open import foundation-core.identity-types -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types ``` diff --git a/src/foundation/connected-maps.lagda.md b/src/foundation/connected-maps.lagda.md index 74bc45c267..a0fb4af1b7 100644 --- a/src/foundation/connected-maps.lagda.md +++ b/src/foundation/connected-maps.lagda.md @@ -1,26 +1,30 @@ # Connected maps ```agda -module foundation.connected-maps where +open import foundation.function-extensionality-axiom + +module + foundation.connected-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.connected-types +open import foundation.connected-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.function-extensionality-axiom +open import foundation.dependent-products-propositions funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.precomposition-dependent-functions +open import foundation.homotopy-induction funext +open import foundation.precomposition-dependent-functions funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels -open import foundation.truncations -open import foundation.univalence -open import foundation.universal-property-family-of-fibers-of-maps +open import foundation.truncations funext +open import foundation.univalence funext +open import foundation.universal-property-family-of-fibers-of-maps funext open import foundation.universe-levels open import foundation-core.contractible-maps @@ -32,9 +36,9 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext ```
diff --git a/src/foundation/connected-types.lagda.md b/src/foundation/connected-types.lagda.md index 433b38821f..b2e349ae7c 100644 --- a/src/foundation/connected-types.lagda.md +++ b/src/foundation/connected-types.lagda.md @@ -1,20 +1,24 @@ # Connected types ```agda -module foundation.connected-types where +open import foundation.function-extensionality-axiom + +module + foundation.connected-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.function-extensionality-axiom -open import foundation.functoriality-truncation -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.truncations +open import foundation.functoriality-truncation funext +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.truncations funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/constant-maps.lagda.md b/src/foundation/constant-maps.lagda.md index ec686e7417..2b418dd759 100644 --- a/src/foundation/constant-maps.lagda.md +++ b/src/foundation/constant-maps.lagda.md @@ -1,7 +1,12 @@ # Constant maps ```agda -module foundation.constant-maps where +open import foundation.function-extensionality-axiom + +module + foundation.constant-maps + (funext : function-extensionality) + where open import foundation-core.constant-maps public ``` @@ -9,28 +14,29 @@ open import foundation-core.constant-maps public
Imports ```agda -open import foundation.0-maps -open import foundation.action-on-homotopies-functions +open import foundation.0-maps funext +open import foundation.action-on-homotopies-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.faithful-maps -open import foundation.function-extensionality -open import foundation.functoriality-dependent-pair-types -open import foundation.images -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.propositional-truncations -open import foundation.retracts-of-maps -open import foundation.retracts-of-types -open import foundation.transposition-identifications-along-equivalences +open import foundation.faithful-maps funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-dependent-pair-types funext +open import foundation.images funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.propositional-truncations funext +open import foundation.retracts-of-maps funext +open import foundation.retracts-of-types funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-unit-type -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.1-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.1-types funext +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.embeddings @@ -43,7 +49,7 @@ open import foundation-core.injective-maps open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/constant-span-diagrams.lagda.md b/src/foundation/constant-span-diagrams.lagda.md index eb2e81061d..8a9a36d8e2 100644 --- a/src/foundation/constant-span-diagrams.lagda.md +++ b/src/foundation/constant-span-diagrams.lagda.md @@ -1,15 +1,20 @@ # Constant span diagrams ```agda -module foundation.constant-span-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.constant-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.span-diagrams +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/constant-type-families.lagda.md b/src/foundation/constant-type-families.lagda.md index 80e1f984df..318489eb31 100644 --- a/src/foundation/constant-type-families.lagda.md +++ b/src/foundation/constant-type-families.lagda.md @@ -1,7 +1,12 @@ # Constant type families ```agda -module foundation.constant-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.constant-type-families + (funext : function-extensionality) + where ```
Imports @@ -10,7 +15,7 @@ module foundation.constant-type-families where open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications diff --git a/src/foundation/continuations.lagda.md b/src/foundation/continuations.lagda.md index 8792570be4..b580a5993e 100644 --- a/src/foundation/continuations.lagda.md +++ b/src/foundation/continuations.lagda.md @@ -1,21 +1,26 @@ # The continuation monad ```agda -module foundation.continuations where +open import foundation.function-extensionality-axiom + +module + foundation.continuations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.empty-types +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext open import foundation.evaluation-functions -open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-arithmetic-dependent-function-types funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.equivalences @@ -23,7 +28,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.propositions -open import orthogonal-factorization-systems.extensions-maps +open import orthogonal-factorization-systems.extensions-maps funext ```
diff --git a/src/foundation/contractible-maps.lagda.md b/src/foundation/contractible-maps.lagda.md index 15c5bb6786..9a195dd4df 100644 --- a/src/foundation/contractible-maps.lagda.md +++ b/src/foundation/contractible-maps.lagda.md @@ -1,7 +1,12 @@ # Contractible maps ```agda -module foundation.contractible-maps where +open import foundation.function-extensionality-axiom + +module + foundation.contractible-maps + (funext : function-extensionality) + where open import foundation-core.contractible-maps public ``` @@ -10,9 +15,9 @@ open import foundation-core.contractible-maps public ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.logical-equivalences -open import foundation.truncated-maps +open import foundation.equivalences funext +open import foundation.logical-equivalences funext +open import foundation.truncated-maps funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/contractible-types.lagda.md b/src/foundation/contractible-types.lagda.md index 0a1a3f297f..e4c85c22fe 100644 --- a/src/foundation/contractible-types.lagda.md +++ b/src/foundation/contractible-types.lagda.md @@ -1,10 +1,15 @@ # Contractible types ```agda -module foundation.contractible-types where +open import foundation.function-extensionality-axiom + +module + foundation.contractible-types + (funext : function-extensionality) + where open import foundation-core.contractible-types public -open import foundation.dependent-products-contractible-types public +open import foundation.dependent-products-contractible-types funext public ```
Imports @@ -12,11 +17,11 @@ open import foundation.dependent-products-contractible-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.logical-equivalences -open import foundation.raising-universe-levels-unit-type -open import foundation.subuniverses +open import foundation.function-extensionality funext + +open import foundation.logical-equivalences funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.subuniverses funext open import foundation.unit-type open import foundation.universe-levels @@ -27,7 +32,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/copartial-elements.lagda.md b/src/foundation/copartial-elements.lagda.md index 857e423d5b..fa271b8e5b 100644 --- a/src/foundation/copartial-elements.lagda.md +++ b/src/foundation/copartial-elements.lagda.md @@ -1,23 +1,28 @@ # Copartial elements ```agda -module foundation.copartial-elements where +open import foundation.function-extensionality-axiom + +module + foundation.copartial-elements + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.negation +open import foundation.empty-types funext +open import foundation.negation funext open import foundation.partial-elements open import foundation.universe-levels open import foundation-core.propositions -open import orthogonal-factorization-systems.closed-modalities +open import orthogonal-factorization-systems.closed-modalities funext -open import synthetic-homotopy-theory.joins-of-types +open import synthetic-homotopy-theory.joins-of-types funext ```
diff --git a/src/foundation/copartial-functions.lagda.md b/src/foundation/copartial-functions.lagda.md index 6b5c611c47..02b2a87745 100644 --- a/src/foundation/copartial-functions.lagda.md +++ b/src/foundation/copartial-functions.lagda.md @@ -1,15 +1,20 @@ # Copartial functions ```agda -module foundation.copartial-functions where +open import foundation.function-extensionality-axiom + +module + foundation.copartial-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.copartial-elements +open import foundation.copartial-elements funext open import foundation.partial-functions -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/foundation/coproduct-decompositions-subuniverse.lagda.md b/src/foundation/coproduct-decompositions-subuniverse.lagda.md index 3d8495b9a1..4ab34bf7f3 100644 --- a/src/foundation/coproduct-decompositions-subuniverse.lagda.md +++ b/src/foundation/coproduct-decompositions-subuniverse.lagda.md @@ -1,26 +1,31 @@ # Coproduct decompositions in a subuniverse ```agda -module foundation.coproduct-decompositions-subuniverse where +open import foundation.function-extensionality-axiom + +module + foundation.coproduct-decompositions-subuniverse + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.functoriality-coproduct-types +open import foundation.empty-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.subuniverses +open import foundation.subuniverses funext open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type -open import foundation.univalence +open import foundation.type-arithmetic-empty-type funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/coproduct-decompositions.lagda.md b/src/foundation/coproduct-decompositions.lagda.md index 4f8dfd14be..bde65ad63b 100644 --- a/src/foundation/coproduct-decompositions.lagda.md +++ b/src/foundation/coproduct-decompositions.lagda.md @@ -1,26 +1,32 @@ # Coproduct decompositions ```agda -module foundation.coproduct-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.coproduct-decompositions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-decompositions-subuniverse +open import foundation.coproduct-decompositions-subuniverse funext open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.functoriality-coproduct-types +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-coproduct-types funext open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.transposition-identifications-along-equivalences -open import foundation.type-arithmetic-coproduct-types +open import foundation.transposition-identifications-along-equivalences funext +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -37,8 +43,8 @@ open import foundation-core.propositions open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/coproduct-types.lagda.md b/src/foundation/coproduct-types.lagda.md index aaadc73d63..3288cf7c32 100644 --- a/src/foundation/coproduct-types.lagda.md +++ b/src/foundation/coproduct-types.lagda.md @@ -1,7 +1,12 @@ # Coproduct types ```agda -module foundation.coproduct-types where +open import foundation.function-extensionality-axiom + +module + foundation.coproduct-types + (funext : function-extensionality) + where open import foundation-core.coproduct-types public ``` @@ -11,9 +16,9 @@ open import foundation-core.coproduct-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.negated-equality -open import foundation.noncontractible-types -open import foundation.subuniverses +open import foundation.negated-equality funext +open import foundation.noncontractible-types funext +open import foundation.subuniverses funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/coproducts-pullbacks.lagda.md b/src/foundation/coproducts-pullbacks.lagda.md index 780fecc445..a778c23153 100644 --- a/src/foundation/coproducts-pullbacks.lagda.md +++ b/src/foundation/coproducts-pullbacks.lagda.md @@ -1,20 +1,25 @@ # Coproducts of pullbacks ```agda -module foundation.coproducts-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.coproducts-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams -open import foundation.coproduct-types +open import foundation.cones-over-cospan-diagrams funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.standard-pullbacks +open import foundation.equality-coproduct-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -22,10 +27,10 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/coslice.lagda.md b/src/foundation/coslice.lagda.md index 20e4829866..ee7a4cb6f8 100644 --- a/src/foundation/coslice.lagda.md +++ b/src/foundation/coslice.lagda.md @@ -1,15 +1,21 @@ # Morphisms in the coslice category of types ```agda -module foundation.coslice where +open import foundation.function-extensionality-axiom + +module + foundation.coslice + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/decidable-dependent-function-types.lagda.md b/src/foundation/decidable-dependent-function-types.lagda.md index efc5cf4919..aaa68b26f1 100644 --- a/src/foundation/decidable-dependent-function-types.lagda.md +++ b/src/foundation/decidable-dependent-function-types.lagda.md @@ -1,17 +1,22 @@ # Decidability of dependent function types ```agda -module foundation.decidable-dependent-function-types where +open import foundation.function-extensionality-axiom + +module + foundation.decidable-dependent-function-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-types -open import foundation.functoriality-dependent-function-types -open import foundation.uniformly-decidable-type-families -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-maybe +open import foundation.decidable-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.uniformly-decidable-type-families funext +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-maybe funext open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/decidable-dependent-pair-types.lagda.md b/src/foundation/decidable-dependent-pair-types.lagda.md index eb012329f7..3d278073e9 100644 --- a/src/foundation/decidable-dependent-pair-types.lagda.md +++ b/src/foundation/decidable-dependent-pair-types.lagda.md @@ -1,17 +1,22 @@ # Decidability of dependent pair types ```agda -module foundation.decidable-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + foundation.decidable-dependent-pair-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-unit-type -open import foundation.uniformly-decidable-type-families +open import foundation.uniformly-decidable-type-families funext open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/decidable-embeddings.lagda.md b/src/foundation/decidable-embeddings.lagda.md index 3b869167e1..b7391dfb6b 100644 --- a/src/foundation/decidable-embeddings.lagda.md +++ b/src/foundation/decidable-embeddings.lagda.md @@ -1,34 +1,39 @@ # Decidable embeddings ```agda -module foundation.decidable-embeddings where +open import foundation.function-extensionality-axiom + +module + foundation.decidable-embeddings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.decidable-maps -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext +open import foundation.decidable-maps funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings -open import foundation.fibers-of-maps -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.retracts-of-maps +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.propositions funext +open import foundation.retracts-of-maps funext open import foundation.subtype-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/decidable-equality.lagda.md b/src/foundation/decidable-equality.lagda.md index dbd26b93ec..8b149f00c1 100644 --- a/src/foundation/decidable-equality.lagda.md +++ b/src/foundation/decidable-equality.lagda.md @@ -1,22 +1,27 @@ # Decidable equality ```agda -module foundation.decidable-equality where +open import foundation.function-extensionality-axiom + +module + foundation.decidable-equality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.double-negation -open import foundation.injective-maps -open import foundation.negation -open import foundation.sections -open import foundation.sets +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext +open import foundation.injective-maps funext +open import foundation.negation funext +open import foundation.sections funext +open import foundation.sets funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/decidable-equivalence-relations.lagda.md b/src/foundation/decidable-equivalence-relations.lagda.md index 935c973f50..3d21272b0a 100644 --- a/src/foundation/decidable-equivalence-relations.lagda.md +++ b/src/foundation/decidable-equivalence-relations.lagda.md @@ -1,37 +1,43 @@ # Decidable equivalence relations ```agda -module foundation.decidable-equivalence-relations where +open import foundation.function-extensionality-axiom + +module + foundation.decidable-equivalence-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-relations -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.decidable-equality funext +open import foundation.decidable-propositions funext +open import foundation.decidable-relations funext +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.effective-maps-equivalence-relations -open import foundation.equivalence-classes -open import foundation.equivalence-relations -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types +open import foundation.dependent-products-propositions funext +open import foundation.effective-maps-equivalence-relations funext +open import foundation.equivalence-classes funext +open import foundation.equivalence-relations funext +open import foundation.existential-quantification funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-cartesian-product-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.images -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.slice -open import foundation.surjective-maps +open import foundation.images funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.sets funext +open import foundation.slice funext +open import foundation.surjective-maps funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-image +open import foundation.universal-property-image funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -44,7 +50,7 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/decidable-maps.lagda.md b/src/foundation/decidable-maps.lagda.md index 926253c0dc..a82e5f1e8d 100644 --- a/src/foundation/decidable-maps.lagda.md +++ b/src/foundation/decidable-maps.lagda.md @@ -1,22 +1,27 @@ # Decidable maps ```agda -module foundation.decidable-maps where +open import foundation.function-extensionality-axiom + +module + foundation.decidable-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.retracts-of-maps +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.retracts-of-maps funext open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/decidable-propositions.lagda.md b/src/foundation/decidable-propositions.lagda.md index 5a6cc27816..00508f519d 100644 --- a/src/foundation/decidable-propositions.lagda.md +++ b/src/foundation/decidable-propositions.lagda.md @@ -1,29 +1,34 @@ # Decidable propositions ```agda -module foundation.decidable-propositions where +open import foundation.function-extensionality-axiom -open import foundation-core.decidable-propositions public +module + foundation.decidable-propositions + (funext : function-extensionality) + where + +open import foundation-core.decidable-propositions funext public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.booleans -open import foundation.decidable-types +open import foundation.booleans funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type -open import foundation.type-arithmetic-coproduct-types +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -35,12 +40,12 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.retracts-of-types open import foundation-core.sets -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext +open import foundation-core.subtypes funext open import foundation-core.transport-along-identifications -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/foundation/decidable-relations.lagda.md b/src/foundation/decidable-relations.lagda.md index 770d4b5f81..c2f9a06686 100644 --- a/src/foundation/decidable-relations.lagda.md +++ b/src/foundation/decidable-relations.lagda.md @@ -1,18 +1,23 @@ # Decidable relations on types ```agda -module foundation.decidable-relations where +open import foundation.function-extensionality-axiom + +module + foundation.decidable-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.propositions diff --git a/src/foundation/decidable-subtypes.lagda.md b/src/foundation/decidable-subtypes.lagda.md index 208d8f6862..052fd88784 100644 --- a/src/foundation/decidable-subtypes.lagda.md +++ b/src/foundation/decidable-subtypes.lagda.md @@ -1,30 +1,35 @@ # Decidable subtypes ```agda -module foundation.decidable-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.decidable-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.1-types -open import foundation.coproduct-types -open import foundation.decidable-embeddings -open import foundation.decidable-maps -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.1-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-embeddings funext +open import foundation.decidable-maps funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equality-dependent-function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.sets -open import foundation.structured-type-duality -open import foundation.subtypes -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.sets funext +open import foundation.structured-type-duality funext +open import foundation.subtypes funext +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation-core.embeddings @@ -38,7 +43,7 @@ open import foundation-core.transport-along-identifications open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import logic.double-negation-stable-subtypes +open import logic.double-negation-stable-subtypes funext ```
diff --git a/src/foundation/decidable-types.lagda.md b/src/foundation/decidable-types.lagda.md index 93bdd1707e..271bc9a714 100644 --- a/src/foundation/decidable-types.lagda.md +++ b/src/foundation/decidable-types.lagda.md @@ -1,25 +1,30 @@ # Decidable types ```agda -module foundation.decidable-types where +open import foundation.function-extensionality-axiom + +module + foundation.decidable-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.equivalences -open import foundation.hilberts-epsilon-operators -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.raising-universe-levels -open import foundation.retracts-of-types -open import foundation.type-arithmetic-empty-type +open import foundation.double-negation funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.hilberts-epsilon-operators funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.raising-universe-levels funext +open import foundation.retracts-of-types funext +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/dependent-binary-homotopies.lagda.md b/src/foundation/dependent-binary-homotopies.lagda.md index affccfbaf5..3ef4030306 100644 --- a/src/foundation/dependent-binary-homotopies.lagda.md +++ b/src/foundation/dependent-binary-homotopies.lagda.md @@ -1,13 +1,18 @@ # Dependent binary homotopies ```agda -module foundation.dependent-binary-homotopies where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-binary-homotopies + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-homotopies +open import foundation.binary-homotopies funext open import foundation.universe-levels open import foundation-core.dependent-identifications diff --git a/src/foundation/dependent-binomial-theorem.lagda.md b/src/foundation/dependent-binomial-theorem.lagda.md index d86a4ac378..23566c7ab9 100644 --- a/src/foundation/dependent-binomial-theorem.lagda.md +++ b/src/foundation/dependent-binomial-theorem.lagda.md @@ -1,23 +1,28 @@ # The dependent binomial theorem for types (distributivity of dependent function types over coproduct types) ```agda -module foundation.dependent-binomial-theorem where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-binomial-theorem + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-decompositions +open import foundation.contractible-types funext +open import foundation.coproduct-decompositions funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.raising-universe-levels +open import foundation.equality-dependent-pair-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.raising-universe-levels funext open import foundation.transport-along-identifications -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -29,8 +34,8 @@ open import foundation-core.homotopies open import foundation-core.type-theoretic-principle-of-choice open import foundation-core.univalence -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md b/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md index 7e107654bd..e2a1ac1b8a 100644 --- a/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md +++ b/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md @@ -1,13 +1,18 @@ # Dependent epimorphisms with respect to truncated types ```agda -module foundation.dependent-epimorphisms-with-respect-to-truncated-types where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-epimorphisms-with-respect-to-truncated-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.epimorphisms-with-respect-to-truncated-types +open import foundation.epimorphisms-with-respect-to-truncated-types funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/dependent-epimorphisms.lagda.md b/src/foundation/dependent-epimorphisms.lagda.md index d4da0dd5e6..5a16b30287 100644 --- a/src/foundation/dependent-epimorphisms.lagda.md +++ b/src/foundation/dependent-epimorphisms.lagda.md @@ -1,13 +1,18 @@ # Dependent epimorphisms ```agda -module foundation.dependent-epimorphisms where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-epimorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.epimorphisms +open import foundation.epimorphisms funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/dependent-function-types.lagda.md b/src/foundation/dependent-function-types.lagda.md index 9ac456c7c7..9d352331cb 100644 --- a/src/foundation/dependent-function-types.lagda.md +++ b/src/foundation/dependent-function-types.lagda.md @@ -1,7 +1,12 @@ # Dependent function types ```agda -module foundation.dependent-function-types where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-function-types + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module foundation.dependent-function-types where ```agda open import foundation.dependent-pair-types open import foundation.spans-families-of-types -open import foundation.terminal-spans-families-of-types -open import foundation.type-arithmetic-dependent-function-types -open import foundation.universal-property-dependent-function-types +open import foundation.terminal-spans-families-of-types funext +open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.universal-property-dependent-function-types funext open import foundation.universe-levels ``` diff --git a/src/foundation/dependent-identifications.lagda.md b/src/foundation/dependent-identifications.lagda.md index 4a1da7c967..b63e3a3dec 100644 --- a/src/foundation/dependent-identifications.lagda.md +++ b/src/foundation/dependent-identifications.lagda.md @@ -1,7 +1,12 @@ # Dependent identifications ```agda -module foundation.dependent-identifications where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-identifications + (funext : function-extensionality) + where open import foundation-core.dependent-identifications public ``` @@ -13,7 +18,7 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.strictly-right-unital-concatenation-identifications -open import foundation.transport-along-higher-identifications +open import foundation.transport-along-higher-identifications funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/dependent-inverse-sequential-diagrams.lagda.md b/src/foundation/dependent-inverse-sequential-diagrams.lagda.md index 7fa699aa8e..8d25d5d93f 100644 --- a/src/foundation/dependent-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/dependent-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Dependent inverse sequential diagrams of types ```agda -module foundation.dependent-inverse-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-inverse-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -10,9 +15,9 @@ module foundation.dependent-inverse-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.inverse-sequential-diagrams -open import foundation.iterating-families-of-maps -open import foundation.raising-universe-levels-unit-type +open import foundation.inverse-sequential-diagrams funext +open import foundation.iterating-families-of-maps funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/dependent-products-contractible-types.lagda.md b/src/foundation/dependent-products-contractible-types.lagda.md index 0cf967700c..c9ff67b98d 100644 --- a/src/foundation/dependent-products-contractible-types.lagda.md +++ b/src/foundation/dependent-products-contractible-types.lagda.md @@ -1,14 +1,20 @@ # Dependent products of contractible types ```agda -module foundation.dependent-products-contractible-types where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-products-contractible-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation/dependent-products-propositions.lagda.md b/src/foundation/dependent-products-propositions.lagda.md index 029f396e8a..2dd021fc2c 100644 --- a/src/foundation/dependent-products-propositions.lagda.md +++ b/src/foundation/dependent-products-propositions.lagda.md @@ -1,14 +1,19 @@ # Dependent products of propositions ```agda -module foundation.dependent-products-propositions where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-products-propositions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-contractible-types funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/dependent-products-pullbacks.lagda.md b/src/foundation/dependent-products-pullbacks.lagda.md index 63b84f2dce..2f3f39caf4 100644 --- a/src/foundation/dependent-products-pullbacks.lagda.md +++ b/src/foundation/dependent-products-pullbacks.lagda.md @@ -1,28 +1,33 @@ # Dependent products of pullbacks ```agda -module foundation.dependent-products-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-products-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.standard-pullbacks +open import foundation.function-extensionality funext + +open import foundation.functoriality-dependent-function-types funext +open import foundation.identity-types funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/dependent-products-truncated-types.lagda.md b/src/foundation/dependent-products-truncated-types.lagda.md index 52960698b7..f9218ed622 100644 --- a/src/foundation/dependent-products-truncated-types.lagda.md +++ b/src/foundation/dependent-products-truncated-types.lagda.md @@ -1,7 +1,12 @@ # Dependent products truncated types ```agda -module foundation.dependent-products-truncated-types where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-products-truncated-types + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module foundation.dependent-products-truncated-types where open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-contractible-types funext open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/dependent-sums-pullbacks.lagda.md b/src/foundation/dependent-sums-pullbacks.lagda.md index c1f09588ee..2ff36f966d 100644 --- a/src/foundation/dependent-sums-pullbacks.lagda.md +++ b/src/foundation/dependent-sums-pullbacks.lagda.md @@ -1,17 +1,22 @@ # Dependent sums of pullbacks ```agda -module foundation.dependent-sums-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-sums-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.standard-pullbacks +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.standard-pullbacks funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -21,10 +26,10 @@ open import foundation-core.families-of-equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/dependent-universal-property-equivalences.lagda.md b/src/foundation/dependent-universal-property-equivalences.lagda.md index e02bb797f2..83c2c5d4b8 100644 --- a/src/foundation/dependent-universal-property-equivalences.lagda.md +++ b/src/foundation/dependent-universal-property-equivalences.lagda.md @@ -1,7 +1,12 @@ # The dependent universal property of equivalences ```agda -module foundation.dependent-universal-property-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.dependent-universal-property-equivalences + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module foundation.dependent-universal-property-equivalences where open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation-core.coherently-invertible-maps diff --git a/src/foundation/descent-coproduct-types.lagda.md b/src/foundation/descent-coproduct-types.lagda.md index 03c1a582ba..22d2325ad3 100644 --- a/src/foundation/descent-coproduct-types.lagda.md +++ b/src/foundation/descent-coproduct-types.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.descent-coproduct-types where +open import foundation.function-extensionality-axiom + +module + foundation.descent-coproduct-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-fibers-of-maps +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-fibers-of-maps funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.coproduct-types open import foundation-core.equality-dependent-pair-types @@ -24,7 +29,7 @@ open import foundation-core.families-of-equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/descent-dependent-pair-types.lagda.md b/src/foundation/descent-dependent-pair-types.lagda.md index 9f3cdfc133..b58c862f09 100644 --- a/src/foundation/descent-dependent-pair-types.lagda.md +++ b/src/foundation/descent-dependent-pair-types.lagda.md @@ -1,15 +1,20 @@ # Descent for dependent pair types ```agda -module foundation.descent-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + foundation.descent-dependent-pair-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.functoriality-fibers-of-maps +open import foundation.functoriality-fibers-of-maps funext open import foundation.universe-levels open import foundation-core.equivalences @@ -17,7 +22,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/descent-empty-types.lagda.md b/src/foundation/descent-empty-types.lagda.md index ca408517a6..7a064fe359 100644 --- a/src/foundation/descent-empty-types.lagda.md +++ b/src/foundation/descent-empty-types.lagda.md @@ -1,18 +1,23 @@ # Descent for the empty type ```agda -module foundation.descent-empty-types where +open import foundation.function-extensionality-axiom + +module + foundation.descent-empty-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation-core.empty-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/descent-equivalences.lagda.md b/src/foundation/descent-equivalences.lagda.md index 2a2da46991..f9c13cd4cf 100644 --- a/src/foundation/descent-equivalences.lagda.md +++ b/src/foundation/descent-equivalences.lagda.md @@ -1,20 +1,25 @@ # Descent for equivalences ```agda -module foundation.descent-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.descent-equivalences + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams -open import foundation.dependent-universal-property-equivalences -open import foundation.equivalences -open import foundation.functoriality-fibers-of-maps +open import foundation.cones-over-cospan-diagrams funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.equivalences funext +open import foundation.functoriality-fibers-of-maps funext open import foundation.universe-levels open import foundation-core.function-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/diaconescus-theorem.lagda.md b/src/foundation/diaconescus-theorem.lagda.md index 246899fdd2..fb523d4f53 100644 --- a/src/foundation/diaconescus-theorem.lagda.md +++ b/src/foundation/diaconescus-theorem.lagda.md @@ -1,30 +1,35 @@ # Diaconescu's theorem ```agda -module foundation.diaconescus-theorem where +open import foundation.function-extensionality-axiom + +module + foundation.diaconescus-theorem + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.axiom-of-choice -open import foundation.booleans -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.axiom-of-choice funext +open import foundation.booleans funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.law-of-excluded-middle -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.law-of-excluded-middle funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.identity-types -open import synthetic-homotopy-theory.suspensions-of-propositions -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.suspensions-of-propositions funext +open import synthetic-homotopy-theory.suspensions-of-types funext ```
diff --git a/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md b/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md index 06fe26c051..11a321cc37 100644 --- a/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md +++ b/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md @@ -1,7 +1,12 @@ # Diagonal maps into cartesian products of types ```agda -module foundation.diagonal-maps-cartesian-products-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.diagonal-maps-cartesian-products-of-types + (funext : function-extensionality) + where open import foundation-core.diagonal-maps-cartesian-products-of-types public ``` @@ -9,12 +14,12 @@ open import foundation-core.diagonal-maps-cartesian-products-of-types public
Imports ```agda -open import foundation.0-maps +open import foundation.0-maps funext open import foundation.dependent-pair-types -open import foundation.faithful-maps +open import foundation.faithful-maps funext open import foundation.universe-levels -open import foundation-core.1-types +open import foundation-core.1-types funext open import foundation-core.cartesian-product-types open import foundation-core.contractible-maps open import foundation-core.embeddings @@ -23,7 +28,7 @@ open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/diagonal-maps-of-types.lagda.md b/src/foundation/diagonal-maps-of-types.lagda.md index ed122f9939..23f9628404 100644 --- a/src/foundation/diagonal-maps-of-types.lagda.md +++ b/src/foundation/diagonal-maps-of-types.lagda.md @@ -1,7 +1,12 @@ # Diagonal maps of types ```agda -module foundation.diagonal-maps-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.diagonal-maps-of-types + (funext : function-extensionality) + where open import foundation-core.diagonal-maps-of-types public ``` @@ -11,9 +16,9 @@ open import foundation-core.diagonal-maps-of-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.transposition-identifications-along-equivalences +open import foundation.function-extensionality funext + +open import foundation.transposition-identifications-along-equivalences funext open import foundation.universe-levels open import foundation-core.constant-maps diff --git a/src/foundation/diagonal-span-diagrams.lagda.md b/src/foundation/diagonal-span-diagrams.lagda.md index bde07d12e9..03a3c1798a 100644 --- a/src/foundation/diagonal-span-diagrams.lagda.md +++ b/src/foundation/diagonal-span-diagrams.lagda.md @@ -1,13 +1,18 @@ # Diagonal span diagrams ```agda -module foundation.diagonal-span-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.diagonal-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.span-diagrams +open import foundation.span-diagrams funext open import foundation.universe-levels ``` diff --git a/src/foundation/diagonals-of-maps.lagda.md b/src/foundation/diagonals-of-maps.lagda.md index a965e62bc4..cb5e519927 100644 --- a/src/foundation/diagonals-of-maps.lagda.md +++ b/src/foundation/diagonals-of-maps.lagda.md @@ -1,7 +1,12 @@ # Diagonals of maps ```agda -module foundation.diagonals-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.diagonals-of-maps + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module foundation.diagonals-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-fibers-of-maps -open import foundation.standard-pullbacks +open import foundation.equality-fibers-of-maps funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation-core.contractible-maps @@ -23,7 +28,7 @@ open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/discrete-binary-relations.lagda.md b/src/foundation/discrete-binary-relations.lagda.md index ef556b6912..3a98bf2009 100644 --- a/src/foundation/discrete-binary-relations.lagda.md +++ b/src/foundation/discrete-binary-relations.lagda.md @@ -1,16 +1,21 @@ # Discrete binary relations ```agda -module foundation.discrete-binary-relations where +open import foundation.function-extensionality-axiom + +module + foundation.discrete-binary-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.dependent-products-propositions -open import foundation.empty-types -open import foundation.propositions +open import foundation.binary-relations funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/foundation/discrete-reflexive-relations.lagda.md b/src/foundation/discrete-reflexive-relations.lagda.md index 2bb6edc906..8ee69b4d05 100644 --- a/src/foundation/discrete-reflexive-relations.lagda.md +++ b/src/foundation/discrete-reflexive-relations.lagda.md @@ -1,18 +1,23 @@ # Discrete reflexive relations ```agda -module foundation.discrete-reflexive-relations where +open import foundation.function-extensionality-axiom + +module + foundation.discrete-reflexive-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.contractible-types +open import foundation.binary-relations funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.reflexive-relations -open import foundation.torsorial-type-families +open import foundation.dependent-products-propositions funext +open import foundation.reflexive-relations funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md index 5c88106f31..0e50275ccc 100644 --- a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md @@ -1,19 +1,24 @@ # Discrete relaxed Σ-decompositions ```agda -module foundation.discrete-relaxed-sigma-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.discrete-relaxed-sigma-decompositions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalences -open import foundation.raising-universe-levels-unit-type -open import foundation.relaxed-sigma-decompositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.relaxed-sigma-decompositions funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -22,7 +27,7 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/discrete-sigma-decompositions.lagda.md b/src/foundation/discrete-sigma-decompositions.lagda.md index 4f46918e5b..cc16457309 100644 --- a/src/foundation/discrete-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-sigma-decompositions.lagda.md @@ -1,20 +1,25 @@ # Discrete Σ-decompositions ```agda -module foundation.discrete-sigma-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.discrete-sigma-decompositions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalences -open import foundation.propositional-truncations -open import foundation.raising-universe-levels-unit-type -open import foundation.sigma-decompositions +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.propositional-truncations funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sigma-decompositions funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -23,7 +28,7 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/discrete-types.lagda.md b/src/foundation/discrete-types.lagda.md index 9f52a992b4..8a13297a89 100644 --- a/src/foundation/discrete-types.lagda.md +++ b/src/foundation/discrete-types.lagda.md @@ -1,21 +1,26 @@ # Discrete types ```agda -module foundation.discrete-types where +open import foundation.function-extensionality-axiom -open import foundation-core.discrete-types public +module + foundation.discrete-types + (funext : function-extensionality) + where + +open import foundation-core.discrete-types funext public ```
Imports ```agda -open import foundation.apartness-relations -open import foundation.binary-relations -open import foundation.decidable-types +open import foundation.apartness-relations funext +open import foundation.binary-relations funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.tight-apartness-relations +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.tight-apartness-relations funext open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/disjoint-subtypes.lagda.md b/src/foundation/disjoint-subtypes.lagda.md index f336231418..55a3e036f0 100644 --- a/src/foundation/disjoint-subtypes.lagda.md +++ b/src/foundation/disjoint-subtypes.lagda.md @@ -1,18 +1,23 @@ # Disjoint subtypes ```agda -module foundation.disjoint-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.disjoint-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.empty-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/foundation/disjunction.lagda.md b/src/foundation/disjunction.lagda.md index 21a764be49..20f80a14c9 100644 --- a/src/foundation/disjunction.lagda.md +++ b/src/foundation/disjunction.lagda.md @@ -1,23 +1,28 @@ # Disjunction ```agda -module foundation.disjunction where +open import foundation.function-extensionality-axiom + +module + foundation.disjunction + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.functoriality-coproduct-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.functoriality-coproduct-types funext +open import foundation.inhabited-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.coproduct-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/double-negation-modality.lagda.md b/src/foundation/double-negation-modality.lagda.md index 89f91c3ee0..c999691859 100644 --- a/src/foundation/double-negation-modality.lagda.md +++ b/src/foundation/double-negation-modality.lagda.md @@ -1,32 +1,37 @@ # The double negation modality ```agda -module foundation.double-negation-modality where +open import foundation.function-extensionality-axiom + +module + foundation.double-negation-modality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositions +open import foundation.double-negation funext +open import foundation.empty-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.transport-along-identifications -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext -open import orthogonal-factorization-systems.continuation-modalities -open import orthogonal-factorization-systems.large-lawvere-tierney-topologies -open import orthogonal-factorization-systems.lawvere-tierney-topologies -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.continuation-modalities funext +open import orthogonal-factorization-systems.large-lawvere-tierney-topologies funext +open import orthogonal-factorization-systems.lawvere-tierney-topologies funext +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext ```
diff --git a/src/foundation/double-negation-stable-equality.lagda.md b/src/foundation/double-negation-stable-equality.lagda.md index 9dced91af2..bc68e52780 100644 --- a/src/foundation/double-negation-stable-equality.lagda.md +++ b/src/foundation/double-negation-stable-equality.lagda.md @@ -1,7 +1,12 @@ # Double negation stable equality ```agda -module foundation.double-negation-stable-equality where +open import foundation.function-extensionality-axiom + +module + foundation.double-negation-stable-equality + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,17 @@ module foundation.double-negation-stable-equality where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.double-negation +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.sets +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels @@ -31,7 +36,7 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.retracts-of-types -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext ```
diff --git a/src/foundation/double-negation-stable-propositions.lagda.md b/src/foundation/double-negation-stable-propositions.lagda.md index 8fb70bf27b..0ddb34a9ec 100644 --- a/src/foundation/double-negation-stable-propositions.lagda.md +++ b/src/foundation/double-negation-stable-propositions.lagda.md @@ -1,35 +1,40 @@ # Double negation stable propositions ```agda -module foundation.double-negation-stable-propositions where +open import foundation.function-extensionality-axiom + +module + foundation.double-negation-stable-propositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.disjunction -open import foundation.double-negation -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext +open import foundation.double-negation funext +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-quantification +open import foundation.universal-quantification funext open import foundation.universe-levels open import foundation-core.contractible-types @@ -37,7 +42,7 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.retracts-of-types -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext ```
diff --git a/src/foundation/double-negation.lagda.md b/src/foundation/double-negation.lagda.md index ee813f6384..0ce9fb6b50 100644 --- a/src/foundation/double-negation.lagda.md +++ b/src/foundation/double-negation.lagda.md @@ -1,14 +1,19 @@ # Double negation ```agda -module foundation.double-negation where +open import foundation.function-extensionality-axiom + +module + foundation.double-negation + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.negation -open import foundation.propositional-truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/double-powersets.lagda.md b/src/foundation/double-powersets.lagda.md index 19aabecf18..22cb3bb998 100644 --- a/src/foundation/double-powersets.lagda.md +++ b/src/foundation/double-powersets.lagda.md @@ -1,24 +1,29 @@ # Double powersets ```agda -module foundation.double-powersets where +open import foundation.function-extensionality-axiom + +module + foundation.double-powersets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.existential-quantification -open import foundation.powersets -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.existential-quantification funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import order-theory.large-posets -open import order-theory.posets +open import order-theory.large-posets funext +open import order-theory.posets funext ```
diff --git a/src/foundation/dubuc-penon-compact-types.lagda.md b/src/foundation/dubuc-penon-compact-types.lagda.md index 6f726c9481..6a275891fe 100644 --- a/src/foundation/dubuc-penon-compact-types.lagda.md +++ b/src/foundation/dubuc-penon-compact-types.lagda.md @@ -1,19 +1,24 @@ # Dubuc-Penon compact types ```agda -module foundation.dubuc-penon-compact-types where +open import foundation.function-extensionality-axiom + +module + foundation.dubuc-penon-compact-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.dependent-products-propositions -open import foundation.disjunction -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext +open import foundation.universal-quantification funext open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/effective-maps-equivalence-relations.lagda.md b/src/foundation/effective-maps-equivalence-relations.lagda.md index 2e7cb51d1b..1009cb4aec 100644 --- a/src/foundation/effective-maps-equivalence-relations.lagda.md +++ b/src/foundation/effective-maps-equivalence-relations.lagda.md @@ -1,17 +1,22 @@ # Effective maps for equivalence relations ```agda -module foundation.effective-maps-equivalence-relations where +open import foundation.function-extensionality-axiom + +module + foundation.effective-maps-equivalence-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.surjective-maps +open import foundation.surjective-maps funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.identity-types ``` diff --git a/src/foundation/embeddings.lagda.md b/src/foundation/embeddings.lagda.md index 16bc0c8d80..3f922fce8c 100644 --- a/src/foundation/embeddings.lagda.md +++ b/src/foundation/embeddings.lagda.md @@ -1,7 +1,12 @@ # Embeddings ```agda -module foundation.embeddings where +open import foundation.function-extensionality-axiom + +module + foundation.embeddings + (funext : function-extensionality) + where open import foundation-core.embeddings public ``` @@ -10,20 +15,20 @@ open import foundation-core.embeddings public ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications -open import foundation.truncated-maps +open import foundation.truncated-maps funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-types open import foundation-core.fibers-of-maps @@ -31,7 +36,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections open import foundation-core.torsorial-type-families diff --git a/src/foundation/empty-types.lagda.md b/src/foundation/empty-types.lagda.md index 28925f767f..912e1f9dc5 100644 --- a/src/foundation/empty-types.lagda.md +++ b/src/foundation/empty-types.lagda.md @@ -1,7 +1,12 @@ # Empty types ```agda -module foundation.empty-types where +open import foundation.function-extensionality-axiom + +module + foundation.empty-types + (funext : function-extensionality) + where open import foundation-core.empty-types public ``` @@ -10,13 +15,13 @@ open import foundation-core.empty-types public ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositional-truncations -open import foundation.raising-universe-levels -open import foundation.subuniverses -open import foundation.univalence +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositional-truncations funext +open import foundation.raising-universe-levels funext +open import foundation.subuniverses funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/endomorphisms.lagda.md b/src/foundation/endomorphisms.lagda.md index 178d2f3786..3d0fd48c5d 100644 --- a/src/foundation/endomorphisms.lagda.md +++ b/src/foundation/endomorphisms.lagda.md @@ -1,9 +1,14 @@ # Endomorphisms ```agda -module foundation.endomorphisms where +open import foundation.function-extensionality-axiom -open import foundation-core.endomorphisms public +module + foundation.endomorphisms + (funext : function-extensionality) + where + +open import foundation-core.endomorphisms funext public ```
Imports @@ -17,10 +22,10 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.sets -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext ```
diff --git a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md index 63bd907d28..a4fcda03d6 100644 --- a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md +++ b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md @@ -1,7 +1,12 @@ # Epimorphisms with respect to maps into sets ```agda -module foundation.epimorphisms-with-respect-to-sets where +open import foundation.function-extensionality-axiom + +module + foundation.epimorphisms-with-respect-to-sets + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module foundation.epimorphisms-with-respect-to-sets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.raising-universe-levels-unit-type -open import foundation.sets -open import foundation.surjective-maps +open import foundation.existential-quantification funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sets funext +open import foundation.surjective-maps funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md b/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md index 3a0d69c835..7cce27197b 100644 --- a/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md +++ b/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md @@ -1,24 +1,30 @@ # Epimorphisms with respect to truncated types ```agda -module foundation.epimorphisms-with-respect-to-truncated-types where +open import foundation.function-extensionality-axiom + +module + foundation.epimorphisms-with-respect-to-truncated-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.connected-maps +open import foundation.commuting-squares-of-maps funext +open import foundation.connected-maps funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings -open import foundation.function-extensionality -open import foundation.functoriality-truncation -open import foundation.precomposition-functions -open import foundation.sections -open import foundation.truncation-equivalences -open import foundation.truncations +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-truncation funext +open import foundation.precomposition-functions funext +open import foundation.sections funext +open import foundation.truncation-equivalences funext +open import foundation.truncations funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -32,9 +38,9 @@ open import foundation-core.propositions open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.codiagonals-of-maps -open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.codiagonals-of-maps funext +open import synthetic-homotopy-theory.pushouts funext ```
diff --git a/src/foundation/epimorphisms.lagda.md b/src/foundation/epimorphisms.lagda.md index b7c5bb9ab4..99e108b528 100644 --- a/src/foundation/epimorphisms.lagda.md +++ b/src/foundation/epimorphisms.lagda.md @@ -1,19 +1,24 @@ # Epimorphisms ```agda -module foundation.epimorphisms where +open import foundation.function-extensionality-axiom + +module + foundation.epimorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.precomposition-functions -open import foundation.sections +open import foundation.embeddings funext +open import foundation.precomposition-functions funext +open import foundation.sections funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types @@ -21,10 +26,10 @@ open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.propositions -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.codiagonals-of-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.codiagonals-of-maps funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/foundation/equality-coproduct-types.lagda.md b/src/foundation/equality-coproduct-types.lagda.md index 83776f0ce3..e84197717d 100644 --- a/src/foundation/equality-coproduct-types.lagda.md +++ b/src/foundation/equality-coproduct-types.lagda.md @@ -1,17 +1,22 @@ # Equality of coproduct types ```agda -module foundation.equality-coproduct-types where +open import foundation.function-extensionality-axiom + +module + foundation.equality-coproduct-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.negated-equality +open import foundation.negated-equality funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/equality-dependent-function-types.lagda.md b/src/foundation/equality-dependent-function-types.lagda.md index 2512259ea6..b15ea08237 100644 --- a/src/foundation/equality-dependent-function-types.lagda.md +++ b/src/foundation/equality-dependent-function-types.lagda.md @@ -1,14 +1,19 @@ # Equality on dependent function types ```agda -module foundation.equality-dependent-function-types where +open import foundation.function-extensionality-axiom + +module + foundation.equality-dependent-function-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-contractible-types funext open import foundation.fundamental-theorem-of-identity-types open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation/equality-dependent-pair-types.lagda.md b/src/foundation/equality-dependent-pair-types.lagda.md index 6ab7a7bbb3..b406c87294 100644 --- a/src/foundation/equality-dependent-pair-types.lagda.md +++ b/src/foundation/equality-dependent-pair-types.lagda.md @@ -1,7 +1,12 @@ # Equality of dependent pair types ```agda -module foundation.equality-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + foundation.equality-dependent-pair-types + (funext : function-extensionality) + where open import foundation-core.equality-dependent-pair-types public ``` @@ -11,7 +16,7 @@ open import foundation-core.equality-dependent-pair-types public ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.dependent-identifications +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/equality-fibers-of-maps.lagda.md b/src/foundation/equality-fibers-of-maps.lagda.md index e5fa8e6684..2e37f3cce3 100644 --- a/src/foundation/equality-fibers-of-maps.lagda.md +++ b/src/foundation/equality-fibers-of-maps.lagda.md @@ -1,7 +1,12 @@ # Equality in the fibers of a map ```agda -module foundation.equality-fibers-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.equality-fibers-of-maps + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module foundation.equality-fibers-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/equivalence-classes.lagda.md b/src/foundation/equivalence-classes.lagda.md index 71954bae57..433573a5fb 100644 --- a/src/foundation/equivalence-classes.lagda.md +++ b/src/foundation/equivalence-classes.lagda.md @@ -1,34 +1,39 @@ # Equivalence classes ```agda -module foundation.equivalence-classes where +open import foundation.function-extensionality-axiom + +module + foundation.equivalence-classes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.existential-quantification -open import foundation.functoriality-propositional-truncation +open import foundation.effective-maps-equivalence-relations funext +open import foundation.existential-quantification funext +open import foundation.functoriality-propositional-truncation funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-subtypes -open import foundation.locally-small-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.slice -open import foundation.small-types +open import foundation.inhabited-subtypes funext +open import foundation.locally-small-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.slice funext +open import foundation.small-types funext open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.surjective-maps -open import foundation.universal-property-image +open import foundation.subtypes funext +open import foundation.surjective-maps funext +open import foundation.universal-property-image funext open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types diff --git a/src/foundation/equivalence-extensionality.lagda.md b/src/foundation/equivalence-extensionality.lagda.md index 6facfb0297..20d32a6cd6 100644 --- a/src/foundation/equivalence-extensionality.lagda.md +++ b/src/foundation/equivalence-extensionality.lagda.md @@ -1,17 +1,22 @@ # Equivalence extensionality ```agda -module foundation.equivalence-extensionality where +open import foundation.function-extensionality-axiom + +module + foundation.equivalence-extensionality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.dependent-universal-property-equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-systems open import foundation.subtype-identity-principle diff --git a/src/foundation/equivalence-induction.lagda.md b/src/foundation/equivalence-induction.lagda.md index a4b437a51f..86e320e314 100644 --- a/src/foundation/equivalence-induction.lagda.md +++ b/src/foundation/equivalence-induction.lagda.md @@ -1,7 +1,12 @@ # Equivalence induction ```agda -module foundation.equivalence-induction where +open import foundation.function-extensionality-axiom + +module + foundation.equivalence-induction + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module foundation.equivalence-induction where ```agda open import foundation.dependent-pair-types open import foundation.identity-systems -open import foundation.subuniverses -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.subuniverses funext +open import foundation.univalence funext +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/equivalence-injective-type-families.lagda.md b/src/foundation/equivalence-injective-type-families.lagda.md index f204fe7573..e912a64a09 100644 --- a/src/foundation/equivalence-injective-type-families.lagda.md +++ b/src/foundation/equivalence-injective-type-families.lagda.md @@ -1,19 +1,24 @@ # Equivalence injective type families ```agda -module foundation.equivalence-injective-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.equivalence-injective-type-families + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.functoriality-dependent-function-types -open import foundation.iterated-dependent-product-types +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.iterated-dependent-product-types funext open import foundation.telescopes -open import foundation.univalence -open import foundation.universal-property-equivalences +open import foundation.univalence funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/equivalence-relations.lagda.md b/src/foundation/equivalence-relations.lagda.md index 931f0e8264..5c00940f7a 100644 --- a/src/foundation/equivalence-relations.lagda.md +++ b/src/foundation/equivalence-relations.lagda.md @@ -1,27 +1,32 @@ # Equivalence relations ```agda -module foundation.equivalence-relations where +open import foundation.function-extensionality-axiom -open import foundation-core.equivalence-relations public +module + foundation.equivalence-relations + (funext : function-extensionality) + where + +open import foundation-core.equivalence-relations funext public ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.fundamental-theorem-of-equivalence-relations -open import foundation.logical-equivalences -open import foundation.partitions -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sigma-decompositions -open import foundation.surjective-maps -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-set-quotients +open import foundation.effective-maps-equivalence-relations funext +open import foundation.fundamental-theorem-of-equivalence-relations funext +open import foundation.logical-equivalences funext +open import foundation.partitions funext +open import foundation.propositional-truncations funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.set-quotients funext +open import foundation.sigma-decompositions funext +open import foundation.surjective-maps funext +open import foundation.uniqueness-set-quotients funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/equivalences-arrows.lagda.md b/src/foundation/equivalences-arrows.lagda.md index 23e82b5948..361657f6f4 100644 --- a/src/foundation/equivalences-arrows.lagda.md +++ b/src/foundation/equivalences-arrows.lagda.md @@ -1,22 +1,27 @@ # Equivalences of arrows ```agda -module foundation.equivalences-arrows where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-morphisms-arrows funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.morphisms-arrows -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.sections -open import foundation.span-diagrams +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext +open import foundation.sections funext +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/equivalences-cospans.lagda.md b/src/foundation/equivalences-cospans.lagda.md index a44b7e3b11..f610c32814 100644 --- a/src/foundation/equivalences-cospans.lagda.md +++ b/src/foundation/equivalences-cospans.lagda.md @@ -1,7 +1,12 @@ # Equivalences of cospans ```agda -module foundation.equivalences-cospans where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences-cospans + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module foundation.equivalences-cospans where open import foundation.cospans open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.morphisms-cospans open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/equivalences-double-arrows.lagda.md b/src/foundation/equivalences-double-arrows.lagda.md index 54c7f508e0..d7c92dc09a 100644 --- a/src/foundation/equivalences-double-arrows.lagda.md +++ b/src/foundation/equivalences-double-arrows.lagda.md @@ -1,20 +1,25 @@ # Equivalences of double arrows ```agda -module foundation.equivalences-double-arrows where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences-double-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-product-types funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.homotopies -open import foundation.morphisms-double-arrows +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.homotopies funext +open import foundation.morphisms-double-arrows funext open import foundation.universe-levels ``` diff --git a/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md b/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md index 3653847a20..98c403b9fa 100644 --- a/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Equivalences of inverse sequential diagrams of types ```agda -module foundation.equivalences-inverse-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences-inverse-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module foundation.equivalences-inverse-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies +open import foundation.binary-homotopies funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.inverse-sequential-diagrams -open import foundation.morphisms-inverse-sequential-diagrams +open import foundation.homotopy-induction funext +open import foundation.inverse-sequential-diagrams funext +open import foundation.morphisms-inverse-sequential-diagrams funext open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/equivalences-maybe.lagda.md b/src/foundation/equivalences-maybe.lagda.md index c656a2d528..1fc49d9bf1 100644 --- a/src/foundation/equivalences-maybe.lagda.md +++ b/src/foundation/equivalences-maybe.lagda.md @@ -1,7 +1,12 @@ # Equivalences on `Maybe` ```agda -module foundation.equivalences-maybe where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences-maybe + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module foundation.equivalences-maybe where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.maybe +open import foundation.equality-coproduct-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext +open import foundation.maybe funext open import foundation.unit-type -open import foundation.universal-property-maybe +open import foundation.universal-property-maybe funext open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md b/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md index 05c24bbdad..deb5820177 100644 --- a/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md +++ b/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md @@ -1,17 +1,22 @@ # Equivalences of span diagrams on families of types ```agda -module foundation.equivalences-span-diagrams-families-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences-span-diagrams-families-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-spans-families-of-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.equivalences funext-spans-families-of-types +open import foundation.homotopies funext open import foundation.operations-spans-families-of-types open import foundation.span-diagrams-families-of-types open import foundation.universe-levels diff --git a/src/foundation/equivalences-span-diagrams.lagda.md b/src/foundation/equivalences-span-diagrams.lagda.md index 92238d6cff..2065e280a5 100644 --- a/src/foundation/equivalences-span-diagrams.lagda.md +++ b/src/foundation/equivalences-span-diagrams.lagda.md @@ -1,29 +1,34 @@ # Equivalences of span diagrams ```agda -module foundation.equivalences-span-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-spans +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.equivalences-spans funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.morphisms-span-diagrams +open import foundation.morphisms-span-diagrams funext open import foundation.morphisms-spans -open import foundation.operations-spans -open import foundation.propositions -open import foundation.span-diagrams +open import foundation.operations-spans funext +open import foundation.propositions funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.torsorial-type-families diff --git a/src/foundation/equivalences-spans-families-of-types.lagda.md b/src/foundation/equivalences-spans-families-of-types.lagda.md index f76bbf5f10..3be364137a 100644 --- a/src/foundation/equivalences-spans-families-of-types.lagda.md +++ b/src/foundation/equivalences-spans-families-of-types.lagda.md @@ -1,22 +1,27 @@ # Equivalences of spans of families of types ```agda -module foundation.equivalences-spans-families-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences-spans-families-of-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.morphisms-spans-families-of-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.morphisms-spans-families-of-types funext open import foundation.spans-families-of-types open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/equivalences-spans.lagda.md b/src/foundation/equivalences-spans.lagda.md index 4e804c318a..f438a7fc5d 100644 --- a/src/foundation/equivalences-spans.lagda.md +++ b/src/foundation/equivalences-spans.lagda.md @@ -1,23 +1,28 @@ # Equivalences of spans ```agda -module foundation.equivalences-spans where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences-spans + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-product-types funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.morphisms-spans open import foundation.spans open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -25,7 +30,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.operations-spans +open import foundation-core.operations-spans funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/equivalences.lagda.md b/src/foundation/equivalences.lagda.md index c7c26fb5c4..b83a093f11 100644 --- a/src/foundation/equivalences.lagda.md +++ b/src/foundation/equivalences.lagda.md @@ -1,7 +1,12 @@ # Equivalences ```agda -module foundation.equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.equivalences + (funext : function-extensionality) + where open import foundation-core.equivalences public ``` @@ -10,17 +15,18 @@ open import foundation-core.equivalences public ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.functoriality-fibers-of-maps -open import foundation.logical-equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-fibers-of-maps funext +open import foundation.logical-equivalences funext open import foundation.transport-along-identifications -open import foundation.transposition-identifications-along-equivalences -open import foundation.truncated-maps -open import foundation.universal-property-equivalences +open import foundation.transposition-identifications-along-equivalences funext +open import foundation.truncated-maps funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -34,11 +40,11 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositions -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.retracts-of-types open import foundation-core.sections -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.truncation-levels open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/exclusive-disjunction.lagda.md b/src/foundation/exclusive-disjunction.lagda.md index 5d95f4c232..4cfd139d2c 100644 --- a/src/foundation/exclusive-disjunction.lagda.md +++ b/src/foundation/exclusive-disjunction.lagda.md @@ -1,28 +1,33 @@ # Exclusive disjunctions ```agda -module foundation.exclusive-disjunction where +open import foundation.function-extensionality-axiom + +module + foundation.exclusive-disjunction + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.equality-coproduct-types -open import foundation.exclusive-sum -open import foundation.functoriality-coproduct-types -open import foundation.propositional-truncations +open import foundation.dependent-products-contractible-types funext +open import foundation.equality-coproduct-types funext +open import foundation.exclusive-sum funext +open import foundation.functoriality-coproduct-types funext +open import foundation.propositional-truncations funext open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types -open import foundation.universal-property-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.embeddings open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions diff --git a/src/foundation/exclusive-sum.lagda.md b/src/foundation/exclusive-sum.lagda.md index d18bfe341a..8afa84bfe8 100644 --- a/src/foundation/exclusive-sum.lagda.md +++ b/src/foundation/exclusive-sum.lagda.md @@ -1,35 +1,40 @@ # Exclusive sums ```agda -module foundation.exclusive-sum where +open import foundation.function-extensionality-axiom + +module + foundation.exclusive-sum + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.conjunction funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.symmetric-operations +open import foundation.dependent-products-propositions funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext +open import foundation.symmetric-operations funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext open import foundation-core.cartesian-product-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.empty-types open import foundation-core.equality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.transport-along-identifications -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/existential-quantification.lagda.md b/src/foundation/existential-quantification.lagda.md index 1cb3523d44..e071eb51f5 100644 --- a/src/foundation/existential-quantification.lagda.md +++ b/src/foundation/existential-quantification.lagda.md @@ -1,18 +1,23 @@ # Existential quantification ```agda -module foundation.existential-quantification where +open import foundation.function-extensionality-axiom + +module + foundation.existential-quantification + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.logical-equivalences -open import foundation.propositional-extensionality -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/exponents-set-quotients.lagda.md b/src/foundation/exponents-set-quotients.lagda.md index 7002792799..82555ca69d 100644 --- a/src/foundation/exponents-set-quotients.lagda.md +++ b/src/foundation/exponents-set-quotients.lagda.md @@ -3,29 +3,34 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.exponents-set-quotients where +open import foundation.function-extensionality-axiom + +module + foundation.exponents-set-quotients + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.functoriality-set-quotients -open import foundation.postcomposition-functions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets -open import foundation.universal-property-set-quotients +open import foundation.dependent-products-propositions funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-set-quotients funext +open import foundation.postcomposition-functions funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.set-quotients funext +open import foundation.sets funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.contractible-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/extensions-types-global-subuniverses.lagda.md b/src/foundation/extensions-types-global-subuniverses.lagda.md index a75184e2aa..1b38266da0 100644 --- a/src/foundation/extensions-types-global-subuniverses.lagda.md +++ b/src/foundation/extensions-types-global-subuniverses.lagda.md @@ -1,32 +1,37 @@ # Extensions of types in a global subuniverse ```agda -module foundation.extensions-types-global-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.extensions-types-global-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.extensions-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.extensions-types funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels ``` diff --git a/src/foundation/extensions-types-subuniverses.lagda.md b/src/foundation/extensions-types-subuniverses.lagda.md index b76a1afee1..95f0b01400 100644 --- a/src/foundation/extensions-types-subuniverses.lagda.md +++ b/src/foundation/extensions-types-subuniverses.lagda.md @@ -1,34 +1,39 @@ # Extensions of types in a subuniverse ```agda -module foundation.extensions-types-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.extensions-types-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.extensions-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.extensions-types funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositions +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositions funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.subuniverses -open import foundation.torsorial-type-families +open import foundation.subuniverses funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels ``` diff --git a/src/foundation/extensions-types.lagda.md b/src/foundation/extensions-types.lagda.md index 7d78a32bdd..c3d388f6f7 100644 --- a/src/foundation/extensions-types.lagda.md +++ b/src/foundation/extensions-types.lagda.md @@ -1,22 +1,27 @@ # Extensions of types ```agda -module foundation.extensions-types where +open import foundation.function-extensionality-axiom + +module + foundation.extensions-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels ``` diff --git a/src/foundation/faithful-maps.lagda.md b/src/foundation/faithful-maps.lagda.md index 0e523f08b3..fccd1c7f7b 100644 --- a/src/foundation/faithful-maps.lagda.md +++ b/src/foundation/faithful-maps.lagda.md @@ -1,13 +1,18 @@ # Faithful maps ```agda -module foundation.faithful-maps where +open import foundation.function-extensionality-axiom + +module + foundation.faithful-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-maps +open import foundation.0-maps funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.universe-levels @@ -20,7 +25,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels ``` diff --git a/src/foundation/families-of-equivalences.lagda.md b/src/foundation/families-of-equivalences.lagda.md index 172bf565b9..fc844cbec0 100644 --- a/src/foundation/families-of-equivalences.lagda.md +++ b/src/foundation/families-of-equivalences.lagda.md @@ -1,7 +1,12 @@ # Families of equivalences ```agda -module foundation.families-of-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.families-of-equivalences + (funext : function-extensionality) + where open import foundation-core.families-of-equivalences public ``` @@ -9,8 +14,8 @@ open import foundation-core.families-of-equivalences public
Imports ```agda -open import foundation.dependent-products-propositions -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/families-of-maps.lagda.md b/src/foundation/families-of-maps.lagda.md index ffcfb2087d..bbde2001ba 100644 --- a/src/foundation/families-of-maps.lagda.md +++ b/src/foundation/families-of-maps.lagda.md @@ -1,28 +1,33 @@ # Families of maps ```agda -module foundation.families-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.families-of-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.families-of-equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/families-over-telescopes.lagda.md b/src/foundation/families-over-telescopes.lagda.md index a6a2844f56..9d9bc64b5d 100644 --- a/src/foundation/families-over-telescopes.lagda.md +++ b/src/foundation/families-over-telescopes.lagda.md @@ -1,7 +1,12 @@ # Families of types over telescopes ```agda -module foundation.families-over-telescopes where +open import foundation.function-extensionality-axiom + +module + foundation.families-over-telescopes + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module foundation.families-over-telescopes where ```agda open import elementary-number-theory.natural-numbers -open import foundation.raising-universe-levels +open import foundation.raising-universe-levels funext open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/foundation/fiber-inclusions.lagda.md b/src/foundation/fiber-inclusions.lagda.md index ca0e8f0ac8..c74d7e0935 100644 --- a/src/foundation/fiber-inclusions.lagda.md +++ b/src/foundation/fiber-inclusions.lagda.md @@ -1,25 +1,30 @@ # Fiber inclusions ```agda -module foundation.fiber-inclusions where +open import foundation.function-extensionality-axiom + +module + foundation.fiber-inclusions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-maps -open import foundation.cones-over-cospan-diagrams +open import foundation.0-maps funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.faithful-maps -open import foundation.fibers-of-maps -open import foundation.raising-universe-levels-unit-type -open import foundation.standard-pullbacks +open import foundation.faithful-maps funext +open import foundation.fibers-of-maps funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.standard-pullbacks funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.1-types +open import foundation-core.1-types funext open import foundation-core.contractible-maps open import foundation-core.embeddings open import foundation-core.equality-dependent-pair-types @@ -29,9 +34,9 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.sets -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/fibered-equivalences.lagda.md b/src/foundation/fibered-equivalences.lagda.md index 3d899df149..f9ef0504c4 100644 --- a/src/foundation/fibered-equivalences.lagda.md +++ b/src/foundation/fibered-equivalences.lagda.md @@ -1,19 +1,24 @@ # Fibered equivalences ```agda -module foundation.fibered-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.fibered-equivalences + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.fibered-maps -open import foundation.logical-equivalences -open import foundation.pullbacks -open import foundation.slice +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.fibered-maps funext +open import foundation.logical-equivalences funext +open import foundation.pullbacks funext +open import foundation.slice funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -23,7 +28,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/fibered-involutions.lagda.md b/src/foundation/fibered-involutions.lagda.md index e00fab4ca6..64e0d7a945 100644 --- a/src/foundation/fibered-involutions.lagda.md +++ b/src/foundation/fibered-involutions.lagda.md @@ -1,15 +1,20 @@ # Fibered involutions ```agda -module foundation.fibered-involutions where +open import foundation.function-extensionality-axiom + +module + foundation.fibered-involutions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibered-maps -open import foundation.involutions +open import foundation.fibered-maps funext +open import foundation.involutions funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/fibered-maps.lagda.md b/src/foundation/fibered-maps.lagda.md index 1ba4249488..39ca646d98 100644 --- a/src/foundation/fibered-maps.lagda.md +++ b/src/foundation/fibered-maps.lagda.md @@ -1,28 +1,34 @@ # Maps fibered over a map ```agda -module foundation.fibered-maps where +open import foundation.function-extensionality-axiom + +module + foundation.fibered-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.dependent-products-truncated-types -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.slice +open import foundation.homotopy-induction funext +open import foundation.slice funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-empty-type +open import foundation.universal-property-empty-type funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.empty-types open import foundation-core.equality-dependent-pair-types @@ -31,7 +37,7 @@ open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.small-types +open import foundation-core.small-types funext open import foundation-core.torsorial-type-families open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/fibers-of-maps.lagda.md b/src/foundation/fibers-of-maps.lagda.md index 01e4a3f77b..6e323a2ee8 100644 --- a/src/foundation/fibers-of-maps.lagda.md +++ b/src/foundation/fibers-of-maps.lagda.md @@ -1,7 +1,12 @@ # Fibers of maps ```agda -module foundation.fibers-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.fibers-of-maps + (funext : function-extensionality) + where open import foundation-core.fibers-of-maps public ``` @@ -10,9 +15,9 @@ open import foundation-core.fibers-of-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.postcomposition-functions +open import foundation.postcomposition-functions funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type @@ -21,13 +26,13 @@ open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.transport-along-identifications -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/finitely-coherent-equivalences.lagda.md b/src/foundation/finitely-coherent-equivalences.lagda.md index ad8dcd5167..46db3d5430 100644 --- a/src/foundation/finitely-coherent-equivalences.lagda.md +++ b/src/foundation/finitely-coherent-equivalences.lagda.md @@ -1,7 +1,12 @@ # Finitely coherent equivalences ```agda -module foundation.finitely-coherent-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.finitely-coherent-equivalences + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module foundation.finitely-coherent-equivalences where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/finitely-coherently-invertible-maps.lagda.md b/src/foundation/finitely-coherently-invertible-maps.lagda.md index a48d827c1e..20c7e997e2 100644 --- a/src/foundation/finitely-coherently-invertible-maps.lagda.md +++ b/src/foundation/finitely-coherently-invertible-maps.lagda.md @@ -1,7 +1,12 @@ # Finitely coherently invertible maps ```agda -module foundation.finitely-coherently-invertible-maps where +open import foundation.function-extensionality-axiom + +module + foundation.finitely-coherently-invertible-maps + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module foundation.finitely-coherently-invertible-maps where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/full-subtypes.lagda.md b/src/foundation/full-subtypes.lagda.md index c2cb38a34f..c94db60b15 100644 --- a/src/foundation/full-subtypes.lagda.md +++ b/src/foundation/full-subtypes.lagda.md @@ -1,23 +1,28 @@ # Full subtypes of types ```agda -module foundation.full-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.full-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-subtypes +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.raising-universe-levels-unit-type +open import foundation.dependent-products-propositions funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/function-extensionality.lagda.md b/src/foundation/function-extensionality.lagda.md index d26c3c48c8..b6ca9801f6 100644 --- a/src/foundation/function-extensionality.lagda.md +++ b/src/foundation/function-extensionality.lagda.md @@ -3,7 +3,10 @@ ```agda open import foundation.function-extensionality-axiom -module foundation.function-extensionality where +module + foundation.function-extensionality + (funext : function-extensionality) + where ```
Imports @@ -12,6 +15,7 @@ module foundation.function-extensionality where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.evaluation-functions open import foundation.implicit-function-types open import foundation.universe-levels @@ -78,23 +82,23 @@ module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} where - postulate - eq-htpy : f ~ g → f ＝ g + eq-htpy : f ~ g → f ＝ g + eq-htpy = map-inv-is-equiv (funext f g) + opaque is-section-eq-htpy : is-section htpy-eq eq-htpy + is-section-eq-htpy = is-section-map-inv-is-equiv (funext f g) - is-retraction-eq-htpy' : is-retraction htpy-eq eq-htpy + is-retraction-eq-htpy : is-retraction htpy-eq eq-htpy + is-retraction-eq-htpy = is-retraction-map-inv-is-equiv (funext f g) - coh-eq-htpy' : + coh-eq-htpy : coherence-is-coherently-invertible ( htpy-eq) ( eq-htpy) ( is-section-eq-htpy) - ( is-retraction-eq-htpy') - -funext : function-extensionality -funext f g = - is-equiv-is-invertible eq-htpy is-section-eq-htpy is-retraction-eq-htpy' + ( is-retraction-eq-htpy) + coh-eq-htpy = coherence-map-inv-is-equiv (funext f g) module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} @@ -107,12 +111,7 @@ module _ is-equiv-eq-htpy : (f g : (x : A) → B x) → is-equiv (eq-htpy {f = f} {g}) is-equiv-eq-htpy f g = - is-equiv-is-invertible htpy-eq is-retraction-eq-htpy' is-section-eq-htpy - - abstract - is-retraction-eq-htpy : - {f g : (x : A) → B x} → is-retraction (htpy-eq {f = f} {g}) eq-htpy - is-retraction-eq-htpy {f} {g} = is-retraction-map-inv-is-equiv (funext f g) + is-equiv-is-invertible htpy-eq is-retraction-eq-htpy is-section-eq-htpy eq-htpy-refl-htpy : (f : (x : A) → B x) → eq-htpy (refl-htpy {f = f}) ＝ refl diff --git a/src/foundation/function-types.lagda.md b/src/foundation/function-types.lagda.md index d6fb4ed16f..09d8ad6fb7 100644 --- a/src/foundation/function-types.lagda.md +++ b/src/foundation/function-types.lagda.md @@ -1,7 +1,12 @@ # Function types ```agda -module foundation.function-types where +open import foundation.function-extensionality-axiom + +module + foundation.function-types + (funext : function-extensionality) + where open import foundation-core.function-types public ``` @@ -13,8 +18,9 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.commuting-pentagons-of-identifications open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopy-induction +open import foundation.function-extensionality funext + +open import foundation.homotopy-induction funext open import foundation.universe-levels open import foundation-core.dependent-identifications diff --git a/src/foundation/functional-correspondences.lagda.md b/src/foundation/functional-correspondences.lagda.md index d2a98ae2fe..2da6d47e8b 100644 --- a/src/foundation/functional-correspondences.lagda.md +++ b/src/foundation/functional-correspondences.lagda.md @@ -1,28 +1,34 @@ # Functional correspondences ```agda -module foundation.functional-correspondences where +open import foundation.function-extensionality-axiom + +module + foundation.functional-correspondences + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equality-dependent-function-types -open import foundation.function-extensionality +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/functoriality-action-on-identifications-functions.lagda.md b/src/foundation/functoriality-action-on-identifications-functions.lagda.md index 987e964955..202eea9a8c 100644 --- a/src/foundation/functoriality-action-on-identifications-functions.lagda.md +++ b/src/foundation/functoriality-action-on-identifications-functions.lagda.md @@ -1,26 +1,31 @@ # Functoriality of the action on identifications of functions ```agda -module foundation.functoriality-action-on-identifications-functions where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-action-on-identifications-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-morphisms-arrows -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-triangles-of-morphisms-arrows funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.homotopies-morphisms-arrows -open import foundation.morphisms-arrows -open import foundation.path-algebra +open import foundation.homotopies-morphisms-arrows funext +open import foundation.morphisms-arrows funext +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equality-dependent-pair-types open import foundation-core.fibers-of-maps open import foundation-core.function-types diff --git a/src/foundation/functoriality-cartesian-product-types.lagda.md b/src/foundation/functoriality-cartesian-product-types.lagda.md index 08be06910b..393e2fd3c2 100644 --- a/src/foundation/functoriality-cartesian-product-types.lagda.md +++ b/src/foundation/functoriality-cartesian-product-types.lagda.md @@ -1,7 +1,12 @@ # Functoriality of cartesian product types ```agda -module foundation.functoriality-cartesian-product-types where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-cartesian-product-types + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module foundation.functoriality-cartesian-product-types where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/functoriality-coproduct-types.lagda.md b/src/foundation/functoriality-coproduct-types.lagda.md index 1c629f6117..3724122c76 100644 --- a/src/foundation/functoriality-coproduct-types.lagda.md +++ b/src/foundation/functoriality-coproduct-types.lagda.md @@ -1,30 +1,36 @@ # Functoriality of coproduct types ```agda -module foundation.functoriality-coproduct-types where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-coproduct-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equality-coproduct-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.negated-equality -open import foundation.propositional-truncations -open import foundation.retractions +open import foundation.equality-coproduct-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.negated-equality funext +open import foundation.propositional-truncations funext +open import foundation.retractions funext open import foundation.structure-identity-principle -open import foundation.surjective-maps +open import foundation.surjective-maps funext open import foundation.unit-type -open import foundation.universal-property-coproduct-types +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -33,7 +39,7 @@ open import foundation-core.embeddings open import foundation-core.empty-types open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/functoriality-dependent-function-types.lagda.md b/src/foundation/functoriality-dependent-function-types.lagda.md index 290c471228..cf3245fc9c 100644 --- a/src/foundation/functoriality-dependent-function-types.lagda.md +++ b/src/foundation/functoriality-dependent-function-types.lagda.md @@ -1,9 +1,14 @@ # Functoriality of dependent function types ```agda -module foundation.functoriality-dependent-function-types where +open import foundation.function-extensionality-axiom -open import foundation-core.functoriality-dependent-function-types public +module + foundation.functoriality-dependent-function-types + (funext : function-extensionality) + where + +open import foundation-core.functoriality-dependent-function-types funext public ```
Imports @@ -11,14 +16,15 @@ open import foundation-core.functoriality-dependent-function-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.dependent-universal-property-equivalences -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.retracts-of-types +open import foundation.dependent-products-truncated-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext + +open import foundation.retracts-of-types funext open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-unit-type funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -32,7 +38,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.precomposition-dependent-functions open import foundation-core.propositional-maps -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/functoriality-dependent-pair-types.lagda.md b/src/foundation/functoriality-dependent-pair-types.lagda.md index beffdd38f2..c8c75ea374 100644 --- a/src/foundation/functoriality-dependent-pair-types.lagda.md +++ b/src/foundation/functoriality-dependent-pair-types.lagda.md @@ -1,7 +1,12 @@ # Functoriality of dependent pair types ```agda -module foundation.functoriality-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-dependent-pair-types + (funext : function-extensionality) + where open import foundation-core.functoriality-dependent-pair-types public ``` @@ -12,10 +17,10 @@ open import foundation-core.functoriality-dependent-pair-types public open import foundation.action-on-identifications-functions open import foundation.dependent-homotopies open import foundation.dependent-pair-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.dependent-identifications @@ -28,7 +33,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositional-maps open import foundation-core.transport-along-identifications -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/functoriality-fibers-of-maps.lagda.md b/src/foundation/functoriality-fibers-of-maps.lagda.md index 5beb6de9e9..2f01630494 100644 --- a/src/foundation/functoriality-fibers-of-maps.lagda.md +++ b/src/foundation/functoriality-fibers-of-maps.lagda.md @@ -1,23 +1,28 @@ # Functoriality of fibers of maps ```agda -module foundation.functoriality-fibers-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-fibers-of-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.homotopies-morphisms-arrows -open import foundation.morphisms-arrows +open import foundation.homotopies-morphisms-arrows funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equality-dependent-pair-types open import foundation-core.fibers-of-maps open import foundation-core.function-types diff --git a/src/foundation/functoriality-function-types.lagda.md b/src/foundation/functoriality-function-types.lagda.md index a86808a6d2..937763a8f4 100644 --- a/src/foundation/functoriality-function-types.lagda.md +++ b/src/foundation/functoriality-function-types.lagda.md @@ -1,7 +1,12 @@ # Functoriality of function types ```agda -module foundation.functoriality-function-types where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-function-types + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module foundation.functoriality-function-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types -open import foundation.postcomposition-functions +open import foundation.functoriality-dependent-function-types funext +open import foundation.postcomposition-functions funext open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.embeddings @@ -21,7 +26,7 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.precomposition-functions open import foundation-core.propositional-maps -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels ``` diff --git a/src/foundation/functoriality-morphisms-arrows.lagda.md b/src/foundation/functoriality-morphisms-arrows.lagda.md index 8ad3592690..8571919b54 100644 --- a/src/foundation/functoriality-morphisms-arrows.lagda.md +++ b/src/foundation/functoriality-morphisms-arrows.lagda.md @@ -1,7 +1,12 @@ # Functoriality of morphisms of arrows ```agda -module foundation.functoriality-morphisms-arrows where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-morphisms-arrows + (funext : function-extensionality) + where ```
Imports @@ -9,32 +14,32 @@ module foundation.functoriality-morphisms-arrows where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.bicomposition-functions -open import foundation.commuting-squares-of-maps -open import foundation.composition-algebra -open import foundation.cones-over-cospan-diagrams +open import foundation.bicomposition-functions funext +open import foundation.commuting-squares-of-maps funext +open import foundation.composition-algebra funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-pullbacks -open import foundation.homotopies -open import foundation.homotopies-morphisms-arrows -open import foundation.homotopies-morphisms-cospan-diagrams -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-pullbacks funext +open import foundation.homotopies funext +open import foundation.homotopies funext-morphisms-arrows +open import foundation.homotopies-morphisms-cospan-diagrams funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.morphisms-cospan-diagrams -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.pullback-cones -open import foundation.pullbacks -open import foundation.retractions -open import foundation.sections -open import foundation.standard-pullbacks +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.pullback-cones funext +open import foundation.pullbacks funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/functoriality-propositional-truncation.lagda.md b/src/foundation/functoriality-propositional-truncation.lagda.md index 32fdfc1b87..65b2c63ee5 100644 --- a/src/foundation/functoriality-propositional-truncation.lagda.md +++ b/src/foundation/functoriality-propositional-truncation.lagda.md @@ -1,7 +1,12 @@ # Functoriality of propositional truncations ```agda -module foundation.functoriality-propositional-truncation where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-propositional-truncation + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,9 @@ module foundation.functoriality-propositional-truncation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.function-extensionality-axiom -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/functoriality-pullbacks.lagda.md b/src/foundation/functoriality-pullbacks.lagda.md index 60e01bf16e..2a19574328 100644 --- a/src/foundation/functoriality-pullbacks.lagda.md +++ b/src/foundation/functoriality-pullbacks.lagda.md @@ -1,29 +1,34 @@ # Functorialty of pullbacks ```agda -module foundation.functoriality-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.homotopies-morphisms-cospan-diagrams +open import foundation.equality-dependent-pair-types funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.homotopies funext-morphisms-cospan-diagrams open import foundation.morphisms-cospan-diagrams -open import foundation.pullback-cones -open import foundation.standard-pullbacks +open import foundation.pullback-cones funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.equivalences open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/functoriality-sequential-limits.lagda.md b/src/foundation/functoriality-sequential-limits.lagda.md index 32979a1d7b..d6b49fe4d2 100644 --- a/src/foundation/functoriality-sequential-limits.lagda.md +++ b/src/foundation/functoriality-sequential-limits.lagda.md @@ -1,7 +1,12 @@ # Functoriality of sequential limits ```agda -module foundation.functoriality-sequential-limits where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-sequential-limits + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module foundation.functoriality-sequential-limits where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cones-over-inverse-sequential-diagrams +open import foundation.cones-over-inverse-sequential-diagrams funext open import foundation.dependent-pair-types -open import foundation.inverse-sequential-diagrams -open import foundation.morphisms-inverse-sequential-diagrams -open import foundation.sequential-limits +open import foundation.inverse-sequential-diagrams funext +open import foundation.morphisms-inverse-sequential-diagrams funext +open import foundation.sequential-limits funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/functoriality-set-quotients.lagda.md b/src/foundation/functoriality-set-quotients.lagda.md index 31b756d2f8..b71732a282 100644 --- a/src/foundation/functoriality-set-quotients.lagda.md +++ b/src/foundation/functoriality-set-quotients.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.functoriality-set-quotients where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-set-quotients + (funext : function-extensionality) + where ```
Imports @@ -11,29 +16,29 @@ module foundation.functoriality-set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalence-extensionality +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-extensionality funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.logical-equivalences -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients +open import foundation.homotopy-induction funext +open import foundation.logical-equivalences funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.set-quotients funext open import foundation.subtype-identity-principle -open import foundation.surjective-maps -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-set-quotients +open import foundation.surjective-maps funext +open import foundation.uniqueness-set-quotients funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/functoriality-set-truncation.lagda.md b/src/foundation/functoriality-set-truncation.lagda.md index e10e05a582..bbaec842be 100644 --- a/src/foundation/functoriality-set-truncation.lagda.md +++ b/src/foundation/functoriality-set-truncation.lagda.md @@ -1,7 +1,12 @@ # Functoriality of set truncation ```agda -module foundation.functoriality-set-truncation where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-set-truncation + (funext : function-extensionality) + where ```
Imports @@ -9,20 +14,20 @@ module foundation.functoriality-set-truncation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.functoriality-truncation -open import foundation.images -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.retracts-of-types -open import foundation.set-truncations -open import foundation.sets -open import foundation.slice -open import foundation.surjective-maps -open import foundation.uniqueness-image -open import foundation.uniqueness-set-truncations -open import foundation.universal-property-image -open import foundation.universal-property-set-truncation +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-truncation funext +open import foundation.images funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext +open import foundation.retracts-of-types funext +open import foundation.set-truncations funext +open import foundation.sets funext +open import foundation.slice funext +open import foundation.surjective-maps funext +open import foundation.uniqueness-image funext +open import foundation.uniqueness-set-truncations funext +open import foundation.universal-property-image funext +open import foundation.universal-property-set-truncation funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/functoriality-truncation.lagda.md b/src/foundation/functoriality-truncation.lagda.md index 86a3aaecad..11f1dd3010 100644 --- a/src/foundation/functoriality-truncation.lagda.md +++ b/src/foundation/functoriality-truncation.lagda.md @@ -1,7 +1,12 @@ # Functoriality of truncations ```agda -module foundation.functoriality-truncation where +open import foundation.function-extensionality-axiom + +module + foundation.functoriality-truncation + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module foundation.functoriality-truncation where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.truncations +open import foundation.function-extensionality funext + +open import foundation.truncations funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md b/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md index 8bd7600e74..69ddb915e5 100644 --- a/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md +++ b/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md @@ -1,28 +1,33 @@ # Fundamental theorem of equivalence relations ```agda -module foundation.fundamental-theorem-of-equivalence-relations where +open import foundation.function-extensionality-axiom + +module + foundation.fundamental-theorem-of-equivalence-relations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-classes -open import foundation.full-subtypes -open import foundation.inhabited-subtypes -open import foundation.logical-equivalences -open import foundation.partitions -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.equivalence-classes funext +open import foundation.full-subtypes funext +open import foundation.inhabited-subtypes funext +open import foundation.logical-equivalences funext +open import foundation.partitions funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.contractible-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types diff --git a/src/foundation/global-choice.lagda.md b/src/foundation/global-choice.lagda.md index dde44fdbc8..581f9a4186 100644 --- a/src/foundation/global-choice.lagda.md +++ b/src/foundation/global-choice.lagda.md @@ -1,22 +1,27 @@ # Global choice ```agda -module foundation.global-choice where +open import foundation.function-extensionality-axiom + +module + foundation.global-choice + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.hilberts-epsilon-operators +open import foundation.functoriality-propositional-truncation funext +open import foundation.hilberts-epsilon-operators funext open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.negation -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/global-subuniverses.lagda.md b/src/foundation/global-subuniverses.lagda.md index 375ab98286..b061ab2cb3 100644 --- a/src/foundation/global-subuniverses.lagda.md +++ b/src/foundation/global-subuniverses.lagda.md @@ -1,15 +1,20 @@ # Global subuniverses ```agda -module foundation.global-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.global-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types -open import foundation.subuniverses +open import foundation.iterated-dependent-product-types funext +open import foundation.subuniverses funext open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/globular-type-of-dependent-functions.lagda.md b/src/foundation/globular-type-of-dependent-functions.lagda.md index c620d17ec1..beb076102e 100644 --- a/src/foundation/globular-type-of-dependent-functions.lagda.md +++ b/src/foundation/globular-type-of-dependent-functions.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module foundation.globular-type-of-dependent-functions where +open import foundation.function-extensionality-axiom + +module + foundation.globular-type-of-dependent-functions + (funext : function-extensionality) + where ```
Imports @@ -14,8 +19,8 @@ open import foundation.universe-levels open import foundation-core.homotopies open import globular-types.globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.reflexive-globular-types funext +open import globular-types.transitive-globular-types funext ```
diff --git a/src/foundation/globular-type-of-functions.lagda.md b/src/foundation/globular-type-of-functions.lagda.md index 41533c9aee..ceab9d078e 100644 --- a/src/foundation/globular-type-of-functions.lagda.md +++ b/src/foundation/globular-type-of-functions.lagda.md @@ -3,20 +3,25 @@ ```agda {-# OPTIONS --guardedness #-} -module foundation.globular-type-of-functions where +open import foundation.function-extensionality-axiom + +module + foundation.globular-type-of-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.globular-type-of-dependent-functions +open import foundation.globular-type-of-dependent-functions funext open import foundation.universe-levels open import foundation-core.homotopies open import globular-types.globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.reflexive-globular-types funext +open import globular-types.transitive-globular-types funext ```
diff --git a/src/foundation/higher-homotopies-morphisms-arrows.lagda.md b/src/foundation/higher-homotopies-morphisms-arrows.lagda.md index 842b83be66..830a4eda4c 100644 --- a/src/foundation/higher-homotopies-morphisms-arrows.lagda.md +++ b/src/foundation/higher-homotopies-morphisms-arrows.lagda.md @@ -1,27 +1,32 @@ # Higher homotopies of morphisms of arrows ```agda -module foundation.higher-homotopies-morphisms-arrows where +open import foundation.function-extensionality-axiom + +module + foundation.higher-homotopies-morphisms-arrows + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies-morphisms-arrows -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.path-algebra +open import foundation.homotopies-morphisms-arrows funext +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import foundation.whiskering-homotopies-concatenation -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-homotopies-concatenation funext +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.equivalences open import foundation-core.homotopies diff --git a/src/foundation/hilberts-epsilon-operators.lagda.md b/src/foundation/hilberts-epsilon-operators.lagda.md index 1c23904a8b..0d7dfd78ae 100644 --- a/src/foundation/hilberts-epsilon-operators.lagda.md +++ b/src/foundation/hilberts-epsilon-operators.lagda.md @@ -1,14 +1,19 @@ # Hilbert's `ε`-operators ```agda -module foundation.hilberts-epsilon-operators where +open import foundation.function-extensionality-axiom + +module + foundation.hilberts-epsilon-operators + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.functoriality-propositional-truncation -open import foundation.propositional-truncations +open import foundation.functoriality-propositional-truncation funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/homotopies-morphisms-arrows.lagda.md b/src/foundation/homotopies-morphisms-arrows.lagda.md index 4eb4eeead5..8f314a55fb 100644 --- a/src/foundation/homotopies-morphisms-arrows.lagda.md +++ b/src/foundation/homotopies-morphisms-arrows.lagda.md @@ -1,29 +1,35 @@ # Homotopies of morphisms of arrows ```agda -module foundation.homotopies-morphisms-arrows where +open import foundation.function-extensionality-axiom + +module + foundation.homotopies-morphisms-arrows + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.commuting-squares-of-homotopies -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies diff --git a/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md b/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md index 0b4e7d6bb5..15afd1e562 100644 --- a/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md +++ b/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md @@ -1,22 +1,28 @@ # Homotopies of morphisms of cospan diagrams ```agda -module foundation.homotopies-morphisms-cospan-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.homotopies-morphisms-cospan-diagrams + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-homotopies funext open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.morphisms-cospan-diagrams open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/homotopies.lagda.md b/src/foundation/homotopies.lagda.md index 54f138533e..c40d62e172 100644 --- a/src/foundation/homotopies.lagda.md +++ b/src/foundation/homotopies.lagda.md @@ -1,7 +1,12 @@ # Homotopies ```agda -module foundation.homotopies where +open import foundation.function-extensionality-axiom + +module + foundation.homotopies + (funext : function-extensionality) + where open import foundation-core.homotopies public ``` @@ -9,22 +14,23 @@ open import foundation-core.homotopies public
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.function-extensionality funext + +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications open import foundation-core.dependent-identifications open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.transport-along-identifications open import foundation-core.whiskering-homotopies-concatenation ``` diff --git a/src/foundation/homotopy-induction.lagda.md b/src/foundation/homotopy-induction.lagda.md index 0e79b789dd..d91803b6e5 100644 --- a/src/foundation/homotopy-induction.lagda.md +++ b/src/foundation/homotopy-induction.lagda.md @@ -1,17 +1,22 @@ # Homotopy induction ```agda -module foundation.homotopy-induction where +open import foundation.function-extensionality-axiom + +module + foundation.homotopy-induction + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.function-extensionality funext + open import foundation.identity-systems -open import foundation.universal-property-identity-systems +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/homotopy-preorder-of-types.lagda.md b/src/foundation/homotopy-preorder-of-types.lagda.md index c6c1e1902e..3b9801d90c 100644 --- a/src/foundation/homotopy-preorder-of-types.lagda.md +++ b/src/foundation/homotopy-preorder-of-types.lagda.md @@ -10,17 +10,17 @@ module ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.mere-functions -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.mere-functions funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.large-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.large-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/foundation/horizontal-composition-spans-of-spans.lagda.md b/src/foundation/horizontal-composition-spans-of-spans.lagda.md index eed1567115..7555b03022 100644 --- a/src/foundation/horizontal-composition-spans-of-spans.lagda.md +++ b/src/foundation/horizontal-composition-spans-of-spans.lagda.md @@ -1,28 +1,33 @@ # Horizontal composition of spans of spans ```agda -module foundation.horizontal-composition-spans-of-spans where +open import foundation.function-extensionality-axiom + +module + foundation.horizontal-composition-spans-of-spans + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps -open import foundation.composition-spans -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-triangles-of-maps funext +open import foundation.composition-spans funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-spans -open import foundation.homotopies -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.equivalences-spans funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.morphisms-spans -open import foundation.pullbacks +open import foundation.pullbacks funext open import foundation.spans -open import foundation.spans-of-spans -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-standard-pullbacks +open import foundation.spans-of-spans funext +open import foundation.standard-pullbacks funext +open import foundation.type-arithmetic-standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/idempotent-maps.lagda.md b/src/foundation/idempotent-maps.lagda.md index 3e0e0adf77..ea94170419 100644 --- a/src/foundation/idempotent-maps.lagda.md +++ b/src/foundation/idempotent-maps.lagda.md @@ -1,14 +1,19 @@ # Idempotent maps ```agda -module foundation.idempotent-maps where +open import foundation.function-extensionality-axiom + +module + foundation.idempotent-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions +open import foundation.dependent-products-propositions funext open import foundation.homotopy-algebra open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/identity-truncated-types.lagda.md b/src/foundation/identity-truncated-types.lagda.md index 0201dea2e3..7d5577f475 100644 --- a/src/foundation/identity-truncated-types.lagda.md +++ b/src/foundation/identity-truncated-types.lagda.md @@ -1,14 +1,19 @@ # Identity types of truncated types ```agda -module foundation.identity-truncated-types where +open import foundation.function-extensionality-axiom + +module + foundation.identity-truncated-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.dependent-products-truncated-types -open import foundation.univalence +open import foundation.dependent-products-truncated-types funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/identity-types.lagda.md b/src/foundation/identity-types.lagda.md index 2f517ddffe..fd892bfdee 100644 --- a/src/foundation/identity-types.lagda.md +++ b/src/foundation/identity-types.lagda.md @@ -1,7 +1,12 @@ # Identity types ```agda -module foundation.identity-types where +open import foundation.function-extensionality-axiom + +module + foundation.identity-types + (funext : function-extensionality) + where open import foundation-core.identity-types public ``` @@ -13,8 +18,9 @@ open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.commuting-pentagons-of-identifications open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/images-subtypes.lagda.md b/src/foundation/images-subtypes.lagda.md index f2959311bd..350f19968e 100644 --- a/src/foundation/images-subtypes.lagda.md +++ b/src/foundation/images-subtypes.lagda.md @@ -1,21 +1,26 @@ # Images of subtypes ```agda -module foundation.images-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.images-subtypes + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.full-subtypes -open import foundation.functoriality-propositional-truncation -open import foundation.images -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.pullbacks-subtypes -open import foundation.subtypes +open import foundation.full-subtypes funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.images funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.pullbacks-subtypes funext +open import foundation.subtypes funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -25,10 +30,10 @@ open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.identity-types -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.galois-connections-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.similarity-of-order-preserving-maps-large-posets funext ```
diff --git a/src/foundation/images.lagda.md b/src/foundation/images.lagda.md index 4ffd596c45..39dbd81d29 100644 --- a/src/foundation/images.lagda.md +++ b/src/foundation/images.lagda.md @@ -1,7 +1,12 @@ # The image of a map ```agda -module foundation.images where +open import foundation.function-extensionality-axiom + +module + foundation.images + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module foundation.images where ```agda open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.propositional-truncations -open import foundation.slice +open import foundation.propositional-truncations funext +open import foundation.slice funext open import foundation.subtype-identity-principle -open import foundation.surjective-maps +open import foundation.surjective-maps funext open import foundation.universe-levels -open import foundation-core.1-types +open import foundation-core.1-types funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-types open import foundation-core.embeddings @@ -26,7 +31,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/impredicative-encodings.lagda.md b/src/foundation/impredicative-encodings.lagda.md index fadc6aea05..604f2594c1 100644 --- a/src/foundation/impredicative-encodings.lagda.md +++ b/src/foundation/impredicative-encodings.lagda.md @@ -1,23 +1,28 @@ # Impredicative encodings of the logical operations ```agda -module foundation.impredicative-encodings where +open import foundation.function-extensionality-axiom + +module + foundation.impredicative-encodings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.disjunction -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.homotopies -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.homotopies funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.universal-quantification funext open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/impredicative-universes.lagda.md b/src/foundation/impredicative-universes.lagda.md index c1f2ed3f59..3145b640c0 100644 --- a/src/foundation/impredicative-universes.lagda.md +++ b/src/foundation/impredicative-universes.lagda.md @@ -1,7 +1,12 @@ # Impredicative universes ```agda -module foundation.impredicative-universes where +open import foundation.function-extensionality-axiom + +module + foundation.impredicative-universes + (funext : function-extensionality) + where ```
Imports @@ -10,7 +15,7 @@ module foundation.impredicative-universes where open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.small-types +open import foundation-core.small-types funext ```
diff --git a/src/foundation/infinitely-coherent-equivalences.lagda.md b/src/foundation/infinitely-coherent-equivalences.lagda.md index a650beffa9..35edb30326 100644 --- a/src/foundation/infinitely-coherent-equivalences.lagda.md +++ b/src/foundation/infinitely-coherent-equivalences.lagda.md @@ -3,22 +3,27 @@ ```agda {-# OPTIONS --guardedness --lossy-unification #-} -module foundation.infinitely-coherent-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.infinitely-coherent-equivalences + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.transposition-identifications-along-equivalences +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.universe-levels ``` diff --git a/src/foundation/inhabited-subtypes.lagda.md b/src/foundation/inhabited-subtypes.lagda.md index 5a4a67c0b3..4d64e0ae5e 100644 --- a/src/foundation/inhabited-subtypes.lagda.md +++ b/src/foundation/inhabited-subtypes.lagda.md @@ -1,17 +1,22 @@ # Inhabited subtypes ```agda -module foundation.inhabited-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.inhabited-subtypes + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.propositional-truncations +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/inhabited-types.lagda.md b/src/foundation/inhabited-types.lagda.md index ff290bc467..caaad0d4b2 100644 --- a/src/foundation/inhabited-types.lagda.md +++ b/src/foundation/inhabited-types.lagda.md @@ -1,20 +1,25 @@ # Inhabited types ```agda -module foundation.inhabited-types where +open import foundation.function-extensionality-axiom + +module + foundation.inhabited-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.functoriality-propositional-truncation +open import foundation.equality-dependent-function-types funext +open import foundation.functoriality-propositional-truncation funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext open import foundation.subtype-identity-principle -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/injective-maps.lagda.md b/src/foundation/injective-maps.lagda.md index 09640c54b1..e5a4ebed7b 100644 --- a/src/foundation/injective-maps.lagda.md +++ b/src/foundation/injective-maps.lagda.md @@ -1,7 +1,12 @@ # Injective maps ```agda -module foundation.injective-maps where +open import foundation.function-extensionality-axiom + +module + foundation.injective-maps + (funext : function-extensionality) + where open import foundation-core.injective-maps public ``` @@ -11,10 +16,10 @@ open import foundation-core.injective-maps public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.logical-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.function-extensionality funext + +open import foundation.logical-equivalences funext open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/intersections-subtypes.lagda.md b/src/foundation/intersections-subtypes.lagda.md index 776056c8e1..7d254d6825 100644 --- a/src/foundation/intersections-subtypes.lagda.md +++ b/src/foundation/intersections-subtypes.lagda.md @@ -1,25 +1,30 @@ # Intersections of subtypes ```agda -module foundation.intersections-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.intersections-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction -open import foundation.decidable-subtypes +open import foundation.conjunction funext +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.large-locale-of-subtypes -open import foundation.powersets +open import foundation.dependent-products-propositions funext +open import foundation.large-locale-of-subtypes funext +open import foundation.powersets funext open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext ```
diff --git a/src/foundation/inverse-sequential-diagrams.lagda.md b/src/foundation/inverse-sequential-diagrams.lagda.md index 553548e870..1007dca5ea 100644 --- a/src/foundation/inverse-sequential-diagrams.lagda.md +++ b/src/foundation/inverse-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Inverse sequential diagrams of types ```agda -module foundation.inverse-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.inverse-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module foundation.inverse-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.iterating-functions -open import foundation.raising-universe-levels-unit-type +open import foundation.iterating-functions funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/invertible-maps.lagda.md b/src/foundation/invertible-maps.lagda.md index 3edb105808..d5f0f8a3eb 100644 --- a/src/foundation/invertible-maps.lagda.md +++ b/src/foundation/invertible-maps.lagda.md @@ -1,7 +1,12 @@ # Invertible maps ```agda -module foundation.invertible-maps where +open import foundation.function-extensionality-axiom + +module + foundation.invertible-maps + (funext : function-extensionality) + where open import foundation-core.invertible-maps public ``` @@ -10,22 +15,23 @@ open import foundation-core.invertible-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types +open import foundation.dependent-products-truncated-types funext open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-cartesian-product-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.postcomposition-functions -open import foundation.retractions -open import foundation.sections +open import foundation.homotopy-induction funext +open import foundation.postcomposition-functions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -41,7 +47,7 @@ open import foundation-core.torsorial-type-families open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.free-loops funext ```
diff --git a/src/foundation/involutions.lagda.md b/src/foundation/involutions.lagda.md index 8f2ad4d544..699b315c0a 100644 --- a/src/foundation/involutions.lagda.md +++ b/src/foundation/involutions.lagda.md @@ -1,21 +1,27 @@ # Involutions ```agda -module foundation.involutions where +open import foundation.function-extensionality-axiom + +module + foundation.involutions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-algebra -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/irrefutable-propositions.lagda.md b/src/foundation/irrefutable-propositions.lagda.md index d89ec3fd7b..1d6ea36e6a 100644 --- a/src/foundation/irrefutable-propositions.lagda.md +++ b/src/foundation/irrefutable-propositions.lagda.md @@ -1,29 +1,34 @@ # Irrefutable propositions ```agda -module foundation.irrefutable-propositions where +open import foundation.function-extensionality-axiom + +module + foundation.irrefutable-propositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.double-negation -open import foundation.empty-types -open import foundation.function-types -open import foundation.negation -open import foundation.propositions -open import foundation.subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.subuniverses funext open import foundation.unit-type open import foundation.universe-levels -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext ```
diff --git a/src/foundation/isolated-elements.lagda.md b/src/foundation/isolated-elements.lagda.md index 994d1a5448..1a022d4a0e 100644 --- a/src/foundation/isolated-elements.lagda.md +++ b/src/foundation/isolated-elements.lagda.md @@ -1,34 +1,39 @@ # Isolated elements ```agda -module foundation.isolated-elements where +open import foundation.function-extensionality-axiom + +module + foundation.isolated-elements + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.constant-maps -open import foundation.decidable-embeddings -open import foundation.decidable-equality -open import foundation.decidable-maps -open import foundation.decidable-types +open import foundation.constant-maps funext +open import foundation.decidable-embeddings funext +open import foundation.decidable-equality funext +open import foundation.decidable-maps funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.sets +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.sets funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.coproduct-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types @@ -36,7 +41,7 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.maybe open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/isomorphisms-of-sets.lagda.md b/src/foundation/isomorphisms-of-sets.lagda.md index c5f46ffa11..4692b5f04a 100644 --- a/src/foundation/isomorphisms-of-sets.lagda.md +++ b/src/foundation/isomorphisms-of-sets.lagda.md @@ -1,7 +1,12 @@ # Isomorphisms of sets ```agda -module foundation.isomorphisms-of-sets where +open import foundation.function-extensionality-axiom + +module + foundation.isomorphisms-of-sets + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,17 @@ module foundation.isomorphisms-of-sets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.sets funext open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/iterated-cartesian-product-types.lagda.md b/src/foundation/iterated-cartesian-product-types.lagda.md index 8a20d00913..d944078297 100644 --- a/src/foundation/iterated-cartesian-product-types.lagda.md +++ b/src/foundation/iterated-cartesian-product-types.lagda.md @@ -1,7 +1,12 @@ # Iterated cartesian product types ```agda -module foundation.iterated-cartesian-product-types where +open import foundation.function-extensionality-axiom + +module + foundation.iterated-cartesian-product-types + (funext : function-extensionality) + where ```
Imports @@ -9,19 +14,19 @@ module foundation.iterated-cartesian-product-types where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.raising-universe-levels-unit-type +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-arithmetic-dependent-function-types funext open import foundation.unit-type -open import foundation.univalence -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-empty-type +open import foundation.univalence funext +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-empty-type funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -31,12 +36,12 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types -open import lists.arrays -open import lists.concatenation-lists +open import lists.arrays funext +open import lists.concatenation-lists funext open import lists.lists -open import lists.permutation-lists +open import lists.permutation-lists funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/iterated-dependent-product-types.lagda.md b/src/foundation/iterated-dependent-product-types.lagda.md index a5cada2333..404f3c5041 100644 --- a/src/foundation/iterated-dependent-product-types.lagda.md +++ b/src/foundation/iterated-dependent-product-types.lagda.md @@ -1,7 +1,12 @@ # Iterated dependent product types ```agda -module foundation.iterated-dependent-product-types where +open import foundation.function-extensionality-axiom + +module + foundation.iterated-dependent-product-types + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module foundation.iterated-dependent-product-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.dependent-products-contractible-types -open import foundation.dependent-products-propositions -open import foundation.dependent-products-truncated-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext open import foundation.implicit-function-types open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.propositions open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/iterating-automorphisms.lagda.md b/src/foundation/iterating-automorphisms.lagda.md index dfae65d2f3..aef82113e6 100644 --- a/src/foundation/iterating-automorphisms.lagda.md +++ b/src/foundation/iterating-automorphisms.lagda.md @@ -1,19 +1,24 @@ # Iterating automorphisms ```agda -module foundation.iterating-automorphisms where +open import foundation.function-extensionality-axiom + +module + foundation.iterating-automorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.automorphisms -open import foundation.equivalence-extensionality -open import foundation.iterating-functions +open import foundation.automorphisms funext +open import foundation.equivalence-extensionality funext +open import foundation.iterating-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/iterating-families-of-maps.lagda.md b/src/foundation/iterating-families-of-maps.lagda.md index 968976eaf1..a94b3ed4c2 100644 --- a/src/foundation/iterating-families-of-maps.lagda.md +++ b/src/foundation/iterating-families-of-maps.lagda.md @@ -1,7 +1,12 @@ # Iterating families of maps over a map ```agda -module foundation.iterating-families-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.iterating-families-of-maps + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module foundation.iterating-families-of-maps where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.dependent-identifications -open import foundation.iterating-functions +open import foundation.dependent-identifications funext +open import foundation.iterating-functions funext open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/iterating-functions.lagda.md b/src/foundation/iterating-functions.lagda.md index 7c6c17cdaf..dad12c698e 100644 --- a/src/foundation/iterating-functions.lagda.md +++ b/src/foundation/iterating-functions.lagda.md @@ -1,32 +1,37 @@ # Iterating functions ```agda -module foundation.iterating-functions where +open import foundation.function-extensionality-axiom + +module + foundation.iterating-functions + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplicative-monoid-of-natural-numbers +open import elementary-number-theory.multiplicative-monoid-of-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.function-extensionality funext + open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps -open import foundation-core.endomorphisms +open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.endomorphisms funext open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.sets -open import group-theory.monoid-actions +open import group-theory.monoid-actions funext ```
diff --git a/src/foundation/iterating-involutions.lagda.md b/src/foundation/iterating-involutions.lagda.md index 06170f10fe..361affaa35 100644 --- a/src/foundation/iterating-involutions.lagda.md +++ b/src/foundation/iterating-involutions.lagda.md @@ -1,24 +1,29 @@ # Iterating involutions ```agda -module foundation.iterating-involutions where +open import foundation.function-extensionality-axiom + +module + foundation.iterating-involutions + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.involutions -open import foundation.iterating-functions +open import foundation.involutions funext +open import foundation.iterating-functions funext open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.identity-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/kernel-span-diagrams-of-maps.lagda.md b/src/foundation/kernel-span-diagrams-of-maps.lagda.md index 37d56efd8d..7eac0660fd 100644 --- a/src/foundation/kernel-span-diagrams-of-maps.lagda.md +++ b/src/foundation/kernel-span-diagrams-of-maps.lagda.md @@ -1,14 +1,19 @@ # Kernel span diagrams of maps ```agda -module foundation.kernel-span-diagrams-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.kernel-span-diagrams-of-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.span-diagrams +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/large-apartness-relations.lagda.md b/src/foundation/large-apartness-relations.lagda.md index b87c9a5b09..9e0e14ae12 100644 --- a/src/foundation/large-apartness-relations.lagda.md +++ b/src/foundation/large-apartness-relations.lagda.md @@ -1,17 +1,22 @@ # Large apartness relations ```agda -module foundation.large-apartness-relations where +open import foundation.function-extensionality-axiom + +module + foundation.large-apartness-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/foundation/large-binary-relations.lagda.md b/src/foundation/large-binary-relations.lagda.md index 2a4b155124..769f60bad2 100644 --- a/src/foundation/large-binary-relations.lagda.md +++ b/src/foundation/large-binary-relations.lagda.md @@ -1,15 +1,20 @@ # Large binary relations ```agda -module foundation.large-binary-relations where +open import foundation.function-extensionality-axiom + +module + foundation.large-binary-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.disjunction +open import foundation.disjunction funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/large-locale-of-propositions.lagda.md b/src/foundation/large-locale-of-propositions.lagda.md index 671ef5ad4b..47a40e65e0 100644 --- a/src/foundation/large-locale-of-propositions.lagda.md +++ b/src/foundation/large-locale-of-propositions.lagda.md @@ -1,34 +1,39 @@ # The large locale of propositions ```agda -module foundation.large-locale-of-propositions where +open import foundation.function-extensionality-axiom + +module + foundation.large-locale-of-propositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction -open import foundation.dependent-products-propositions -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.propositional-extensionality +open import foundation.conjunction funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.propositions -open import order-theory.bottom-elements-large-posets -open import order-theory.large-frames -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.bottom-elements-large-posets funext +open import order-theory.large-frames funext +open import order-theory.large-locales funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/foundation/large-locale-of-subtypes.lagda.md b/src/foundation/large-locale-of-subtypes.lagda.md index 2661d3c83d..bf32155c73 100644 --- a/src/foundation/large-locale-of-subtypes.lagda.md +++ b/src/foundation/large-locale-of-subtypes.lagda.md @@ -1,29 +1,34 @@ # The large locale of subtypes ```agda -module foundation.large-locale-of-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.large-locale-of-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.large-locale-of-propositions +open import foundation.large-binary-relations funext +open import foundation.large-locale-of-propositions funext open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.sets -open import order-theory.bottom-elements-large-posets -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.powers-of-large-locales -open import order-theory.top-elements-large-posets +open import order-theory.bottom-elements-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-locales funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.powers-of-large-locales funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/foundation/law-of-excluded-middle.lagda.md b/src/foundation/law-of-excluded-middle.lagda.md index 2a3935ebdc..f9b832cb1a 100644 --- a/src/foundation/law-of-excluded-middle.lagda.md +++ b/src/foundation/law-of-excluded-middle.lagda.md @@ -1,22 +1,27 @@ # The law of excluded middle ```agda -module foundation.law-of-excluded-middle where +open import foundation.function-extensionality-axiom + +module + foundation.law-of-excluded-middle + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions +open import foundation.dependent-products-propositions funext open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.negation open import foundation-core.propositions -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext ```
diff --git a/src/foundation/lawveres-fixed-point-theorem.lagda.md b/src/foundation/lawveres-fixed-point-theorem.lagda.md index 603c14897d..b4733c3d77 100644 --- a/src/foundation/lawveres-fixed-point-theorem.lagda.md +++ b/src/foundation/lawveres-fixed-point-theorem.lagda.md @@ -1,17 +1,21 @@ # Lawvere's fixed point theorem ```agda -module foundation.lawveres-fixed-point-theorem where +open import foundation.function-extensionality-axiom + +module + foundation.lawveres-fixed-point-theorem + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-extensionality-axiom -open import foundation.propositional-truncations -open import foundation.surjective-maps +open import foundation.existential-quantification funext +open import foundation.propositional-truncations funext +open import foundation.surjective-maps funext open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md index 5c9d5e9e71..9abc4e611e 100644 --- a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md +++ b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md @@ -1,19 +1,24 @@ # The lesser limited principle of omniscience ```agda -module foundation.lesser-limited-principle-of-omniscience where +open import foundation.function-extensionality-axiom + +module + foundation.lesser-limited-principle-of-omniscience + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.disjunction -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext +open import foundation.universal-quantification funext open import foundation.universe-levels open import foundation-core.booleans diff --git a/src/foundation/limited-principle-of-omniscience.lagda.md b/src/foundation/limited-principle-of-omniscience.lagda.md index 58bfd6a8d7..3d6dd83878 100644 --- a/src/foundation/limited-principle-of-omniscience.lagda.md +++ b/src/foundation/limited-principle-of-omniscience.lagda.md @@ -1,7 +1,12 @@ # The limited principle of omniscience ```agda -module foundation.limited-principle-of-omniscience where +open import foundation.function-extensionality-axiom + +module + foundation.limited-principle-of-omniscience + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module foundation.limited-principle-of-omniscience where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.negation -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext +open import foundation.existential-quantification funext +open import foundation.negation funext +open import foundation.universal-quantification funext open import foundation.universe-levels open import foundation-core.booleans @@ -23,7 +28,7 @@ open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/locale-of-propositions.lagda.md b/src/foundation/locale-of-propositions.lagda.md index dd65321505..9a2de3f6ca 100644 --- a/src/foundation/locale-of-propositions.lagda.md +++ b/src/foundation/locale-of-propositions.lagda.md @@ -1,33 +1,38 @@ # The locale of propositions ```agda -module foundation.locale-of-propositions where +open import foundation.function-extensionality-axiom + +module + foundation.locale-of-propositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.large-locale-of-propositions -open import foundation.logical-equivalences -open import foundation.raising-universe-levels-unit-type +open import foundation.existential-quantification funext +open import foundation.large-locale-of-propositions funext +open import foundation.logical-equivalences funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.function-types -open import order-theory.frames -open import order-theory.greatest-lower-bounds-posets -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.meet-semilattices -open import order-theory.meet-suplattices -open import order-theory.posets -open import order-theory.preorders -open import order-theory.suplattices -open import order-theory.top-elements-posets +open import order-theory.frames funext +open import order-theory.greatest-lower-bounds-posets funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.meet-semilattices funext +open import order-theory.meet-suplattices funext +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.suplattices funext +open import order-theory.top-elements-posets funext ```
diff --git a/src/foundation/locally-small-types.lagda.md b/src/foundation/locally-small-types.lagda.md index 2c54ced78e..f4e69c151b 100644 --- a/src/foundation/locally-small-types.lagda.md +++ b/src/foundation/locally-small-types.lagda.md @@ -1,20 +1,26 @@ # Locally small types ```agda -module foundation.locally-small-types where +open import foundation.function-extensionality-axiom + +module + foundation.locally-small-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.dependent-products-truncated-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.inhabited-subtypes -open import foundation.subuniverses -open import foundation.univalence +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.inhabited-subtypes funext +open import foundation.subuniverses funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.embeddings @@ -23,8 +29,8 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext +open import foundation-core.subtypes funext open import foundation-core.transport-along-identifications open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/logical-equivalences.lagda.md b/src/foundation/logical-equivalences.lagda.md index f95d0aacb7..929afb8780 100644 --- a/src/foundation/logical-equivalences.lagda.md +++ b/src/foundation/logical-equivalences.lagda.md @@ -1,7 +1,12 @@ # Logical equivalences ```agda -module foundation.logical-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.logical-equivalences + (funext : function-extensionality) + where open import foundation-core.logical-equivalences public ``` @@ -10,11 +15,12 @@ open import foundation-core.logical-equivalences public ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions +open import foundation.dependent-products-propositions funext open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-cartesian-product-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/maps-in-global-subuniverses.lagda.md b/src/foundation/maps-in-global-subuniverses.lagda.md index 93a167a49c..e92a945013 100644 --- a/src/foundation/maps-in-global-subuniverses.lagda.md +++ b/src/foundation/maps-in-global-subuniverses.lagda.md @@ -1,18 +1,23 @@ # Maps in global subuniverses ```agda -module foundation.maps-in-global-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.maps-in-global-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows +open import foundation.cartesian-morphisms-arrows funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.fibers-of-maps -open import foundation.functoriality-fibers-of-maps -open import foundation.global-subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.global-subuniverses funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/maps-in-subuniverses.lagda.md b/src/foundation/maps-in-subuniverses.lagda.md index 52c43cb7cc..8cbf3758bd 100644 --- a/src/foundation/maps-in-subuniverses.lagda.md +++ b/src/foundation/maps-in-subuniverses.lagda.md @@ -1,14 +1,19 @@ # Maps in subuniverses ```agda -module foundation.maps-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.maps-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.subuniverses +open import foundation.homotopies funext +open import foundation.subuniverses funext open import foundation.universe-levels open import foundation-core.fibers-of-maps diff --git a/src/foundation/maybe.lagda.md b/src/foundation/maybe.lagda.md index a7c8ed3e01..149520a637 100644 --- a/src/foundation/maybe.lagda.md +++ b/src/foundation/maybe.lagda.md @@ -1,7 +1,12 @@ # The maybe monad ```agda -module foundation.maybe where +open import foundation.function-extensionality-axiom + +module + foundation.maybe + (funext : function-extensionality) + where open import foundation-core.maybe public ``` @@ -10,14 +15,14 @@ open import foundation-core.maybe public ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.existential-quantification -open import foundation.propositional-truncations -open import foundation.surjective-maps -open import foundation.type-arithmetic-empty-type +open import foundation.equality-coproduct-types funext +open import foundation.existential-quantification funext +open import foundation.propositional-truncations funext +open import foundation.surjective-maps funext +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/mere-embeddings.lagda.md b/src/foundation/mere-embeddings.lagda.md index 4fbccc13d4..0215657878 100644 --- a/src/foundation/mere-embeddings.lagda.md +++ b/src/foundation/mere-embeddings.lagda.md @@ -1,22 +1,27 @@ # Mere embeddings ```agda -module foundation.mere-embeddings where +open import foundation.function-extensionality-axiom + +module + foundation.mere-embeddings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cantor-schroder-bernstein-escardo -open import foundation.embeddings -open import foundation.law-of-excluded-middle -open import foundation.mere-equivalences -open import foundation.propositional-truncations +open import foundation.cantor-schroder-bernstein-escardo funext +open import foundation.embeddings funext +open import foundation.law-of-excluded-middle funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.propositions -open import order-theory.large-preorders +open import order-theory.large-preorders funext ```
diff --git a/src/foundation/mere-equality.lagda.md b/src/foundation/mere-equality.lagda.md index d5319cae0a..77b75565f0 100644 --- a/src/foundation/mere-equality.lagda.md +++ b/src/foundation/mere-equality.lagda.md @@ -1,21 +1,26 @@ # Mere equality ```agda -module foundation.mere-equality where +open import foundation.function-extensionality-axiom + +module + foundation.mere-equality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations +open import foundation.functoriality-propositional-truncation funext +open import foundation.propositional-truncations funext +open import foundation.reflecting-maps-equivalence-relations funext open import foundation.universe-levels -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets diff --git a/src/foundation/mere-equivalences.lagda.md b/src/foundation/mere-equivalences.lagda.md index 27fecbd0f1..b4e91b45a0 100644 --- a/src/foundation/mere-equivalences.lagda.md +++ b/src/foundation/mere-equivalences.lagda.md @@ -1,19 +1,24 @@ # Mere equivalences ```agda -module foundation.mere-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.mere-equivalences + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-equality -open import foundation.dependent-products-truncated-types -open import foundation.functoriality-propositional-truncation -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.univalence +open import foundation.binary-relations funext +open import foundation.decidable-equality funext +open import foundation.dependent-products-truncated-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/mere-functions.lagda.md b/src/foundation/mere-functions.lagda.md index 4597357ccd..6a5c87b810 100644 --- a/src/foundation/mere-functions.lagda.md +++ b/src/foundation/mere-functions.lagda.md @@ -1,13 +1,18 @@ # Mere functions ```agda -module foundation.mere-functions where +open import foundation.function-extensionality-axiom + +module + foundation.mere-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/mere-logical-equivalences.lagda.md b/src/foundation/mere-logical-equivalences.lagda.md index 5bf9ebe781..5490b4e7c2 100644 --- a/src/foundation/mere-logical-equivalences.lagda.md +++ b/src/foundation/mere-logical-equivalences.lagda.md @@ -1,18 +1,23 @@ # Mere logical equivalences ```agda -module foundation.mere-logical-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.mere-logical-equivalences + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.mere-functions -open import foundation.propositional-truncations +open import foundation.inhabited-types funext +open import foundation.logical-equivalences funext +open import foundation.mere-functions funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/mere-path-cosplit-maps.lagda.md b/src/foundation/mere-path-cosplit-maps.lagda.md index 5cd5644ffe..ac3addf472 100644 --- a/src/foundation/mere-path-cosplit-maps.lagda.md +++ b/src/foundation/mere-path-cosplit-maps.lagda.md @@ -1,7 +1,12 @@ # Mere path-cosplit maps ```agda -module foundation.mere-path-cosplit-maps where +open import foundation.function-extensionality-axiom + +module + foundation.mere-path-cosplit-maps + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module foundation.mere-path-cosplit-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalences-arrows -open import foundation.inhabited-types -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.truncated-maps +open import foundation.dependent-products-propositions funext +open import foundation.equivalences-arrows funext +open import foundation.inhabited-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.truncated-maps funext open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/foundation/monomorphisms.lagda.md b/src/foundation/monomorphisms.lagda.md index 9fc0e6bd82..eb98657ed8 100644 --- a/src/foundation/monomorphisms.lagda.md +++ b/src/foundation/monomorphisms.lagda.md @@ -1,7 +1,12 @@ # Monomorphisms ```agda -module foundation.monomorphisms where +open import foundation.function-extensionality-axiom + +module + foundation.monomorphisms + (funext : function-extensionality) + where ```
Imports @@ -9,11 +14,12 @@ module foundation.monomorphisms where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings -open import foundation.function-extensionality -open import foundation.functoriality-function-types -open import foundation.postcomposition-functions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-function-types funext +open import foundation.postcomposition-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/morphisms-arrows.lagda.md b/src/foundation/morphisms-arrows.lagda.md index b80513a416..04cbfd8dce 100644 --- a/src/foundation/morphisms-arrows.lagda.md +++ b/src/foundation/morphisms-arrows.lagda.md @@ -1,21 +1,27 @@ # Morphisms of arrows ```agda -module foundation.morphisms-arrows where +open import foundation.function-extensionality-axiom + +module + foundation.morphisms-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/morphisms-binary-relations.lagda.md b/src/foundation/morphisms-binary-relations.lagda.md index 5e9c42e904..06b0427747 100644 --- a/src/foundation/morphisms-binary-relations.lagda.md +++ b/src/foundation/morphisms-binary-relations.lagda.md @@ -1,14 +1,19 @@ # Morphisms of binary relations ```agda -module foundation.morphisms-binary-relations where +open import foundation.function-extensionality-axiom + +module + foundation.morphisms-binary-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-homotopies -open import foundation.binary-relations +open import foundation.binary-homotopies funext +open import foundation.binary-relations funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/morphisms-coalgebras-maybe.lagda.md b/src/foundation/morphisms-coalgebras-maybe.lagda.md index 41c03ed586..049b157edf 100644 --- a/src/foundation/morphisms-coalgebras-maybe.lagda.md +++ b/src/foundation/morphisms-coalgebras-maybe.lagda.md @@ -1,20 +1,25 @@ # Morphisms of coalgebras of the maybe monad ```agda -module foundation.morphisms-coalgebras-maybe where +open import foundation.function-extensionality-axiom + +module + foundation.morphisms-coalgebras-maybe + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coalgebras-maybe -open import foundation.commuting-squares-of-maps +open import foundation.coalgebras-maybe funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation-core.maybe -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext ```
diff --git a/src/foundation/morphisms-double-arrows.lagda.md b/src/foundation/morphisms-double-arrows.lagda.md index 33810a5de8..0e80732b07 100644 --- a/src/foundation/morphisms-double-arrows.lagda.md +++ b/src/foundation/morphisms-double-arrows.lagda.md @@ -1,19 +1,24 @@ # Morphisms of double arrows ```agda -module foundation.morphisms-double-arrows where +open import foundation.function-extensionality-axiom + +module + foundation.morphisms-double-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps +open import foundation.cartesian-product-types funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.function-types -open import foundation.homotopies -open import foundation.morphisms-arrows +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels ``` diff --git a/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md b/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md index 515f06b8ce..255776a6b5 100644 --- a/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Morphisms of inverse sequential diagrams of types ```agda -module foundation.morphisms-inverse-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.morphisms-inverse-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -10,13 +15,13 @@ module foundation.morphisms-inverse-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-homotopies -open import foundation.dependent-inverse-sequential-diagrams +open import foundation.binary-homotopies funext +open import foundation.dependent-inverse-sequential-diagrams funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.inverse-sequential-diagrams +open import foundation.homotopy-induction funext +open import foundation.inverse-sequential-diagrams funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/morphisms-span-diagrams.lagda.md b/src/foundation/morphisms-span-diagrams.lagda.md index 604d0c6d6e..0f93f1d095 100644 --- a/src/foundation/morphisms-span-diagrams.lagda.md +++ b/src/foundation/morphisms-span-diagrams.lagda.md @@ -1,20 +1,25 @@ # Morphisms of span diagrams ```agda -module foundation.morphisms-span-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.morphisms-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.morphisms-spans -open import foundation.operations-spans -open import foundation.span-diagrams +open import foundation.operations-spans funext +open import foundation.span-diagrams funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext ```
diff --git a/src/foundation/morphisms-spans-families-of-types.lagda.md b/src/foundation/morphisms-spans-families-of-types.lagda.md index 8c372f1a61..310d245cbc 100644 --- a/src/foundation/morphisms-spans-families-of-types.lagda.md +++ b/src/foundation/morphisms-spans-families-of-types.lagda.md @@ -1,17 +1,22 @@ # Morphisms of spans on families of types ```agda -module foundation.morphisms-spans-families-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.morphisms-spans-families-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.spans-families-of-types open import foundation.structure-identity-principle open import foundation.universe-levels diff --git a/src/foundation/multisubsets.lagda.md b/src/foundation/multisubsets.lagda.md index 3819e8ba69..f0a5cc7cc1 100644 --- a/src/foundation/multisubsets.lagda.md +++ b/src/foundation/multisubsets.lagda.md @@ -1,7 +1,12 @@ # Multisubsets ```agda -module foundation.multisubsets where +open import foundation.function-extensionality-axiom + +module + foundation.multisubsets + (funext : function-extensionality) + where ```
Imports @@ -10,14 +15,14 @@ module foundation.multisubsets where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.images -open import foundation.negated-equality +open import foundation.images funext +open import foundation.negated-equality funext open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.sets -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/foundation/multivariable-correspondences.lagda.md b/src/foundation/multivariable-correspondences.lagda.md index 817901c593..1148321a72 100644 --- a/src/foundation/multivariable-correspondences.lagda.md +++ b/src/foundation/multivariable-correspondences.lagda.md @@ -1,7 +1,12 @@ # Multivariable correspondences ```agda -module foundation.multivariable-correspondences where +open import foundation.function-extensionality-axiom + +module + foundation.multivariable-correspondences + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/multivariable-decidable-relations.lagda.md b/src/foundation/multivariable-decidable-relations.lagda.md index 9a5467028e..80cf44621b 100644 --- a/src/foundation/multivariable-decidable-relations.lagda.md +++ b/src/foundation/multivariable-decidable-relations.lagda.md @@ -1,7 +1,12 @@ # Multivariable decidable relations ```agda -module foundation.multivariable-decidable-relations where +open import foundation.function-extensionality-axiom + +module + foundation.multivariable-decidable-relations + (funext : function-extensionality) + where ```
Imports @@ -9,12 +14,12 @@ module foundation.multivariable-decidable-relations where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-subtypes -open import foundation.multivariable-correspondences -open import foundation.multivariable-relations +open import foundation.decidable-subtypes funext +open import foundation.multivariable-correspondences funext +open import foundation.multivariable-relations funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/multivariable-functoriality-set-quotients.lagda.md b/src/foundation/multivariable-functoriality-set-quotients.lagda.md index 62cad9dc12..aec02ce5ae 100644 --- a/src/foundation/multivariable-functoriality-set-quotients.lagda.md +++ b/src/foundation/multivariable-functoriality-set-quotients.lagda.md @@ -1,7 +1,12 @@ # Multivariable functoriality of set quotients ```agda -module foundation.multivariable-functoriality-set-quotients where +open import foundation.function-extensionality-axiom + +module + foundation.multivariable-functoriality-set-quotients + (funext : function-extensionality) + where ```
Imports @@ -9,18 +14,18 @@ module foundation.multivariable-functoriality-set-quotients where ```agda open import elementary-number-theory.natural-numbers -open import foundation.functoriality-set-quotients -open import foundation.set-quotients +open import foundation.functoriality-set-quotients funext +open import foundation.set-quotients funext open import foundation.universe-levels -open import foundation.vectors-set-quotients +open import foundation.vectors-set-quotients funext -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.function-types open import foundation-core.homotopies -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/multivariable-homotopies.lagda.md b/src/foundation/multivariable-homotopies.lagda.md index 3d3588b02c..83ec67d484 100644 --- a/src/foundation/multivariable-homotopies.lagda.md +++ b/src/foundation/multivariable-homotopies.lagda.md @@ -1,7 +1,12 @@ # Multivariable homotopies ```agda -module foundation.multivariable-homotopies where +open import foundation.function-extensionality-axiom + +module + foundation.multivariable-homotopies + (funext : function-extensionality) + where ```
Imports @@ -10,17 +15,17 @@ module foundation.multivariable-homotopies where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.equality-dependent-function-types funext +open import foundation.function-extensionality funext + open import foundation.implicit-function-types -open import foundation.iterated-dependent-product-types +open import foundation.iterated-dependent-product-types funext open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.torsorial-type-families diff --git a/src/foundation/multivariable-operations.lagda.md b/src/foundation/multivariable-operations.lagda.md index fd82bdc4d4..3dfa907628 100644 --- a/src/foundation/multivariable-operations.lagda.md +++ b/src/foundation/multivariable-operations.lagda.md @@ -1,7 +1,12 @@ # Multivariable operations ```agda -module foundation.multivariable-operations where +open import foundation.function-extensionality-axiom + +module + foundation.multivariable-operations + (funext : function-extensionality) + where ```
Imports @@ -12,8 +17,8 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type open import foundation.unit-type open import foundation.universe-levels @@ -24,7 +29,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import linear-algebra.vectors +open import linear-algebra.vectors funext ```
diff --git a/src/foundation/multivariable-relations.lagda.md b/src/foundation/multivariable-relations.lagda.md index 630c453e97..9b1d2bfbce 100644 --- a/src/foundation/multivariable-relations.lagda.md +++ b/src/foundation/multivariable-relations.lagda.md @@ -1,7 +1,12 @@ # Multivariable relations ```agda -module foundation.multivariable-relations where +open import foundation.function-extensionality-axiom + +module + foundation.multivariable-relations + (funext : function-extensionality) + where ```
Imports @@ -9,12 +14,12 @@ module foundation.multivariable-relations where ```agda open import elementary-number-theory.natural-numbers -open import foundation.multivariable-correspondences +open import foundation.multivariable-correspondences funext open import foundation.universe-levels -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/multivariable-sections.lagda.md b/src/foundation/multivariable-sections.lagda.md index f3fd8820d7..5c317627b2 100644 --- a/src/foundation/multivariable-sections.lagda.md +++ b/src/foundation/multivariable-sections.lagda.md @@ -1,7 +1,12 @@ # Multivariable sections ```agda -module foundation.multivariable-sections where +open import foundation.function-extensionality-axiom + +module + foundation.multivariable-sections + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module foundation.multivariable-sections where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types -open import foundation.multivariable-homotopies +open import foundation.iterated-dependent-product-types funext +open import foundation.multivariable-homotopies funext open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/negated-equality.lagda.md b/src/foundation/negated-equality.lagda.md index 6978557244..3469298fcc 100644 --- a/src/foundation/negated-equality.lagda.md +++ b/src/foundation/negated-equality.lagda.md @@ -1,17 +1,21 @@ # Negated equality ```agda -module foundation.negated-equality where +open import foundation.function-extensionality-axiom + +module + foundation.negated-equality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.function-extensionality-axiom -open import foundation.negation +open import foundation.negation funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/negation.lagda.md b/src/foundation/negation.lagda.md index 6e01b1d0a1..d3574d49fc 100644 --- a/src/foundation/negation.lagda.md +++ b/src/foundation/negation.lagda.md @@ -1,7 +1,12 @@ # Negation ```agda -module foundation.negation where +open import foundation.function-extensionality-axiom + +module + foundation.negation + (funext : function-extensionality) + where open import foundation-core.negation public ``` @@ -10,8 +15,8 @@ open import foundation-core.negation public ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.logical-equivalences +open import foundation.dependent-products-propositions funext +open import foundation.logical-equivalences funext open import foundation.universe-levels open import foundation-core.empty-types diff --git a/src/foundation/noncontractible-types.lagda.md b/src/foundation/noncontractible-types.lagda.md index 98d2d49311..56e62a8088 100644 --- a/src/foundation/noncontractible-types.lagda.md +++ b/src/foundation/noncontractible-types.lagda.md @@ -1,7 +1,12 @@ # Noncontractible types ```agda -module foundation.noncontractible-types where +open import foundation.function-extensionality-axiom + +module + foundation.noncontractible-types + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module foundation.noncontractible-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.inhabited-types +open import foundation.empty-types funext +open import foundation.inhabited-types funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/null-homotopic-maps.lagda.md b/src/foundation/null-homotopic-maps.lagda.md index 2500c019f4..7b73047a38 100644 --- a/src/foundation/null-homotopic-maps.lagda.md +++ b/src/foundation/null-homotopic-maps.lagda.md @@ -1,33 +1,38 @@ # Null-homotopic maps ```agda -module foundation.null-homotopic-maps where +open import foundation.function-extensionality-axiom + +module + foundation.null-homotopic-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-identifications -open import foundation.constant-maps +open import foundation.commuting-triangles-of-identifications funext +open import foundation.constant-maps funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.functoriality-dependent-pair-types +open import foundation.empty-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.images -open import foundation.inhabited-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.inhabited-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-empty-type +open import foundation.universal-property-empty-type funext open import foundation.universe-levels -open import foundation.weakly-constant-maps +open import foundation.weakly-constant-maps funext open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/operations-span-diagrams.lagda.md b/src/foundation/operations-span-diagrams.lagda.md index 9337e9f12a..6896795247 100644 --- a/src/foundation/operations-span-diagrams.lagda.md +++ b/src/foundation/operations-span-diagrams.lagda.md @@ -1,18 +1,23 @@ # Operations on span diagrams ```agda -module foundation.operations-span-diagrams where +open import foundation.function-extensionality-axiom -open import foundation-core.operations-span-diagrams public +module + foundation.operations-span-diagrams + (funext : function-extensionality) + where + +open import foundation-core.operations-span-diagrams funext public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences-arrows -open import foundation.operations-spans -open import foundation.span-diagrams +open import foundation.equivalences-arrows funext +open import foundation.operations-spans funext +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels ``` diff --git a/src/foundation/operations-spans.lagda.md b/src/foundation/operations-spans.lagda.md index 6562513941..9f589ec323 100644 --- a/src/foundation/operations-spans.lagda.md +++ b/src/foundation/operations-spans.lagda.md @@ -1,17 +1,22 @@ # Operations on spans ```agda -module foundation.operations-spans where +open import foundation.function-extensionality-axiom -open import foundation-core.operations-spans public +module + foundation.operations-spans + (funext : function-extensionality) + where + +open import foundation-core.operations-spans funext public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences-arrows -open import foundation.morphisms-arrows +open import foundation.equivalences-arrows funext +open import foundation.morphisms-arrows funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/pairs-of-distinct-elements.lagda.md b/src/foundation/pairs-of-distinct-elements.lagda.md index 8b152f6408..7d52cab993 100644 --- a/src/foundation/pairs-of-distinct-elements.lagda.md +++ b/src/foundation/pairs-of-distinct-elements.lagda.md @@ -1,18 +1,23 @@ # Pairs of distinct elements ```agda -module foundation.pairs-of-distinct-elements where +open import foundation.function-extensionality-axiom + +module + foundation.pairs-of-distinct-elements + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences +open import foundation.embeddings funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.negated-equality -open import foundation.negation +open import foundation.negated-equality funext +open import foundation.negation funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle open import foundation.universe-levels diff --git a/src/foundation/partitions.lagda.md b/src/foundation/partitions.lagda.md index b46f3f5c10..51af928f19 100644 --- a/src/foundation/partitions.lagda.md +++ b/src/foundation/partitions.lagda.md @@ -1,32 +1,37 @@ # Partitions ```agda -module foundation.partitions where +open import foundation.function-extensionality-axiom + +module + foundation.partitions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.conjunction -open import foundation.contractible-types +open import foundation.conjunction funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.fiber-inclusions +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.fiber-inclusions funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-subtypes -open import foundation.inhabited-types -open import foundation.locally-small-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.sigma-decompositions -open import foundation.small-types +open import foundation.inhabited-subtypes funext +open import foundation.inhabited-types funext +open import foundation.locally-small-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.sigma-decompositions funext +open import foundation.small-types funext open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -34,7 +39,7 @@ open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/path-algebra.lagda.md b/src/foundation/path-algebra.lagda.md index 471a4d85e1..1e09e92baa 100644 --- a/src/foundation/path-algebra.lagda.md +++ b/src/foundation/path-algebra.lagda.md @@ -1,7 +1,12 @@ # Path algebra ```agda -module foundation.path-algebra where +open import foundation.function-extensionality-axiom + +module + foundation.path-algebra + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module foundation.path-algebra where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications diff --git a/src/foundation/path-cosplit-maps.lagda.md b/src/foundation/path-cosplit-maps.lagda.md index cf0e458b12..b46909a175 100644 --- a/src/foundation/path-cosplit-maps.lagda.md +++ b/src/foundation/path-cosplit-maps.lagda.md @@ -1,7 +1,12 @@ # Path-cosplit maps ```agda -module foundation.path-cosplit-maps where +open import foundation.function-extensionality-axiom + +module + foundation.path-cosplit-maps + (funext : function-extensionality) + where ```
Imports @@ -10,38 +15,39 @@ module foundation.path-cosplit-maps where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.coproduct-types +open import foundation.commuting-triangles-of-maps funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.dependent-products-propositions -open import foundation.dependent-products-truncated-types -open import foundation.empty-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-truncated-types funext +open import foundation.empty-types funext open import foundation.equality-cartesian-product-types -open import foundation.equality-coproduct-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences-arrows -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-action-on-identifications-functions -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.mere-path-cosplit-maps -open import foundation.morphisms-arrows -open import foundation.negated-equality -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.truncated-maps +open import foundation.equality-coproduct-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences-arrows funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-action-on-identifications-functions funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.mere-path-cosplit-maps funext +open import foundation.morphisms-arrows funext +open import foundation.negated-equality funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext +open import foundation.truncated-maps funext open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/foundation/path-split-maps.lagda.md b/src/foundation/path-split-maps.lagda.md index 28223aec36..4a9e40a544 100644 --- a/src/foundation/path-split-maps.lagda.md +++ b/src/foundation/path-split-maps.lagda.md @@ -1,7 +1,12 @@ # Path-split maps ```agda -module foundation.path-split-maps where +open import foundation.function-extensionality-axiom + +module + foundation.path-split-maps + (funext : function-extensionality) + where open import foundation-core.path-split-maps public ``` @@ -10,9 +15,9 @@ open import foundation-core.path-split-maps public ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences +open import foundation.equivalences funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/path-split-type-families.lagda.md b/src/foundation/path-split-type-families.lagda.md index 0aad6110c8..3c2d33fac1 100644 --- a/src/foundation/path-split-type-families.lagda.md +++ b/src/foundation/path-split-type-families.lagda.md @@ -1,7 +1,12 @@ # Path-split type families ```agda -module foundation.path-split-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.path-split-type-families + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module foundation.path-split-type-families where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.embeddings +open import foundation.dependent-products-contractible-types funext +open import foundation.embeddings funext open import foundation.transport-along-identifications open import foundation.universe-levels @@ -21,7 +26,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositions open import foundation-core.sections -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/perfect-images.lagda.md b/src/foundation/perfect-images.lagda.md index 2a0569e866..9db1a591ef 100644 --- a/src/foundation/perfect-images.lagda.md +++ b/src/foundation/perfect-images.lagda.md @@ -1,7 +1,12 @@ # Perfect images ```agda -module foundation.perfect-images where +open import foundation.function-extensionality-axiom + +module + foundation.perfect-images + (funext : function-extensionality) + where ```
Imports @@ -10,14 +15,14 @@ module foundation.perfect-images where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.iterated-dependent-product-types -open import foundation.iterating-functions -open import foundation.law-of-excluded-middle -open import foundation.negated-equality -open import foundation.negation +open import foundation.double-negation funext +open import foundation.iterated-dependent-product-types funext +open import foundation.iterating-functions funext +open import foundation.law-of-excluded-middle funext +open import foundation.negated-equality funext +open import foundation.negation funext open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/pi-decompositions-subuniverse.lagda.md b/src/foundation/pi-decompositions-subuniverse.lagda.md index 940decfffb..b204251f70 100644 --- a/src/foundation/pi-decompositions-subuniverse.lagda.md +++ b/src/foundation/pi-decompositions-subuniverse.lagda.md @@ -1,15 +1,20 @@ # Π-decompositions of types into types in a subuniverse ```agda -module foundation.pi-decompositions-subuniverse where +open import foundation.function-extensionality-axiom + +module + foundation.pi-decompositions-subuniverse + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.pi-decompositions -open import foundation.subuniverses +open import foundation.pi-decompositions funext +open import foundation.subuniverses funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/pi-decompositions.lagda.md b/src/foundation/pi-decompositions.lagda.md index dcbbb9f548..a47a21b6f6 100644 --- a/src/foundation/pi-decompositions.lagda.md +++ b/src/foundation/pi-decompositions.lagda.md @@ -3,20 +3,25 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.pi-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.pi-decompositions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/pointed-torsorial-type-families.lagda.md b/src/foundation/pointed-torsorial-type-families.lagda.md index ac06797f4c..a6e533b8d1 100644 --- a/src/foundation/pointed-torsorial-type-families.lagda.md +++ b/src/foundation/pointed-torsorial-type-families.lagda.md @@ -1,23 +1,28 @@ # Pointed torsorial type families ```agda -module foundation.pointed-torsorial-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.pointed-torsorial-type-families + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalences +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.locally-small-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.locally-small-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext open import foundation.sorial-type-families open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -25,7 +30,7 @@ open import foundation-core.contractible-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.small-types +open import foundation-core.small-types funext open import foundation-core.torsorial-type-families open import structured-types.pointed-types diff --git a/src/foundation/postcomposition-dependent-functions.lagda.md b/src/foundation/postcomposition-dependent-functions.lagda.md index f01cde3833..a6f88b40db 100644 --- a/src/foundation/postcomposition-dependent-functions.lagda.md +++ b/src/foundation/postcomposition-dependent-functions.lagda.md @@ -1,7 +1,12 @@ # Postcomposition of dependent functions ```agda -module foundation.postcomposition-dependent-functions where +open import foundation.function-extensionality-axiom + +module + foundation.postcomposition-dependent-functions + (funext : function-extensionality) + where open import foundation-core.postcomposition-dependent-functions public ``` @@ -10,12 +15,12 @@ open import foundation-core.postcomposition-dependent-functions public ```agda open import foundation.action-on-identifications-functions -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.identity-types ``` diff --git a/src/foundation/postcomposition-functions.lagda.md b/src/foundation/postcomposition-functions.lagda.md index 247b3d1eb1..5fc3bc233f 100644 --- a/src/foundation/postcomposition-functions.lagda.md +++ b/src/foundation/postcomposition-functions.lagda.md @@ -1,7 +1,12 @@ # Postcomposition of functions ```agda -module foundation.postcomposition-functions where +open import foundation.function-extensionality-axiom + +module + foundation.postcomposition-functions + (funext : function-extensionality) + where open import foundation-core.postcomposition-functions public ``` @@ -11,20 +16,20 @@ open import foundation-core.postcomposition-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.postcomposition-dependent-functions +open import foundation.function-extensionality funext + +open import foundation.postcomposition-dependent-functions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/postcomposition-pullbacks.lagda.md b/src/foundation/postcomposition-pullbacks.lagda.md index 7b3dc4fee2..bacad23184 100644 --- a/src/foundation/postcomposition-pullbacks.lagda.md +++ b/src/foundation/postcomposition-pullbacks.lagda.md @@ -1,18 +1,23 @@ # Postcomposition of pullbacks ```agda -module foundation.postcomposition-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.postcomposition-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.standard-pullbacks +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -22,8 +27,8 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.postcomposition-functions -open import foundation-core.pullbacks -open import foundation-core.universal-property-pullbacks +open import foundation-core.pullbacks funext +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/powersets.lagda.md b/src/foundation/powersets.lagda.md index e195cf37f9..18d5056158 100644 --- a/src/foundation/powersets.lagda.md +++ b/src/foundation/powersets.lagda.md @@ -1,41 +1,46 @@ # Powersets ```agda -module foundation.powersets where +open import foundation.function-extensionality-axiom + +module + foundation.powersets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.large-locale-of-propositions -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.large-locale-of-propositions funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.subtypes funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.sets -open import order-theory.bottom-elements-large-posets -open import order-theory.bottom-elements-posets -open import order-theory.dependent-products-large-meet-semilattices -open import order-theory.dependent-products-large-posets -open import order-theory.dependent-products-large-preorders -open import order-theory.dependent-products-large-suplattices -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.posets -open import order-theory.preorders -open import order-theory.similarity-of-elements-large-posets -open import order-theory.suplattices -open import order-theory.top-elements-large-posets -open import order-theory.top-elements-posets +open import order-theory.bottom-elements-large-posets funext +open import order-theory.bottom-elements-posets funext +open import order-theory.dependent-products-large-meet-semilattices funext +open import order-theory.dependent-products-large-posets funext +open import order-theory.dependent-products-large-preorders funext +open import order-theory.dependent-products-large-suplattices funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.large-suplattices funext +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.suplattices funext +open import order-theory.top-elements-large-posets funext +open import order-theory.top-elements-posets funext ```
diff --git a/src/foundation/precomposition-dependent-functions.lagda.md b/src/foundation/precomposition-dependent-functions.lagda.md index f7a092edc9..cb45239ca4 100644 --- a/src/foundation/precomposition-dependent-functions.lagda.md +++ b/src/foundation/precomposition-dependent-functions.lagda.md @@ -1,7 +1,12 @@ # Precomposition of dependent functions ```agda -module foundation.precomposition-dependent-functions where +open import foundation.function-extensionality-axiom + +module + foundation.precomposition-dependent-functions + (funext : function-extensionality) + where open import foundation-core.precomposition-dependent-functions public ``` @@ -11,18 +16,18 @@ open import foundation-core.precomposition-dependent-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.dependent-universal-property-equivalences funext +open import foundation.function-extensionality funext + open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/precomposition-functions-into-subuniverses.lagda.md b/src/foundation/precomposition-functions-into-subuniverses.lagda.md index c6dcd9527c..75cf74b2bb 100644 --- a/src/foundation/precomposition-functions-into-subuniverses.lagda.md +++ b/src/foundation/precomposition-functions-into-subuniverses.lagda.md @@ -1,7 +1,12 @@ # Precomposition of functions into subuniverses ```agda -module foundation.precomposition-functions-into-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.precomposition-functions-into-subuniverses + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,7 @@ module foundation.precomposition-functions-into-subuniverses where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality-axiom -open import foundation.precomposition-functions +open import foundation.precomposition-functions funext open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/precomposition-functions.lagda.md b/src/foundation/precomposition-functions.lagda.md index c8216b79b9..4aac6bfe01 100644 --- a/src/foundation/precomposition-functions.lagda.md +++ b/src/foundation/precomposition-functions.lagda.md @@ -1,7 +1,12 @@ # Precomposition of functions ```agda -module foundation.precomposition-functions where +open import foundation.function-extensionality-axiom + +module + foundation.precomposition-functions + (funext : function-extensionality) + where open import foundation-core.precomposition-functions public ``` @@ -11,14 +16,14 @@ open import foundation-core.precomposition-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.precomposition-dependent-functions -open import foundation.sections +open import foundation.function-extensionality funext + +open import foundation.precomposition-dependent-functions funext +open import foundation.sections funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.commuting-triangles-of-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation/precomposition-type-families.lagda.md b/src/foundation/precomposition-type-families.lagda.md index 0d86dd8b97..52d180ac99 100644 --- a/src/foundation/precomposition-type-families.lagda.md +++ b/src/foundation/precomposition-type-families.lagda.md @@ -1,14 +1,19 @@ # Precomposition of type families ```agda -module foundation.precomposition-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.precomposition-type-families + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.homotopy-induction -open import foundation.transport-along-homotopies +open import foundation.homotopy-induction funext +open import foundation.transport-along-homotopies funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/preunivalence.lagda.md b/src/foundation/preunivalence.lagda.md index 9fe3c4409c..6832bf367d 100644 --- a/src/foundation/preunivalence.lagda.md +++ b/src/foundation/preunivalence.lagda.md @@ -1,21 +1,26 @@ # The preunivalence axiom ```agda -module foundation.preunivalence where +open import foundation.function-extensionality-axiom + +module + foundation.preunivalence + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.sets -open import foundation.univalence +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.sets funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.identity-types -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/preunivalent-type-families.lagda.md b/src/foundation/preunivalent-type-families.lagda.md index 933a182ad5..2efee40de9 100644 --- a/src/foundation/preunivalent-type-families.lagda.md +++ b/src/foundation/preunivalent-type-families.lagda.md @@ -1,24 +1,29 @@ # Preunivalent type families ```agda -module foundation.preunivalent-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.preunivalent-type-families + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-maps +open import foundation.0-maps funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-injective-type-families -open import foundation.faithful-maps -open import foundation.function-types -open import foundation.injective-maps -open import foundation.preunivalence -open import foundation.retractions -open import foundation.sets -open import foundation.subuniverses +open import foundation.embeddings funext +open import foundation.equivalence-injective-type-families funext +open import foundation.faithful-maps funext +open import foundation.function-types funext +open import foundation.injective-maps funext +open import foundation.preunivalence funext +open import foundation.retractions funext +open import foundation.sets funext +open import foundation.subuniverses funext open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/principle-of-omniscience.lagda.md b/src/foundation/principle-of-omniscience.lagda.md index 6b5ce7a3d1..0b7bc97076 100644 --- a/src/foundation/principle-of-omniscience.lagda.md +++ b/src/foundation/principle-of-omniscience.lagda.md @@ -1,18 +1,23 @@ # The principle of omniscience ```agda -module foundation.principle-of-omniscience where +open import foundation.function-extensionality-axiom + +module + foundation.principle-of-omniscience + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-subtypes -open import foundation.dependent-products-propositions -open import foundation.propositional-truncations +open import foundation.decidable-subtypes funext +open import foundation.dependent-products-propositions funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.propositions ``` diff --git a/src/foundation/product-decompositions-subuniverse.lagda.md b/src/foundation/product-decompositions-subuniverse.lagda.md index cb4513fe87..dcedaf6118 100644 --- a/src/foundation/product-decompositions-subuniverse.lagda.md +++ b/src/foundation/product-decompositions-subuniverse.lagda.md @@ -1,23 +1,28 @@ # Product decompositions of types in a subuniverse ```agda -module foundation.product-decompositions-subuniverse where +open import foundation.function-extensionality-axiom + +module + foundation.product-decompositions-subuniverse + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.dependent-products-propositions -open import foundation.equivalences -open import foundation.raising-universe-levels-unit-type -open import foundation.subuniverses +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.subuniverses funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/products-binary-relations.lagda.md b/src/foundation/products-binary-relations.lagda.md index 93f4ce0c07..8c051bf627 100644 --- a/src/foundation/products-binary-relations.lagda.md +++ b/src/foundation/products-binary-relations.lagda.md @@ -1,13 +1,18 @@ # Products of binary relations ```agda -module foundation.products-binary-relations where +open import foundation.function-extensionality-axiom + +module + foundation.products-binary-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/products-equivalence-relations.lagda.md b/src/foundation/products-equivalence-relations.lagda.md index 37e2364b6d..73bb6f7de8 100644 --- a/src/foundation/products-equivalence-relations.lagda.md +++ b/src/foundation/products-equivalence-relations.lagda.md @@ -1,19 +1,24 @@ # Products of equivalence relataions ```agda -module foundation.products-equivalence-relations where +open import foundation.function-extensionality-axiom + +module + foundation.products-equivalence-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.products-binary-relations +open import foundation.products-binary-relations funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext ```
diff --git a/src/foundation/products-of-tuples-of-types.lagda.md b/src/foundation/products-of-tuples-of-types.lagda.md index 0fc4d95508..64591a9c2b 100644 --- a/src/foundation/products-of-tuples-of-types.lagda.md +++ b/src/foundation/products-of-tuples-of-types.lagda.md @@ -1,7 +1,12 @@ # Products of tuples of types ```agda -module foundation.products-of-tuples-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.products-of-tuples-of-types + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module foundation.products-of-tuples-of-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.tuples-of-types +open import foundation.tuples-of-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/products-pullbacks.lagda.md b/src/foundation/products-pullbacks.lagda.md index acd174310d..7cf32c29b7 100644 --- a/src/foundation/products-pullbacks.lagda.md +++ b/src/foundation/products-pullbacks.lagda.md @@ -1,20 +1,25 @@ # Products of pullbacks ```agda -module foundation.products-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.products-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.pullbacks -open import foundation.standard-pullbacks +open import foundation.functoriality-cartesian-product-types funext +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext +open import foundation.pullbacks funext +open import foundation.standard-pullbacks funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -24,7 +29,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/products-unordered-pairs-of-types.lagda.md b/src/foundation/products-unordered-pairs-of-types.lagda.md index 73d194ded8..9e3fe90acb 100644 --- a/src/foundation/products-unordered-pairs-of-types.lagda.md +++ b/src/foundation/products-unordered-pairs-of-types.lagda.md @@ -1,28 +1,33 @@ # Products of unordered pairs of types ```agda -module foundation.products-unordered-pairs-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.products-unordered-pairs-of-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.symmetric-operations +open import foundation.dependent-universal-property-equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.symmetric-operations funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.unordered-pairs -open import foundation.unordered-pairs-of-types +open import foundation.unordered-pairs funext +open import foundation.unordered-pairs funext-of-types open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.universal-property-standard-finite-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.universal-property-standard-finite-types funext ```
diff --git a/src/foundation/products-unordered-tuples-of-types.lagda.md b/src/foundation/products-unordered-tuples-of-types.lagda.md index c33e6374ef..ccceace7d7 100644 --- a/src/foundation/products-unordered-tuples-of-types.lagda.md +++ b/src/foundation/products-unordered-tuples-of-types.lagda.md @@ -1,7 +1,12 @@ # Products of unordered tuples of types ```agda -module foundation.products-unordered-tuples-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.products-unordered-tuples-of-types + (funext : function-extensionality) + where ```
Imports @@ -10,16 +15,16 @@ module foundation.products-unordered-tuples-of-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types -open import foundation.universal-property-maybe +open import foundation.functoriality-dependent-function-types funext +open import foundation.universal-property-maybe funext open import foundation.universe-levels -open import foundation.unordered-tuples -open import foundation.unordered-tuples-of-types +open import foundation.unordered-tuples funext +open import foundation.unordered-tuples funext-of-types open import foundation-core.cartesian-product-types open import foundation-core.equivalences -open import univalent-combinatorics.complements-isolated-elements +open import univalent-combinatorics.complements-isolated-elements funext ```
diff --git a/src/foundation/projective-types.lagda.md b/src/foundation/projective-types.lagda.md index f537366853..30fea2599e 100644 --- a/src/foundation/projective-types.lagda.md +++ b/src/foundation/projective-types.lagda.md @@ -1,7 +1,12 @@ # Projective types ```agda -module foundation.projective-types where +open import foundation.function-extensionality-axiom + +module + foundation.projective-types + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module foundation.projective-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-maps -open import foundation.postcomposition-functions -open import foundation.surjective-maps +open import foundation.connected-maps funext +open import foundation.postcomposition-functions funext +open import foundation.surjective-maps funext open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/foundation/proper-subtypes.lagda.md b/src/foundation/proper-subtypes.lagda.md index 2ca5864332..d1183221ee 100644 --- a/src/foundation/proper-subtypes.lagda.md +++ b/src/foundation/proper-subtypes.lagda.md @@ -1,18 +1,23 @@ # Proper subsets ```agda -module foundation.proper-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.proper-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.complements-subtypes -open import foundation.inhabited-subtypes +open import foundation.complements-subtypes funext +open import foundation.inhabited-subtypes funext open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/propositional-extensionality.lagda.md b/src/foundation/propositional-extensionality.lagda.md index 3d3e72c471..7965ff0291 100644 --- a/src/foundation/propositional-extensionality.lagda.md +++ b/src/foundation/propositional-extensionality.lagda.md @@ -1,30 +1,35 @@ # Propositional extensionality ```agda -module foundation.propositional-extensionality where +open import foundation.function-extensionality-axiom + +module + foundation.propositional-extensionality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.dependent-products-propositions -open import foundation.empty-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type open import foundation.subtype-identity-principle open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type -open import foundation.univalence -open import foundation.univalent-type-families -open import foundation.universal-property-contractible-types -open import foundation.universal-property-empty-type +open import foundation.univalence funext +open import foundation.univalent-type-families funext +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-empty-type funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/propositional-maps.lagda.md b/src/foundation/propositional-maps.lagda.md index 00de80bd25..3e12f14837 100644 --- a/src/foundation/propositional-maps.lagda.md +++ b/src/foundation/propositional-maps.lagda.md @@ -1,7 +1,12 @@ # Propositional maps ```agda -module foundation.propositional-maps where +open import foundation.function-extensionality-axiom + +module + foundation.propositional-maps + (funext : function-extensionality) + where open import foundation-core.propositional-maps public ``` @@ -10,10 +15,10 @@ open import foundation-core.propositional-maps public ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings -open import foundation.logical-equivalences -open import foundation.truncated-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.logical-equivalences funext +open import foundation.truncated-maps funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/propositional-resizing.lagda.md b/src/foundation/propositional-resizing.lagda.md index 22cb73035d..5c4017d869 100644 --- a/src/foundation/propositional-resizing.lagda.md +++ b/src/foundation/propositional-resizing.lagda.md @@ -1,20 +1,25 @@ # Propositional resizing ```agda -module foundation.propositional-resizing where +open import foundation.function-extensionality-axiom + +module + foundation.propositional-resizing + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions +open import foundation.dependent-products-propositions funext open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.propositions -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/propositional-truncations.lagda.md b/src/foundation/propositional-truncations.lagda.md index c9ae9be7fc..4c48cc036f 100644 --- a/src/foundation/propositional-truncations.lagda.md +++ b/src/foundation/propositional-truncations.lagda.md @@ -1,7 +1,12 @@ # Propositional truncations ```agda -module foundation.propositional-truncations where +open import foundation.function-extensionality-axiom + +module + foundation.propositional-truncations + (funext : function-extensionality) + where ```
Imports @@ -9,12 +14,12 @@ module foundation.propositional-truncations where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.functoriality-cartesian-product-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.truncations -open import foundation.universal-property-propositional-truncation +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.truncations funext +open import foundation.universal-property-propositional-truncation funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/propositions.lagda.md b/src/foundation/propositions.lagda.md index 75b2a12684..3df756f6f0 100644 --- a/src/foundation/propositions.lagda.md +++ b/src/foundation/propositions.lagda.md @@ -1,20 +1,25 @@ # Propositions ```agda -module foundation.propositions where +open import foundation.function-extensionality-axiom + +module + foundation.propositions + (funext : function-extensionality) + where open import foundation-core.propositions public -open import foundation.dependent-products-propositions public +open import foundation.dependent-products-propositions funext public ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.logical-equivalences -open import foundation.retracts-of-types +open import foundation.fibers-of-maps funext +open import foundation.logical-equivalences funext +open import foundation.retracts-of-types funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/pullback-cones.lagda.md b/src/foundation/pullback-cones.lagda.md index 5a098e4403..648277cb32 100644 --- a/src/foundation/pullback-cones.lagda.md +++ b/src/foundation/pullback-cones.lagda.md @@ -1,29 +1,34 @@ # Pullback cones ```agda -module foundation.pullback-cones where +open import foundation.function-extensionality-axiom + +module + foundation.pullback-cones + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams +open import foundation.cartesian-product-types funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.pullbacks -open import foundation.standard-pullbacks +open import foundation.identity-types funext +open import foundation.pullbacks funext +open import foundation.standard-pullbacks funext open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/pullbacks-subtypes.lagda.md b/src/foundation/pullbacks-subtypes.lagda.md index f2f6b26b72..a963732d28 100644 --- a/src/foundation/pullbacks-subtypes.lagda.md +++ b/src/foundation/pullbacks-subtypes.lagda.md @@ -1,22 +1,27 @@ # Pullbacks of subtypes ```agda -module foundation.pullbacks-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.pullbacks-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.logical-equivalences -open import foundation.powersets +open import foundation.logical-equivalences funext +open import foundation.powersets funext open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext ```
diff --git a/src/foundation/pullbacks.lagda.md b/src/foundation/pullbacks.lagda.md index db2de5b6a1..ace892e282 100644 --- a/src/foundation/pullbacks.lagda.md +++ b/src/foundation/pullbacks.lagda.md @@ -1,9 +1,14 @@ # Pullbacks ```agda -module foundation.pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.pullbacks + (funext : function-extensionality) + where -open import foundation-core.pullbacks public +open import foundation-core.pullbacks funext public ```
Imports @@ -11,17 +16,17 @@ open import foundation-core.pullbacks public ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-cubes-of-maps -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-cubes-of-maps funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.dependent-sums-pullbacks -open import foundation.descent-equivalences +open import foundation.dependent-sums-pullbacks funext +open import foundation.descent-equivalences funext open import foundation.equality-cartesian-product-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.standard-pullbacks -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.standard-pullbacks funext +open import foundation.subtypes funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/quasicoherently-idempotent-maps.lagda.md b/src/foundation/quasicoherently-idempotent-maps.lagda.md index 0cda3d0440..8eb8001436 100644 --- a/src/foundation/quasicoherently-idempotent-maps.lagda.md +++ b/src/foundation/quasicoherently-idempotent-maps.lagda.md @@ -1,27 +1,32 @@ # Quasicoherently idempotent maps ```agda -module foundation.quasicoherently-idempotent-maps where +open import foundation.function-extensionality-axiom + +module + foundation.quasicoherently-idempotent-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.1-types +open import foundation.1-types funext open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equality-dependent-pair-types +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.idempotent-maps -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation +open import foundation.homotopy-induction funext +open import foundation.idempotent-maps funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition @@ -34,8 +39,8 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.sets -open import synthetic-homotopy-theory.circle -open import synthetic-homotopy-theory.loop-homotopy-circle +open import synthetic-homotopy-theory.circle funext +open import synthetic-homotopy-theory.loop-homotopy-circle funext ```
diff --git a/src/foundation/raising-universe-levels-booleans.lagda.md b/src/foundation/raising-universe-levels-booleans.lagda.md index a94fd6c0e0..c904cc43e7 100644 --- a/src/foundation/raising-universe-levels-booleans.lagda.md +++ b/src/foundation/raising-universe-levels-booleans.lagda.md @@ -1,13 +1,18 @@ # Raising universe levels of the booleans ```agda -module foundation.raising-universe-levels-booleans where +open import foundation.function-extensionality-axiom + +module + foundation.raising-universe-levels-booleans + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.raising-universe-levels +open import foundation.raising-universe-levels funext open import foundation.universe-levels open import foundation-core.booleans diff --git a/src/foundation/raising-universe-levels-unit-type.lagda.md b/src/foundation/raising-universe-levels-unit-type.lagda.md index c8315fa606..4b5e5bb9a8 100644 --- a/src/foundation/raising-universe-levels-unit-type.lagda.md +++ b/src/foundation/raising-universe-levels-unit-type.lagda.md @@ -1,7 +1,12 @@ # Raising universe levels for the unit type ```agda -module foundation.raising-universe-levels-unit-type where +open import foundation.function-extensionality-axiom + +module + foundation.raising-universe-levels-unit-type + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module foundation.raising-universe-levels-unit-type where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.raising-universe-levels +open import foundation.raising-universe-levels funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/raising-universe-levels.lagda.md b/src/foundation/raising-universe-levels.lagda.md index 052c944420..1516f42d0b 100644 --- a/src/foundation/raising-universe-levels.lagda.md +++ b/src/foundation/raising-universe-levels.lagda.md @@ -1,7 +1,12 @@ # Raising universe levels ```agda -module foundation.raising-universe-levels where +open import foundation.function-extensionality-axiom + +module + foundation.raising-universe-levels + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module foundation.raising-universe-levels where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.univalence +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.contractible-types @@ -22,7 +27,7 @@ open import foundation-core.homotopies open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/reflecting-maps-equivalence-relations.lagda.md b/src/foundation/reflecting-maps-equivalence-relations.lagda.md index dda9020f8c..9f794d93b0 100644 --- a/src/foundation/reflecting-maps-equivalence-relations.lagda.md +++ b/src/foundation/reflecting-maps-equivalence-relations.lagda.md @@ -1,21 +1,26 @@ # Reflecting maps for equivalence relations ```agda -module foundation.reflecting-maps-equivalence-relations where +open import foundation.function-extensionality-axiom + +module + foundation.reflecting-maps-equivalence-relations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.effective-maps-equivalence-relations +open import foundation.dependent-products-propositions funext +open import foundation.effective-maps-equivalence-relations funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction +open import foundation.homotopy-induction funext open import foundation.subtype-identity-principle open import foundation.universe-levels -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/reflexive-relations.lagda.md b/src/foundation/reflexive-relations.lagda.md index 0953b7c3f4..b29536521c 100644 --- a/src/foundation/reflexive-relations.lagda.md +++ b/src/foundation/reflexive-relations.lagda.md @@ -1,14 +1,19 @@ # Reflexive relations ```agda -module foundation.reflexive-relations where +open import foundation.function-extensionality-axiom + +module + foundation.reflexive-relations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.binary-dependent-identifications -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md b/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md index c830446ce5..4567c1f572 100644 --- a/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md +++ b/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md @@ -9,30 +9,30 @@ module
Imports ```agda -open import foundation.0-connected-types -open import foundation.connected-maps -open import foundation.connected-types +open import foundation.0-connected-types funext +open import foundation.connected-maps funext +open import foundation.connected-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fiber-inclusions -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.functoriality-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.maps-in-subuniverses -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.separated-types-subuniverses -open import foundation.structured-equality-duality -open import foundation.subuniverses -open import foundation.surjective-maps -open import foundation.truncated-maps -open import foundation.truncated-types +open import foundation.equivalences funext +open import foundation.fiber-inclusions funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.functoriality-truncation funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.logical-equivalences funext +open import foundation.maps-in-subuniverses funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.separated-types-subuniverses funext +open import foundation.structured-equality-duality funext +open import foundation.subuniverses funext +open import foundation.surjective-maps funext +open import foundation.truncated-maps funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels ``` @@ -89,7 +89,12 @@ agda-unimath. ### The extended fundamental theorem of identity types ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {l1 l2 l3 : Level} (𝒫 : subuniverse (l1 ⊔ l2) l3) {A : UU l1} (a : A) {B : A → UU l2} where diff --git a/src/foundation/relaxed-sigma-decompositions.lagda.md b/src/foundation/relaxed-sigma-decompositions.lagda.md index 9280f10597..4076fe726c 100644 --- a/src/foundation/relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/relaxed-sigma-decompositions.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.relaxed-sigma-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.relaxed-sigma-decompositions + (funext : function-extensionality) + where ```
Imports @@ -11,14 +16,14 @@ module foundation.relaxed-sigma-decompositions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.equivalence-extensionality -open import foundation.equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.transposition-identifications-along-equivalences +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/repetitions-of-values.lagda.md b/src/foundation/repetitions-of-values.lagda.md index cbecce73b5..790013c514 100644 --- a/src/foundation/repetitions-of-values.lagda.md +++ b/src/foundation/repetitions-of-values.lagda.md @@ -1,7 +1,12 @@ # Repetitions of values of maps ```agda -module foundation.repetitions-of-values where +open import foundation.function-extensionality-axiom + +module + foundation.repetitions-of-values + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module foundation.repetitions-of-values where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.pairs-of-distinct-elements +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.pairs-of-distinct-elements funext open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies diff --git a/src/foundation/repetitions-sequences.lagda.md b/src/foundation/repetitions-sequences.lagda.md index c52b33a71d..7a05dd2225 100644 --- a/src/foundation/repetitions-sequences.lagda.md +++ b/src/foundation/repetitions-sequences.lagda.md @@ -1,20 +1,25 @@ # Repetitions in sequences ```agda -module foundation.repetitions-sequences where +open import foundation.function-extensionality-axiom + +module + foundation.repetitions-sequences + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers +open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.negated-equality -open import foundation.pairs-of-distinct-elements -open import foundation.repetitions-of-values +open import foundation.negated-equality funext +open import foundation.pairs-of-distinct-elements funext +open import foundation.repetitions-of-values funext open import foundation.sequences open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/replacement.lagda.md b/src/foundation/replacement.lagda.md index f399430bcb..41f27cbe3b 100644 --- a/src/foundation/replacement.lagda.md +++ b/src/foundation/replacement.lagda.md @@ -1,17 +1,22 @@ # The type theoretic replacement axiom ```agda -module foundation.replacement where +open import foundation.function-extensionality-axiom + +module + foundation.replacement + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.images -open import foundation.locally-small-types +open import foundation.images funext +open import foundation.locally-small-types funext open import foundation.universe-levels -open import foundation-core.small-types +open import foundation-core.small-types funext ```
diff --git a/src/foundation/retractions.lagda.md b/src/foundation/retractions.lagda.md index afabb0426b..c5fa68eb0d 100644 --- a/src/foundation/retractions.lagda.md +++ b/src/foundation/retractions.lagda.md @@ -1,7 +1,12 @@ # Retractions ```agda -module foundation.retractions where +open import foundation.function-extensionality-axiom + +module + foundation.retractions + (funext : function-extensionality) + where open import foundation-core.retractions public ``` @@ -10,9 +15,9 @@ open import foundation-core.retractions public ```agda open import foundation.action-on-identifications-functions -open import foundation.coslice +open import foundation.coslice funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types +open import foundation.dependent-products-truncated-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/retracts-of-maps.lagda.md b/src/foundation/retracts-of-maps.lagda.md index 4a6ba64557..878bf112f5 100644 --- a/src/foundation/retracts-of-maps.lagda.md +++ b/src/foundation/retracts-of-maps.lagda.md @@ -1,29 +1,35 @@ # Retracts of maps ```agda -module foundation.retracts-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.retracts-of-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-triangles-of-morphisms-arrows +open import foundation.commuting-prisms-of-maps funext +open import foundation.commuting-triangles-of-morphisms-arrows funext open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.function-extensionality -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies-morphisms-arrows +open import foundation.diagonal-maps-of-types funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies-morphisms-arrows funext open import foundation.homotopy-algebra -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.retracts-of-types +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.retracts-of-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.constant-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation/retracts-of-types.lagda.md b/src/foundation/retracts-of-types.lagda.md index e180da55c5..3d81ed7742 100644 --- a/src/foundation/retracts-of-types.lagda.md +++ b/src/foundation/retracts-of-types.lagda.md @@ -1,7 +1,12 @@ # Retracts of types ```agda -module foundation.retracts-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.retracts-of-types + (funext : function-extensionality) + where open import foundation-core.retracts-of-types public ``` @@ -10,15 +15,16 @@ open import foundation-core.retracts-of-types public ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.equivalences funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.logical-equivalences +open import foundation.homotopy-induction funext +open import foundation.logical-equivalences funext open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/sections.lagda.md b/src/foundation/sections.lagda.md index 0ec87899b6..d978649891 100644 --- a/src/foundation/sections.lagda.md +++ b/src/foundation/sections.lagda.md @@ -1,7 +1,12 @@ # Sections ```agda -module foundation.sections where +open import foundation.function-extensionality-axiom + +module + foundation.sections + (funext : function-extensionality) + where open import foundation-core.sections public ``` @@ -10,10 +15,11 @@ open import foundation-core.sections public ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.function-extensionality +open import foundation.dependent-products-contractible-types funext +open import foundation.function-extensionality funext + open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/separated-types-subuniverses.lagda.md b/src/foundation/separated-types-subuniverses.lagda.md index cb0571d472..4cc9ff08b8 100644 --- a/src/foundation/separated-types-subuniverses.lagda.md +++ b/src/foundation/separated-types-subuniverses.lagda.md @@ -1,14 +1,19 @@ # Types separated at subuniverses ```agda -module foundation.separated-types-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.separated-types-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.dependent-products-propositions -open import foundation.subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.subuniverses funext open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/sequential-limits.lagda.md b/src/foundation/sequential-limits.lagda.md index f2891ee0db..c37321519a 100644 --- a/src/foundation/sequential-limits.lagda.md +++ b/src/foundation/sequential-limits.lagda.md @@ -1,7 +1,12 @@ # Sequential limits ```agda -module foundation.sequential-limits where +open import foundation.function-extensionality-axiom + +module + foundation.sequential-limits + (funext : function-extensionality) + where ```
Imports @@ -10,15 +15,15 @@ module foundation.sequential-limits where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cones-over-inverse-sequential-diagrams +open import foundation.cones-over-inverse-sequential-diagrams funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.inverse-sequential-diagrams +open import foundation.homotopy-induction funext +open import foundation.inverse-sequential-diagrams funext open import foundation.structure-identity-principle -open import foundation.universal-property-sequential-limits +open import foundation.universal-property-sequential-limits funext open import foundation.universe-levels open import foundation-core.commuting-squares-of-homotopies diff --git a/src/foundation/set-presented-types.lagda.md b/src/foundation/set-presented-types.lagda.md index ae88a8fae8..d5b6a411a5 100644 --- a/src/foundation/set-presented-types.lagda.md +++ b/src/foundation/set-presented-types.lagda.md @@ -1,31 +1,36 @@ # Set presented types ```agda -module foundation.set-presented-types where +open import foundation.function-extensionality-axiom + +module + foundation.set-presented-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.fibers-of-maps -open import foundation.functoriality-coproduct-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.images -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.set-truncations -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equality-coproduct-types funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-coproduct-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext +open import foundation.set-truncations funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/set-quotients.lagda.md b/src/foundation/set-quotients.lagda.md index 883cf8111f..3cd4071dff 100644 --- a/src/foundation/set-quotients.lagda.md +++ b/src/foundation/set-quotients.lagda.md @@ -1,7 +1,12 @@ # Set quotients ```agda -module foundation.set-quotients where +open import foundation.function-extensionality-axiom + +module + foundation.set-quotients + (funext : function-extensionality) + where ```
Imports @@ -9,31 +14,30 @@ module foundation.set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.effective-maps-equivalence-relations -open import foundation.embeddings -open import foundation.equivalence-classes -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.slice -open import foundation.surjective-maps -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-image -open import foundation.universal-property-set-quotients +open import foundation.dependent-products-propositions funext +open import foundation.effective-maps-equivalence-relations funext +open import foundation.embeddings funext +open import foundation.equivalence-classes funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.sets funext +open import foundation.slice funext +open import foundation.surjective-maps funext +open import foundation.uniqueness-set-quotients funext +open import foundation.universal-property-image funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.homotopies open import foundation-core.propositions -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/set-truncations.lagda.md b/src/foundation/set-truncations.lagda.md index 154cc2d2b5..8eb92139c8 100644 --- a/src/foundation/set-truncations.lagda.md +++ b/src/foundation/set-truncations.lagda.md @@ -3,31 +3,36 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.set-truncations where +open import foundation.function-extensionality-axiom + +module + foundation.set-truncations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.equality-coproduct-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.mere-equality -open import foundation.postcomposition-functions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.slice -open import foundation.surjective-maps -open import foundation.truncations -open import foundation.uniqueness-set-truncations +open import foundation.effective-maps-equivalence-relations funext +open import foundation.equality-coproduct-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.mere-equality funext +open import foundation.postcomposition-functions funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.sets funext +open import foundation.slice funext +open import foundation.surjective-maps funext +open import foundation.truncations funext +open import foundation.uniqueness-set-truncations funext open import foundation.unit-type -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-image -open import foundation.universal-property-set-quotients -open import foundation.universal-property-set-truncation +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-image funext +open import foundation.universal-property-set-quotients funext +open import foundation.universal-property-set-truncation funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -37,7 +42,7 @@ open import foundation-core.embeddings open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/sets.lagda.md b/src/foundation/sets.lagda.md index f486be35a9..98b29c759f 100644 --- a/src/foundation/sets.lagda.md +++ b/src/foundation/sets.lagda.md @@ -1,7 +1,12 @@ # Sets ```agda -module foundation.sets where +open import foundation.function-extensionality-axiom + +module + foundation.sets + (funext : function-extensionality) + where open import foundation-core.sets public ``` @@ -9,16 +14,16 @@ open import foundation-core.sets public
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.logical-equivalences -open import foundation.subuniverses -open import foundation.truncated-types -open import foundation.univalent-type-families +open import foundation.dependent-products-truncated-types funext +open import foundation.logical-equivalences funext +open import foundation.subuniverses funext +open import foundation.truncated-types funext +open import foundation.univalent-type-families funext open import foundation.universe-levels -open import foundation-core.1-types +open import foundation-core.1-types funext open import foundation-core.cartesian-product-types open import foundation-core.embeddings open import foundation-core.equivalences @@ -27,7 +32,7 @@ open import foundation-core.injective-maps open import foundation-core.precomposition-functions open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.truncation-levels ``` diff --git a/src/foundation/sigma-closed-subuniverses.lagda.md b/src/foundation/sigma-closed-subuniverses.lagda.md index 29e8d7b87a..b9ce18011c 100644 --- a/src/foundation/sigma-closed-subuniverses.lagda.md +++ b/src/foundation/sigma-closed-subuniverses.lagda.md @@ -1,14 +1,19 @@ # Σ-closed subuniverses ```agda -module foundation.sigma-closed-subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.sigma-closed-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.subuniverses +open import foundation.subuniverses funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/sigma-decomposition-subuniverse.lagda.md b/src/foundation/sigma-decomposition-subuniverse.lagda.md index ef0e6e73f6..168d2c9160 100644 --- a/src/foundation/sigma-decomposition-subuniverse.lagda.md +++ b/src/foundation/sigma-decomposition-subuniverse.lagda.md @@ -1,15 +1,20 @@ # Σ-decompositions of types into types in a subuniverse ```agda -module foundation.sigma-decomposition-subuniverse where +open import foundation.function-extensionality-axiom + +module + foundation.sigma-decomposition-subuniverse + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.relaxed-sigma-decompositions -open import foundation.subuniverses +open import foundation.relaxed-sigma-decompositions funext +open import foundation.subuniverses funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/sigma-decompositions.lagda.md b/src/foundation/sigma-decompositions.lagda.md index b3c759f936..6ba7a4e9cf 100644 --- a/src/foundation/sigma-decompositions.lagda.md +++ b/src/foundation/sigma-decompositions.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.sigma-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.sigma-decompositions + (funext : function-extensionality) + where ```
Imports @@ -11,17 +16,17 @@ module foundation.sigma-decompositions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.equivalence-extensionality -open import foundation.equivalences +open import foundation.dependent-products-contractible-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.structure-identity-principle -open import foundation.transposition-identifications-along-equivalences +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/singleton-subtypes.lagda.md b/src/foundation/singleton-subtypes.lagda.md index b624eca1cc..655f085729 100644 --- a/src/foundation/singleton-subtypes.lagda.md +++ b/src/foundation/singleton-subtypes.lagda.md @@ -1,24 +1,29 @@ # Singleton subtypes ```agda -module foundation.singleton-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.singleton-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.connected-components -open import foundation.contractible-types +open import foundation.connected-components funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.images-subtypes -open import foundation.inhabited-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.functoriality-propositional-truncation funext +open import foundation.images-subtypes funext +open import foundation.inhabited-subtypes funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.singleton-induction -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/slice.lagda.md b/src/foundation/slice.lagda.md index 621d6af8f9..bd0e0c899a 100644 --- a/src/foundation/slice.lagda.md +++ b/src/foundation/slice.lagda.md @@ -1,24 +1,30 @@ # Morphisms in the slice category of types ```agda -module foundation.slice where +open import foundation.function-extensionality-axiom + +module + foundation.slice + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.logical-equivalences +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.logical-equivalences funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -35,7 +41,7 @@ open import foundation-core.propositions open import foundation-core.torsorial-type-families open import foundation-core.type-theoretic-principle-of-choice -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext ```
diff --git a/src/foundation/small-maps.lagda.md b/src/foundation/small-maps.lagda.md index 4084071783..9f5131f628 100644 --- a/src/foundation/small-maps.lagda.md +++ b/src/foundation/small-maps.lagda.md @@ -1,22 +1,27 @@ # Small maps ```agda -module foundation.small-maps where +open import foundation.function-extensionality-axiom + +module + foundation.small-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.locally-small-types -open import foundation.retracts-of-maps -open import foundation.split-idempotent-maps +open import foundation.dependent-products-propositions funext +open import foundation.locally-small-types funext +open import foundation.retracts-of-maps funext +open import foundation.split-idempotent-maps funext open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.propositions -open import foundation-core.small-types +open import foundation-core.small-types funext ```
diff --git a/src/foundation/small-types.lagda.md b/src/foundation/small-types.lagda.md index 2d60593a75..ead1b928bf 100644 --- a/src/foundation/small-types.lagda.md +++ b/src/foundation/small-types.lagda.md @@ -1,21 +1,26 @@ # Small types ```agda -module foundation.small-types where +open import foundation.function-extensionality-axiom -open import foundation-core.small-types public +module + foundation.small-types + (funext : function-extensionality) + where + +open import foundation-core.small-types funext public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.images -open import foundation.locally-small-types -open import foundation.replacement -open import foundation.surjective-maps -open import foundation.uniqueness-image -open import foundation.universal-property-image +open import foundation.images funext +open import foundation.locally-small-types funext +open import foundation.replacement funext +open import foundation.surjective-maps funext +open import foundation.uniqueness-image funext +open import foundation.universal-property-image funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/small-universes.lagda.md b/src/foundation/small-universes.lagda.md index fda8cb43a0..f73e0ee038 100644 --- a/src/foundation/small-universes.lagda.md +++ b/src/foundation/small-universes.lagda.md @@ -1,7 +1,12 @@ # Small universes ```agda -module foundation.small-universes where +open import foundation.function-extensionality-axiom + +module + foundation.small-universes + (funext : function-extensionality) + where ```
Imports @@ -10,7 +15,7 @@ module foundation.small-universes where open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.small-types +open import foundation-core.small-types funext ```
diff --git a/src/foundation/span-diagrams.lagda.md b/src/foundation/span-diagrams.lagda.md index 3356a17241..9738936202 100644 --- a/src/foundation/span-diagrams.lagda.md +++ b/src/foundation/span-diagrams.lagda.md @@ -1,14 +1,19 @@ # Span diagrams ```agda -module foundation.span-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows +open import foundation.morphisms-arrows funext open import foundation.spans open import foundation.universe-levels ``` diff --git a/src/foundation/spans-of-spans.lagda.md b/src/foundation/spans-of-spans.lagda.md index 792737abe6..6e228fe989 100644 --- a/src/foundation/spans-of-spans.lagda.md +++ b/src/foundation/spans-of-spans.lagda.md @@ -1,15 +1,20 @@ # Spans of spans ```agda -module foundation.spans-of-spans where +open import foundation.function-extensionality-axiom + +module + foundation.spans-of-spans + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/split-idempotent-maps.lagda.md b/src/foundation/split-idempotent-maps.lagda.md index e3a320b622..6e775f6a01 100644 --- a/src/foundation/split-idempotent-maps.lagda.md +++ b/src/foundation/split-idempotent-maps.lagda.md @@ -1,7 +1,12 @@ # Split idempotent maps ```agda -module foundation.split-idempotent-maps where +open import foundation.function-extensionality-axiom + +module + foundation.split-idempotent-maps + (funext : function-extensionality) + where ```
Imports @@ -9,29 +14,29 @@ module foundation.split-idempotent-maps where ```agda open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fixed-points-endofunctions open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.idempotent-maps -open import foundation.inverse-sequential-diagrams -open import foundation.locally-small-types -open import foundation.path-cosplit-maps -open import foundation.quasicoherently-idempotent-maps -open import foundation.retracts-of-types -open import foundation.sequential-limits +open import foundation.homotopy-induction funext +open import foundation.idempotent-maps funext +open import foundation.inverse-sequential-diagrams funext +open import foundation.locally-small-types funext +open import foundation.path-cosplit-maps funext +open import foundation.quasicoherently-idempotent-maps funext +open import foundation.retracts-of-types funext +open import foundation.sequential-limits funext open import foundation.structure-identity-principle open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import foundation.weakly-constant-maps +open import foundation.weakly-constant-maps funext open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies @@ -44,7 +49,7 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.sections open import foundation-core.sets -open import foundation-core.small-types +open import foundation-core.small-types funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/standard-apartness-relations.lagda.md b/src/foundation/standard-apartness-relations.lagda.md index 3a3df40ac0..0cb656f8cb 100644 --- a/src/foundation/standard-apartness-relations.lagda.md +++ b/src/foundation/standard-apartness-relations.lagda.md @@ -1,19 +1,24 @@ # Standard apartness relations ```agda -module foundation.standard-apartness-relations where +open import foundation.function-extensionality-axiom + +module + foundation.standard-apartness-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.apartness-relations -open import foundation.decidable-types +open import foundation.apartness-relations funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.law-of-excluded-middle -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.tight-apartness-relations +open import foundation.law-of-excluded-middle funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext +open import foundation.tight-apartness-relations funext open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/standard-pullbacks.lagda.md b/src/foundation/standard-pullbacks.lagda.md index 8f0db009ca..350bb426a1 100644 --- a/src/foundation/standard-pullbacks.lagda.md +++ b/src/foundation/standard-pullbacks.lagda.md @@ -1,23 +1,28 @@ # Standard pullbacks ```agda -module foundation.standard-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.standard-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.diagonal-maps-cartesian-products-of-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences @@ -27,7 +32,7 @@ open import foundation-core.homotopies open import foundation-core.retractions open import foundation-core.sections open import foundation-core.type-theoretic-principle-of-choice -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext open import foundation-core.whiskering-identifications-concatenation ``` diff --git a/src/foundation/standard-ternary-pullbacks.lagda.md b/src/foundation/standard-ternary-pullbacks.lagda.md index 6ca4fd1596..8aeefb1d20 100644 --- a/src/foundation/standard-ternary-pullbacks.lagda.md +++ b/src/foundation/standard-ternary-pullbacks.lagda.md @@ -1,23 +1,28 @@ # Standard ternary pullbacks ```agda -module foundation.standard-ternary-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.standard-ternary-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.diagonal-maps-cartesian-products-of-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences @@ -27,7 +32,7 @@ open import foundation-core.homotopies open import foundation-core.retractions open import foundation-core.sections open import foundation-core.type-theoretic-principle-of-choice -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext open import foundation-core.whiskering-identifications-concatenation ``` diff --git a/src/foundation/strict-symmetrization-binary-relations.lagda.md b/src/foundation/strict-symmetrization-binary-relations.lagda.md index 1c316d7ad4..8e0b26ad29 100644 --- a/src/foundation/strict-symmetrization-binary-relations.lagda.md +++ b/src/foundation/strict-symmetrization-binary-relations.lagda.md @@ -1,15 +1,20 @@ # Strict symmetrization of binary relations ```agda -module foundation.strict-symmetrization-binary-relations where +open import foundation.function-extensionality-axiom + +module + foundation.strict-symmetrization-binary-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.binary-relations-with-extensions -open import foundation.binary-relations-with-lifts +open import foundation.binary-relations funext +open import foundation.binary-relations funext-with-extensions +open import foundation.binary-relations-with-lifts funext open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/strictly-involutive-identity-types.lagda.md b/src/foundation/strictly-involutive-identity-types.lagda.md index f6cd949dd5..5e1d22cbc2 100644 --- a/src/foundation/strictly-involutive-identity-types.lagda.md +++ b/src/foundation/strictly-involutive-identity-types.lagda.md @@ -1,7 +1,12 @@ # Strictly involutive identity types ```agda -module foundation.strictly-involutive-identity-types where +open import foundation.function-extensionality-axiom + +module + foundation.strictly-involutive-identity-types + (funext : function-extensionality) + where ```
Imports @@ -11,13 +16,13 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.multivariable-homotopies +open import foundation.function-extensionality funext + +open import foundation.multivariable-homotopies funext open import foundation.strictly-right-unital-concatenation-identifications open import foundation.telescopes -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.univalence funext +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/strong-preunivalence.lagda.md b/src/foundation/strong-preunivalence.lagda.md index 051e55fa52..2148624632 100644 --- a/src/foundation/strong-preunivalence.lagda.md +++ b/src/foundation/strong-preunivalence.lagda.md @@ -1,23 +1,28 @@ # The strong preunivalence axiom ```agda -module foundation.strong-preunivalence where +open import foundation.function-extensionality-axiom + +module + foundation.strong-preunivalence + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.preunivalence -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.sets -open import foundation.small-types -open import foundation.structured-equality-duality -open import foundation.univalence +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.preunivalence funext +open import foundation.propositional-maps funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.small-types funext +open import foundation.structured-equality-duality funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/strongly-extensional-maps.lagda.md b/src/foundation/strongly-extensional-maps.lagda.md index 9b5bfa198f..6a902e9b19 100644 --- a/src/foundation/strongly-extensional-maps.lagda.md +++ b/src/foundation/strongly-extensional-maps.lagda.md @@ -1,13 +1,18 @@ # Strongly extensional maps ```agda -module foundation.strongly-extensional-maps where +open import foundation.function-extensionality-axiom + +module + foundation.strongly-extensional-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.apartness-relations +open import foundation.apartness-relations funext open import foundation.universe-levels ``` diff --git a/src/foundation/structure.lagda.md b/src/foundation/structure.lagda.md index 6a5b9217b7..15969aa801 100644 --- a/src/foundation/structure.lagda.md +++ b/src/foundation/structure.lagda.md @@ -1,14 +1,19 @@ # Structure ```agda -module foundation.structure where +open import foundation.function-extensionality-axiom + +module + foundation.structure + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/structured-equality-duality.lagda.md b/src/foundation/structured-equality-duality.lagda.md index 534bf63cd7..4ce8de15f0 100644 --- a/src/foundation/structured-equality-duality.lagda.md +++ b/src/foundation/structured-equality-duality.lagda.md @@ -1,19 +1,24 @@ # Structured equality duality ```agda -module foundation.structured-equality-duality where +open import foundation.function-extensionality-axiom + +module + foundation.structured-equality-duality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.maps-in-subuniverses -open import foundation.separated-types-subuniverses -open import foundation.structure -open import foundation.subuniverses +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.maps-in-subuniverses funext +open import foundation.separated-types-subuniverses funext +open import foundation.structure funext +open import foundation.subuniverses funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/structured-type-duality.lagda.md b/src/foundation/structured-type-duality.lagda.md index e7d04bcb07..188e375c32 100644 --- a/src/foundation/structured-type-duality.lagda.md +++ b/src/foundation/structured-type-duality.lagda.md @@ -1,23 +1,28 @@ # Structured type duality ```agda -module foundation.structured-type-duality where +open import foundation.function-extensionality-axiom + +module + foundation.structured-type-duality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.structure +open import foundation.equivalences funext +open import foundation.structure funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-duality -open import foundation.univalence +open import foundation.type-duality funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/subtype-duality.lagda.md b/src/foundation/subtype-duality.lagda.md index abd64501e7..fd1118c059 100644 --- a/src/foundation/subtype-duality.lagda.md +++ b/src/foundation/subtype-duality.lagda.md @@ -1,17 +1,22 @@ # Subtype duality ```agda -module foundation.subtype-duality where +open import foundation.function-extensionality-axiom + +module + foundation.subtype-duality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.propositional-maps -open import foundation.structured-type-duality -open import foundation.surjective-maps +open import foundation.inhabited-types funext +open import foundation.propositional-maps funext +open import foundation.structured-type-duality funext +open import foundation.surjective-maps funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/subtypes.lagda.md b/src/foundation/subtypes.lagda.md index 20def667fe..e62aa97232 100644 --- a/src/foundation/subtypes.lagda.md +++ b/src/foundation/subtypes.lagda.md @@ -1,21 +1,26 @@ # Subtypes ```agda -module foundation.subtypes where +open import foundation.function-extensionality-axiom -open import foundation-core.subtypes public +module + foundation.subtypes + (funext : function-extensionality) + where + +open import foundation-core.subtypes funext public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings -open import foundation.equality-dependent-function-types +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext +open import foundation.equality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences -open import foundation.propositional-extensionality +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/subuniverses.lagda.md b/src/foundation/subuniverses.lagda.md index ddeb1e28d6..1bb3f6ee17 100644 --- a/src/foundation/subuniverses.lagda.md +++ b/src/foundation/subuniverses.lagda.md @@ -1,18 +1,23 @@ # Subuniverses ```agda -module foundation.subuniverses where +open import foundation.function-extensionality-axiom + +module + foundation.subuniverses + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types open import foundation.subtype-identity-principle -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.contractible-types @@ -21,7 +26,7 @@ open import foundation-core.fibers-of-maps open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/surjective-maps.lagda.md b/src/foundation/surjective-maps.lagda.md index 6296eb39df..a2fcd62661 100644 --- a/src/foundation/surjective-maps.lagda.md +++ b/src/foundation/surjective-maps.lagda.md @@ -1,33 +1,38 @@ # Surjective maps ```agda -module foundation.surjective-maps where +open import foundation.function-extensionality-axiom + +module + foundation.surjective-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.connected-maps -open import foundation.contractible-types +open import foundation.connected-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.embeddings +open import foundation.dependent-products-propositions funext +open import foundation.embeddings funext open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-cartesian-product-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.postcomposition-dependent-functions -open import foundation.propositional-truncations +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.postcomposition-dependent-functions funext +open import foundation.propositional-truncations funext open import foundation.split-surjective-maps open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.truncated-types -open import foundation.univalence -open import foundation.universal-property-family-of-fibers-of-maps -open import foundation.universal-property-propositional-truncation +open import foundation.truncated-types funext +open import foundation.univalence funext +open import foundation.universal-property-family-of-fibers-of-maps funext +open import foundation.universal-property-propositional-truncation funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -37,19 +42,19 @@ open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.homotopies open import foundation-core.precomposition-dependent-functions open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sections open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels -open import orthogonal-factorization-systems.extensions-maps +open import orthogonal-factorization-systems.extensions-maps funext ```
diff --git a/src/foundation/symmetric-binary-relations.lagda.md b/src/foundation/symmetric-binary-relations.lagda.md index 19d488fdc8..47b07f6c8d 100644 --- a/src/foundation/symmetric-binary-relations.lagda.md +++ b/src/foundation/symmetric-binary-relations.lagda.md @@ -1,21 +1,25 @@ # Symmetric binary relations ```agda -module foundation.symmetric-binary-relations where +open import foundation.function-extensionality-axiom + +module + foundation.symmetric-binary-relations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.function-extensionality-axiom -open import foundation.morphisms-binary-relations -open import foundation.symmetric-operations +open import foundation.equivalence-extensionality funext +open import foundation.morphisms-binary-relations funext +open import foundation.symmetric-operations funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext open import foundation-core.equivalences open import foundation-core.function-types @@ -23,7 +27,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.transport-along-identifications -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/symmetric-cores-binary-relations.lagda.md b/src/foundation/symmetric-cores-binary-relations.lagda.md index 95c56d21dd..17f920d654 100644 --- a/src/foundation/symmetric-cores-binary-relations.lagda.md +++ b/src/foundation/symmetric-cores-binary-relations.lagda.md @@ -1,25 +1,30 @@ # Symmetric cores of binary relations ```agda -module foundation.symmetric-cores-binary-relations where +open import foundation.function-extensionality-axiom + +module + foundation.symmetric-cores-binary-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.morphisms-binary-relations -open import foundation.postcomposition-functions -open import foundation.symmetric-binary-relations +open import foundation.binary-relations funext +open import foundation.morphisms-binary-relations funext +open import foundation.postcomposition-functions funext +open import foundation.symmetric-binary-relations funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-arithmetic-dependent-function-types funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/symmetric-difference.lagda.md b/src/foundation/symmetric-difference.lagda.md index 13308cf30a..f605a3b0f4 100644 --- a/src/foundation/symmetric-difference.lagda.md +++ b/src/foundation/symmetric-difference.lagda.md @@ -1,26 +1,31 @@ # Symmetric difference of subtypes ```agda -module foundation.symmetric-difference where +open import foundation.function-extensionality-axiom + +module + foundation.symmetric-difference + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.exclusive-sum -open import foundation.intersections-subtypes +open import foundation.exclusive-sum funext +open import foundation.intersections-subtypes funext open import foundation.universe-levels open import foundation-core.coproduct-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/symmetric-identity-types.lagda.md b/src/foundation/symmetric-identity-types.lagda.md index 7b34c892e3..688a7e1e21 100644 --- a/src/foundation/symmetric-identity-types.lagda.md +++ b/src/foundation/symmetric-identity-types.lagda.md @@ -1,7 +1,12 @@ # The symmetric identity types ```agda -module foundation.symmetric-identity-types where +open import foundation.function-extensionality-axiom + +module + foundation.symmetric-identity-types + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,15 @@ module foundation.symmetric-identity-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types +open import foundation.function-extensionality funext + +open import foundation.functoriality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext open import foundation-core.contractible-types open import foundation-core.coproduct-types @@ -27,7 +33,7 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.torsorial-type-families -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/symmetric-operations.lagda.md b/src/foundation/symmetric-operations.lagda.md index 317c977990..69d03ebdb9 100644 --- a/src/foundation/symmetric-operations.lagda.md +++ b/src/foundation/symmetric-operations.lagda.md @@ -1,7 +1,12 @@ # Symmetric operations ```agda -module foundation.symmetric-operations where +open import foundation.function-extensionality-axiom + +module + foundation.symmetric-operations + (funext : function-extensionality) + where ```
Imports @@ -10,15 +15,16 @@ module foundation.symmetric-operations where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalence-extensionality -open import foundation.function-extensionality -open import foundation.functoriality-coproduct-types +open import foundation.dependent-products-propositions funext +open import foundation.equivalence-extensionality funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-coproduct-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.propositional-truncations -open import foundation.universal-property-propositional-truncation-into-sets +open import foundation.propositional-truncations funext +open import foundation.universal-property-propositional-truncation-into-sets funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext open import foundation-core.coproduct-types open import foundation-core.equivalences @@ -27,12 +33,12 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/terminal-spans-families-of-types.lagda.md b/src/foundation/terminal-spans-families-of-types.lagda.md index 697d998b8e..830c19b404 100644 --- a/src/foundation/terminal-spans-families-of-types.lagda.md +++ b/src/foundation/terminal-spans-families-of-types.lagda.md @@ -1,13 +1,18 @@ # Terminal spans on families of types ```agda -module foundation.terminal-spans-families-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.terminal-spans-families-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.morphisms-spans-families-of-types +open import foundation.morphisms-spans-families-of-types funext open import foundation.spans-families-of-types open import foundation.universe-levels diff --git a/src/foundation/tight-apartness-relations.lagda.md b/src/foundation/tight-apartness-relations.lagda.md index f848664137..7fb6473906 100644 --- a/src/foundation/tight-apartness-relations.lagda.md +++ b/src/foundation/tight-apartness-relations.lagda.md @@ -1,17 +1,23 @@ # Tight apartness relations ```agda -module foundation.tight-apartness-relations where +open import foundation.function-extensionality-axiom + +module + foundation.tight-apartness-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.apartness-relations -open import foundation.binary-relations +open import foundation.apartness-relations funext +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.propositional-truncations +open import foundation.function-extensionality funext + +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/torsorial-type-families.lagda.md b/src/foundation/torsorial-type-families.lagda.md index 0929568e83..0618fff39d 100644 --- a/src/foundation/torsorial-type-families.lagda.md +++ b/src/foundation/torsorial-type-families.lagda.md @@ -1,7 +1,12 @@ # Torsorial type families ```agda -module foundation.torsorial-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.torsorial-type-families + (funext : function-extensionality) + where open import foundation-core.torsorial-type-families public ``` @@ -9,11 +14,11 @@ open import foundation-core.torsorial-type-families public
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences -open import foundation.universal-property-identity-types +open import foundation.logical-equivalences funext +open import foundation.universal-property-identity-types funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/total-partial-functions.lagda.md b/src/foundation/total-partial-functions.lagda.md index 7b1083887d..13df6f2194 100644 --- a/src/foundation/total-partial-functions.lagda.md +++ b/src/foundation/total-partial-functions.lagda.md @@ -1,14 +1,19 @@ # Total partial functions ```agda -module foundation.total-partial-functions where +open import foundation.function-extensionality-axiom + +module + foundation.total-partial-functions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions +open import foundation.dependent-products-propositions funext open import foundation.partial-functions open import foundation.universe-levels diff --git a/src/foundation/transfinite-cocomposition-of-maps.lagda.md b/src/foundation/transfinite-cocomposition-of-maps.lagda.md index 9d3f7d02ca..6dba5a2eeb 100644 --- a/src/foundation/transfinite-cocomposition-of-maps.lagda.md +++ b/src/foundation/transfinite-cocomposition-of-maps.lagda.md @@ -1,14 +1,19 @@ # Transfinite cocomposition of maps ```agda -module foundation.transfinite-cocomposition-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.transfinite-cocomposition-of-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.inverse-sequential-diagrams -open import foundation.sequential-limits +open import foundation.inverse-sequential-diagrams funext +open import foundation.sequential-limits funext open import foundation.universe-levels ``` diff --git a/src/foundation/transport-along-equivalences.lagda.md b/src/foundation/transport-along-equivalences.lagda.md index f46c28bfa9..c44902f1b1 100644 --- a/src/foundation/transport-along-equivalences.lagda.md +++ b/src/foundation/transport-along-equivalences.lagda.md @@ -1,22 +1,28 @@ # Transport along equivalences ```agda -module foundation.transport-along-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.transport-along-equivalences + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-equivalences-functions -open import foundation.action-on-equivalences-type-families +open import foundation.action-on-equivalences-functions funext +open import foundation.action-on-equivalences-type-families funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalence-induction -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-induction funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/transport-along-higher-identifications.lagda.md b/src/foundation/transport-along-higher-identifications.lagda.md index f031e7713c..b5db400ea0 100644 --- a/src/foundation/transport-along-higher-identifications.lagda.md +++ b/src/foundation/transport-along-higher-identifications.lagda.md @@ -1,22 +1,27 @@ # Transport along higher identifications ```agda -module foundation.transport-along-higher-identifications where +open import foundation.function-extensionality-axiom + +module + foundation.transport-along-higher-identifications + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-identifications -open import foundation.function-types -open import foundation.homotopies +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-identifications funext +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.path-algebra +open import foundation.path-algebra funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.identity-types open import foundation-core.transport-along-identifications diff --git a/src/foundation/transport-along-homotopies.lagda.md b/src/foundation/transport-along-homotopies.lagda.md index 8308d97123..0e41ff7d8a 100644 --- a/src/foundation/transport-along-homotopies.lagda.md +++ b/src/foundation/transport-along-homotopies.lagda.md @@ -1,17 +1,22 @@ # Transport along homotopies ```agda -module foundation.transport-along-homotopies where +open import foundation.function-extensionality-axiom + +module + foundation.transport-along-homotopies + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.homotopy-induction -open import foundation.transport-along-higher-identifications +open import foundation.function-extensionality funext + +open import foundation.homotopy-induction funext +open import foundation.transport-along-higher-identifications funext open import foundation.universe-levels open import foundation-core.homotopies diff --git a/src/foundation/transport-split-type-families.lagda.md b/src/foundation/transport-split-type-families.lagda.md index ff883a366f..7358b6596b 100644 --- a/src/foundation/transport-split-type-families.lagda.md +++ b/src/foundation/transport-split-type-families.lagda.md @@ -1,20 +1,25 @@ # Transport-split type families ```agda -module foundation.transport-split-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.transport-split-type-families + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalence-injective-type-families -open import foundation.equivalences +open import foundation.equivalence-injective-type-families funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.iterated-dependent-product-types +open import foundation.iterated-dependent-product-types funext open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalent-type-families -open import foundation.universal-property-identity-systems +open import foundation.univalent-type-families funext +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/transposition-identifications-along-equivalences.lagda.md b/src/foundation/transposition-identifications-along-equivalences.lagda.md index 9870736681..1981015681 100644 --- a/src/foundation/transposition-identifications-along-equivalences.lagda.md +++ b/src/foundation/transposition-identifications-along-equivalences.lagda.md @@ -1,15 +1,20 @@ # Transposing identifications along equivalences ```agda -module foundation.transposition-identifications-along-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.transposition-identifications-along-equivalences + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-identifications -open import foundation.identity-types +open import foundation.commuting-triangles-of-identifications funext +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/transposition-identifications-along-retractions.lagda.md b/src/foundation/transposition-identifications-along-retractions.lagda.md index 2dfe11e3cb..f0bfecbc2a 100644 --- a/src/foundation/transposition-identifications-along-retractions.lagda.md +++ b/src/foundation/transposition-identifications-along-retractions.lagda.md @@ -1,7 +1,12 @@ # Transposing identifications along retractions ```agda -module foundation.transposition-identifications-along-retractions where +open import foundation.function-extensionality-axiom + +module + foundation.transposition-identifications-along-retractions + (funext : function-extensionality) + where ```
@@ -9,7 +14,8 @@ module foundation.transposition-identifications-along-retractions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/transposition-identifications-along-sections.lagda.md b/src/foundation/transposition-identifications-along-sections.lagda.md index 9cffc6452a..a1ede27639 100644 --- a/src/foundation/transposition-identifications-along-sections.lagda.md +++ b/src/foundation/transposition-identifications-along-sections.lagda.md @@ -1,7 +1,12 @@ # Transposing identifications along sections ```agda -module foundation.transposition-identifications-along-sections where +open import foundation.function-extensionality-axiom + +module + foundation.transposition-identifications-along-sections + (funext : function-extensionality) + where ```
@@ -9,7 +14,8 @@ module foundation.transposition-identifications-along-sections where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/transposition-span-diagrams.lagda.md b/src/foundation/transposition-span-diagrams.lagda.md index 1d9df617ee..12b150c1af 100644 --- a/src/foundation/transposition-span-diagrams.lagda.md +++ b/src/foundation/transposition-span-diagrams.lagda.md @@ -1,7 +1,12 @@ # Transposition of span diagrams ```agda -module foundation.transposition-span-diagrams where +open import foundation.function-extensionality-axiom + +module + foundation.transposition-span-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module foundation.transposition-span-diagrams where ```agda open import foundation.dependent-pair-types open import foundation.opposite-spans -open import foundation.span-diagrams +open import foundation.span-diagrams funext open import foundation.spans open import foundation.universe-levels ``` diff --git a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md index 905d56a633..5930f3e499 100644 --- a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md @@ -1,17 +1,22 @@ # Trivial relaxed Σ-decompositions ```agda -module foundation.trivial-relaxed-sigma-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.trivial-relaxed-sigma-decompositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.raising-universe-levels-unit-type -open import foundation.relaxed-sigma-decompositions -open import foundation.transposition-identifications-along-equivalences +open import foundation.raising-universe-levels-unit-type funext +open import foundation.relaxed-sigma-decompositions funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -21,7 +26,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/trivial-sigma-decompositions.lagda.md b/src/foundation/trivial-sigma-decompositions.lagda.md index d7a099583f..1863f92e63 100644 --- a/src/foundation/trivial-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-sigma-decompositions.lagda.md @@ -1,21 +1,26 @@ # Trivial Σ-decompositions ```agda -module foundation.trivial-sigma-decompositions where +open import foundation.function-extensionality-axiom + +module + foundation.trivial-sigma-decompositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.inhabited-types -open import foundation.raising-universe-levels-unit-type -open import foundation.sigma-decompositions -open import foundation.transposition-identifications-along-equivalences +open import foundation.functoriality-propositional-truncation funext +open import foundation.inhabited-types funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sigma-decompositions funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type open import foundation.universe-levels @@ -25,7 +30,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/truncated-equality.lagda.md b/src/foundation/truncated-equality.lagda.md index c88cab61f7..25d8f7c1d6 100644 --- a/src/foundation/truncated-equality.lagda.md +++ b/src/foundation/truncated-equality.lagda.md @@ -1,13 +1,18 @@ # Truncated equality ```agda -module foundation.truncated-equality where +open import foundation.function-extensionality-axiom + +module + foundation.truncated-equality + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.truncations +open import foundation.truncations funext open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/truncated-maps.lagda.md b/src/foundation/truncated-maps.lagda.md index 05f95a7187..b8c1940299 100644 --- a/src/foundation/truncated-maps.lagda.md +++ b/src/foundation/truncated-maps.lagda.md @@ -1,24 +1,29 @@ # Truncated maps ```agda -module foundation.truncated-maps where +open import foundation.function-extensionality-axiom -open import foundation.dependent-products-truncated-types public -open import foundation-core.truncated-maps public +module + foundation.truncated-maps + (funext : function-extensionality) + where + +open import foundation.dependent-products-truncated-types funext public +open import foundation-core.truncated-maps funext public ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.functoriality-fibers-of-maps +open import foundation.dependent-products-propositions funext +open import foundation.functoriality-fibers-of-maps funext open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.propositions -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/truncated-types.lagda.md b/src/foundation/truncated-types.lagda.md index 4233ee729d..64436f7f0d 100644 --- a/src/foundation/truncated-types.lagda.md +++ b/src/foundation/truncated-types.lagda.md @@ -1,10 +1,15 @@ # Truncated types ```agda -module foundation.truncated-types where +open import foundation.function-extensionality-axiom + +module + foundation.truncated-types + (funext : function-extensionality) + where open import foundation-core.truncated-types public -open import foundation.dependent-products-truncated-types public +open import foundation.dependent-products-truncated-types funext public ```
Imports @@ -13,17 +18,17 @@ open import foundation.dependent-products-truncated-types public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.logical-equivalences +open import foundation.equivalences funext +open import foundation.logical-equivalences funext open import foundation.subtype-identity-principle open import foundation.truncation-levels -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.embeddings open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/truncation-equivalences.lagda.md b/src/foundation/truncation-equivalences.lagda.md index 95d6169280..c2a4c41d62 100644 --- a/src/foundation/truncation-equivalences.lagda.md +++ b/src/foundation/truncation-equivalences.lagda.md @@ -1,27 +1,32 @@ # `k`-Equivalences ```agda -module foundation.truncation-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.truncation-equivalences + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.connected-maps -open import foundation.connected-types -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.connected-maps funext +open import foundation.connected-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.functoriality-truncation -open import foundation.identity-types -open import foundation.precomposition-functions-into-subuniverses -open import foundation.propositional-truncations -open import foundation.truncations +open import foundation.dependent-products-truncated-types funext +open import foundation.functoriality-truncation funext +open import foundation.identity-types funext +open import foundation.precomposition-functions-into-subuniverses funext +open import foundation.propositional-truncations funext +open import foundation.truncations funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-equivalences -open import foundation.universal-property-truncation +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-truncation funext open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/truncation-images-of-maps.lagda.md b/src/foundation/truncation-images-of-maps.lagda.md index 2aa88a1be2..4d320800b2 100644 --- a/src/foundation/truncation-images-of-maps.lagda.md +++ b/src/foundation/truncation-images-of-maps.lagda.md @@ -1,26 +1,31 @@ # Truncation images of maps ```agda -module foundation.truncation-images-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.truncation-images-of-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.connected-maps +open import foundation.connected-maps funext open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.functoriality-truncation -open import foundation.identity-types -open import foundation.truncations +open import foundation.fibers-of-maps funext +open import foundation.functoriality-truncation funext +open import foundation.identity-types funext +open import foundation.truncations funext open import foundation.universe-levels open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.transport-along-identifications -open import foundation-core.truncated-maps +open import foundation-core.truncated-maps funext open import foundation-core.truncation-levels ``` diff --git a/src/foundation/truncation-modalities.lagda.md b/src/foundation/truncation-modalities.lagda.md index 4c38c783fb..90470ac5de 100644 --- a/src/foundation/truncation-modalities.lagda.md +++ b/src/foundation/truncation-modalities.lagda.md @@ -1,20 +1,25 @@ # The truncation modalities ```agda -module foundation.truncation-modalities where +open import foundation.function-extensionality-axiom + +module + foundation.truncation-modalities + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.truncations +open import foundation.truncations funext open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.truncation-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext ```
diff --git a/src/foundation/truncations.lagda.md b/src/foundation/truncations.lagda.md index d7bed98e65..4aaa890fce 100644 --- a/src/foundation/truncations.lagda.md +++ b/src/foundation/truncations.lagda.md @@ -1,22 +1,27 @@ # Truncations ```agda -module foundation.truncations where +open import foundation.function-extensionality-axiom + +module + foundation.truncations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.functoriality-dependent-function-types +open import foundation.function-extensionality funext + +open import foundation.functoriality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.truncated-types -open import foundation.universal-property-dependent-pair-types +open import foundation.identity-types funext +open import foundation.truncated-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -30,7 +35,7 @@ open import foundation-core.homotopies open import foundation-core.propositions open import foundation-core.torsorial-type-families open import foundation-core.truncation-levels -open import foundation-core.universal-property-truncation +open import foundation-core.universal-property-truncation funext ```
diff --git a/src/foundation/tuples-of-types.lagda.md b/src/foundation/tuples-of-types.lagda.md index 49b8e03fc5..3b9bc8ee2f 100644 --- a/src/foundation/tuples-of-types.lagda.md +++ b/src/foundation/tuples-of-types.lagda.md @@ -1,7 +1,12 @@ # Tuples of types ```agda -module foundation.tuples-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.tuples-of-types + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/type-arithmetic-coproduct-types.lagda.md b/src/foundation/type-arithmetic-coproduct-types.lagda.md index 4bfa836a20..77379c8cee 100644 --- a/src/foundation/type-arithmetic-coproduct-types.lagda.md +++ b/src/foundation/type-arithmetic-coproduct-types.lagda.md @@ -1,15 +1,20 @@ # Type arithmetic for coproduct types ```agda -module foundation.type-arithmetic-coproduct-types where +open import foundation.function-extensionality-axiom + +module + foundation.type-arithmetic-coproduct-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types +open import foundation.equality-coproduct-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/type-arithmetic-dependent-function-types.lagda.md b/src/foundation/type-arithmetic-dependent-function-types.lagda.md index 27533716f7..98993d5d4d 100644 --- a/src/foundation/type-arithmetic-dependent-function-types.lagda.md +++ b/src/foundation/type-arithmetic-dependent-function-types.lagda.md @@ -1,7 +1,12 @@ # Type arithmetic with dependent function types ```agda -module foundation.type-arithmetic-dependent-function-types where +open import foundation.function-extensionality-axiom + +module + foundation.type-arithmetic-dependent-function-types + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module foundation.type-arithmetic-dependent-function-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-function-types funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/type-arithmetic-empty-type.lagda.md b/src/foundation/type-arithmetic-empty-type.lagda.md index 3e65340797..28df76dcbe 100644 --- a/src/foundation/type-arithmetic-empty-type.lagda.md +++ b/src/foundation/type-arithmetic-empty-type.lagda.md @@ -1,13 +1,18 @@ # Type arithmetic with the empty type ```agda -module foundation.type-arithmetic-empty-type where +open import foundation.function-extensionality-axiom + +module + foundation.type-arithmetic-empty-type + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/type-arithmetic-standard-pullbacks.lagda.md b/src/foundation/type-arithmetic-standard-pullbacks.lagda.md index 09335074fa..a73a6743f1 100644 --- a/src/foundation/type-arithmetic-standard-pullbacks.lagda.md +++ b/src/foundation/type-arithmetic-standard-pullbacks.lagda.md @@ -1,17 +1,22 @@ # Type arithmetic with standard pullbacks ```agda -module foundation.type-arithmetic-standard-pullbacks where +open import foundation.function-extensionality-axiom + +module + foundation.type-arithmetic-standard-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.standard-pullbacks -open import foundation.standard-ternary-pullbacks +open import foundation.equality-dependent-pair-types funext +open import foundation.standard-pullbacks funext +open import foundation.standard-ternary-pullbacks funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/type-duality.lagda.md b/src/foundation/type-duality.lagda.md index 50d1ca1b70..61ca8cdeda 100644 --- a/src/foundation/type-duality.lagda.md +++ b/src/foundation/type-duality.lagda.md @@ -1,7 +1,12 @@ # Type duality ```agda -module foundation.type-duality where +open import foundation.function-extensionality-axiom + +module + foundation.type-duality + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,17 @@ module foundation.type-duality where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality +open import foundation.equivalences funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.locally-small-types -open import foundation.raising-universe-levels-unit-type -open import foundation.slice +open import foundation.locally-small-types funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.slice funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence -open import foundation.universal-property-equivalences +open import foundation.univalence funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-maps @@ -26,15 +32,15 @@ open import foundation-core.contractible-types open import foundation-core.embeddings open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.injective-maps -open import foundation-core.small-types +open import foundation-core.small-types funext open import foundation-core.torsorial-type-families -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext ```
diff --git a/src/foundation/type-theoretic-principle-of-choice.lagda.md b/src/foundation/type-theoretic-principle-of-choice.lagda.md index 984e3fd557..73a5beb31f 100644 --- a/src/foundation/type-theoretic-principle-of-choice.lagda.md +++ b/src/foundation/type-theoretic-principle-of-choice.lagda.md @@ -1,7 +1,12 @@ # The type theoretic principle of choice ```agda -module foundation.type-theoretic-principle-of-choice where +open import foundation.function-extensionality-axiom + +module + foundation.type-theoretic-principle-of-choice + (funext : function-extensionality) + where open import foundation-core.type-theoretic-principle-of-choice public ``` @@ -10,7 +15,8 @@ open import foundation-core.type-theoretic-principle-of-choice public ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.implicit-function-types open import foundation.structure-identity-principle open import foundation.universe-levels diff --git a/src/foundation/uniformly-decidable-type-families.lagda.md b/src/foundation/uniformly-decidable-type-families.lagda.md index 9beb5f6b51..e2118e8af6 100644 --- a/src/foundation/uniformly-decidable-type-families.lagda.md +++ b/src/foundation/uniformly-decidable-type-families.lagda.md @@ -1,26 +1,31 @@ # Uniformly decidable type families ```agda -module foundation.uniformly-decidable-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.uniformly-decidable-type-families + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.dependent-products-truncated-types -open import foundation.equality-coproduct-types -open import foundation.inhabited-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.truncated-types +open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-truncated-types funext +open import foundation.equality-coproduct-types funext +open import foundation.inhabited-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.truncated-types funext open import foundation.truncation-levels -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/unions-subtypes.lagda.md b/src/foundation/unions-subtypes.lagda.md index a3ae84790a..0d98ac4e8c 100644 --- a/src/foundation/unions-subtypes.lagda.md +++ b/src/foundation/unions-subtypes.lagda.md @@ -1,27 +1,32 @@ # Unions of subtypes ```agda -module foundation.unions-subtypes where +open import foundation.function-extensionality-axiom + +module + foundation.unions-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-subtypes +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.large-locale-of-subtypes -open import foundation.powersets -open import foundation.propositional-truncations +open import foundation.disjunction funext +open import foundation.large-locale-of-subtypes funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import logic.de-morgan-propositions -open import logic.de-morgan-subtypes -open import logic.double-negation-stable-subtypes +open import logic.de-morgan-propositions funext +open import logic.de-morgan-subtypes funext +open import logic.double-negation-stable-subtypes funext -open import order-theory.least-upper-bounds-large-posets +open import order-theory.least-upper-bounds-large-posets funext ```
diff --git a/src/foundation/uniqueness-image.lagda.md b/src/foundation/uniqueness-image.lagda.md index 4711b5a4d1..f7a3962959 100644 --- a/src/foundation/uniqueness-image.lagda.md +++ b/src/foundation/uniqueness-image.lagda.md @@ -1,18 +1,23 @@ # Uniqueness of the image of a map ```agda -module foundation.uniqueness-image where +open import foundation.function-extensionality-axiom + +module + foundation.uniqueness-image + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.images -open import foundation.slice +open import foundation.equivalences funext +open import foundation.images funext +open import foundation.slice funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-image +open import foundation.universal-property-image funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/uniqueness-quantification.lagda.md b/src/foundation/uniqueness-quantification.lagda.md index dbbce2a023..08f9d9b66d 100644 --- a/src/foundation/uniqueness-quantification.lagda.md +++ b/src/foundation/uniqueness-quantification.lagda.md @@ -1,14 +1,19 @@ # Uniqueness quantification ```agda -module foundation.uniqueness-quantification where +open import foundation.function-extensionality-axiom + +module + foundation.uniqueness-quantification + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/uniqueness-set-quotients.lagda.md b/src/foundation/uniqueness-set-quotients.lagda.md index 386076acce..7b375f4933 100644 --- a/src/foundation/uniqueness-set-quotients.lagda.md +++ b/src/foundation/uniqueness-set-quotients.lagda.md @@ -1,7 +1,12 @@ # The uniqueness of set quotients ```agda -module foundation.uniqueness-set-quotients where +open import foundation.function-extensionality-axiom + +module + foundation.uniqueness-set-quotients + (funext : function-extensionality) + where ```
Imports @@ -9,18 +14,17 @@ module foundation.uniqueness-set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets +open import foundation.equivalences funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.universal-property-equivalences -open import foundation.universal-property-set-quotients +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.contractible-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/uniqueness-set-truncations.lagda.md b/src/foundation/uniqueness-set-truncations.lagda.md index 604c442e9f..d30e5dd395 100644 --- a/src/foundation/uniqueness-set-truncations.lagda.md +++ b/src/foundation/uniqueness-set-truncations.lagda.md @@ -1,17 +1,22 @@ # Uniqueness of set truncations ```agda -module foundation.uniqueness-set-truncations where +open import foundation.function-extensionality-axiom + +module + foundation.uniqueness-set-truncations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.mere-equality -open import foundation.sets -open import foundation.uniqueness-set-quotients -open import foundation.universal-property-set-truncation +open import foundation.mere-equality funext +open import foundation.sets funext +open import foundation.uniqueness-set-quotients funext +open import foundation.universal-property-set-truncation funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/uniqueness-truncation.lagda.md b/src/foundation/uniqueness-truncation.lagda.md index d14c70219d..05ac46d0f5 100644 --- a/src/foundation/uniqueness-truncation.lagda.md +++ b/src/foundation/uniqueness-truncation.lagda.md @@ -1,13 +1,18 @@ # Uniqueness of the truncations ```agda -module foundation.uniqueness-truncation where +open import foundation.function-extensionality-axiom + +module + foundation.uniqueness-truncation + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.dependent-products-truncated-types +open import foundation.dependent-products-truncated-types funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/univalence-implies-function-extensionality.lagda.md b/src/foundation/univalence-implies-function-extensionality.lagda.md index a0d8b50ddc..63958f244c 100644 --- a/src/foundation/univalence-implies-function-extensionality.lagda.md +++ b/src/foundation/univalence-implies-function-extensionality.lagda.md @@ -1,19 +1,23 @@ # The univalence axiom implies function extensionality ```agda -module foundation.univalence-implies-function-extensionality where +open import foundation.function-extensionality-axiom + +module + foundation.univalence-implies-function-extensionality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalence-induction -open import foundation.function-extensionality-axiom -open import foundation.postcomposition-functions +open import foundation.equivalence-induction funext +open import foundation.postcomposition-functions funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import foundation.weak-function-extensionality +open import foundation.weak-function-extensionality funext open import foundation-core.contractible-maps open import foundation-core.contractible-types diff --git a/src/foundation/univalence.lagda.md b/src/foundation/univalence.lagda.md index 7b5a2bf621..657bab60cc 100644 --- a/src/foundation/univalence.lagda.md +++ b/src/foundation/univalence.lagda.md @@ -1,7 +1,12 @@ # The univalence axiom ```agda -module foundation.univalence where +open import foundation.function-extensionality-axiom + +module + foundation.univalence + (funext : function-extensionality) + where open import foundation-core.univalence public ``` @@ -11,8 +16,8 @@ open import foundation-core.univalence public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation/univalent-type-families.lagda.md b/src/foundation/univalent-type-families.lagda.md index 0a3999846c..1364a89300 100644 --- a/src/foundation/univalent-type-families.lagda.md +++ b/src/foundation/univalent-type-families.lagda.md @@ -1,7 +1,12 @@ # Univalent type families ```agda -module foundation.univalent-type-families where +open import foundation.function-extensionality-axiom + +module + foundation.univalent-type-families + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,17 @@ module foundation.univalent-type-families where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-systems -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.subuniverses +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.subuniverses funext open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.univalence funext +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/universal-property-booleans.lagda.md b/src/foundation/universal-property-booleans.lagda.md index bcb23bb57a..1c2bb788a2 100644 --- a/src/foundation/universal-property-booleans.lagda.md +++ b/src/foundation/universal-property-booleans.lagda.md @@ -1,7 +1,12 @@ # The universal property of booleans ```agda -module foundation.universal-property-booleans where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-booleans + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,8 @@ module foundation.universal-property-booleans where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation-core.booleans diff --git a/src/foundation/universal-property-cartesian-product-types.lagda.md b/src/foundation/universal-property-cartesian-product-types.lagda.md index c2053eae40..3bb8c4c0be 100644 --- a/src/foundation/universal-property-cartesian-product-types.lagda.md +++ b/src/foundation/universal-property-cartesian-product-types.lagda.md @@ -1,18 +1,23 @@ # The universal properties of cartesian product types ```agda -module foundation.universal-property-cartesian-product-types where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-cartesian-product-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.standard-pullbacks +open import foundation.logical-equivalences funext +open import foundation.standard-pullbacks funext open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -21,10 +26,10 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/universal-property-contractible-types.lagda.md b/src/foundation/universal-property-contractible-types.lagda.md index d73ff1f0f2..c02455b43f 100644 --- a/src/foundation/universal-property-contractible-types.lagda.md +++ b/src/foundation/universal-property-contractible-types.lagda.md @@ -1,7 +1,12 @@ # Universal property of contractible types ```agda -module foundation.universal-property-contractible-types where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-contractible-types + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module foundation.universal-property-contractible-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.function-extensionality funext + open import foundation.singleton-induction open import foundation.universe-levels diff --git a/src/foundation/universal-property-coproduct-types.lagda.md b/src/foundation/universal-property-coproduct-types.lagda.md index 893e864163..f353140115 100644 --- a/src/foundation/universal-property-coproduct-types.lagda.md +++ b/src/foundation/universal-property-coproduct-types.lagda.md @@ -1,7 +1,12 @@ # The universal property of coproduct types ```agda -module foundation.universal-property-coproduct-types where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-coproduct-types + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,9 @@ module foundation.universal-property-coproduct-types where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.universal-property-equivalences +open import foundation.function-extensionality funext + +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/universal-property-dependent-function-types.lagda.md b/src/foundation/universal-property-dependent-function-types.lagda.md index 9f7b72e52a..fcbbf8ce0a 100644 --- a/src/foundation/universal-property-dependent-function-types.lagda.md +++ b/src/foundation/universal-property-dependent-function-types.lagda.md @@ -1,23 +1,29 @@ # The universal property of dependent function types ```agda -module foundation.universal-property-dependent-function-types where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-dependent-function-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext + +open import foundation.identity-types funext open import foundation.spans-families-of-types -open import foundation.terminal-spans-families-of-types +open import foundation.terminal-spans-families-of-types funext open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types ``` diff --git a/src/foundation/universal-property-dependent-pair-types.lagda.md b/src/foundation/universal-property-dependent-pair-types.lagda.md index dcd8364df1..1374eae79b 100644 --- a/src/foundation/universal-property-dependent-pair-types.lagda.md +++ b/src/foundation/universal-property-dependent-pair-types.lagda.md @@ -1,14 +1,20 @@ # The universal property of dependent pair types ```agda -module foundation.universal-property-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-dependent-pair-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/universal-property-empty-type.lagda.md b/src/foundation/universal-property-empty-type.lagda.md index c3fe4f7374..4421e9fe8b 100644 --- a/src/foundation/universal-property-empty-type.lagda.md +++ b/src/foundation/universal-property-empty-type.lagda.md @@ -1,15 +1,21 @@ # The universal property of the empty type ```agda -module foundation.universal-property-empty-type where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-empty-type + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.universal-property-equivalences +open import foundation.function-extensionality funext + +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/universal-property-equivalences.lagda.md b/src/foundation/universal-property-equivalences.lagda.md index 4f4300ef98..7611184631 100644 --- a/src/foundation/universal-property-equivalences.lagda.md +++ b/src/foundation/universal-property-equivalences.lagda.md @@ -1,15 +1,20 @@ # The universal property of equivalences ```agda -module foundation.universal-property-equivalences where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-equivalences + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.precomposition-functions-into-subuniverses +open import foundation.dependent-universal-property-equivalences funext +open import foundation.precomposition-functions-into-subuniverses funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md index 82c10540aa..40f1377b76 100644 --- a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md +++ b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md @@ -1,7 +1,12 @@ # The universal property of the family of fibers of maps ```agda -module foundation.universal-property-family-of-fibers-of-maps where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-family-of-fibers-of-maps + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module foundation.universal-property-family-of-fibers-of-maps where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.families-of-equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.families-of-equivalences funext +open import foundation.function-extensionality funext + open import foundation.subtype-identity-principle open import foundation.universe-levels @@ -21,7 +26,7 @@ open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types @@ -29,8 +34,8 @@ open import foundation-core.precomposition-dependent-functions open import foundation-core.retractions open import foundation-core.sections -open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements funext +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
diff --git a/src/foundation/universal-property-fiber-products.lagda.md b/src/foundation/universal-property-fiber-products.lagda.md index 9c0b864ad8..a403c1787c 100644 --- a/src/foundation/universal-property-fiber-products.lagda.md +++ b/src/foundation/universal-property-fiber-products.lagda.md @@ -1,16 +1,21 @@ # The universal property of fiber products ```agda -module foundation.universal-property-fiber-products where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-fiber-products + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.standard-pullbacks +open import foundation.standard-pullbacks funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -21,8 +26,8 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks -open import foundation-core.universal-property-pullbacks +open import foundation-core.pullbacks funext +open import foundation-core.universal-property-pullbacks funext ```
diff --git a/src/foundation/universal-property-identity-systems.lagda.md b/src/foundation/universal-property-identity-systems.lagda.md index b0e32181a0..39be921752 100644 --- a/src/foundation/universal-property-identity-systems.lagda.md +++ b/src/foundation/universal-property-identity-systems.lagda.md @@ -1,7 +1,12 @@ # The universal property of identity systems ```agda -module foundation.universal-property-identity-systems where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-identity-systems + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module foundation.universal-property-identity-systems where ```agda open import foundation.dependent-pair-types open import foundation.identity-systems -open import foundation.universal-property-contractible-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/universal-property-identity-types.lagda.md b/src/foundation/universal-property-identity-types.lagda.md index 1e4268ca8f..daba01e9c9 100644 --- a/src/foundation/universal-property-identity-types.lagda.md +++ b/src/foundation/universal-property-identity-types.lagda.md @@ -1,7 +1,12 @@ # The universal property of identity types ```agda -module foundation.universal-property-identity-types where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-identity-types + (funext : function-extensionality) + where ```
Imports @@ -9,18 +14,19 @@ module foundation.universal-property-identity-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.dependent-universal-property-equivalences -open import foundation.embeddings -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types +open import foundation.dependent-products-propositions funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-dependent-function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.preunivalence -open import foundation.univalence +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.preunivalence funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/universal-property-image.lagda.md b/src/foundation/universal-property-image.lagda.md index d3ce89ffd0..8a945fb291 100644 --- a/src/foundation/universal-property-image.lagda.md +++ b/src/foundation/universal-property-image.lagda.md @@ -1,21 +1,26 @@ # The universal property of the image of a map ```agda -module foundation.universal-property-image where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-image + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.images -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.slice -open import foundation.surjective-maps +open import foundation.embeddings funext +open import foundation.images funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.slice funext +open import foundation.surjective-maps funext open import foundation.transport-along-identifications -open import foundation.universal-property-family-of-fibers-of-maps +open import foundation.universal-property-family-of-fibers-of-maps funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -24,7 +29,7 @@ open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types @@ -32,7 +37,7 @@ open import foundation-core.injective-maps open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sections -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/universal-property-maybe.lagda.md b/src/foundation/universal-property-maybe.lagda.md index f55128fdfa..27564028ad 100644 --- a/src/foundation/universal-property-maybe.lagda.md +++ b/src/foundation/universal-property-maybe.lagda.md @@ -1,14 +1,20 @@ # The universal property of the maybe monad ```agda -module foundation.universal-property-maybe where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-maybe + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md b/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md index 124181f37d..2ae5b12dc0 100644 --- a/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md +++ b/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md @@ -1,7 +1,12 @@ # The universal property of propositional truncations with respect to sets ```agda -module foundation.universal-property-propositional-truncation-into-sets where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-propositional-truncation-into-sets + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,11 @@ module foundation.universal-property-propositional-truncation-into-sets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.propositional-truncations +open import foundation.function-extensionality funext + +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import foundation.weakly-constant-maps +open import foundation.weakly-constant-maps funext open import foundation-core.equivalences open import foundation-core.fibers-of-maps @@ -21,7 +27,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes +open import foundation-core.subtypes funext ```
diff --git a/src/foundation/universal-property-propositional-truncation.lagda.md b/src/foundation/universal-property-propositional-truncation.lagda.md index 1cadb2f5f2..ed662964de 100644 --- a/src/foundation/universal-property-propositional-truncation.lagda.md +++ b/src/foundation/universal-property-propositional-truncation.lagda.md @@ -1,29 +1,35 @@ # The universal property of propositional truncations ```agda -module foundation.universal-property-propositional-truncation where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-propositional-truncation + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types -open import foundation.logical-equivalences -open import foundation.precomposition-functions-into-subuniverses +open import foundation.dependent-products-propositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-cartesian-product-types funext +open import foundation.logical-equivalences funext +open import foundation.precomposition-functions-into-subuniverses funext open import foundation.subtype-identity-principle open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-equivalences +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/universal-property-pullbacks.lagda.md b/src/foundation/universal-property-pullbacks.lagda.md index 0b97e575fa..3fe1ee145a 100644 --- a/src/foundation/universal-property-pullbacks.lagda.md +++ b/src/foundation/universal-property-pullbacks.lagda.md @@ -1,23 +1,28 @@ # The universal property of pullbacks ```agda -module foundation.universal-property-pullbacks where +open import foundation.function-extensionality-axiom -open import foundation-core.universal-property-pullbacks public +module + foundation.universal-property-pullbacks + (funext : function-extensionality) + where + +open import foundation-core.universal-property-pullbacks funext public ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.subtype-identity-principle open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.function-types -open import foundation-core.pullbacks +open import foundation-core.pullbacks funext ```
diff --git a/src/foundation/universal-property-sequential-limits.lagda.md b/src/foundation/universal-property-sequential-limits.lagda.md index d7377fae19..d2b09b774d 100644 --- a/src/foundation/universal-property-sequential-limits.lagda.md +++ b/src/foundation/universal-property-sequential-limits.lagda.md @@ -1,18 +1,23 @@ # The universal property of sequential limits ```agda -module foundation.universal-property-sequential-limits where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-sequential-limits + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-inverse-sequential-diagrams +open import foundation.cones-over-inverse-sequential-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.inverse-sequential-diagrams -open import foundation.postcomposition-functions +open import foundation.equivalences funext +open import foundation.inverse-sequential-diagrams funext +open import foundation.postcomposition-functions funext open import foundation.subtype-identity-principle open import foundation.universe-levels diff --git a/src/foundation/universal-property-set-quotients.lagda.md b/src/foundation/universal-property-set-quotients.lagda.md index 8ff5cf6b79..747d57b3d4 100644 --- a/src/foundation/universal-property-set-quotients.lagda.md +++ b/src/foundation/universal-property-set-quotients.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.universal-property-set-quotients where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-set-quotients + (funext : function-extensionality) + where ```
Imports @@ -11,28 +16,28 @@ module foundation.universal-property-set-quotients where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.dependent-universal-property-equivalences -open import foundation.effective-maps-equivalence-relations -open import foundation.epimorphisms-with-respect-to-sets -open import foundation.equivalence-classes -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom +open import foundation.dependent-products-propositions funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.effective-maps-equivalence-relations funext +open import foundation.epimorphisms-with-respect-to-sets funext +open import foundation.equivalence-classes funext +open import foundation.existential-quantification funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.images -open import foundation.injective-maps -open import foundation.locally-small-types -open import foundation.logical-equivalences -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.surjective-maps +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.injective-maps funext +open import foundation.locally-small-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.sets funext +open import foundation.surjective-maps funext open import foundation.transport-along-identifications -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-image +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-image funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -41,7 +46,7 @@ open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types @@ -49,8 +54,8 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.small-types -open import foundation-core.subtypes +open import foundation-core.small-types funext +open import foundation-core.subtypes funext open import foundation-core.torsorial-type-families open import foundation-core.type-theoretic-principle-of-choice open import foundation-core.univalence diff --git a/src/foundation/universal-property-set-truncation.lagda.md b/src/foundation/universal-property-set-truncation.lagda.md index c6a4069b7b..1ac282d263 100644 --- a/src/foundation/universal-property-set-truncation.lagda.md +++ b/src/foundation/universal-property-set-truncation.lagda.md @@ -1,20 +1,26 @@ # The universal property of set truncations ```agda -module foundation.universal-property-set-truncation where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-set-truncation + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.mere-equality -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.mere-equality funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.sets funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-equivalences -open import foundation.universal-property-set-quotients +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/universal-property-truncation.lagda.md b/src/foundation/universal-property-truncation.lagda.md index 3a47918c45..fe3a531d07 100644 --- a/src/foundation/universal-property-truncation.lagda.md +++ b/src/foundation/universal-property-truncation.lagda.md @@ -1,31 +1,37 @@ # The universal property of truncations ```agda -module foundation.universal-property-truncation where +open import foundation.function-extensionality-axiom -open import foundation-core.universal-property-truncation public +module + foundation.universal-property-truncation + (funext : function-extensionality) + where + +open import foundation-core.universal-property-truncation funext public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.surjective-maps -open import foundation.type-arithmetic-dependent-function-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-identity-types +open import foundation.dependent-products-contractible-types funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.surjective-maps funext +open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-identity-types funext open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.torsorial-type-families open import foundation-core.truncated-types diff --git a/src/foundation/universal-property-unit-type.lagda.md b/src/foundation/universal-property-unit-type.lagda.md index 20149383b1..823ca72740 100644 --- a/src/foundation/universal-property-unit-type.lagda.md +++ b/src/foundation/universal-property-unit-type.lagda.md @@ -1,7 +1,12 @@ # The universal property of the unit type ```agda -module foundation.universal-property-unit-type where +open import foundation.function-extensionality-axiom + +module + foundation.universal-property-unit-type + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module foundation.universal-property-unit-type where ```agda open import foundation.dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-contractible-types -open import foundation.universal-property-equivalences +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.constant-maps diff --git a/src/foundation/universal-quantification.lagda.md b/src/foundation/universal-quantification.lagda.md index 63a9a9e0e7..043f646f4a 100644 --- a/src/foundation/universal-quantification.lagda.md +++ b/src/foundation/universal-quantification.lagda.md @@ -1,17 +1,22 @@ # Universal quantification ```agda -module foundation.universal-quantification where +open import foundation.function-extensionality-axiom + +module + foundation.universal-quantification + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions +open import foundation.dependent-products-propositions funext open import foundation.evaluation-functions -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/unordered-pairs-of-types.lagda.md b/src/foundation/unordered-pairs-of-types.lagda.md index ccefe96921..fd833b65f2 100644 --- a/src/foundation/unordered-pairs-of-types.lagda.md +++ b/src/foundation/unordered-pairs-of-types.lagda.md @@ -1,7 +1,12 @@ # Unordered pairs of types ```agda -module foundation.unordered-pairs-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.unordered-pairs-of-types + (funext : function-extensionality) + where ```
Imports @@ -10,15 +15,15 @@ module foundation.unordered-pairs-of-types where open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.torsorial-type-families -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext ```
diff --git a/src/foundation/unordered-pairs.lagda.md b/src/foundation/unordered-pairs.lagda.md index 764054eed8..14a446f15c 100644 --- a/src/foundation/unordered-pairs.lagda.md +++ b/src/foundation/unordered-pairs.lagda.md @@ -1,29 +1,35 @@ # Unordered pairs of elements in a type ```agda -module foundation.unordered-pairs where +open import foundation.function-extensionality-axiom + +module + foundation.unordered-pairs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types -open import foundation.decidable-equality +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-types funext +open import foundation.decidable-equality funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality +open import foundation.dependent-universal-property-equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.mere-equivalences -open import foundation.postcomposition-functions -open import foundation.propositional-truncations +open import foundation.homotopy-induction funext +open import foundation.mere-equivalences funext +open import foundation.postcomposition-functions funext +open import foundation.propositional-truncations funext open import foundation.structure-identity-principle -open import foundation.type-arithmetic-dependent-function-types -open import foundation.universal-property-contractible-types -open import foundation.universal-property-dependent-pair-types +open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -32,7 +38,7 @@ open import foundation-core.coproduct-types open import foundation-core.embeddings open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types @@ -41,11 +47,11 @@ open import foundation-core.propositions open import foundation-core.sets open import foundation-core.torsorial-type-families -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.universal-property-standard-finite-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.universal-property-standard-finite-types funext ```
diff --git a/src/foundation/unordered-tuples-of-types.lagda.md b/src/foundation/unordered-tuples-of-types.lagda.md index b208cabd92..58aea7bda5 100644 --- a/src/foundation/unordered-tuples-of-types.lagda.md +++ b/src/foundation/unordered-tuples-of-types.lagda.md @@ -1,7 +1,12 @@ # Unordered tuples of types ```agda -module foundation.unordered-tuples-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.unordered-tuples-of-types + (funext : function-extensionality) + where ```
Imports @@ -12,15 +17,15 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import foundation.unordered-tuples +open import foundation.unordered-tuples funext open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.torsorial-type-families -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/foundation/unordered-tuples.lagda.md b/src/foundation/unordered-tuples.lagda.md index d3ce033256..a857805559 100644 --- a/src/foundation/unordered-tuples.lagda.md +++ b/src/foundation/unordered-tuples.lagda.md @@ -1,7 +1,12 @@ # Unordered `n`-tuples of elements in a type ```agda -module foundation.unordered-tuples where +open import foundation.function-extensionality-axiom + +module + foundation.unordered-tuples + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module foundation.unordered-tuples where ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types -open import foundation.decidable-equality +open import foundation.1-types funext +open import foundation.decidable-equality funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types +open import foundation.dependent-products-truncated-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.postcomposition-functions +open import foundation.homotopy-induction funext +open import foundation.postcomposition-functions funext open import foundation.structure-identity-principle -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -30,10 +35,10 @@ open import foundation-core.identity-types open import foundation-core.sets open import foundation-core.torsorial-type-families -open import univalent-combinatorics.complements-isolated-elements -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.complements-isolated-elements funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/vectors-set-quotients.lagda.md b/src/foundation/vectors-set-quotients.lagda.md index d9652fc385..d979430018 100644 --- a/src/foundation/vectors-set-quotients.lagda.md +++ b/src/foundation/vectors-set-quotients.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module foundation.vectors-set-quotients where +open import foundation.function-extensionality-axiom + +module + foundation.vectors-set-quotients + (funext : function-extensionality) + where ```
Imports @@ -12,26 +17,26 @@ module foundation.vectors-set-quotients where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-products-set-quotients +open import foundation.cartesian-products-set-quotients funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.multivariable-operations -open import foundation.products-equivalence-relations -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.multivariable-operations funext +open import foundation.products-equivalence-relations funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.set-quotients funext +open import foundation.sets funext open import foundation.unit-type -open import foundation.universal-property-set-quotients +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.coproduct-types open import foundation-core.equality-dependent-pair-types -open import foundation-core.equivalence-relations +open import foundation-core.equivalence-relations funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies @@ -40,9 +45,9 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.sections -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/foundation/vertical-composition-spans-of-spans.lagda.md b/src/foundation/vertical-composition-spans-of-spans.lagda.md index 785b482745..dffbda6cba 100644 --- a/src/foundation/vertical-composition-spans-of-spans.lagda.md +++ b/src/foundation/vertical-composition-spans-of-spans.lagda.md @@ -1,27 +1,32 @@ # Vertical composition of spans of spans ```agda -module foundation.vertical-composition-spans-of-spans where +open import foundation.function-extensionality-axiom + +module + foundation.vertical-composition-spans-of-spans + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps -open import foundation.composition-spans +open import foundation.commuting-triangles-of-maps funext +open import foundation.composition-spans funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-spans -open import foundation.homotopies -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.equivalences-spans funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.morphisms-spans -open import foundation.pullbacks +open import foundation.pullbacks funext open import foundation.spans -open import foundation.spans-of-spans -open import foundation.standard-pullbacks -open import foundation.type-arithmetic-standard-pullbacks +open import foundation.spans-of-spans funext +open import foundation.standard-pullbacks funext +open import foundation.type-arithmetic-standard-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/weak-function-extensionality.lagda.md b/src/foundation/weak-function-extensionality.lagda.md index 39801af669..06c9312502 100644 --- a/src/foundation/weak-function-extensionality.lagda.md +++ b/src/foundation/weak-function-extensionality.lagda.md @@ -1,17 +1,21 @@ # Weak function extensionality ```agda -module foundation.weak-function-extensionality where +open import foundation.function-extensionality-axiom + +module + foundation.weak-function-extensionality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation/weak-limited-principle-of-omniscience.lagda.md b/src/foundation/weak-limited-principle-of-omniscience.lagda.md index abef45248f..19ced2b51c 100644 --- a/src/foundation/weak-limited-principle-of-omniscience.lagda.md +++ b/src/foundation/weak-limited-principle-of-omniscience.lagda.md @@ -1,7 +1,12 @@ # The weak limited principle of omniscience ```agda -module foundation.weak-limited-principle-of-omniscience where +open import foundation.function-extensionality-axiom + +module + foundation.weak-limited-principle-of-omniscience + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module foundation.weak-limited-principle-of-omniscience where ```agda open import elementary-number-theory.natural-numbers -open import foundation.disjunction -open import foundation.negation -open import foundation.universal-quantification +open import foundation.disjunction funext +open import foundation.negation funext +open import foundation.universal-quantification funext open import foundation.universe-levels open import foundation-core.booleans -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.propositions open import foundation-core.sets ``` diff --git a/src/foundation/weakly-constant-maps.lagda.md b/src/foundation/weakly-constant-maps.lagda.md index e2d2c88d58..0c48713b47 100644 --- a/src/foundation/weakly-constant-maps.lagda.md +++ b/src/foundation/weakly-constant-maps.lagda.md @@ -1,7 +1,12 @@ # Weakly constant maps ```agda -module foundation.weakly-constant-maps where +open import foundation.function-extensionality-axiom + +module + foundation.weakly-constant-maps + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module foundation.weakly-constant-maps where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.identity-types -open import foundation.iterated-dependent-product-types +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/whiskering-homotopies-concatenation.lagda.md b/src/foundation/whiskering-homotopies-concatenation.lagda.md index ef61dcad5c..d84e1d82d0 100644 --- a/src/foundation/whiskering-homotopies-concatenation.lagda.md +++ b/src/foundation/whiskering-homotopies-concatenation.lagda.md @@ -1,7 +1,12 @@ # Whiskering homotopies with respect to concatenation ```agda -module foundation.whiskering-homotopies-concatenation where +open import foundation.function-extensionality-axiom + +module + foundation.whiskering-homotopies-concatenation + (funext : function-extensionality) + where open import foundation-core.whiskering-homotopies-concatenation public ``` @@ -10,10 +15,10 @@ open import foundation-core.whiskering-homotopies-concatenation public ```agda open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types +open import foundation-core.functoriality-dependent-function-types funext open import foundation-core.homotopies ``` diff --git a/src/foundation/whiskering-identifications-concatenation.lagda.md b/src/foundation/whiskering-identifications-concatenation.lagda.md index c37fbc64cc..79c68c4137 100644 --- a/src/foundation/whiskering-identifications-concatenation.lagda.md +++ b/src/foundation/whiskering-identifications-concatenation.lagda.md @@ -1,7 +1,12 @@ # Whiskering identifications with respect to concatenation ```agda -module foundation.whiskering-identifications-concatenation where +open import foundation.function-extensionality-axiom + +module + foundation.whiskering-identifications-concatenation + (funext : function-extensionality) + where open import foundation-core.whiskering-identifications-concatenation public ``` @@ -10,7 +15,7 @@ open import foundation-core.whiskering-identifications-concatenation public ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/wild-category-of-types.lagda.md b/src/foundation/wild-category-of-types.lagda.md index 60277a29a4..6e496cd7e4 100644 --- a/src/foundation/wild-category-of-types.lagda.md +++ b/src/foundation/wild-category-of-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module foundation.wild-category-of-types where +open import foundation.function-extensionality-axiom + +module + foundation.wild-category-of-types + (funext : function-extensionality) + where ```
Imports @@ -11,11 +16,11 @@ module foundation.wild-category-of-types where ```agda open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.globular-type-of-functions -open import foundation.homotopies -open import foundation.isomorphisms-of-sets -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.globular-type-of-functions funext +open import foundation.homotopies funext +open import foundation.isomorphisms-of-sets funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels open import foundation-core.contractible-types @@ -26,13 +31,13 @@ open import foundation-core.identity-types open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.large-reflexive-globular-types -open import globular-types.large-transitive-globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.large-reflexive-globular-types funext +open import globular-types.large-transitive-globular-types funext +open import globular-types.reflexive-globular-types funext +open import globular-types.transitive-globular-types funext -open import wild-category-theory.noncoherent-large-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-large-omega-precategories funext +open import wild-category-theory.noncoherent-omega-precategories funext ```
diff --git a/src/foundation/yoneda-identity-types.lagda.md b/src/foundation/yoneda-identity-types.lagda.md index f9064f5122..74133c02d2 100644 --- a/src/foundation/yoneda-identity-types.lagda.md +++ b/src/foundation/yoneda-identity-types.lagda.md @@ -1,7 +1,12 @@ # Yoneda identity types ```agda -module foundation.yoneda-identity-types where +open import foundation.function-extensionality-axiom + +module + foundation.yoneda-identity-types + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module foundation.yoneda-identity-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.multivariable-homotopies +open import foundation.function-extensionality funext + +open import foundation.multivariable-homotopies funext open import foundation.strictly-right-unital-concatenation-identifications open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalence -open import foundation.universal-property-identity-systems +open import foundation.univalence funext +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/globular-types.lagda.md b/src/globular-types.lagda.md index 260995b614..688a7344ee 100644 --- a/src/globular-types.lagda.md +++ b/src/globular-types.lagda.md @@ -7,61 +7,66 @@ ## Modules in the globular types namespace ```agda -module globular-types where +open import foundation.function-extensionality-axiom -open import globular-types.base-change-dependent-globular-types public -open import globular-types.base-change-dependent-reflexive-globular-types public -open import globular-types.binary-dependent-globular-types public -open import globular-types.binary-dependent-reflexive-globular-types public +module + globular-types + (funext : function-extensionality) + where + +open import globular-types.base-change-dependent-globular-types funext public +open import globular-types.base-change-dependent-reflexive-globular-types funext public +open import globular-types.binary-dependent-globular-types funext public +open import globular-types.binary-dependent-reflexive-globular-types funext public open import globular-types.binary-globular-maps public -open import globular-types.colax-reflexive-globular-maps public -open import globular-types.colax-transitive-globular-maps public +open import globular-types.colax-reflexive-globular-maps funext public +open import globular-types.colax-transitive-globular-maps funext public open import globular-types.composition-structure-globular-types public open import globular-types.constant-globular-types public -open import globular-types.dependent-globular-types public -open import globular-types.dependent-reflexive-globular-types public -open import globular-types.dependent-sums-globular-types public -open import globular-types.discrete-dependent-reflexive-globular-types public -open import globular-types.discrete-globular-types public -open import globular-types.discrete-reflexive-globular-types public -open import globular-types.empty-globular-types public -open import globular-types.equality-globular-types public -open import globular-types.exponentials-globular-types public -open import globular-types.fibers-globular-maps public -open import globular-types.globular-equivalences public -open import globular-types.globular-maps public +open import globular-types.dependent-globular-types funext public +open import globular-types.dependent-reflexive-globular-types funext public +open import globular-types.dependent-sums-globular-types funext public +open import globular-types.discrete-dependent-reflexive-globular-types funext public +open import globular-types.discrete-globular-types funext public +open import globular-types.discrete-reflexive-globular-types funext public +open import globular-types.empty-globular-types funext public +open import globular-types.equality-globular-types funext public +open import globular-types.exponentials-globular-types funext public +open import globular-types.fibers-globular-maps funext public +open import globular-types.globular-equivalences funext public +open import globular-types.globular-maps funext public open import globular-types.globular-types public -open import globular-types.large-colax-reflexive-globular-maps public -open import globular-types.large-colax-transitive-globular-maps public -open import globular-types.large-globular-maps public +open import globular-types.large-colax-reflexive-globular-maps funext public +open import globular-types.large-colax-transitive-globular-maps funext public +open import globular-types.large-globular-maps funext public open import globular-types.large-globular-types public -open import globular-types.large-lax-reflexive-globular-maps public -open import globular-types.large-lax-transitive-globular-maps public -open import globular-types.large-reflexive-globular-maps public -open import globular-types.large-reflexive-globular-types public -open import globular-types.large-symmetric-globular-types public -open import globular-types.large-transitive-globular-maps public -open import globular-types.large-transitive-globular-types public -open import globular-types.lax-reflexive-globular-maps public -open import globular-types.lax-transitive-globular-maps public -open import globular-types.points-globular-types public -open import globular-types.points-reflexive-globular-types public -open import globular-types.pointwise-extensions-binary-families-globular-types public -open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types public -open import globular-types.pointwise-extensions-families-globular-types public -open import globular-types.pointwise-extensions-families-reflexive-globular-types public -open import globular-types.products-families-of-globular-types public -open import globular-types.reflexive-globular-equivalences public -open import globular-types.reflexive-globular-maps public -open import globular-types.reflexive-globular-types public -open import globular-types.sections-dependent-globular-types public -open import globular-types.superglobular-types public -open import globular-types.symmetric-globular-types public -open import globular-types.terminal-globular-types public -open import globular-types.transitive-globular-maps public -open import globular-types.transitive-globular-types public +open import globular-types.large-lax-reflexive-globular-maps funext public +open import globular-types.large-lax-transitive-globular-maps funext public +open import globular-types.large-reflexive-globular-maps funext public +open import globular-types.large-reflexive-globular-types funext public +open import globular-types.large-symmetric-globular-types funext public +open import globular-types.large-transitive-globular-maps funext public +open import globular-types.large-transitive-globular-types funext public +open import globular-types.lax-reflexive-globular-maps funext public +open import globular-types.lax-transitive-globular-maps funext public +open import globular-types.points-globular-types funext public +open import globular-types.points-reflexive-globular-types funext public +open import globular-types.pointwise-extensions-binary-families-globular-types funext public +open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types funext public +open import globular-types.pointwise-extensions-families-globular-types funext public +open import globular-types.pointwise-extensions-families-reflexive-globular-types funext public +open import globular-types.products-families-of-globular-types funext public +open import globular-types.reflexive-globular-equivalences funext public +open import globular-types.reflexive-globular-maps funext public +open import globular-types.reflexive-globular-types funext public +open import globular-types.sections-dependent-globular-types funext public +open import globular-types.superglobular-types funext public +open import globular-types.symmetric-globular-types funext public +open import globular-types.terminal-globular-types funext public +open import globular-types.transitive-globular-maps funext public +open import globular-types.transitive-globular-types funext public open import globular-types.unit-globular-type public -open import globular-types.unit-reflexive-globular-type public -open import globular-types.universal-globular-type public -open import globular-types.universal-reflexive-globular-type public +open import globular-types.unit-reflexive-globular-type funext public +open import globular-types.universal-globular-type funext public +open import globular-types.universal-reflexive-globular-type funext public ``` diff --git a/src/globular-types/base-change-dependent-globular-types.lagda.md b/src/globular-types/base-change-dependent-globular-types.lagda.md index c0408459c0..d000158db8 100644 --- a/src/globular-types/base-change-dependent-globular-types.lagda.md +++ b/src/globular-types/base-change-dependent-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.base-change-dependent-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.base-change-dependent-globular-types + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ module globular-types.base-change-dependent-globular-types where ```agda open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.globular-maps +open import globular-types.dependent-globular-types funext +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md b/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md index f1507037dd..709a13fd92 100644 --- a/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md @@ -3,22 +3,27 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.base-change-dependent-reflexive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.base-change-dependent-reflexive-globular-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import globular-types.base-change-dependent-globular-types -open import globular-types.dependent-globular-types -open import globular-types.dependent-reflexive-globular-types +open import globular-types.base-change-dependent-globular-types funext +open import globular-types.dependent-globular-types funext +open import globular-types.dependent-reflexive-globular-types funext open import globular-types.globular-types -open import globular-types.reflexive-globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-maps funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/binary-dependent-globular-types.lagda.md b/src/globular-types/binary-dependent-globular-types.lagda.md index de718af1c3..0ac6db2f7a 100644 --- a/src/globular-types/binary-dependent-globular-types.lagda.md +++ b/src/globular-types/binary-dependent-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.binary-dependent-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.binary-dependent-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ module globular-types.binary-dependent-globular-types where open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.points-globular-types +open import globular-types.points-globular-types funext ```
diff --git a/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md b/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md index 234b035227..4d9d40343a 100644 --- a/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.binary-dependent-reflexive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.binary-dependent-reflexive-globular-types + (funext : function-extensionality) + where ```
Imports @@ -11,10 +16,10 @@ module globular-types.binary-dependent-reflexive-globular-types where ```agda open import foundation.universe-levels -open import globular-types.binary-dependent-globular-types +open import globular-types.binary-dependent-globular-types funext open import globular-types.globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.points-reflexive-globular-types funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/colax-reflexive-globular-maps.lagda.md b/src/globular-types/colax-reflexive-globular-maps.lagda.md index 1e834a12a5..ddd1b65791 100644 --- a/src/globular-types/colax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/colax-reflexive-globular-maps.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.colax-reflexive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.colax-reflexive-globular-maps + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ module globular-types.colax-reflexive-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.globular-maps funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/colax-transitive-globular-maps.lagda.md b/src/globular-types/colax-transitive-globular-maps.lagda.md index cb012086d5..8f037f92c4 100644 --- a/src/globular-types/colax-transitive-globular-maps.lagda.md +++ b/src/globular-types/colax-transitive-globular-maps.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.colax-transitive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.colax-transitive-globular-maps + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ module globular-types.colax-transitive-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.transitive-globular-types +open import globular-types.globular-maps funext +open import globular-types.transitive-globular-types funext ```
diff --git a/src/globular-types/dependent-globular-types.lagda.md b/src/globular-types/dependent-globular-types.lagda.md index 41d4806001..8f8725a6e1 100644 --- a/src/globular-types/dependent-globular-types.lagda.md +++ b/src/globular-types/dependent-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.dependent-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.dependent-globular-types + (funext : function-extensionality) + where ```
Imports @@ -13,7 +18,7 @@ open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.points-globular-types +open import globular-types.points-globular-types funext ```
diff --git a/src/globular-types/dependent-reflexive-globular-types.lagda.md b/src/globular-types/dependent-reflexive-globular-types.lagda.md index b82c493c5e..dd5c0ec871 100644 --- a/src/globular-types/dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/dependent-reflexive-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.dependent-reflexive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.dependent-reflexive-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,10 +17,10 @@ module globular-types.dependent-reflexive-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.dependent-globular-types +open import globular-types.dependent-globular-types funext open import globular-types.globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.points-reflexive-globular-types funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/dependent-sums-globular-types.lagda.md b/src/globular-types/dependent-sums-globular-types.lagda.md index ead7b91cb5..83e39e0b54 100644 --- a/src/globular-types/dependent-sums-globular-types.lagda.md +++ b/src/globular-types/dependent-sums-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.dependent-sums-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.dependent-sums-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,11 +17,11 @@ module globular-types.dependent-sums-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.base-change-dependent-globular-types -open import globular-types.dependent-globular-types -open import globular-types.globular-maps +open import globular-types.base-change-dependent-globular-types funext +open import globular-types.dependent-globular-types funext +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.sections-dependent-globular-types +open import globular-types.sections-dependent-globular-types funext ```
diff --git a/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md b/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md index 782d45590d..b002492c96 100644 --- a/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.discrete-dependent-reflexive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.discrete-dependent-reflexive-globular-types + (funext : function-extensionality) + where ```
Imports @@ -11,10 +16,10 @@ module globular-types.discrete-dependent-reflexive-globular-types where ```agda open import foundation.universe-levels -open import globular-types.dependent-reflexive-globular-types -open import globular-types.discrete-reflexive-globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.dependent-reflexive-globular-types funext +open import globular-types.discrete-reflexive-globular-types funext +open import globular-types.points-reflexive-globular-types funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/discrete-globular-types.lagda.md b/src/globular-types/discrete-globular-types.lagda.md index 77b4dd1141..8883dade06 100644 --- a/src/globular-types/discrete-globular-types.lagda.md +++ b/src/globular-types/discrete-globular-types.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.discrete-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.discrete-globular-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.discrete-binary-relations -open import foundation.propositions +open import foundation.discrete-binary-relations funext +open import foundation.propositions funext open import foundation.universe-levels -open import globular-types.empty-globular-types +open import globular-types.empty-globular-types funext open import globular-types.globular-types ``` diff --git a/src/globular-types/discrete-reflexive-globular-types.lagda.md b/src/globular-types/discrete-reflexive-globular-types.lagda.md index 9e45c68d20..cbd898c3ff 100644 --- a/src/globular-types/discrete-reflexive-globular-types.lagda.md +++ b/src/globular-types/discrete-reflexive-globular-types.lagda.md @@ -3,20 +3,25 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.discrete-reflexive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.discrete-reflexive-globular-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.reflexive-globular-types -open import globular-types.symmetric-globular-types -open import globular-types.transitive-globular-types +open import globular-types.reflexive-globular-types funext +open import globular-types.symmetric-globular-types funext +open import globular-types.transitive-globular-types funext ```
diff --git a/src/globular-types/empty-globular-types.lagda.md b/src/globular-types/empty-globular-types.lagda.md index 9e19f67f78..f612cfcc1a 100644 --- a/src/globular-types/empty-globular-types.lagda.md +++ b/src/globular-types/empty-globular-types.lagda.md @@ -3,13 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.empty-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.empty-globular-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.empty-types +open import foundation.empty-types funext open import foundation.universe-levels open import globular-types.constant-globular-types diff --git a/src/globular-types/equality-globular-types.lagda.md b/src/globular-types/equality-globular-types.lagda.md index a93f6bde6f..92ae709ea6 100644 --- a/src/globular-types/equality-globular-types.lagda.md +++ b/src/globular-types/equality-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.equality-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.equality-globular-types + (funext : function-extensionality) + where ```
Imports @@ -11,13 +16,13 @@ module globular-types.equality-globular-types where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-homotopies -open import foundation.cartesian-product-types +open import foundation.binary-homotopies funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.coherently-invertible-maps diff --git a/src/globular-types/exponentials-globular-types.lagda.md b/src/globular-types/exponentials-globular-types.lagda.md index 85458109da..a6e30ae583 100644 --- a/src/globular-types/exponentials-globular-types.lagda.md +++ b/src/globular-types/exponentials-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.exponentials-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.exponentials-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,9 +17,9 @@ module globular-types.exponentials-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.products-families-of-globular-types +open import globular-types.products-families-of-globular-types funext ```
diff --git a/src/globular-types/fibers-globular-maps.lagda.md b/src/globular-types/fibers-globular-maps.lagda.md index 62022c561b..21ece5fd89 100644 --- a/src/globular-types/fibers-globular-maps.lagda.md +++ b/src/globular-types/fibers-globular-maps.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.fibers-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.fibers-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.identity-types +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.globular-maps +open import globular-types.dependent-globular-types funext +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/globular-equivalences.lagda.md b/src/globular-types/globular-equivalences.lagda.md index 5afece9603..14f5f46142 100644 --- a/src/globular-types/globular-equivalences.lagda.md +++ b/src/globular-types/globular-equivalences.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.globular-equivalences where +open import foundation.function-extensionality-axiom + +module + globular-types.globular-equivalences + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/globular-maps.lagda.md b/src/globular-types/globular-maps.lagda.md index 4cdc042698..44bbe7cd7b 100644 --- a/src/globular-types/globular-maps.lagda.md +++ b/src/globular-types/globular-maps.lagda.md @@ -3,15 +3,20 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.globular-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels open import globular-types.globular-types diff --git a/src/globular-types/large-colax-reflexive-globular-maps.lagda.md b/src/globular-types/large-colax-reflexive-globular-maps.lagda.md index a293af9b2d..adff192737 100644 --- a/src/globular-types/large-colax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/large-colax-reflexive-globular-maps.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-colax-reflexive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.large-colax-reflexive-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import globular-types.colax-reflexive-globular-maps -open import globular-types.large-globular-maps -open import globular-types.large-reflexive-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.colax-reflexive-globular-maps funext +open import globular-types.large-globular-maps funext +open import globular-types.large-reflexive-globular-types funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/large-colax-transitive-globular-maps.lagda.md b/src/globular-types/large-colax-transitive-globular-maps.lagda.md index 89aa77b7db..96479e7cfe 100644 --- a/src/globular-types/large-colax-transitive-globular-maps.lagda.md +++ b/src/globular-types/large-colax-transitive-globular-maps.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-colax-transitive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.large-colax-transitive-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import globular-types.colax-transitive-globular-maps -open import globular-types.large-globular-maps -open import globular-types.large-transitive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.colax-transitive-globular-maps funext +open import globular-types.large-globular-maps funext +open import globular-types.large-transitive-globular-types funext +open import globular-types.transitive-globular-types funext ```
diff --git a/src/globular-types/large-globular-maps.lagda.md b/src/globular-types/large-globular-maps.lagda.md index de2899cac3..79ff02150b 100644 --- a/src/globular-types/large-globular-maps.lagda.md +++ b/src/globular-types/large-globular-maps.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.large-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types open import globular-types.large-globular-types ``` diff --git a/src/globular-types/large-lax-reflexive-globular-maps.lagda.md b/src/globular-types/large-lax-reflexive-globular-maps.lagda.md index 4bde0a6526..47fe404b1d 100644 --- a/src/globular-types/large-lax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/large-lax-reflexive-globular-maps.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-lax-reflexive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.large-lax-reflexive-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import globular-types.large-globular-maps -open import globular-types.large-reflexive-globular-types -open import globular-types.lax-reflexive-globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.large-globular-maps funext +open import globular-types.large-reflexive-globular-types funext +open import globular-types.lax-reflexive-globular-maps funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/large-lax-transitive-globular-maps.lagda.md b/src/globular-types/large-lax-transitive-globular-maps.lagda.md index d2534bf35f..e41dd02a81 100644 --- a/src/globular-types/large-lax-transitive-globular-maps.lagda.md +++ b/src/globular-types/large-lax-transitive-globular-maps.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-lax-transitive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.large-lax-transitive-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import globular-types.large-globular-maps -open import globular-types.large-transitive-globular-types -open import globular-types.lax-transitive-globular-maps -open import globular-types.transitive-globular-types +open import globular-types.large-globular-maps funext +open import globular-types.large-transitive-globular-types funext +open import globular-types.lax-transitive-globular-maps funext +open import globular-types.transitive-globular-types funext ```
diff --git a/src/globular-types/large-reflexive-globular-maps.lagda.md b/src/globular-types/large-reflexive-globular-maps.lagda.md index 38cada0b7b..a5278af3a8 100644 --- a/src/globular-types/large-reflexive-globular-maps.lagda.md +++ b/src/globular-types/large-reflexive-globular-maps.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-reflexive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.large-reflexive-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.large-globular-maps -open import globular-types.large-reflexive-globular-types -open import globular-types.reflexive-globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.large-globular-maps funext +open import globular-types.large-reflexive-globular-types funext +open import globular-types.reflexive-globular-maps funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/large-reflexive-globular-types.lagda.md b/src/globular-types/large-reflexive-globular-types.lagda.md index 5c87033440..143220a0b8 100644 --- a/src/globular-types/large-reflexive-globular-types.lagda.md +++ b/src/globular-types/large-reflexive-globular-types.lagda.md @@ -3,20 +3,25 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-reflexive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.large-reflexive-globular-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.large-binary-relations +open import foundation.binary-relations funext +open import foundation.large-binary-relations funext open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.large-globular-maps +open import globular-types.large-globular-maps funext open import globular-types.large-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/large-symmetric-globular-types.lagda.md b/src/globular-types/large-symmetric-globular-types.lagda.md index 02e84ade5f..fd2a165495 100644 --- a/src/globular-types/large-symmetric-globular-types.lagda.md +++ b/src/globular-types/large-symmetric-globular-types.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-symmetric-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.large-symmetric-globular-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.large-binary-relations +open import foundation.large-binary-relations funext open import foundation.universe-levels open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.symmetric-globular-types +open import globular-types.symmetric-globular-types funext ```
diff --git a/src/globular-types/large-transitive-globular-maps.lagda.md b/src/globular-types/large-transitive-globular-maps.lagda.md index c4800f5c99..6e5d4245c4 100644 --- a/src/globular-types/large-transitive-globular-maps.lagda.md +++ b/src/globular-types/large-transitive-globular-maps.lagda.md @@ -3,21 +3,26 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-transitive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.large-transitive-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.large-globular-maps -open import globular-types.large-transitive-globular-types -open import globular-types.transitive-globular-maps -open import globular-types.transitive-globular-types +open import globular-types.large-globular-maps funext +open import globular-types.large-transitive-globular-types funext +open import globular-types.transitive-globular-maps funext +open import globular-types.transitive-globular-types funext ```
diff --git a/src/globular-types/large-transitive-globular-types.lagda.md b/src/globular-types/large-transitive-globular-types.lagda.md index 7981f454ba..b34f28e915 100644 --- a/src/globular-types/large-transitive-globular-types.lagda.md +++ b/src/globular-types/large-transitive-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.large-transitive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.large-transitive-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,9 +17,9 @@ module globular-types.large-transitive-globular-types where open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.large-globular-maps +open import globular-types.large-globular-maps funext open import globular-types.large-globular-types -open import globular-types.transitive-globular-types +open import globular-types.transitive-globular-types funext ```
diff --git a/src/globular-types/lax-reflexive-globular-maps.lagda.md b/src/globular-types/lax-reflexive-globular-maps.lagda.md index 910fa5260d..89cb31719d 100644 --- a/src/globular-types/lax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/lax-reflexive-globular-maps.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.lax-reflexive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.lax-reflexive-globular-maps + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ module globular-types.lax-reflexive-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.globular-maps funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/lax-transitive-globular-maps.lagda.md b/src/globular-types/lax-transitive-globular-maps.lagda.md index d06760ce39..e6a8ff4cac 100644 --- a/src/globular-types/lax-transitive-globular-maps.lagda.md +++ b/src/globular-types/lax-transitive-globular-maps.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.lax-transitive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.lax-transitive-globular-maps + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ module globular-types.lax-transitive-globular-maps where ```agda open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.transitive-globular-types +open import globular-types.globular-maps funext +open import globular-types.transitive-globular-types funext ```
diff --git a/src/globular-types/points-globular-types.lagda.md b/src/globular-types/points-globular-types.lagda.md index 94e81c6f56..7d1dbb0af4 100644 --- a/src/globular-types/points-globular-types.lagda.md +++ b/src/globular-types/points-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.points-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.points-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ module globular-types.points-globular-types where open import foundation.unit-type open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types open import globular-types.unit-globular-type ``` diff --git a/src/globular-types/points-reflexive-globular-types.lagda.md b/src/globular-types/points-reflexive-globular-types.lagda.md index c18a467757..4f0fe2e779 100644 --- a/src/globular-types/points-reflexive-globular-types.lagda.md +++ b/src/globular-types/points-reflexive-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.points-reflexive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.points-reflexive-globular-types + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ module globular-types.points-reflexive-globular-types where ```agda open import foundation.universe-levels -open import globular-types.points-globular-types -open import globular-types.reflexive-globular-types +open import globular-types.points-globular-types funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md b/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md index 904d9b312f..b1cc9ec0ba 100644 --- a/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md @@ -14,10 +14,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.binary-dependent-globular-types -open import globular-types.globular-equivalences +open import globular-types.binary-dependent-globular-types funext +open import globular-types.globular-equivalences funext open import globular-types.globular-types -open import globular-types.points-globular-types +open import globular-types.points-globular-types funext ```
@@ -48,7 +48,12 @@ of `K` if it comes equipped with a family of ### The predicate of being a pointwise extension of a binary family of globular types ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {l1 l2 l3 l4 l5 l6 l7 l8 : Level} {G : Globular-Type l1 l2} {H : Globular-Type l3 l4} (K : 0-cell-Globular-Type G → 0-cell-Globular-Type H → Globular-Type l5 l6) diff --git a/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md b/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md index c593d0e0a3..1023ced2d4 100644 --- a/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md @@ -14,10 +14,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.binary-dependent-reflexive-globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-equivalences -open import globular-types.reflexive-globular-types +open import globular-types.binary-dependent-reflexive-globular-types funext +open import globular-types.points-reflexive-globular-types funext +open import globular-types.reflexive-globular-equivalences funext +open import globular-types.reflexive-globular-types funext ```
@@ -49,7 +49,12 @@ of `K` if it comes equipped with a family of ### The predicate of being a pointwise extension of a binary family of reflexive globular types ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {l1 l2 l3 l4 l5 l6 l7 l8 : Level} {G : Reflexive-Globular-Type l1 l2} {H : Reflexive-Globular-Type l3 l4} (K : diff --git a/src/globular-types/pointwise-extensions-families-globular-types.lagda.md b/src/globular-types/pointwise-extensions-families-globular-types.lagda.md index 05d14be3df..a531212472 100644 --- a/src/globular-types/pointwise-extensions-families-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-families-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.pointwise-extensions-families-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.pointwise-extensions-families-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,10 +17,10 @@ module globular-types.pointwise-extensions-families-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.globular-equivalences +open import globular-types.dependent-globular-types funext +open import globular-types.globular-equivalences funext open import globular-types.globular-types -open import globular-types.points-globular-types +open import globular-types.points-globular-types funext ```
diff --git a/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md b/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md index 195002b2fe..10e14d29a1 100644 --- a/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md @@ -14,13 +14,13 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.dependent-reflexive-globular-types +open import globular-types.dependent-globular-types funext +open import globular-types.dependent-reflexive-globular-types funext open import globular-types.globular-types -open import globular-types.points-globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.reflexive-globular-equivalences -open import globular-types.reflexive-globular-types +open import globular-types.points-globular-types funext +open import globular-types.points-reflexive-globular-types funext +open import globular-types.reflexive-globular-equivalences funext +open import globular-types.reflexive-globular-types funext ```
@@ -49,7 +49,12 @@ indexed by the [points](globular-types.points-reflexive-globular-types.md) of ### The predicate of being a pointwise extension of a family of reflexive globular types ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {l1 l2 l3 l4 l5 l6 : Level} {G : Reflexive-Globular-Type l1 l2} (H : 0-cell-Reflexive-Globular-Type G → Reflexive-Globular-Type l3 l4) (K : Dependent-Reflexive-Globular-Type l5 l6 G) diff --git a/src/globular-types/products-families-of-globular-types.lagda.md b/src/globular-types/products-families-of-globular-types.lagda.md index a3c5ae1d63..2f0f276f63 100644 --- a/src/globular-types/products-families-of-globular-types.lagda.md +++ b/src/globular-types/products-families-of-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.products-families-of-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.products-families-of-globular-types + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ module globular-types.products-families-of-globular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/reflexive-globular-equivalences.lagda.md b/src/globular-types/reflexive-globular-equivalences.lagda.md index 8d154f39af..6ef59adcc3 100644 --- a/src/globular-types/reflexive-globular-equivalences.lagda.md +++ b/src/globular-types/reflexive-globular-equivalences.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.reflexive-globular-equivalences where +open import foundation.function-extensionality-axiom + +module + globular-types.reflexive-globular-equivalences + (funext : function-extensionality) + where ```
Imports @@ -11,15 +16,15 @@ module globular-types.reflexive-globular-equivalences where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-equivalences -open import globular-types.globular-maps -open import globular-types.reflexive-globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.globular-equivalences funext +open import globular-types.globular-maps funext +open import globular-types.reflexive-globular-maps funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/reflexive-globular-maps.lagda.md b/src/globular-types/reflexive-globular-maps.lagda.md index 92bd88780a..3eb226d886 100644 --- a/src/globular-types/reflexive-globular-maps.lagda.md +++ b/src/globular-types/reflexive-globular-maps.lagda.md @@ -3,17 +3,22 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.reflexive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.reflexive-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.reflexive-globular-types +open import globular-types.globular-maps funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/reflexive-globular-types.lagda.md b/src/globular-types/reflexive-globular-types.lagda.md index 8eec1e2951..8005795203 100644 --- a/src/globular-types/reflexive-globular-types.lagda.md +++ b/src/globular-types/reflexive-globular-types.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.reflexive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.reflexive-globular-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/sections-dependent-globular-types.lagda.md b/src/globular-types/sections-dependent-globular-types.lagda.md index 382d8719a1..eb1340404d 100644 --- a/src/globular-types/sections-dependent-globular-types.lagda.md +++ b/src/globular-types/sections-dependent-globular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.sections-dependent-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.sections-dependent-globular-types + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ module globular-types.sections-dependent-globular-types where ```agda open import foundation.universe-levels -open import globular-types.dependent-globular-types +open import globular-types.dependent-globular-types funext open import globular-types.globular-types ``` diff --git a/src/globular-types/superglobular-types.lagda.md b/src/globular-types/superglobular-types.lagda.md index eb34024fd4..6819e1a9fe 100644 --- a/src/globular-types/superglobular-types.lagda.md +++ b/src/globular-types/superglobular-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.superglobular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.superglobular-types + (funext : function-extensionality) + where ```
Imports @@ -12,12 +17,12 @@ module globular-types.superglobular-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.binary-dependent-reflexive-globular-types +open import globular-types.binary-dependent-reflexive-globular-types funext open import globular-types.globular-types -open import globular-types.points-reflexive-globular-types -open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types -open import globular-types.reflexive-globular-equivalences -open import globular-types.reflexive-globular-types +open import globular-types.points-reflexive-globular-types funext +open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types funext +open import globular-types.reflexive-globular-equivalences funext +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/globular-types/symmetric-globular-types.lagda.md b/src/globular-types/symmetric-globular-types.lagda.md index f8b627002c..a1708f579d 100644 --- a/src/globular-types/symmetric-globular-types.lagda.md +++ b/src/globular-types/symmetric-globular-types.lagda.md @@ -3,15 +3,20 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.symmetric-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.symmetric-globular-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import globular-types.globular-types diff --git a/src/globular-types/terminal-globular-types.lagda.md b/src/globular-types/terminal-globular-types.lagda.md index b9007c4347..192b92c3a1 100644 --- a/src/globular-types/terminal-globular-types.lagda.md +++ b/src/globular-types/terminal-globular-types.lagda.md @@ -3,16 +3,21 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.terminal-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.terminal-globular-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/transitive-globular-maps.lagda.md b/src/globular-types/transitive-globular-maps.lagda.md index 3d7d093665..6c330292f1 100644 --- a/src/globular-types/transitive-globular-maps.lagda.md +++ b/src/globular-types/transitive-globular-maps.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.transitive-globular-maps where +open import foundation.function-extensionality-axiom + +module + globular-types.transitive-globular-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps -open import globular-types.transitive-globular-types +open import globular-types.globular-maps funext +open import globular-types.transitive-globular-types funext ```
diff --git a/src/globular-types/transitive-globular-types.lagda.md b/src/globular-types/transitive-globular-types.lagda.md index 368bad45fc..4756a13f95 100644 --- a/src/globular-types/transitive-globular-types.lagda.md +++ b/src/globular-types/transitive-globular-types.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.transitive-globular-types where +open import foundation.function-extensionality-axiom + +module + globular-types.transitive-globular-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/unit-reflexive-globular-type.lagda.md b/src/globular-types/unit-reflexive-globular-type.lagda.md index 1c3e8752c0..ac0c4127d4 100644 --- a/src/globular-types/unit-reflexive-globular-type.lagda.md +++ b/src/globular-types/unit-reflexive-globular-type.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.unit-reflexive-globular-type where +open import foundation.function-extensionality-axiom + +module + globular-types.unit-reflexive-globular-type + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ module globular-types.unit-reflexive-globular-type where open import foundation.unit-type open import foundation.universe-levels -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-types funext open import globular-types.unit-globular-type ``` diff --git a/src/globular-types/universal-globular-type.lagda.md b/src/globular-types/universal-globular-type.lagda.md index 2d67afcbf1..ac7317b7c8 100644 --- a/src/globular-types/universal-globular-type.lagda.md +++ b/src/globular-types/universal-globular-type.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.universal-globular-type where +open import foundation.function-extensionality-axiom + +module + globular-types.universal-globular-type + (funext : function-extensionality) + where ```
Imports @@ -13,9 +18,9 @@ open import foundation.dependent-pair-types open import foundation.spans open import foundation.universe-levels -open import globular-types.dependent-globular-types -open import globular-types.exponentials-globular-types -open import globular-types.globular-maps +open import globular-types.dependent-globular-types funext +open import globular-types.exponentials-globular-types funext +open import globular-types.globular-maps funext open import globular-types.globular-types ``` diff --git a/src/globular-types/universal-reflexive-globular-type.lagda.md b/src/globular-types/universal-reflexive-globular-type.lagda.md index d704e71b34..92b9da49af 100644 --- a/src/globular-types/universal-reflexive-globular-type.lagda.md +++ b/src/globular-types/universal-reflexive-globular-type.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module globular-types.universal-reflexive-globular-type where +open import foundation.function-extensionality-axiom + +module + globular-types.universal-reflexive-globular-type + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ module globular-types.universal-reflexive-globular-type where open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-types funext ```
diff --git a/src/graph-theory.lagda.md b/src/graph-theory.lagda.md index c873b5ded2..c4c8add1ae 100644 --- a/src/graph-theory.lagda.md +++ b/src/graph-theory.lagda.md @@ -3,85 +3,90 @@ ## Modules in the graph theory namespace ```agda -module graph-theory where +open import foundation.function-extensionality-axiom -open import graph-theory.acyclic-undirected-graphs public -open import graph-theory.base-change-dependent-directed-graphs public -open import graph-theory.base-change-dependent-reflexive-graphs public -open import graph-theory.cartesian-products-directed-graphs public -open import graph-theory.cartesian-products-reflexive-graphs public -open import graph-theory.circuits-undirected-graphs public -open import graph-theory.closed-walks-undirected-graphs public -open import graph-theory.complete-bipartite-graphs public -open import graph-theory.complete-multipartite-graphs public -open import graph-theory.complete-undirected-graphs public -open import graph-theory.connected-undirected-graphs public -open import graph-theory.cycles-undirected-graphs public -open import graph-theory.dependent-directed-graphs public -open import graph-theory.dependent-products-directed-graphs public -open import graph-theory.dependent-products-reflexive-graphs public -open import graph-theory.dependent-reflexive-graphs public -open import graph-theory.dependent-sums-directed-graphs public -open import graph-theory.dependent-sums-reflexive-graphs public -open import graph-theory.directed-graph-duality public -open import graph-theory.directed-graph-structures-on-standard-finite-sets public -open import graph-theory.directed-graphs public -open import graph-theory.discrete-dependent-reflexive-graphs public -open import graph-theory.discrete-directed-graphs public -open import graph-theory.discrete-reflexive-graphs public -open import graph-theory.displayed-large-reflexive-graphs public -open import graph-theory.edge-coloured-undirected-graphs public -open import graph-theory.embeddings-directed-graphs public -open import graph-theory.embeddings-undirected-graphs public -open import graph-theory.enriched-undirected-graphs public -open import graph-theory.equivalences-dependent-directed-graphs public -open import graph-theory.equivalences-dependent-reflexive-graphs public -open import graph-theory.equivalences-directed-graphs public -open import graph-theory.equivalences-enriched-undirected-graphs public -open import graph-theory.equivalences-reflexive-graphs public -open import graph-theory.equivalences-undirected-graphs public -open import graph-theory.eulerian-circuits-undirected-graphs public -open import graph-theory.faithful-morphisms-undirected-graphs public -open import graph-theory.fibers-directed-graphs public -open import graph-theory.fibers-morphisms-directed-graphs public -open import graph-theory.fibers-morphisms-reflexive-graphs public -open import graph-theory.finite-graphs public -open import graph-theory.geometric-realizations-undirected-graphs public -open import graph-theory.higher-directed-graphs public -open import graph-theory.hypergraphs public -open import graph-theory.internal-hom-directed-graphs public -open import graph-theory.large-higher-directed-graphs public +module + graph-theory + (funext : function-extensionality) + where + +open import graph-theory.acyclic-undirected-graphs funext public +open import graph-theory.base-change-dependent-directed-graphs funext public +open import graph-theory.base-change-dependent-reflexive-graphs funext public +open import graph-theory.cartesian-products-directed-graphs funext public +open import graph-theory.cartesian-products-reflexive-graphs funext public +open import graph-theory.circuits-undirected-graphs funext public +open import graph-theory.closed-walks-undirected-graphs funext public +open import graph-theory.complete-bipartite-graphs funext public +open import graph-theory.complete-multipartite-graphs funext public +open import graph-theory.complete-undirected-graphs funext public +open import graph-theory.connected-undirected-graphs funext public +open import graph-theory.cycles-undirected-graphs funext public +open import graph-theory.dependent-directed-graphs funext public +open import graph-theory.dependent-products-directed-graphs funext public +open import graph-theory.dependent-products-reflexive-graphs funext public +open import graph-theory.dependent-reflexive-graphs funext public +open import graph-theory.dependent-sums-directed-graphs funext public +open import graph-theory.dependent-sums-reflexive-graphs funext public +open import graph-theory.directed-graph-duality funext public +open import graph-theory.directed-graph-structures-on-standard-finite-sets funext public +open import graph-theory.directed-graphs funext public +open import graph-theory.discrete-dependent-reflexive-graphs funext public +open import graph-theory.discrete-directed-graphs funext public +open import graph-theory.discrete-reflexive-graphs funext public +open import graph-theory.displayed-large-reflexive-graphs funext public +open import graph-theory.edge-coloured-undirected-graphs funext public +open import graph-theory.embeddings-directed-graphs funext public +open import graph-theory.embeddings-undirected-graphs funext public +open import graph-theory.enriched-undirected-graphs funext public +open import graph-theory.equivalences-dependent-directed-graphs funext public +open import graph-theory.equivalences-dependent-reflexive-graphs funext public +open import graph-theory.equivalences-directed-graphs funext public +open import graph-theory.equivalences-enriched-undirected-graphs funext public +open import graph-theory.equivalences-reflexive-graphs funext public +open import graph-theory.equivalences-undirected-graphs funext public +open import graph-theory.eulerian-circuits-undirected-graphs funext public +open import graph-theory.faithful-morphisms-undirected-graphs funext public +open import graph-theory.fibers-directed-graphs funext public +open import graph-theory.fibers-morphisms-directed-graphs funext public +open import graph-theory.fibers-morphisms-reflexive-graphs funext public +open import graph-theory.finite-graphs funext public +open import graph-theory.geometric-realizations-undirected-graphs funext public +open import graph-theory.higher-directed-graphs funext public +open import graph-theory.hypergraphs funext public +open import graph-theory.internal-hom-directed-graphs funext public +open import graph-theory.large-higher-directed-graphs funext public open import graph-theory.large-reflexive-graphs public -open import graph-theory.matchings public -open import graph-theory.mere-equivalences-undirected-graphs public -open import graph-theory.morphisms-dependent-directed-graphs public -open import graph-theory.morphisms-directed-graphs public -open import graph-theory.morphisms-reflexive-graphs public -open import graph-theory.morphisms-undirected-graphs public -open import graph-theory.neighbors-undirected-graphs public -open import graph-theory.orientations-undirected-graphs public -open import graph-theory.paths-undirected-graphs public -open import graph-theory.polygons public -open import graph-theory.raising-universe-levels-directed-graphs public -open import graph-theory.reflecting-maps-undirected-graphs public -open import graph-theory.reflexive-graphs public -open import graph-theory.regular-undirected-graphs public -open import graph-theory.sections-dependent-directed-graphs public -open import graph-theory.sections-dependent-reflexive-graphs public -open import graph-theory.simple-undirected-graphs public -open import graph-theory.stereoisomerism-enriched-undirected-graphs public -open import graph-theory.terminal-directed-graphs public -open import graph-theory.terminal-reflexive-graphs public -open import graph-theory.totally-faithful-morphisms-undirected-graphs public -open import graph-theory.trails-directed-graphs public -open import graph-theory.trails-undirected-graphs public -open import graph-theory.undirected-graph-structures-on-standard-finite-sets public -open import graph-theory.undirected-graphs public -open import graph-theory.universal-directed-graph public -open import graph-theory.universal-reflexive-graph public -open import graph-theory.vertex-covers public -open import graph-theory.voltage-graphs public -open import graph-theory.walks-directed-graphs public -open import graph-theory.walks-undirected-graphs public -open import graph-theory.wide-displayed-large-reflexive-graphs public +open import graph-theory.matchings funext public +open import graph-theory.mere-equivalences-undirected-graphs funext public +open import graph-theory.morphisms-dependent-directed-graphs funext public +open import graph-theory.morphisms-directed-graphs funext public +open import graph-theory.morphisms-reflexive-graphs funext public +open import graph-theory.morphisms-undirected-graphs funext public +open import graph-theory.neighbors-undirected-graphs funext public +open import graph-theory.orientations-undirected-graphs funext public +open import graph-theory.paths-undirected-graphs funext public +open import graph-theory.polygons funext public +open import graph-theory.raising-universe-levels-directed-graphs funext public +open import graph-theory.reflecting-maps-undirected-graphs funext public +open import graph-theory.reflexive-graphs funext public +open import graph-theory.regular-undirected-graphs funext public +open import graph-theory.sections-dependent-directed-graphs funext public +open import graph-theory.sections-dependent-reflexive-graphs funext public +open import graph-theory.simple-undirected-graphs funext public +open import graph-theory.stereoisomerism-enriched-undirected-graphs funext public +open import graph-theory.terminal-directed-graphs funext public +open import graph-theory.terminal-reflexive-graphs funext public +open import graph-theory.totally-faithful-morphisms-undirected-graphs funext public +open import graph-theory.trails-directed-graphs funext public +open import graph-theory.trails-undirected-graphs funext public +open import graph-theory.undirected-graph-structures-on-standard-finite-sets funext public +open import graph-theory.undirected-graphs funext public +open import graph-theory.universal-directed-graph funext public +open import graph-theory.universal-reflexive-graph funext public +open import graph-theory.vertex-covers funext public +open import graph-theory.voltage-graphs funext public +open import graph-theory.walks-directed-graphs funext public +open import graph-theory.walks-undirected-graphs funext public +open import graph-theory.wide-displayed-large-reflexive-graphs funext public ``` diff --git a/src/graph-theory/acyclic-undirected-graphs.lagda.md b/src/graph-theory/acyclic-undirected-graphs.lagda.md index 300bd4eda8..6bf8e4eb8b 100644 --- a/src/graph-theory/acyclic-undirected-graphs.lagda.md +++ b/src/graph-theory/acyclic-undirected-graphs.lagda.md @@ -1,7 +1,12 @@ # Acyclic undirected graphs ```agda -module graph-theory.acyclic-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.acyclic-undirected-graphs + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module graph-theory.acyclic-undirected-graphs where ```agda open import foundation.universe-levels -open import graph-theory.geometric-realizations-undirected-graphs -open import graph-theory.reflecting-maps-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.geometric-realizations-undirected-graphs funext +open import graph-theory.reflecting-maps-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/base-change-dependent-directed-graphs.lagda.md b/src/graph-theory/base-change-dependent-directed-graphs.lagda.md index 839b1619cd..7cad3529cf 100644 --- a/src/graph-theory/base-change-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/base-change-dependent-directed-graphs.lagda.md @@ -1,7 +1,12 @@ # Base change of dependent directed graphs ```agda -module graph-theory.base-change-dependent-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.base-change-dependent-directed-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,9 +15,9 @@ module graph-theory.base-change-dependent-directed-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md b/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md index d1168be9c8..9f11a28a05 100644 --- a/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md @@ -1,22 +1,27 @@ # Base change of dependent reflexive graphs ```agda -module graph-theory.base-change-dependent-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.base-change-dependent-reflexive-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.base-change-dependent-directed-graphs funext +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.dependent-reflexive-graphs funext +open import graph-theory.morphisms-reflexive-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/cartesian-products-directed-graphs.lagda.md b/src/graph-theory/cartesian-products-directed-graphs.lagda.md index 50840f8b15..5746251702 100644 --- a/src/graph-theory/cartesian-products-directed-graphs.lagda.md +++ b/src/graph-theory/cartesian-products-directed-graphs.lagda.md @@ -1,18 +1,23 @@ # Cartesian products of directed graphs ```agda -module graph-theory.cartesian-products-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.cartesian-products-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md b/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md index f68342b1c5..ee2eba1fc4 100644 --- a/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md +++ b/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md @@ -1,22 +1,27 @@ # Cartesian products of reflexive graphs ```agda -module graph-theory.cartesian-products-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.cartesian-products-reflexive-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.cartesian-products-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.cartesian-products-directed-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.morphisms-reflexive-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/circuits-undirected-graphs.lagda.md b/src/graph-theory/circuits-undirected-graphs.lagda.md index e3a8ea7dcc..9338ca4cb8 100644 --- a/src/graph-theory/circuits-undirected-graphs.lagda.md +++ b/src/graph-theory/circuits-undirected-graphs.lagda.md @@ -1,7 +1,12 @@ # Circuits in undirected graphs ```agda -module graph-theory.circuits-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.circuits-undirected-graphs + (funext : function-extensionality) + where ```
Imports @@ -12,9 +17,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.polygons -open import graph-theory.totally-faithful-morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.polygons funext +open import graph-theory.totally-faithful-morphisms-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/closed-walks-undirected-graphs.lagda.md b/src/graph-theory/closed-walks-undirected-graphs.lagda.md index 54484b5def..3f6ec3cb82 100644 --- a/src/graph-theory/closed-walks-undirected-graphs.lagda.md +++ b/src/graph-theory/closed-walks-undirected-graphs.lagda.md @@ -1,7 +1,12 @@ # Closed walks in undirected graphs ```agda -module graph-theory.closed-walks-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.closed-walks-undirected-graphs + (funext : function-extensionality) + where ```
Imports @@ -12,9 +17,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.polygons -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext +open import graph-theory.polygons funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/complete-bipartite-graphs.lagda.md b/src/graph-theory/complete-bipartite-graphs.lagda.md index d671a66be1..89b024de4a 100644 --- a/src/graph-theory/complete-bipartite-graphs.lagda.md +++ b/src/graph-theory/complete-bipartite-graphs.lagda.md @@ -1,24 +1,29 @@ # Complete bipartite graphs ```agda -module graph-theory.complete-bipartite-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.complete-bipartite-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.finite-graphs +open import graph-theory.finite-graphs funext -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.fibers-of-maps -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.fibers-of-maps funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/graph-theory/complete-multipartite-graphs.lagda.md b/src/graph-theory/complete-multipartite-graphs.lagda.md index eafcab5fa0..86f03e5e27 100644 --- a/src/graph-theory/complete-multipartite-graphs.lagda.md +++ b/src/graph-theory/complete-multipartite-graphs.lagda.md @@ -1,23 +1,28 @@ # Complete multipartite graphs ```agda -module graph-theory.complete-multipartite-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.complete-multipartite-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.finite-graphs +open import graph-theory.finite-graphs funext -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.function-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.function-types funext ```
diff --git a/src/graph-theory/complete-undirected-graphs.lagda.md b/src/graph-theory/complete-undirected-graphs.lagda.md index 6adb8963c1..e16175238a 100644 --- a/src/graph-theory/complete-undirected-graphs.lagda.md +++ b/src/graph-theory/complete-undirected-graphs.lagda.md @@ -1,7 +1,12 @@ # Complete undirected graphs ```agda -module graph-theory.complete-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.complete-undirected-graphs + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module graph-theory.complete-undirected-graphs where ```agda open import foundation.universe-levels -open import graph-theory.complete-multipartite-graphs -open import graph-theory.finite-graphs +open import graph-theory.complete-multipartite-graphs funext +open import graph-theory.finite-graphs funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/graph-theory/connected-undirected-graphs.lagda.md b/src/graph-theory/connected-undirected-graphs.lagda.md index fafe80a55b..50f6931ec6 100644 --- a/src/graph-theory/connected-undirected-graphs.lagda.md +++ b/src/graph-theory/connected-undirected-graphs.lagda.md @@ -1,18 +1,23 @@ # Connected graphs ```agda -module graph-theory.connected-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.connected-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.universe-levels -open import graph-theory.undirected-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.undirected-graphs funext +open import graph-theory.walks-undirected-graphs funext ```
diff --git a/src/graph-theory/cycles-undirected-graphs.lagda.md b/src/graph-theory/cycles-undirected-graphs.lagda.md index 2dd455a2f4..9ad87205f2 100644 --- a/src/graph-theory/cycles-undirected-graphs.lagda.md +++ b/src/graph-theory/cycles-undirected-graphs.lagda.md @@ -1,7 +1,12 @@ # Cycles in undirected graphs ```agda -module graph-theory.cycles-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.cycles-undirected-graphs + (funext : function-extensionality) + where ```
Imports @@ -12,9 +17,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.embeddings-undirected-graphs -open import graph-theory.polygons -open import graph-theory.undirected-graphs +open import graph-theory.embeddings-undirected-graphs funext +open import graph-theory.polygons funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/dependent-directed-graphs.lagda.md b/src/graph-theory/dependent-directed-graphs.lagda.md index bd7a43b39d..f865864cad 100644 --- a/src/graph-theory/dependent-directed-graphs.lagda.md +++ b/src/graph-theory/dependent-directed-graphs.lagda.md @@ -1,7 +1,12 @@ # Dependent directed graphs ```agda -module graph-theory.dependent-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.dependent-directed-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,7 +15,7 @@ module graph-theory.dependent-directed-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext ```
diff --git a/src/graph-theory/dependent-products-directed-graphs.lagda.md b/src/graph-theory/dependent-products-directed-graphs.lagda.md index 5e0174ead8..273bbc998c 100644 --- a/src/graph-theory/dependent-products-directed-graphs.lagda.md +++ b/src/graph-theory/dependent-products-directed-graphs.lagda.md @@ -1,25 +1,30 @@ # Dependent products of directed graphs ```agda -module graph-theory.dependent-products-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.dependent-products-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs -open import graph-theory.cartesian-products-directed-graphs -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.sections-dependent-directed-graphs +open import graph-theory.base-change-dependent-directed-graphs funext +open import graph-theory.cartesian-products-directed-graphs funext +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.sections-dependent-directed-graphs funext ```
diff --git a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md index 562665d1c4..9612955f7e 100644 --- a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md @@ -1,7 +1,12 @@ # Dependent products of reflexive graphs ```agda -module graph-theory.dependent-products-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.dependent-products-reflexive-graphs + (funext : function-extensionality) + where ```
Imports @@ -9,33 +14,33 @@ module graph-theory.dependent-products-reflexive-graphs where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-types +open import foundation.commuting-squares-of-identifications funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import graph-theory.base-change-dependent-reflexive-graphs -open import graph-theory.cartesian-products-reflexive-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs -open import graph-theory.sections-dependent-reflexive-graphs +open import graph-theory.base-change-dependent-reflexive-graphs funext +open import graph-theory.cartesian-products-reflexive-graphs funext +open import graph-theory.dependent-reflexive-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.morphisms-reflexive-graphs funext +open import graph-theory.reflexive-graphs funext +open import graph-theory.sections-dependent-reflexive-graphs funext ```
diff --git a/src/graph-theory/dependent-reflexive-graphs.lagda.md b/src/graph-theory/dependent-reflexive-graphs.lagda.md index 76136f1504..937d08b635 100644 --- a/src/graph-theory/dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-reflexive-graphs.lagda.md @@ -1,18 +1,23 @@ # Dependent reflexive graphs ```agda -module graph-theory.dependent-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.dependent-reflexive-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/dependent-sums-directed-graphs.lagda.md b/src/graph-theory/dependent-sums-directed-graphs.lagda.md index 3c0ab314b5..0090655e84 100644 --- a/src/graph-theory/dependent-sums-directed-graphs.lagda.md +++ b/src/graph-theory/dependent-sums-directed-graphs.lagda.md @@ -1,7 +1,12 @@ # Dependent sums directed graphs ```agda -module graph-theory.dependent-sums-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.dependent-sums-directed-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module graph-theory.dependent-sums-directed-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.sections-dependent-directed-graphs +open import graph-theory.base-change-dependent-directed-graphs funext +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.sections-dependent-directed-graphs funext ```
diff --git a/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md b/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md index f8b5131441..e9fb1ecffc 100644 --- a/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md @@ -1,31 +1,36 @@ # Dependent sums reflexive graphs ```agda -module graph-theory.dependent-sums-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.dependent-sums-reflexive-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import graph-theory.base-change-dependent-reflexive-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.dependent-sums-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.discrete-dependent-reflexive-graphs -open import graph-theory.discrete-reflexive-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs -open import graph-theory.sections-dependent-directed-graphs -open import graph-theory.sections-dependent-reflexive-graphs +open import graph-theory.base-change-dependent-reflexive-graphs funext +open import graph-theory.dependent-reflexive-graphs funext +open import graph-theory.dependent-sums-directed-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.discrete-dependent-reflexive-graphs funext +open import graph-theory.discrete-reflexive-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.morphisms-reflexive-graphs funext +open import graph-theory.reflexive-graphs funext +open import graph-theory.sections-dependent-directed-graphs funext +open import graph-theory.sections-dependent-reflexive-graphs funext ```
diff --git a/src/graph-theory/directed-graph-duality.lagda.md b/src/graph-theory/directed-graph-duality.lagda.md index 26a89c50fc..927cc9b64a 100644 --- a/src/graph-theory/directed-graph-duality.lagda.md +++ b/src/graph-theory/directed-graph-duality.lagda.md @@ -1,29 +1,34 @@ # Directed graph duality ```agda -module graph-theory.directed-graph-duality where +open import foundation.function-extensionality-axiom + +module + graph-theory.directed-graph-duality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-sums-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.equivalences-directed-graphs -open import graph-theory.fibers-morphisms-directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.dependent-sums-directed-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.equivalences-dependent-directed-graphs funext +open import graph-theory.equivalences-directed-graphs funext +open import graph-theory.fibers-morphisms-directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md b/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md index 79f8ee66f1..56d7d926b2 100644 --- a/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md +++ b/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md @@ -1,7 +1,12 @@ # Directed graph structures on standard finite sets ```agda -module graph-theory.directed-graph-structures-on-standard-finite-sets where +open import foundation.function-extensionality-axiom + +module + graph-theory.directed-graph-structures-on-standard-finite-sets + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/graph-theory/directed-graphs.lagda.md b/src/graph-theory/directed-graphs.lagda.md index 798b5afeb6..e7f9367184 100644 --- a/src/graph-theory/directed-graphs.lagda.md +++ b/src/graph-theory/directed-graphs.lagda.md @@ -1,16 +1,21 @@ # Directed graphs ```agda -module graph-theory.directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md b/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md index 9d43af0730..d25ec3fb85 100644 --- a/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md @@ -1,18 +1,23 @@ # Discrete dependent reflexive graphs ```agda -module graph-theory.discrete-dependent-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.discrete-dependent-reflexive-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.discrete-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-reflexive-graphs funext +open import graph-theory.discrete-reflexive-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/discrete-directed-graphs.lagda.md b/src/graph-theory/discrete-directed-graphs.lagda.md index c3ff8a436b..a55fe0a3e9 100644 --- a/src/graph-theory/discrete-directed-graphs.lagda.md +++ b/src/graph-theory/discrete-directed-graphs.lagda.md @@ -1,29 +1,34 @@ # Discrete directed graphs ```agda -module graph-theory.discrete-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.discrete-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.discrete-binary-relations -open import foundation.empty-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.retractions -open import foundation.sections +open import foundation.discrete-binary-relations funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.torsorial-type-families -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/discrete-reflexive-graphs.lagda.md b/src/graph-theory/discrete-reflexive-graphs.lagda.md index e750402ea7..9af8d77e65 100644 --- a/src/graph-theory/discrete-reflexive-graphs.lagda.md +++ b/src/graph-theory/discrete-reflexive-graphs.lagda.md @@ -1,23 +1,28 @@ # Discrete reflexive graphs ```agda -module graph-theory.discrete-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.discrete-reflexive-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.discrete-reflexive-relations +open import foundation.discrete-reflexive-relations funext open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.torsorial-type-families -open import graph-theory.directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/displayed-large-reflexive-graphs.lagda.md b/src/graph-theory/displayed-large-reflexive-graphs.lagda.md index 7040f628b1..94bd052223 100644 --- a/src/graph-theory/displayed-large-reflexive-graphs.lagda.md +++ b/src/graph-theory/displayed-large-reflexive-graphs.lagda.md @@ -1,7 +1,12 @@ # Displayed large reflexive graphs ```agda -module graph-theory.displayed-large-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.displayed-large-reflexive-graphs + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ open import foundation.dependent-pair-types open import foundation.universe-levels open import graph-theory.large-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/edge-coloured-undirected-graphs.lagda.md b/src/graph-theory/edge-coloured-undirected-graphs.lagda.md index fe22d6bcf3..4a2ba3381c 100644 --- a/src/graph-theory/edge-coloured-undirected-graphs.lagda.md +++ b/src/graph-theory/edge-coloured-undirected-graphs.lagda.md @@ -1,19 +1,24 @@ # Edge-coloured undirected graphs ```agda -module graph-theory.edge-coloured-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.edge-coloured-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.neighbors-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.neighbors-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/embeddings-directed-graphs.lagda.md b/src/graph-theory/embeddings-directed-graphs.lagda.md index e483f06dc2..cfd9a759d2 100644 --- a/src/graph-theory/embeddings-directed-graphs.lagda.md +++ b/src/graph-theory/embeddings-directed-graphs.lagda.md @@ -1,19 +1,24 @@ # Embeddings of directed graphs ```agda -module graph-theory.embeddings-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.embeddings-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.propositions funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/embeddings-undirected-graphs.lagda.md b/src/graph-theory/embeddings-undirected-graphs.lagda.md index db07969f1c..f29cad1f13 100644 --- a/src/graph-theory/embeddings-undirected-graphs.lagda.md +++ b/src/graph-theory/embeddings-undirected-graphs.lagda.md @@ -1,19 +1,24 @@ # Embeddings of undirected graphs ```agda -module graph-theory.embeddings-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.embeddings-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.propositions funext open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/enriched-undirected-graphs.lagda.md b/src/graph-theory/enriched-undirected-graphs.lagda.md index 1f74332982..a9a046e258 100644 --- a/src/graph-theory/enriched-undirected-graphs.lagda.md +++ b/src/graph-theory/enriched-undirected-graphs.lagda.md @@ -1,26 +1,31 @@ # Enriched undirected graphs ```agda -module graph-theory.enriched-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.enriched-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.connected-components +open import foundation.connected-components funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.neighbors-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.neighbors-undirected-graphs funext +open import graph-theory.undirected-graphs funext -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-group-actions funext +open import higher-group-theory.higher-groups funext ```
diff --git a/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md b/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md index 2876ea23fa..89ecf974de 100644 --- a/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md @@ -1,26 +1,31 @@ # Equivalences of dependent directed graphs ```agda -module graph-theory.equivalences-dependent-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.equivalences-dependent-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.families-of-equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.directed-graphs funext ```
diff --git a/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md b/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md index 4197698468..079cdb41d6 100644 --- a/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md @@ -1,27 +1,32 @@ # Equivalences of dependent reflexive graphs ```agda -module graph-theory.equivalences-dependent-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.equivalences-dependent-reflexive-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.dependent-identifications +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.families-of-equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-reflexive-graphs funext +open import graph-theory.equivalences-dependent-directed-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/equivalences-directed-graphs.lagda.md b/src/graph-theory/equivalences-directed-graphs.lagda.md index a95e1ea270..fd6909a73e 100644 --- a/src/graph-theory/equivalences-directed-graphs.lagda.md +++ b/src/graph-theory/equivalences-directed-graphs.lagda.md @@ -1,7 +1,12 @@ # Equivalences of directed graphs ```agda -module graph-theory.equivalences-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.equivalences-directed-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,28 +15,28 @@ module graph-theory.equivalences-directed-graphs where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.transposition-identifications-along-equivalences +open import foundation.torsorial-type-families funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.univalence +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.univalence funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md b/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md index 5655fafc9d..2039e13fb8 100644 --- a/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md +++ b/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md @@ -1,29 +1,34 @@ # Equivalences of enriched undirected graphs ```agda -module graph-theory.equivalences-enriched-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.equivalences-enriched-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.enriched-undirected-graphs -open import graph-theory.equivalences-undirected-graphs -open import graph-theory.neighbors-undirected-graphs +open import graph-theory.enriched-undirected-graphs funext +open import graph-theory.equivalences-undirected-graphs funext +open import graph-theory.neighbors-undirected-graphs funext ```
diff --git a/src/graph-theory/equivalences-reflexive-graphs.lagda.md b/src/graph-theory/equivalences-reflexive-graphs.lagda.md index ae2ff0ebab..c693eaba6d 100644 --- a/src/graph-theory/equivalences-reflexive-graphs.lagda.md +++ b/src/graph-theory/equivalences-reflexive-graphs.lagda.md @@ -1,20 +1,25 @@ # Equivalences of reflexive graphs ```agda -module graph-theory.equivalences-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.equivalences-reflexive-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.equivalences-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.equivalences-directed-graphs funext +open import graph-theory.morphisms-reflexive-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/equivalences-undirected-graphs.lagda.md b/src/graph-theory/equivalences-undirected-graphs.lagda.md index 4b98ef0d5e..d8553c2fff 100644 --- a/src/graph-theory/equivalences-undirected-graphs.lagda.md +++ b/src/graph-theory/equivalences-undirected-graphs.lagda.md @@ -1,33 +1,38 @@ # Equivalences of undirected graphs ```agda -module graph-theory.equivalences-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.equivalences-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md b/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md index 5503cf3128..15ce7dc365 100644 --- a/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md +++ b/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md @@ -1,7 +1,12 @@ # Eulerian circuits in undirected graphs ```agda -module graph-theory.eulerian-circuits-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.eulerian-circuits-undirected-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,13 +15,13 @@ module graph-theory.eulerian-circuits-undirected-graphs where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.polygons -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext +open import graph-theory.polygons funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md b/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md index 685ec29151..a303a3d40d 100644 --- a/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md @@ -1,19 +1,24 @@ # Faithful morphisms of undirected graphs ```agda -module graph-theory.faithful-morphisms-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.faithful-morphisms-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.propositions funext open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/fibers-directed-graphs.lagda.md b/src/graph-theory/fibers-directed-graphs.lagda.md index ed82be7273..36461f54a3 100644 --- a/src/graph-theory/fibers-directed-graphs.lagda.md +++ b/src/graph-theory/fibers-directed-graphs.lagda.md @@ -1,29 +1,34 @@ # Fibers of directed graphs ```agda -module graph-theory.fibers-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.fibers-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.walks-directed-graphs funext -open import trees.directed-trees +open import trees.directed-trees funext ```
diff --git a/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md b/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md index c6e11c4da1..766e9b3865 100644 --- a/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md +++ b/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md @@ -1,25 +1,30 @@ # Fibers of morphisms into directed graphs ```agda -module graph-theory.fibers-morphisms-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.fibers-morphisms-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.families-of-equivalences -open import foundation.fibers-of-maps -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-sums-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.equivalences-directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.dependent-sums-directed-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.equivalences-dependent-directed-graphs funext +open import graph-theory.equivalences-directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md b/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md index 8ffde96bc4..4e84053970 100644 --- a/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md +++ b/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md @@ -1,7 +1,12 @@ # Fibers of morphisms into reflexive graphs ```agda -module graph-theory.fibers-morphisms-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.fibers-morphisms-reflexive-graphs + (funext : function-extensionality) + where ```
Imports @@ -9,25 +14,25 @@ module graph-theory.fibers-morphisms-reflexive-graphs where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.families-of-equivalences -open import foundation.fibers-of-maps -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.dependent-sums-reflexive-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.equivalences-dependent-reflexive-graphs -open import graph-theory.equivalences-reflexive-graphs -open import graph-theory.fibers-morphisms-directed-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.dependent-reflexive-graphs funext +open import graph-theory.dependent-sums-reflexive-graphs funext +open import graph-theory.equivalences-dependent-directed-graphs funext +open import graph-theory.equivalences-dependent-reflexive-graphs funext +open import graph-theory.equivalences-reflexive-graphs funext +open import graph-theory.fibers-morphisms-directed-graphs funext +open import graph-theory.morphisms-reflexive-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/finite-graphs.lagda.md b/src/graph-theory/finite-graphs.lagda.md index 6aff626a25..c5cd6f2f79 100644 --- a/src/graph-theory/finite-graphs.lagda.md +++ b/src/graph-theory/finite-graphs.lagda.md @@ -1,23 +1,28 @@ # Finite graphs ```agda -module graph-theory.finite-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.finite-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md b/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md index bb8fa6abfc..df19ae0e8a 100644 --- a/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md +++ b/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md @@ -1,20 +1,25 @@ # Geometric realizations of undirected graphs ```agda -module graph-theory.geometric-realizations-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.geometric-realizations-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.symmetric-identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.symmetric-identity-types funext open import foundation.universe-levels -open import graph-theory.reflecting-maps-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.reflecting-maps-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/higher-directed-graphs.lagda.md b/src/graph-theory/higher-directed-graphs.lagda.md index 3357611b21..a73f8d6185 100644 --- a/src/graph-theory/higher-directed-graphs.lagda.md +++ b/src/graph-theory/higher-directed-graphs.lagda.md @@ -1,7 +1,12 @@ # Higher directed graphs ```agda -module graph-theory.higher-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.higher-directed-graphs + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module graph-theory.higher-directed-graphs where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext ```
diff --git a/src/graph-theory/hypergraphs.lagda.md b/src/graph-theory/hypergraphs.lagda.md index 018e504f13..a55531b153 100644 --- a/src/graph-theory/hypergraphs.lagda.md +++ b/src/graph-theory/hypergraphs.lagda.md @@ -1,7 +1,12 @@ # Hypergraphs ```agda -module graph-theory.hypergraphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.hypergraphs + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation.unordered-tuples +open import foundation.unordered-tuples funext ```
diff --git a/src/graph-theory/internal-hom-directed-graphs.lagda.md b/src/graph-theory/internal-hom-directed-graphs.lagda.md index c4625f214c..23a6834e72 100644 --- a/src/graph-theory/internal-hom-directed-graphs.lagda.md +++ b/src/graph-theory/internal-hom-directed-graphs.lagda.md @@ -1,22 +1,27 @@ # Internal homs of directed graphs ```agda -module graph-theory.internal-hom-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.internal-hom-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import graph-theory.cartesian-products-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.cartesian-products-directed-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/large-higher-directed-graphs.lagda.md b/src/graph-theory/large-higher-directed-graphs.lagda.md index 6d805cf1a8..8c01b1b29f 100644 --- a/src/graph-theory/large-higher-directed-graphs.lagda.md +++ b/src/graph-theory/large-higher-directed-graphs.lagda.md @@ -1,7 +1,12 @@ # Large higher directed graphs ```agda -module graph-theory.large-higher-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.large-higher-directed-graphs + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,17 @@ module graph-theory.large-higher-directed-graphs where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.raising-universe-levels +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.raising-universe-levels funext open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.higher-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.higher-directed-graphs funext ```
diff --git a/src/graph-theory/matchings.lagda.md b/src/graph-theory/matchings.lagda.md index 66d2d1cc2c..c80a5ead6e 100644 --- a/src/graph-theory/matchings.lagda.md +++ b/src/graph-theory/matchings.lagda.md @@ -1,24 +1,29 @@ # Matchings ```agda -module graph-theory.matchings where +open import foundation.function-extensionality-axiom + +module + graph-theory.matchings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md b/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md index 9376ae4058..8e240c26a5 100644 --- a/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md +++ b/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md @@ -1,18 +1,23 @@ # Mere equivalences of undirected graphs ```agda -module graph-theory.mere-equivalences-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.mere-equivalences-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.universe-levels -open import graph-theory.equivalences-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.equivalences-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md b/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md index ef0c365ed0..222c55ecec 100644 --- a/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md @@ -1,18 +1,23 @@ # Morphisms of dependent directed graphs ```agda -module graph-theory.morphisms-dependent-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.morphisms-dependent-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.directed-graphs funext ```
diff --git a/src/graph-theory/morphisms-directed-graphs.lagda.md b/src/graph-theory/morphisms-directed-graphs.lagda.md index 9c85662c76..98b63abf0e 100644 --- a/src/graph-theory/morphisms-directed-graphs.lagda.md +++ b/src/graph-theory/morphisms-directed-graphs.lagda.md @@ -1,7 +1,12 @@ # Morphisms of directed graphs ```agda -module graph-theory.morphisms-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.morphisms-directed-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,19 +15,19 @@ module graph-theory.morphisms-directed-graphs where open import foundation.binary-dependent-identifications open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext ```
diff --git a/src/graph-theory/morphisms-reflexive-graphs.lagda.md b/src/graph-theory/morphisms-reflexive-graphs.lagda.md index 855700002e..3825329b02 100644 --- a/src/graph-theory/morphisms-reflexive-graphs.lagda.md +++ b/src/graph-theory/morphisms-reflexive-graphs.lagda.md @@ -1,7 +1,12 @@ # Morphisms of reflexive graphs ```agda -module graph-theory.morphisms-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.morphisms-reflexive-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,22 +15,22 @@ module graph-theory.morphisms-reflexive-graphs where open import foundation.action-on-identifications-binary-dependent-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import graph-theory.morphisms-directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/morphisms-undirected-graphs.lagda.md b/src/graph-theory/morphisms-undirected-graphs.lagda.md index aa80fba80a..09e5dbc957 100644 --- a/src/graph-theory/morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/morphisms-undirected-graphs.lagda.md @@ -1,31 +1,36 @@ # Morphisms of undirected graphs ```agda -module graph-theory.morphisms-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.morphisms-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/neighbors-undirected-graphs.lagda.md b/src/graph-theory/neighbors-undirected-graphs.lagda.md index 9b6fba97e3..4f23c9a277 100644 --- a/src/graph-theory/neighbors-undirected-graphs.lagda.md +++ b/src/graph-theory/neighbors-undirected-graphs.lagda.md @@ -1,24 +1,29 @@ # Incidence in undirected graphs ```agda -module graph-theory.neighbors-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.neighbors-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.equivalences-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.equivalences-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/orientations-undirected-graphs.lagda.md b/src/graph-theory/orientations-undirected-graphs.lagda.md index cdabb031fa..1a905eaceb 100644 --- a/src/graph-theory/orientations-undirected-graphs.lagda.md +++ b/src/graph-theory/orientations-undirected-graphs.lagda.md @@ -1,7 +1,12 @@ # Orientations of undirected graphs ```agda -module graph-theory.orientations-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.orientations-undirected-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,9 +15,9 @@ module graph-theory.orientations-undirected-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/graph-theory/paths-undirected-graphs.lagda.md b/src/graph-theory/paths-undirected-graphs.lagda.md index b811c34281..aaafacb98d 100644 --- a/src/graph-theory/paths-undirected-graphs.lagda.md +++ b/src/graph-theory/paths-undirected-graphs.lagda.md @@ -1,7 +1,12 @@ # Paths in undirected graphs ```agda -module graph-theory.paths-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.paths-undirected-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module graph-theory.paths-undirected-graphs where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.injective-maps +open import foundation.injective-maps funext open import foundation.universe-levels -open import graph-theory.undirected-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.undirected-graphs funext +open import graph-theory.walks-undirected-graphs funext ```
diff --git a/src/graph-theory/polygons.lagda.md b/src/graph-theory/polygons.lagda.md index 68f0117f77..0efd1014d9 100644 --- a/src/graph-theory/polygons.lagda.md +++ b/src/graph-theory/polygons.lagda.md @@ -1,29 +1,34 @@ # Polygons ```agda -module graph-theory.polygons where +open import foundation.function-extensionality-axiom + +module + graph-theory.polygons + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic funext open import elementary-number-theory.natural-numbers -open import foundation.decidable-equality +open import foundation.decidable-equality funext open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.functoriality-propositional-truncation -open import foundation.mere-equivalences -open import foundation.sets +open import foundation.fibers-of-maps funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.mere-equivalences funext +open import foundation.sets funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.equivalences-undirected-graphs -open import graph-theory.mere-equivalences-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.equivalences-undirected-graphs funext +open import graph-theory.mere-equivalences-undirected-graphs funext +open import graph-theory.undirected-graphs funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md b/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md index ff763cffc0..ac64b1117d 100644 --- a/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md +++ b/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md @@ -1,20 +1,25 @@ # Raising universe levels of directed graphs ```agda -module graph-theory.raising-universe-levels-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.raising-universe-levels-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.raising-universe-levels +open import foundation.equivalences funext +open import foundation.raising-universe-levels funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.equivalences-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.equivalences-directed-graphs funext +open import graph-theory.walks-directed-graphs funext ```
diff --git a/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md b/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md index 5be62477ee..c4dfa41d1d 100644 --- a/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md +++ b/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md @@ -1,20 +1,25 @@ # Reflecting maps of undirected graphs ```agda -module graph-theory.reflecting-maps-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.reflecting-maps-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.symmetric-identity-types +open import foundation.symmetric-identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/reflexive-graphs.lagda.md b/src/graph-theory/reflexive-graphs.lagda.md index 1ab53e86e5..ebfa77f653 100644 --- a/src/graph-theory/reflexive-graphs.lagda.md +++ b/src/graph-theory/reflexive-graphs.lagda.md @@ -1,7 +1,12 @@ # Reflexive graphs ```agda -module graph-theory.reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.reflexive-graphs + (funext : function-extensionality) + where ```
Imports @@ -9,11 +14,11 @@ module graph-theory.reflexive-graphs where ```agda open import foundation.binary-dependent-identifications open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.reflexive-relations +open import foundation.identity-types funext +open import foundation.reflexive-relations funext open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext ```
diff --git a/src/graph-theory/regular-undirected-graphs.lagda.md b/src/graph-theory/regular-undirected-graphs.lagda.md index 295ec95081..b5b08ebc73 100644 --- a/src/graph-theory/regular-undirected-graphs.lagda.md +++ b/src/graph-theory/regular-undirected-graphs.lagda.md @@ -1,18 +1,23 @@ # Regular undirected graph ```agda -module graph-theory.regular-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.regular-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.mere-equivalences -open import foundation.propositions +open import foundation.mere-equivalences funext +open import foundation.propositions funext open import foundation.universe-levels -open import graph-theory.neighbors-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.neighbors-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/sections-dependent-directed-graphs.lagda.md b/src/graph-theory/sections-dependent-directed-graphs.lagda.md index c8ca8c42d4..4400e8a100 100644 --- a/src/graph-theory/sections-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/sections-dependent-directed-graphs.lagda.md @@ -1,26 +1,31 @@ # Sections of dependent directed graphs ```agda -module graph-theory.sections-dependent-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.sections-dependent-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.directed-graphs funext ```
diff --git a/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md b/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md index 792b3557f8..ff4182136e 100644 --- a/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md @@ -1,7 +1,12 @@ # Sections of dependent reflexive graphs ```agda -module graph-theory.sections-dependent-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.sections-dependent-reflexive-graphs + (funext : function-extensionality) + where ```
Imports @@ -11,24 +16,24 @@ open import foundation.action-on-identifications-binary-dependent-functions open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.reflexive-relations +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.reflexive-relations funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.reflexive-graphs -open import graph-theory.sections-dependent-directed-graphs +open import graph-theory.dependent-reflexive-graphs funext +open import graph-theory.reflexive-graphs funext +open import graph-theory.sections-dependent-directed-graphs funext ```
diff --git a/src/graph-theory/simple-undirected-graphs.lagda.md b/src/graph-theory/simple-undirected-graphs.lagda.md index b81f7668e6..e7da69dc88 100644 --- a/src/graph-theory/simple-undirected-graphs.lagda.md +++ b/src/graph-theory/simple-undirected-graphs.lagda.md @@ -1,22 +1,27 @@ # Simple undirected graphs ```agda -module graph-theory.simple-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.simple-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.negation -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md b/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md index 1fd241fbed..3c201d24e8 100644 --- a/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md +++ b/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md @@ -1,19 +1,24 @@ # Stereoisomerism for enriched undirected graphs ```agda -module graph-theory.stereoisomerism-enriched-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.stereoisomerism-enriched-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import graph-theory.enriched-undirected-graphs -open import graph-theory.equivalences-undirected-graphs +open import graph-theory.enriched-undirected-graphs funext +open import graph-theory.equivalences-undirected-graphs funext ```
diff --git a/src/graph-theory/terminal-directed-graphs.lagda.md b/src/graph-theory/terminal-directed-graphs.lagda.md index d49804435a..23a6ff1841 100644 --- a/src/graph-theory/terminal-directed-graphs.lagda.md +++ b/src/graph-theory/terminal-directed-graphs.lagda.md @@ -1,20 +1,25 @@ # Terminal directed graphs ```agda -module graph-theory.terminal-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.terminal-directed-graphs + (funext : function-extensionality) + where ```
Idea ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/terminal-reflexive-graphs.lagda.md b/src/graph-theory/terminal-reflexive-graphs.lagda.md index 31ff8ae60a..689794d0bf 100644 --- a/src/graph-theory/terminal-reflexive-graphs.lagda.md +++ b/src/graph-theory/terminal-reflexive-graphs.lagda.md @@ -1,22 +1,27 @@ # Terminal reflexive graphs ```agda -module graph-theory.terminal-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.terminal-reflexive-graphs + (funext : function-extensionality) + where ```
Idea ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.reflexive-graphs -open import graph-theory.morphisms-reflexive-graphs -open import graph-theory.terminal-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.reflexive-graphs funext +open import graph-theory.morphisms-reflexive-graphs funext +open import graph-theory.terminal-directed-graphs funext ```
diff --git a/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md b/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md index 7127494138..2fe137c05b 100644 --- a/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md @@ -1,19 +1,24 @@ # Totally faithful morphisms of undirected graphs ```agda -module graph-theory.totally-faithful-morphisms-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.totally-faithful-morphisms-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.functoriality-dependent-pair-types +open import foundation.embeddings funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.morphisms-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/graph-theory/trails-directed-graphs.lagda.md b/src/graph-theory/trails-directed-graphs.lagda.md index 19c803955e..abcdaf5508 100644 --- a/src/graph-theory/trails-directed-graphs.lagda.md +++ b/src/graph-theory/trails-directed-graphs.lagda.md @@ -1,18 +1,23 @@ # Trails in directed graphs ```agda -module graph-theory.trails-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.trails-directed-graphs + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.injective-maps +open import foundation.injective-maps funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.walks-directed-graphs funext ```
diff --git a/src/graph-theory/trails-undirected-graphs.lagda.md b/src/graph-theory/trails-undirected-graphs.lagda.md index 3aaaa397cc..f5db11d07a 100644 --- a/src/graph-theory/trails-undirected-graphs.lagda.md +++ b/src/graph-theory/trails-undirected-graphs.lagda.md @@ -1,7 +1,12 @@ # Trails in undirected graphs ```agda -module graph-theory.trails-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.trails-undirected-graphs + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module graph-theory.trails-undirected-graphs where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.injective-maps -open import foundation.propositions +open import foundation.injective-maps funext +open import foundation.propositions funext open import foundation.universe-levels -open import graph-theory.undirected-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.undirected-graphs funext +open import graph-theory.walks-undirected-graphs funext ```
diff --git a/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md b/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md index b16324d61e..24e3ab01e7 100644 --- a/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md +++ b/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md @@ -1,7 +1,12 @@ # Undirected graph structures on standard finite sets ```agda -module graph-theory.undirected-graph-structures-on-standard-finite-sets where +open import foundation.function-extensionality-axiom + +module + graph-theory.undirected-graph-structures-on-standard-finite-sets + (funext : function-extensionality) + where ```
Imports @@ -11,9 +16,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/graph-theory/undirected-graphs.lagda.md b/src/graph-theory/undirected-graphs.lagda.md index dda08c3492..5ceb37a9b3 100644 --- a/src/graph-theory/undirected-graphs.lagda.md +++ b/src/graph-theory/undirected-graphs.lagda.md @@ -1,20 +1,25 @@ # Undirected graphs ```agda -module graph-theory.undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext ```
diff --git a/src/graph-theory/universal-directed-graph.lagda.md b/src/graph-theory/universal-directed-graph.lagda.md index d7242623d2..167fd3c608 100644 --- a/src/graph-theory/universal-directed-graph.lagda.md +++ b/src/graph-theory/universal-directed-graph.lagda.md @@ -1,7 +1,12 @@ # The universal directed graph ```agda -module graph-theory.universal-directed-graph where +open import foundation.function-extensionality-axiom + +module + graph-theory.universal-directed-graph + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module graph-theory.universal-directed-graph where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs -open import graph-theory.dependent-directed-graphs -open import graph-theory.directed-graphs -open import graph-theory.equivalences-dependent-directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.base-change-dependent-directed-graphs funext +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.equivalences-dependent-directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/universal-reflexive-graph.lagda.md b/src/graph-theory/universal-reflexive-graph.lagda.md index 3b3fd8042f..a0ab6c1819 100644 --- a/src/graph-theory/universal-reflexive-graph.lagda.md +++ b/src/graph-theory/universal-reflexive-graph.lagda.md @@ -1,7 +1,12 @@ # The universal reflexive graph ```agda -module graph-theory.universal-reflexive-graph where +open import foundation.function-extensionality-axiom + +module + graph-theory.universal-reflexive-graph + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module graph-theory.universal-reflexive-graph where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs -open import graph-theory.dependent-reflexive-graphs -open import graph-theory.directed-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.dependent-directed-graphs funext +open import graph-theory.dependent-reflexive-graphs funext +open import graph-theory.directed-graphs funext +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/graph-theory/vertex-covers.lagda.md b/src/graph-theory/vertex-covers.lagda.md index 462cda70c8..2dcce33e22 100644 --- a/src/graph-theory/vertex-covers.lagda.md +++ b/src/graph-theory/vertex-covers.lagda.md @@ -1,24 +1,29 @@ # Vertex covers ```agda -module graph-theory.vertex-covers where +open import foundation.function-extensionality-axiom + +module + graph-theory.vertex-covers + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/graph-theory/voltage-graphs.lagda.md b/src/graph-theory/voltage-graphs.lagda.md index bc99323d60..bf53f23fd5 100644 --- a/src/graph-theory/voltage-graphs.lagda.md +++ b/src/graph-theory/voltage-graphs.lagda.md @@ -1,7 +1,12 @@ # Voltage graphs ```agda -module graph-theory.voltage-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.voltage-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,9 +15,9 @@ module graph-theory.voltage-graphs where open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext -open import group-theory.groups +open import group-theory.groups funext ```
diff --git a/src/graph-theory/walks-directed-graphs.lagda.md b/src/graph-theory/walks-directed-graphs.lagda.md index b7e9537b73..ea770b217d 100644 --- a/src/graph-theory/walks-directed-graphs.lagda.md +++ b/src/graph-theory/walks-directed-graphs.lagda.md @@ -1,7 +1,12 @@ # Walks in directed graphs ```agda -module graph-theory.walks-directed-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.walks-directed-graphs + (funext : function-extensionality) + where ```
Imports @@ -10,27 +15,27 @@ module graph-theory.walks-directed-graphs where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.raising-universe-levels -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.raising-universe-levels funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.equivalences-directed-graphs -open import graph-theory.morphisms-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.equivalences-directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext ```
diff --git a/src/graph-theory/walks-undirected-graphs.lagda.md b/src/graph-theory/walks-undirected-graphs.lagda.md index b73510b8b4..80f19afcad 100644 --- a/src/graph-theory/walks-undirected-graphs.lagda.md +++ b/src/graph-theory/walks-undirected-graphs.lagda.md @@ -1,36 +1,41 @@ # Walks in undirected graphs ```agda -module graph-theory.walks-undirected-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.walks-undirected-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families -open import foundation.type-arithmetic-coproduct-types +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext +open import foundation.type-arithmetic-coproduct-types funext open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.undirected-graphs +open import graph-theory.undirected-graphs funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md b/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md index 4392870452..51bb50e037 100644 --- a/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md +++ b/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md @@ -1,20 +1,25 @@ # Wide displayed large reflexive graphs ```agda -module graph-theory.wide-displayed-large-reflexive-graphs where +open import foundation.function-extensionality-axiom + +module + graph-theory.wide-displayed-large-reflexive-graphs + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import graph-theory.large-reflexive-graphs -open import graph-theory.reflexive-graphs +open import graph-theory.reflexive-graphs funext ```
diff --git a/src/group-theory.lagda.md b/src/group-theory.lagda.md index 6d7a7e8e31..27c6f34059 100644 --- a/src/group-theory.lagda.md +++ b/src/group-theory.lagda.md @@ -3,203 +3,208 @@ ## Modules in the group theory namespace ```agda -module group-theory where +open import foundation.function-extensionality-axiom -open import group-theory.abelian-groups public -open import group-theory.abelianization-groups public -open import group-theory.addition-homomorphisms-abelian-groups public -open import group-theory.automorphism-groups public -open import group-theory.cartesian-products-abelian-groups public -open import group-theory.cartesian-products-concrete-groups public -open import group-theory.cartesian-products-groups public -open import group-theory.cartesian-products-monoids public -open import group-theory.cartesian-products-semigroups public -open import group-theory.category-of-abelian-groups public +module + group-theory + (funext : function-extensionality) + where + +open import group-theory.abelian-groups funext public +open import group-theory.abelianization-groups funext public +open import group-theory.addition-homomorphisms-abelian-groups funext public +open import group-theory.automorphism-groups funext public +open import group-theory.cartesian-products-abelian-groups funext public +open import group-theory.cartesian-products-concrete-groups funext public +open import group-theory.cartesian-products-groups funext public +open import group-theory.cartesian-products-monoids funext public +open import group-theory.cartesian-products-semigroups funext public +open import group-theory.category-of-abelian-groups funext public open import group-theory.category-of-concrete-groups public -open import group-theory.category-of-group-actions public -open import group-theory.category-of-groups public -open import group-theory.category-of-orbits-groups public -open import group-theory.category-of-semigroups public -open import group-theory.cayleys-theorem public -open import group-theory.centers-groups public -open import group-theory.centers-monoids public -open import group-theory.centers-semigroups public -open import group-theory.central-elements-groups public -open import group-theory.central-elements-monoids public -open import group-theory.central-elements-semigroups public -open import group-theory.centralizer-subgroups public -open import group-theory.characteristic-subgroups public -open import group-theory.commutative-monoids public -open import group-theory.commutator-subgroups public -open import group-theory.commutators-of-elements-groups public -open import group-theory.commuting-elements-groups public -open import group-theory.commuting-elements-monoids public -open import group-theory.commuting-elements-semigroups public -open import group-theory.commuting-squares-of-group-homomorphisms public -open import group-theory.concrete-group-actions public -open import group-theory.concrete-groups public -open import group-theory.concrete-monoids public -open import group-theory.congruence-relations-abelian-groups public -open import group-theory.congruence-relations-commutative-monoids public -open import group-theory.congruence-relations-groups public -open import group-theory.congruence-relations-monoids public -open import group-theory.congruence-relations-semigroups public -open import group-theory.conjugation public -open import group-theory.conjugation-concrete-groups public -open import group-theory.contravariant-pushforward-concrete-group-actions public -open import group-theory.cores-monoids public -open import group-theory.cyclic-groups public -open import group-theory.decidable-subgroups public -open import group-theory.dependent-products-abelian-groups public -open import group-theory.dependent-products-commutative-monoids public -open import group-theory.dependent-products-groups public -open import group-theory.dependent-products-monoids public -open import group-theory.dependent-products-semigroups public -open import group-theory.dihedral-group-construction public -open import group-theory.dihedral-groups public -open import group-theory.e8-lattice public -open import group-theory.elements-of-finite-order-groups public -open import group-theory.embeddings-abelian-groups public -open import group-theory.embeddings-groups public -open import group-theory.endomorphism-rings-abelian-groups public -open import group-theory.epimorphisms-groups public -open import group-theory.equivalences-concrete-group-actions public -open import group-theory.equivalences-concrete-groups public -open import group-theory.equivalences-group-actions public -open import group-theory.equivalences-semigroups public -open import group-theory.exponents-abelian-groups public -open import group-theory.exponents-groups public -open import group-theory.free-concrete-group-actions public -open import group-theory.free-groups-with-one-generator public -open import group-theory.full-subgroups public -open import group-theory.full-subsemigroups public -open import group-theory.function-abelian-groups public -open import group-theory.function-commutative-monoids public -open import group-theory.function-groups public -open import group-theory.function-monoids public -open import group-theory.function-semigroups public -open import group-theory.functoriality-quotient-groups public -open import group-theory.furstenberg-groups public -open import group-theory.generating-elements-groups public -open import group-theory.generating-sets-groups public -open import group-theory.group-actions public -open import group-theory.groups public -open import group-theory.homomorphisms-abelian-groups public -open import group-theory.homomorphisms-commutative-monoids public -open import group-theory.homomorphisms-concrete-group-actions public -open import group-theory.homomorphisms-concrete-groups public -open import group-theory.homomorphisms-generated-subgroups public -open import group-theory.homomorphisms-group-actions public -open import group-theory.homomorphisms-groups public -open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups public -open import group-theory.homomorphisms-monoids public -open import group-theory.homomorphisms-semigroups public -open import group-theory.homotopy-automorphism-groups public -open import group-theory.images-of-group-homomorphisms public -open import group-theory.images-of-semigroup-homomorphisms public -open import group-theory.integer-multiples-of-elements-abelian-groups public -open import group-theory.integer-powers-of-elements-groups public -open import group-theory.intersections-subgroups-abelian-groups public -open import group-theory.intersections-subgroups-groups public -open import group-theory.inverse-semigroups public -open import group-theory.invertible-elements-monoids public -open import group-theory.isomorphisms-abelian-groups public -open import group-theory.isomorphisms-concrete-groups public -open import group-theory.isomorphisms-group-actions public -open import group-theory.isomorphisms-groups public -open import group-theory.isomorphisms-monoids public -open import group-theory.isomorphisms-semigroups public -open import group-theory.iterated-cartesian-products-concrete-groups public -open import group-theory.kernels-homomorphisms-abelian-groups public -open import group-theory.kernels-homomorphisms-concrete-groups public -open import group-theory.kernels-homomorphisms-groups public -open import group-theory.large-semigroups public -open import group-theory.loop-groups-sets public -open import group-theory.mere-equivalences-concrete-group-actions public -open import group-theory.mere-equivalences-group-actions public -open import group-theory.minkowski-multiplication-commutative-monoids public -open import group-theory.minkowski-multiplication-monoids public -open import group-theory.minkowski-multiplication-semigroups public -open import group-theory.monoid-actions public -open import group-theory.monoids public -open import group-theory.monomorphisms-concrete-groups public -open import group-theory.monomorphisms-groups public -open import group-theory.multiples-of-elements-abelian-groups public -open import group-theory.nontrivial-groups public -open import group-theory.normal-closures-subgroups public -open import group-theory.normal-cores-subgroups public -open import group-theory.normal-subgroups public -open import group-theory.normal-subgroups-concrete-groups public -open import group-theory.normal-submonoids public -open import group-theory.normal-submonoids-commutative-monoids public -open import group-theory.normalizer-subgroups public -open import group-theory.nullifying-group-homomorphisms public -open import group-theory.opposite-groups public -open import group-theory.opposite-semigroups public -open import group-theory.orbit-stabilizer-theorem-concrete-groups public -open import group-theory.orbits-concrete-group-actions public -open import group-theory.orbits-group-actions public -open import group-theory.orders-of-elements-groups public -open import group-theory.perfect-cores public -open import group-theory.perfect-groups public -open import group-theory.perfect-subgroups public -open import group-theory.powers-of-elements-commutative-monoids public -open import group-theory.powers-of-elements-groups public -open import group-theory.powers-of-elements-monoids public -open import group-theory.precategory-of-commutative-monoids public -open import group-theory.precategory-of-concrete-groups public -open import group-theory.precategory-of-group-actions public -open import group-theory.precategory-of-groups public -open import group-theory.precategory-of-monoids public -open import group-theory.precategory-of-orbits-monoid-actions public -open import group-theory.precategory-of-semigroups public -open import group-theory.principal-group-actions public -open import group-theory.principal-torsors-concrete-groups public -open import group-theory.products-of-elements-monoids public -open import group-theory.products-of-tuples-of-elements-commutative-monoids public -open import group-theory.pullbacks-subgroups public -open import group-theory.pullbacks-subsemigroups public -open import group-theory.quotient-groups public -open import group-theory.quotient-groups-concrete-groups public -open import group-theory.quotients-abelian-groups public -open import group-theory.rational-commutative-monoids public -open import group-theory.representations-monoids-precategories public -open import group-theory.saturated-congruence-relations-commutative-monoids public -open import group-theory.saturated-congruence-relations-monoids public -open import group-theory.semigroups public -open import group-theory.sheargroups public -open import group-theory.shriek-concrete-group-actions public -open import group-theory.stabilizer-groups public -open import group-theory.stabilizer-groups-concrete-group-actions public -open import group-theory.subgroups public -open import group-theory.subgroups-abelian-groups public -open import group-theory.subgroups-concrete-groups public -open import group-theory.subgroups-generated-by-elements-groups public -open import group-theory.subgroups-generated-by-families-of-elements-groups public -open import group-theory.subgroups-generated-by-subsets-groups public -open import group-theory.submonoids public -open import group-theory.submonoids-commutative-monoids public -open import group-theory.subsemigroups public -open import group-theory.subsets-abelian-groups public -open import group-theory.subsets-commutative-monoids public -open import group-theory.subsets-groups public -open import group-theory.subsets-monoids public -open import group-theory.subsets-semigroups public -open import group-theory.substitution-functor-concrete-group-actions public -open import group-theory.substitution-functor-group-actions public -open import group-theory.surjective-group-homomorphisms public -open import group-theory.surjective-semigroup-homomorphisms public -open import group-theory.symmetric-concrete-groups public -open import group-theory.symmetric-groups public -open import group-theory.torsion-elements-groups public -open import group-theory.torsion-free-groups public -open import group-theory.torsors public -open import group-theory.transitive-concrete-group-actions public -open import group-theory.transitive-group-actions public -open import group-theory.trivial-concrete-groups public -open import group-theory.trivial-group-homomorphisms public -open import group-theory.trivial-groups public -open import group-theory.trivial-subgroups public -open import group-theory.unordered-tuples-of-elements-commutative-monoids public -open import group-theory.wild-representations-monoids public +open import group-theory.category-of-group-actions funext public +open import group-theory.category-of-groups funext public +open import group-theory.category-of-orbits-groups funext public +open import group-theory.category-of-semigroups funext public +open import group-theory.cayleys-theorem funext public +open import group-theory.centers-groups funext public +open import group-theory.centers-monoids funext public +open import group-theory.centers-semigroups funext public +open import group-theory.central-elements-groups funext public +open import group-theory.central-elements-monoids funext public +open import group-theory.central-elements-semigroups funext public +open import group-theory.centralizer-subgroups funext public +open import group-theory.characteristic-subgroups funext public +open import group-theory.commutative-monoids funext public +open import group-theory.commutator-subgroups funext public +open import group-theory.commutators-of-elements-groups funext public +open import group-theory.commuting-elements-groups funext public +open import group-theory.commuting-elements-monoids funext public +open import group-theory.commuting-elements-semigroups funext public +open import group-theory.commuting-squares-of-group-homomorphisms funext public +open import group-theory.concrete-group-actions funext public +open import group-theory.concrete-groups funext public +open import group-theory.concrete-monoids funext public +open import group-theory.congruence-relations-abelian-groups funext public +open import group-theory.congruence-relations-commutative-monoids funext public +open import group-theory.congruence-relations-groups funext public +open import group-theory.congruence-relations-monoids funext public +open import group-theory.congruence-relations-semigroups funext public +open import group-theory.conjugation funext public +open import group-theory.conjugation-concrete-groups funext public +open import group-theory.contravariant-pushforward-concrete-group-actions funext public +open import group-theory.cores-monoids funext public +open import group-theory.cyclic-groups funext public +open import group-theory.decidable-subgroups funext public +open import group-theory.dependent-products-abelian-groups funext public +open import group-theory.dependent-products-commutative-monoids funext public +open import group-theory.dependent-products-groups funext public +open import group-theory.dependent-products-monoids funext public +open import group-theory.dependent-products-semigroups funext public +open import group-theory.dihedral-group-construction funext public +open import group-theory.dihedral-groups funext public +open import group-theory.e8-lattice funext public +open import group-theory.elements-of-finite-order-groups funext public +open import group-theory.embeddings-abelian-groups funext public +open import group-theory.embeddings-groups funext public +open import group-theory.endomorphism-rings-abelian-groups funext public +open import group-theory.epimorphisms-groups funext public +open import group-theory.equivalences-concrete-group-actions funext public +open import group-theory.equivalences-concrete-groups funext public +open import group-theory.equivalences-group-actions funext public +open import group-theory.equivalences-semigroups funext public +open import group-theory.exponents-abelian-groups funext public +open import group-theory.exponents-groups funext public +open import group-theory.free-concrete-group-actions funext public +open import group-theory.free-groups-with-one-generator funext public +open import group-theory.full-subgroups funext public +open import group-theory.full-subsemigroups funext public +open import group-theory.function-abelian-groups funext public +open import group-theory.function-commutative-monoids funext public +open import group-theory.function-groups funext public +open import group-theory.function-monoids funext public +open import group-theory.function-semigroups funext public +open import group-theory.functoriality-quotient-groups funext public +open import group-theory.furstenberg-groups funext public +open import group-theory.generating-elements-groups funext public +open import group-theory.generating-sets-groups funext public +open import group-theory.group-actions funext public +open import group-theory.groups funext public +open import group-theory.homomorphisms-abelian-groups funext public +open import group-theory.homomorphisms-commutative-monoids funext public +open import group-theory.homomorphisms-concrete-group-actions funext public +open import group-theory.homomorphisms-concrete-groups funext public +open import group-theory.homomorphisms-generated-subgroups funext public +open import group-theory.homomorphisms-group-actions funext public +open import group-theory.homomorphisms-groups funext public +open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups funext public +open import group-theory.homomorphisms-monoids funext public +open import group-theory.homomorphisms-semigroups funext public +open import group-theory.homotopy-automorphism-groups funext public +open import group-theory.images-of-group-homomorphisms funext public +open import group-theory.images-of-semigroup-homomorphisms funext public +open import group-theory.integer-multiples-of-elements-abelian-groups funext public +open import group-theory.integer-powers-of-elements-groups funext public +open import group-theory.intersections-subgroups-abelian-groups funext public +open import group-theory.intersections-subgroups-groups funext public +open import group-theory.inverse-semigroups funext public +open import group-theory.invertible-elements-monoids funext public +open import group-theory.isomorphisms-abelian-groups funext public +open import group-theory.isomorphisms-concrete-groups funext public +open import group-theory.isomorphisms-group-actions funext public +open import group-theory.isomorphisms-groups funext public +open import group-theory.isomorphisms-monoids funext public +open import group-theory.isomorphisms-semigroups funext public +open import group-theory.iterated-cartesian-products-concrete-groups funext public +open import group-theory.kernels-homomorphisms-abelian-groups funext public +open import group-theory.kernels-homomorphisms-concrete-groups funext public +open import group-theory.kernels-homomorphisms-groups funext public +open import group-theory.large-semigroups funext public +open import group-theory.loop-groups-sets funext public +open import group-theory.mere-equivalences-concrete-group-actions funext public +open import group-theory.mere-equivalences-group-actions funext public +open import group-theory.minkowski-multiplication-commutative-monoids funext public +open import group-theory.minkowski-multiplication-monoids funext public +open import group-theory.minkowski-multiplication-semigroups funext public +open import group-theory.monoid-actions funext public +open import group-theory.monoids funext public +open import group-theory.monomorphisms-concrete-groups funext public +open import group-theory.monomorphisms-groups funext public +open import group-theory.multiples-of-elements-abelian-groups funext public +open import group-theory.nontrivial-groups funext public +open import group-theory.normal-closures-subgroups funext public +open import group-theory.normal-cores-subgroups funext public +open import group-theory.normal-subgroups funext public +open import group-theory.normal-subgroups-concrete-groups funext public +open import group-theory.normal-submonoids funext public +open import group-theory.normal-submonoids-commutative-monoids funext public +open import group-theory.normalizer-subgroups funext public +open import group-theory.nullifying-group-homomorphisms funext public +open import group-theory.opposite-groups funext public +open import group-theory.opposite-semigroups funext public +open import group-theory.orbit-stabilizer-theorem-concrete-groups funext public +open import group-theory.orbits-concrete-group-actions funext public +open import group-theory.orbits-group-actions funext public +open import group-theory.orders-of-elements-groups funext public +open import group-theory.perfect-cores funext public +open import group-theory.perfect-groups funext public +open import group-theory.perfect-subgroups funext public +open import group-theory.powers-of-elements-commutative-monoids funext public +open import group-theory.powers-of-elements-groups funext public +open import group-theory.powers-of-elements-monoids funext public +open import group-theory.precategory-of-commutative-monoids funext public +open import group-theory.precategory-of-concrete-groups funext public +open import group-theory.precategory-of-group-actions funext public +open import group-theory.precategory-of-groups funext public +open import group-theory.precategory-of-monoids funext public +open import group-theory.precategory-of-orbits-monoid-actions funext public +open import group-theory.precategory-of-semigroups funext public +open import group-theory.principal-group-actions funext public +open import group-theory.principal-torsors-concrete-groups funext public +open import group-theory.products-of-elements-monoids funext public +open import group-theory.products-of-tuples-of-elements-commutative-monoids funext public +open import group-theory.pullbacks-subgroups funext public +open import group-theory.pullbacks-subsemigroups funext public +open import group-theory.quotient-groups funext public +open import group-theory.quotient-groups-concrete-groups funext public +open import group-theory.quotients-abelian-groups funext public +open import group-theory.rational-commutative-monoids funext public +open import group-theory.representations-monoids-precategories funext public +open import group-theory.saturated-congruence-relations-commutative-monoids funext public +open import group-theory.saturated-congruence-relations-monoids funext public +open import group-theory.semigroups funext public +open import group-theory.sheargroups funext public +open import group-theory.shriek-concrete-group-actions funext public +open import group-theory.stabilizer-groups funext public +open import group-theory.stabilizer-groups-concrete-group-actions funext public +open import group-theory.subgroups funext public +open import group-theory.subgroups-abelian-groups funext public +open import group-theory.subgroups-concrete-groups funext public +open import group-theory.subgroups-generated-by-elements-groups funext public +open import group-theory.subgroups-generated-by-families-of-elements-groups funext public +open import group-theory.subgroups-generated-by-subsets-groups funext public +open import group-theory.submonoids funext public +open import group-theory.submonoids-commutative-monoids funext public +open import group-theory.subsemigroups funext public +open import group-theory.subsets-abelian-groups funext public +open import group-theory.subsets-commutative-monoids funext public +open import group-theory.subsets-groups funext public +open import group-theory.subsets-monoids funext public +open import group-theory.subsets-semigroups funext public +open import group-theory.substitution-functor-concrete-group-actions funext public +open import group-theory.substitution-functor-group-actions funext public +open import group-theory.surjective-group-homomorphisms funext public +open import group-theory.surjective-semigroup-homomorphisms funext public +open import group-theory.symmetric-concrete-groups funext public +open import group-theory.symmetric-groups funext public +open import group-theory.torsion-elements-groups funext public +open import group-theory.torsion-free-groups funext public +open import group-theory.torsors funext public +open import group-theory.transitive-concrete-group-actions funext public +open import group-theory.transitive-group-actions funext public +open import group-theory.trivial-concrete-groups funext public +open import group-theory.trivial-group-homomorphisms funext public +open import group-theory.trivial-groups funext public +open import group-theory.trivial-subgroups funext public +open import group-theory.unordered-tuples-of-elements-commutative-monoids funext public +open import group-theory.wild-representations-monoids funext public ``` diff --git a/src/group-theory/abelian-groups.lagda.md b/src/group-theory/abelian-groups.lagda.md index 6023e6276d..050d547706 100644 --- a/src/group-theory/abelian-groups.lagda.md +++ b/src/group-theory/abelian-groups.lagda.md @@ -1,7 +1,12 @@ # Abelian groups ```agda -module group-theory.abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.abelian-groups + (funext : function-extensionality) + where ```
Imports @@ -9,41 +14,41 @@ module group-theory.abelian-groups where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.full-subtypes funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.interchange-law -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.central-elements-groups -open import group-theory.commutative-monoids -open import group-theory.commutator-subgroups -open import group-theory.commutators-of-elements-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.monoids -open import group-theory.nullifying-group-homomorphisms -open import group-theory.pullbacks-subgroups -open import group-theory.semigroups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-families-of-elements-groups -open import group-theory.trivial-subgroups - -open import lists.concatenation-lists +open import group-theory.central-elements-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.commutator-subgroups funext +open import group-theory.commutators-of-elements-groups funext +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.monoids funext +open import group-theory.nullifying-group-homomorphisms funext +open import group-theory.pullbacks-subgroups funext +open import group-theory.semigroups funext +open import group-theory.subgroups funext +open import group-theory.subgroups funext-generated-by-families-of-elements-groups +open import group-theory.trivial-subgroups funext + +open import lists.concatenation-lists funext open import lists.lists -open import structured-types.pointed-types-equipped-with-automorphisms +open import structured-types.pointed-types-equipped-with-automorphisms funext ```
diff --git a/src/group-theory/abelianization-groups.lagda.md b/src/group-theory/abelianization-groups.lagda.md index 5698ee542f..c28d0833c9 100644 --- a/src/group-theory/abelianization-groups.lagda.md +++ b/src/group-theory/abelianization-groups.lagda.md @@ -3,41 +3,46 @@ ```agda {-# OPTIONS --lossy-unification #-} -module group-theory.abelianization-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.abelianization-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.adjunctions-large-categories -open import category-theory.adjunctions-large-precategories -open import category-theory.functors-large-categories -open import category-theory.functors-large-precategories -open import category-theory.natural-transformations-functors-large-categories -open import category-theory.natural-transformations-functors-large-precategories - -open import foundation.commuting-squares-of-maps +open import category-theory.adjunctions-large-categories funext +open import category-theory.adjunctions-large-precategories funext +open import category-theory.functors-large-categories funext +open import category-theory.functors-large-precategories funext +open import category-theory.natural-transformations-functors-large-categories funext +open import category-theory.natural-transformations-functors-large-precategories funext + +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.set-quotients -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.set-quotients funext +open import foundation.sets funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import group-theory.abelian-groups -open import group-theory.category-of-abelian-groups -open import group-theory.category-of-groups -open import group-theory.commutator-subgroups -open import group-theory.commuting-squares-of-group-homomorphisms -open import group-theory.functoriality-quotient-groups -open import group-theory.groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.nullifying-group-homomorphisms -open import group-theory.quotient-groups +open import group-theory.abelian-groups funext +open import group-theory.category-of-abelian-groups funext +open import group-theory.category-of-groups funext +open import group-theory.commutator-subgroups funext +open import group-theory.commuting-squares-of-group-homomorphisms funext +open import group-theory.functoriality-quotient-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.normal-subgroups funext +open import group-theory.nullifying-group-homomorphisms funext +open import group-theory.quotient-groups funext ```
diff --git a/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md b/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md index 8c5fd68978..d3de9771ba 100644 --- a/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md @@ -1,7 +1,12 @@ # Pointwise addition of morphisms of abelian groups ```agda -module group-theory.addition-homomorphisms-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.addition-homomorphisms-abelian-groups + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module group-theory.addition-homomorphisms-abelian-groups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/automorphism-groups.lagda.md b/src/group-theory/automorphism-groups.lagda.md index 668dde054a..65c6335a6c 100644 --- a/src/group-theory/automorphism-groups.lagda.md +++ b/src/group-theory/automorphism-groups.lagda.md @@ -1,27 +1,32 @@ # Automorphism groups ```agda -module group-theory.automorphism-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.automorphism-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.1-types -open import foundation.connected-components +open import foundation.1-types funext +open import foundation.connected-components funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.equivalences-concrete-groups funext -open import higher-group-theory.automorphism-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.automorphism-groups funext +open import higher-group-theory.higher-groups funext ```
diff --git a/src/group-theory/cartesian-products-abelian-groups.lagda.md b/src/group-theory/cartesian-products-abelian-groups.lagda.md index 2bf663196b..21868c8edc 100644 --- a/src/group-theory/cartesian-products-abelian-groups.lagda.md +++ b/src/group-theory/cartesian-products-abelian-groups.lagda.md @@ -1,7 +1,12 @@ # Cartesian products of abelian groups ```agda -module group-theory.cartesian-products-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.cartesian-products-abelian-groups + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module group-theory.cartesian-products-abelian-groups where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.cartesian-products-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.cartesian-products-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/cartesian-products-concrete-groups.lagda.md b/src/group-theory/cartesian-products-concrete-groups.lagda.md index a60202281c..2280a032ab 100644 --- a/src/group-theory/cartesian-products-concrete-groups.lagda.md +++ b/src/group-theory/cartesian-products-concrete-groups.lagda.md @@ -1,31 +1,36 @@ # Cartesian products of concrete groups ```agda -module group-theory.cartesian-products-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.cartesian-products-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.1-types -open import foundation.cartesian-product-types +open import foundation.0-connected-types funext +open import foundation.1-types funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.groups +open import group-theory.concrete-groups funext +open import group-theory.groups funext -open import higher-group-theory.cartesian-products-higher-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.cartesian-products-higher-groups funext +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types ``` diff --git a/src/group-theory/cartesian-products-groups.lagda.md b/src/group-theory/cartesian-products-groups.lagda.md index 84748d8b87..43ca52a66a 100644 --- a/src/group-theory/cartesian-products-groups.lagda.md +++ b/src/group-theory/cartesian-products-groups.lagda.md @@ -1,7 +1,12 @@ # Cartesian products of groups ```agda -module group-theory.cartesian-products-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.cartesian-products-groups + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module group-theory.cartesian-products-groups where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.cartesian-products-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.cartesian-products-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/cartesian-products-monoids.lagda.md b/src/group-theory/cartesian-products-monoids.lagda.md index c83c132714..7880bfd202 100644 --- a/src/group-theory/cartesian-products-monoids.lagda.md +++ b/src/group-theory/cartesian-products-monoids.lagda.md @@ -1,7 +1,12 @@ # Cartesian products of monoids ```agda -module group-theory.cartesian-products-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.cartesian-products-monoids + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module group-theory.cartesian-products-monoids where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.cartesian-products-semigroups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.cartesian-products-semigroups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/cartesian-products-semigroups.lagda.md b/src/group-theory/cartesian-products-semigroups.lagda.md index e14a38dbc2..a57864f7eb 100644 --- a/src/group-theory/cartesian-products-semigroups.lagda.md +++ b/src/group-theory/cartesian-products-semigroups.lagda.md @@ -1,7 +1,12 @@ # Cartesian products of semigroups ```agda -module group-theory.cartesian-products-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.cartesian-products-semigroups + (funext : function-extensionality) + where ```
Imports @@ -9,11 +14,11 @@ module group-theory.cartesian-products-semigroups where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/category-of-abelian-groups.lagda.md b/src/group-theory/category-of-abelian-groups.lagda.md index abb1ac4341..bca9cd26b5 100644 --- a/src/group-theory/category-of-abelian-groups.lagda.md +++ b/src/group-theory/category-of-abelian-groups.lagda.md @@ -1,23 +1,28 @@ # The category of abelian groups ```agda -module group-theory.category-of-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.category-of-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.full-large-subcategories -open import category-theory.functors-large-categories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.full-large-subcategories funext +open import category-theory.functors-large-categories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.category-of-groups +open import group-theory.abelian-groups funext +open import group-theory.category-of-groups funext ```
diff --git a/src/group-theory/category-of-group-actions.lagda.md b/src/group-theory/category-of-group-actions.lagda.md index 1205990345..08c74e94be 100644 --- a/src/group-theory/category-of-group-actions.lagda.md +++ b/src/group-theory/category-of-group-actions.lagda.md @@ -1,27 +1,32 @@ # The category of group actions ```agda -module group-theory.category-of-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.category-of-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.isomorphisms-group-actions -open import group-theory.precategory-of-group-actions +open import group-theory.group-actions funext +open import group-theory.groups funext +open import group-theory.homomorphisms-group-actions funext +open import group-theory.isomorphisms-group-actions funext +open import group-theory.precategory-of-group-actions funext ```
diff --git a/src/group-theory/category-of-groups.lagda.md b/src/group-theory/category-of-groups.lagda.md index 5b7a7ec268..b6c21be780 100644 --- a/src/group-theory/category-of-groups.lagda.md +++ b/src/group-theory/category-of-groups.lagda.md @@ -1,24 +1,29 @@ # The category of groups ```agda -module group-theory.category-of-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.category-of-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories +open import category-theory.categories funext +open import category-theory.large-categories funext -open import foundation.1-types -open import foundation.equivalences +open import foundation.1-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.isomorphisms-groups -open import group-theory.precategory-of-groups +open import group-theory.groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.precategory-of-groups funext ```
diff --git a/src/group-theory/category-of-orbits-groups.lagda.md b/src/group-theory/category-of-orbits-groups.lagda.md index e8ddd2bdc0..93a09223ec 100644 --- a/src/group-theory/category-of-orbits-groups.lagda.md +++ b/src/group-theory/category-of-orbits-groups.lagda.md @@ -1,30 +1,35 @@ # The orbit category of a group ```agda -module group-theory.category-of-orbits-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.category-of-orbits-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.full-large-subcategories -open import category-theory.isomorphisms-in-large-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.full-large-subcategories funext +open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels -open import group-theory.category-of-group-actions -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.isomorphisms-group-actions -open import group-theory.precategory-of-group-actions -open import group-theory.transitive-group-actions +open import group-theory.category-of-group-actions funext +open import group-theory.group-actions funext +open import group-theory.groups funext +open import group-theory.homomorphisms-group-actions funext +open import group-theory.isomorphisms-group-actions funext +open import group-theory.precategory-of-group-actions funext +open import group-theory.transitive-group-actions funext ```
diff --git a/src/group-theory/category-of-semigroups.lagda.md b/src/group-theory/category-of-semigroups.lagda.md index a610b13437..034a13422e 100644 --- a/src/group-theory/category-of-semigroups.lagda.md +++ b/src/group-theory/category-of-semigroups.lagda.md @@ -1,25 +1,30 @@ # The category of semigroups ```agda -module group-theory.category-of-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.category-of-semigroups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories +open import category-theory.categories funext +open import category-theory.large-categories funext -open import foundation.1-types +open import foundation.1-types funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.isomorphisms-semigroups -open import group-theory.precategory-of-semigroups -open import group-theory.semigroups +open import group-theory.isomorphisms-semigroups funext +open import group-theory.precategory-of-semigroups funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/cayleys-theorem.lagda.md b/src/group-theory/cayleys-theorem.lagda.md index b770b023ac..bc24466f32 100644 --- a/src/group-theory/cayleys-theorem.lagda.md +++ b/src/group-theory/cayleys-theorem.lagda.md @@ -1,23 +1,28 @@ # Cayley's theorem ```agda -module group-theory.cayleys-theorem where +open import foundation.function-extensionality-axiom + +module + group-theory.cayleys-theorem + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-extensionality -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.embeddings funext +open import foundation.equivalence-extensionality funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.universe-levels -open import group-theory.embeddings-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.symmetric-groups +open import group-theory.embeddings-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.symmetric-groups funext ```
diff --git a/src/group-theory/centers-groups.lagda.md b/src/group-theory/centers-groups.lagda.md index a92e3af960..2634f73aac 100644 --- a/src/group-theory/centers-groups.lagda.md +++ b/src/group-theory/centers-groups.lagda.md @@ -1,22 +1,27 @@ # The center of a group ```agda -module group-theory.centers-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.centers-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.central-elements-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.subgroups +open import group-theory.central-elements-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.normal-subgroups funext +open import group-theory.subgroups funext ```
diff --git a/src/group-theory/centers-monoids.lagda.md b/src/group-theory/centers-monoids.lagda.md index 39deb28916..f40e75d76a 100644 --- a/src/group-theory/centers-monoids.lagda.md +++ b/src/group-theory/centers-monoids.lagda.md @@ -1,21 +1,26 @@ # Center of a monoid ```agda -module group-theory.centers-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.centers-monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.central-elements-monoids -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.submonoids +open import group-theory.central-elements-monoids funext +open import group-theory.homomorphisms-monoids funext +open import group-theory.monoids funext +open import group-theory.submonoids funext ```
diff --git a/src/group-theory/centers-semigroups.lagda.md b/src/group-theory/centers-semigroups.lagda.md index 9997e96a0c..5e24d95ec4 100644 --- a/src/group-theory/centers-semigroups.lagda.md +++ b/src/group-theory/centers-semigroups.lagda.md @@ -1,21 +1,26 @@ # Center of a semigroup ```agda -module group-theory.centers-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.centers-semigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.central-elements-semigroups -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups -open import group-theory.subsemigroups +open import group-theory.central-elements-semigroups funext +open import group-theory.homomorphisms-semigroups funext +open import group-theory.semigroups funext +open import group-theory.subsemigroups funext ```
diff --git a/src/group-theory/central-elements-groups.lagda.md b/src/group-theory/central-elements-groups.lagda.md index 21cd4b9353..698682c85b 100644 --- a/src/group-theory/central-elements-groups.lagda.md +++ b/src/group-theory/central-elements-groups.lagda.md @@ -1,21 +1,26 @@ # Central elements of groups ```agda -module group-theory.central-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.central-elements-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.central-elements-monoids -open import group-theory.conjugation -open import group-theory.groups +open import group-theory.central-elements-monoids funext +open import group-theory.conjugation funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/central-elements-monoids.lagda.md b/src/group-theory/central-elements-monoids.lagda.md index bece727ced..a759cd76b5 100644 --- a/src/group-theory/central-elements-monoids.lagda.md +++ b/src/group-theory/central-elements-monoids.lagda.md @@ -1,18 +1,23 @@ # Central elements of monoids ```agda -module group-theory.central-elements-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.central-elements-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.central-elements-semigroups -open import group-theory.monoids +open import group-theory.central-elements-semigroups funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/central-elements-semigroups.lagda.md b/src/group-theory/central-elements-semigroups.lagda.md index cedeca3a11..2ade7477b3 100644 --- a/src/group-theory/central-elements-semigroups.lagda.md +++ b/src/group-theory/central-elements-semigroups.lagda.md @@ -1,19 +1,24 @@ # Central elements of semirings ```agda -module group-theory.central-elements-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.central-elements-semigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/centralizer-subgroups.lagda.md b/src/group-theory/centralizer-subgroups.lagda.md index 9e44de697c..e5cff01755 100644 --- a/src/group-theory/centralizer-subgroups.lagda.md +++ b/src/group-theory/centralizer-subgroups.lagda.md @@ -1,7 +1,12 @@ # Centralizer subgroups ```agda -module group-theory.centralizer-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.centralizer-subgroups + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module group-theory.centralizer-subgroups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext ```
diff --git a/src/group-theory/characteristic-subgroups.lagda.md b/src/group-theory/characteristic-subgroups.lagda.md index 023e2b5cee..5073691e85 100644 --- a/src/group-theory/characteristic-subgroups.lagda.md +++ b/src/group-theory/characteristic-subgroups.lagda.md @@ -1,19 +1,24 @@ # Characteristic subgroups ```agda -module group-theory.characteristic-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.characteristic-subgroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.isomorphisms-groups -open import group-theory.subgroups +open import group-theory.groups funext +open import group-theory.images-of-group-homomorphisms funext +open import group-theory.isomorphisms-groups funext +open import group-theory.subgroups funext ```
diff --git a/src/group-theory/commutative-monoids.lagda.md b/src/group-theory/commutative-monoids.lagda.md index ad42cb9e4f..670467cd5c 100644 --- a/src/group-theory/commutative-monoids.lagda.md +++ b/src/group-theory/commutative-monoids.lagda.md @@ -1,7 +1,12 @@ # Commutative monoids ```agda -module group-theory.commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.commutative-monoids + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,17 @@ module group-theory.commutative-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.interchange-law -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.telescopes open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/commutator-subgroups.lagda.md b/src/group-theory/commutator-subgroups.lagda.md index 1300e1e9be..051b0fbb3b 100644 --- a/src/group-theory/commutator-subgroups.lagda.md +++ b/src/group-theory/commutator-subgroups.lagda.md @@ -1,31 +1,36 @@ # Commutator subgroups ```agda -module group-theory.commutator-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.commutator-subgroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import group-theory.commutators-of-elements-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.normal-subgroups -open import group-theory.pullbacks-subgroups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-families-of-elements-groups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups +open import group-theory.commutators-of-elements-groups funext +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.images-of-group-homomorphisms funext +open import group-theory.normal-subgroups funext +open import group-theory.pullbacks-subgroups funext +open import group-theory.subgroups funext +open import group-theory.subgroups funext-generated-by-families-of-elements-groups +open import group-theory.subgroups-generated-by-subsets-groups funext +open import group-theory.subsets-groups funext ```
diff --git a/src/group-theory/commutators-of-elements-groups.lagda.md b/src/group-theory/commutators-of-elements-groups.lagda.md index 086b8fcc4d..ae33e500e3 100644 --- a/src/group-theory/commutators-of-elements-groups.lagda.md +++ b/src/group-theory/commutators-of-elements-groups.lagda.md @@ -1,20 +1,25 @@ # Commutators of elements in groups ```agda -module group-theory.commutators-of-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.commutators-of-elements-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commuting-elements-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups +open import group-theory.commuting-elements-groups funext +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext ```
diff --git a/src/group-theory/commuting-elements-groups.lagda.md b/src/group-theory/commuting-elements-groups.lagda.md index 9e76af7d68..b1c539a3f8 100644 --- a/src/group-theory/commuting-elements-groups.lagda.md +++ b/src/group-theory/commuting-elements-groups.lagda.md @@ -1,18 +1,23 @@ # Commuting elements of groups ```agda -module group-theory.commuting-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.commuting-elements-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.commuting-elements-monoids -open import group-theory.groups +open import group-theory.commuting-elements-monoids funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/commuting-elements-monoids.lagda.md b/src/group-theory/commuting-elements-monoids.lagda.md index 3f74bcc1d1..3590439529 100644 --- a/src/group-theory/commuting-elements-monoids.lagda.md +++ b/src/group-theory/commuting-elements-monoids.lagda.md @@ -1,18 +1,23 @@ # Commuting elements of monoids ```agda -module group-theory.commuting-elements-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.commuting-elements-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.commuting-elements-semigroups -open import group-theory.monoids +open import group-theory.commuting-elements-semigroups funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/commuting-elements-semigroups.lagda.md b/src/group-theory/commuting-elements-semigroups.lagda.md index 4c5d7998e8..d0672f59e1 100644 --- a/src/group-theory/commuting-elements-semigroups.lagda.md +++ b/src/group-theory/commuting-elements-semigroups.lagda.md @@ -1,19 +1,24 @@ # Commuting elements of semigroups ```agda -module group-theory.commuting-elements-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.commuting-elements-semigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md b/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md index e8e02a54ec..6740052c23 100644 --- a/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md +++ b/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md @@ -1,17 +1,22 @@ # Commuting squares of group homomorphisms ```agda -module group-theory.commuting-squares-of-group-homomorphisms where +open import foundation.function-extensionality-axiom + +module + group-theory.commuting-squares-of-group-homomorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext ```
diff --git a/src/group-theory/concrete-group-actions.lagda.md b/src/group-theory/concrete-group-actions.lagda.md index a379534da8..8e6fadf7da 100644 --- a/src/group-theory/concrete-group-actions.lagda.md +++ b/src/group-theory/concrete-group-actions.lagda.md @@ -1,18 +1,23 @@ # Concrete group actions ```agda -module group-theory.concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.concrete-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.function-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.concrete-groups +open import group-theory.concrete-groups funext ```
diff --git a/src/group-theory/concrete-groups.lagda.md b/src/group-theory/concrete-groups.lagda.md index 17b5b67ad6..7075446bfc 100644 --- a/src/group-theory/concrete-groups.lagda.md +++ b/src/group-theory/concrete-groups.lagda.md @@ -1,31 +1,36 @@ # Concrete groups ```agda -module group-theory.concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.1-types +open import foundation.0-connected-types funext +open import foundation.1-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.groups -open import group-theory.monoids -open import group-theory.opposite-groups -open import group-theory.opposite-semigroups -open import group-theory.semigroups +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.opposite-groups funext +open import group-theory.opposite-semigroups funext +open import group-theory.semigroups funext -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types ``` diff --git a/src/group-theory/concrete-monoids.lagda.md b/src/group-theory/concrete-monoids.lagda.md index 702c2b25d3..aae3ff369a 100644 --- a/src/group-theory/concrete-monoids.lagda.md +++ b/src/group-theory/concrete-monoids.lagda.md @@ -1,22 +1,27 @@ # Concrete monoids ```agda -module group-theory.concrete-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.concrete-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories +open import category-theory.categories funext -open import foundation.0-connected-types -open import foundation.cartesian-product-types +open import foundation.0-connected-types funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.cores-monoids -open import group-theory.monoids -open import group-theory.torsors +open import group-theory.cores-monoids funext +open import group-theory.monoids funext +open import group-theory.torsors funext ```
diff --git a/src/group-theory/congruence-relations-abelian-groups.lagda.md b/src/group-theory/congruence-relations-abelian-groups.lagda.md index f9f130587d..ac7ad2bc61 100644 --- a/src/group-theory/congruence-relations-abelian-groups.lagda.md +++ b/src/group-theory/congruence-relations-abelian-groups.lagda.md @@ -1,22 +1,27 @@ # Congruence relations on abelian groups ```agda -module group-theory.congruence-relations-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.congruence-relations-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.binary-relations funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.congruence-relations-groups +open import group-theory.abelian-groups funext +open import group-theory.congruence-relations-groups funext ```
diff --git a/src/group-theory/congruence-relations-commutative-monoids.lagda.md b/src/group-theory/congruence-relations-commutative-monoids.lagda.md index 2b79291e89..d4c9bc9d88 100644 --- a/src/group-theory/congruence-relations-commutative-monoids.lagda.md +++ b/src/group-theory/congruence-relations-commutative-monoids.lagda.md @@ -1,22 +1,27 @@ # Congruence relations on commutative monoids ```agda -module group-theory.congruence-relations-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.congruence-relations-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.binary-relations funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.congruence-relations-monoids +open import group-theory.commutative-monoids funext +open import group-theory.congruence-relations-monoids funext ```
diff --git a/src/group-theory/congruence-relations-groups.lagda.md b/src/group-theory/congruence-relations-groups.lagda.md index ca3018bb5d..60a2e2da69 100644 --- a/src/group-theory/congruence-relations-groups.lagda.md +++ b/src/group-theory/congruence-relations-groups.lagda.md @@ -1,26 +1,31 @@ # Congruence relations on groups ```agda -module group-theory.congruence-relations-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.congruence-relations-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.congruence-relations-semigroups -open import group-theory.conjugation -open import group-theory.groups +open import group-theory.congruence-relations-semigroups funext +open import group-theory.conjugation funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/congruence-relations-monoids.lagda.md b/src/group-theory/congruence-relations-monoids.lagda.md index ce5778b509..8639cbe0fa 100644 --- a/src/group-theory/congruence-relations-monoids.lagda.md +++ b/src/group-theory/congruence-relations-monoids.lagda.md @@ -1,23 +1,28 @@ # Congruence relations on monoids ```agda -module group-theory.congruence-relations-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.congruence-relations-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.congruence-relations-semigroups -open import group-theory.monoids +open import group-theory.congruence-relations-semigroups funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/congruence-relations-semigroups.lagda.md b/src/group-theory/congruence-relations-semigroups.lagda.md index 5ebc48e734..24831cd8e9 100644 --- a/src/group-theory/congruence-relations-semigroups.lagda.md +++ b/src/group-theory/congruence-relations-semigroups.lagda.md @@ -1,24 +1,29 @@ # Congruence relations on semigroups ```agda -module group-theory.congruence-relations-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.congruence-relations-semigroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences +open import foundation.equivalence-relations funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/conjugation-concrete-groups.lagda.md b/src/group-theory/conjugation-concrete-groups.lagda.md index 4b3aa4c395..55ab7f63f0 100644 --- a/src/group-theory/conjugation-concrete-groups.lagda.md +++ b/src/group-theory/conjugation-concrete-groups.lagda.md @@ -1,21 +1,26 @@ # Conjugation on concrete groups ```agda -module group-theory.conjugation-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.conjugation-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.conjugation -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.conjugation funext +open import group-theory.homomorphisms-concrete-groups funext -open import higher-group-theory.conjugation +open import higher-group-theory.conjugation funext ```
diff --git a/src/group-theory/conjugation.lagda.md b/src/group-theory/conjugation.lagda.md index 55baaed82e..927dfa5700 100644 --- a/src/group-theory/conjugation.lagda.md +++ b/src/group-theory/conjugation.lagda.md @@ -1,7 +1,12 @@ # Conjugation in groups ```agda -module group-theory.conjugation where +open import foundation.function-extensionality-axiom + +module + group-theory.conjugation + (funext : function-extensionality) + where ```
Imports @@ -11,24 +16,24 @@ open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections -open import foundation.subtypes -open import foundation.transposition-identifications-along-retractions -open import foundation.transposition-identifications-along-sections +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.subtypes funext +open import foundation.transposition-identifications-along-retractions funext +open import foundation.transposition-identifications-along-sections funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.isomorphisms-groups -open import group-theory.subsets-groups +open import group-theory.group-actions funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.integer-powers-of-elements-groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.subsets-groups funext ```
diff --git a/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md b/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md index a9aa640c3c..ef3a41ba66 100644 --- a/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md +++ b/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md @@ -1,7 +1,12 @@ # Contravariant pushforwards of concrete group actions ```agda -module group-theory.contravariant-pushforward-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.contravariant-pushforward-concrete-group-actions + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module group-theory.contravariant-pushforward-concrete-group-actions where ```agda open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.homomorphisms-concrete-groups funext ```
diff --git a/src/group-theory/cores-monoids.lagda.md b/src/group-theory/cores-monoids.lagda.md index 50328b33a1..33bb201f66 100644 --- a/src/group-theory/cores-monoids.lagda.md +++ b/src/group-theory/cores-monoids.lagda.md @@ -1,29 +1,34 @@ # Cores of monoids ```agda -module group-theory.cores-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.cores-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories +open import category-theory.functors-large-precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-monoids -open import group-theory.invertible-elements-monoids -open import group-theory.monoids -open import group-theory.precategory-of-groups -open import group-theory.precategory-of-monoids -open import group-theory.semigroups -open import group-theory.submonoids +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-monoids funext +open import group-theory.invertible-elements-monoids funext +open import group-theory.monoids funext +open import group-theory.precategory-of-groups funext +open import group-theory.precategory-of-monoids funext +open import group-theory.semigroups funext +open import group-theory.submonoids funext ```
diff --git a/src/group-theory/cyclic-groups.lagda.md b/src/group-theory/cyclic-groups.lagda.md index 08c862b1fc..47ada889bb 100644 --- a/src/group-theory/cyclic-groups.lagda.md +++ b/src/group-theory/cyclic-groups.lagda.md @@ -1,25 +1,30 @@ # Cyclic groups ```agda -module group-theory.cyclic-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.cyclic-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.generating-elements-groups -open import group-theory.groups +open import group-theory.abelian-groups funext +open import group-theory.generating-elements-groups funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/decidable-subgroups.lagda.md b/src/group-theory/decidable-subgroups.lagda.md index e523eb23cb..dd5c5ef933 100644 --- a/src/group-theory/decidable-subgroups.lagda.md +++ b/src/group-theory/decidable-subgroups.lagda.md @@ -1,31 +1,36 @@ # Decidable subgroups of groups ```agda -module group-theory.decidable-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.decidable-subgroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-subtypes +open import foundation.binary-relations funext +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.semigroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.semigroups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext ```
diff --git a/src/group-theory/dependent-products-abelian-groups.lagda.md b/src/group-theory/dependent-products-abelian-groups.lagda.md index 94aa816e80..ce63053a52 100644 --- a/src/group-theory/dependent-products-abelian-groups.lagda.md +++ b/src/group-theory/dependent-products-abelian-groups.lagda.md @@ -1,23 +1,29 @@ # Dependent products of abelian groups ```agda -module group-theory.dependent-products-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.dependent-products-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.dependent-products-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.dependent-products-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/dependent-products-commutative-monoids.lagda.md b/src/group-theory/dependent-products-commutative-monoids.lagda.md index 6d9fdd11e9..c0f1835639 100644 --- a/src/group-theory/dependent-products-commutative-monoids.lagda.md +++ b/src/group-theory/dependent-products-commutative-monoids.lagda.md @@ -1,21 +1,27 @@ # Dependent products of commutative monoids ```agda -module group-theory.dependent-products-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.dependent-products-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.dependent-products-monoids -open import group-theory.monoids +open import group-theory.commutative-monoids funext +open import group-theory.dependent-products-monoids funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/dependent-products-groups.lagda.md b/src/group-theory/dependent-products-groups.lagda.md index 6c0d59730a..90daf2af78 100644 --- a/src/group-theory/dependent-products-groups.lagda.md +++ b/src/group-theory/dependent-products-groups.lagda.md @@ -1,22 +1,28 @@ # Dependent products of groups ```agda -module group-theory.dependent-products-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.dependent-products-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.dependent-products-semigroups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.dependent-products-semigroups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/dependent-products-monoids.lagda.md b/src/group-theory/dependent-products-monoids.lagda.md index f2602a6622..504bdf5238 100644 --- a/src/group-theory/dependent-products-monoids.lagda.md +++ b/src/group-theory/dependent-products-monoids.lagda.md @@ -1,21 +1,27 @@ # Dependent products of monoids ```agda -module group-theory.dependent-products-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.dependent-products-monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.dependent-products-semigroups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.dependent-products-semigroups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/dependent-products-semigroups.lagda.md b/src/group-theory/dependent-products-semigroups.lagda.md index 5194e020a4..987257ff92 100644 --- a/src/group-theory/dependent-products-semigroups.lagda.md +++ b/src/group-theory/dependent-products-semigroups.lagda.md @@ -1,19 +1,25 @@ # Dependent products of semigroups ```agda -module group-theory.dependent-products-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.dependent-products-semigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/dihedral-group-construction.lagda.md b/src/group-theory/dihedral-group-construction.lagda.md index 6aba36c7df..8530ab3444 100644 --- a/src/group-theory/dihedral-group-construction.lagda.md +++ b/src/group-theory/dihedral-group-construction.lagda.md @@ -1,24 +1,29 @@ # The dihedral group construction ```agda -module group-theory.dihedral-group-construction where +open import foundation.function-extensionality-axiom + +module + group-theory.dihedral-group-construction + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types -open import foundation.identity-types -open import foundation.sets +open import foundation.equality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/dihedral-groups.lagda.md b/src/group-theory/dihedral-groups.lagda.md index 83fd4ee34a..353ecf5064 100644 --- a/src/group-theory/dihedral-groups.lagda.md +++ b/src/group-theory/dihedral-groups.lagda.md @@ -1,19 +1,24 @@ # The dihedral groups ```agda -module group-theory.dihedral-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.dihedral-groups + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.standard-cyclic-groups +open import elementary-number-theory.standard-cyclic-groups funext open import foundation.universe-levels -open import group-theory.dihedral-group-construction -open import group-theory.groups +open import group-theory.dihedral-group-construction funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/e8-lattice.lagda.md b/src/group-theory/e8-lattice.lagda.md index 85b7ccc933..f54f1a79fb 100644 --- a/src/group-theory/e8-lattice.lagda.md +++ b/src/group-theory/e8-lattice.lagda.md @@ -1,20 +1,25 @@ # The `E₈`-lattice ```agda -module group-theory.e8-lattice where +open import foundation.function-extensionality-axiom + +module + group-theory.e8-lattice + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers -open import foundation.equality-coproduct-types -open import foundation.sets +open import foundation.equality-coproduct-types funext +open import foundation.sets funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/group-theory/elements-of-finite-order-groups.lagda.md b/src/group-theory/elements-of-finite-order-groups.lagda.md index de05cf476b..52ce753ef8 100644 --- a/src/group-theory/elements-of-finite-order-groups.lagda.md +++ b/src/group-theory/elements-of-finite-order-groups.lagda.md @@ -1,23 +1,28 @@ # Elements of finite order ```agda -module group-theory.elements-of-finite-order-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.elements-of-finite-order-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.nonzero-integers funext -open import foundation.existential-quantification -open import foundation.propositions +open import foundation.existential-quantification funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.orders-of-elements-groups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-elements-groups +open import group-theory.groups funext +open import group-theory.orders-of-elements-groups funext +open import group-theory.subgroups funext +open import group-theory.subgroups funext-generated-by-elements-groups ```
diff --git a/src/group-theory/embeddings-abelian-groups.lagda.md b/src/group-theory/embeddings-abelian-groups.lagda.md index 9061f2dbe1..2e027bd62e 100644 --- a/src/group-theory/embeddings-abelian-groups.lagda.md +++ b/src/group-theory/embeddings-abelian-groups.lagda.md @@ -1,19 +1,24 @@ # Embeddings of abelian groups ```agda -module group-theory.embeddings-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.embeddings-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.embeddings-groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.subgroups-abelian-groups +open import group-theory.abelian-groups funext +open import group-theory.embeddings-groups funext +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.subgroups-abelian-groups funext ```
diff --git a/src/group-theory/embeddings-groups.lagda.md b/src/group-theory/embeddings-groups.lagda.md index 9d7b7c5dab..c034efab85 100644 --- a/src/group-theory/embeddings-groups.lagda.md +++ b/src/group-theory/embeddings-groups.lagda.md @@ -1,19 +1,24 @@ # Embeddings of groups ```agda -module group-theory.embeddings-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.embeddings-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.subgroups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.subgroups funext ```
diff --git a/src/group-theory/endomorphism-rings-abelian-groups.lagda.md b/src/group-theory/endomorphism-rings-abelian-groups.lagda.md index d3dfb679a9..f1e2034d14 100644 --- a/src/group-theory/endomorphism-rings-abelian-groups.lagda.md +++ b/src/group-theory/endomorphism-rings-abelian-groups.lagda.md @@ -1,7 +1,12 @@ # The endomorphism rings of abelian groups ```agda -module group-theory.endomorphism-rings-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.endomorphism-rings-abelian-groups + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module group-theory.endomorphism-rings-abelian-groups where open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.addition-homomorphisms-abelian-groups -open import group-theory.homomorphisms-abelian-groups +open import group-theory.abelian-groups funext +open import group-theory.addition-homomorphisms-abelian-groups funext +open import group-theory.homomorphisms-abelian-groups funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/group-theory/epimorphisms-groups.lagda.md b/src/group-theory/epimorphisms-groups.lagda.md index be41b90450..c590731345 100644 --- a/src/group-theory/epimorphisms-groups.lagda.md +++ b/src/group-theory/epimorphisms-groups.lagda.md @@ -1,21 +1,26 @@ # Epimorphisms in groups ```agda -module group-theory.epimorphisms-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.epimorphisms-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.epimorphisms-in-large-precategories +open import category-theory.epimorphisms-in-large-precategories funext -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.precategory-of-groups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.precategory-of-groups funext ```
diff --git a/src/group-theory/equivalences-concrete-group-actions.lagda.md b/src/group-theory/equivalences-concrete-group-actions.lagda.md index 27c37431a5..ed39de48f7 100644 --- a/src/group-theory/equivalences-concrete-group-actions.lagda.md +++ b/src/group-theory/equivalences-concrete-group-actions.lagda.md @@ -1,27 +1,32 @@ # Equivalences of concrete group actions ```agda -module group-theory.equivalences-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.equivalences-concrete-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.1-types +open import foundation.1-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.embeddings funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-group-actions +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext +open import group-theory.homomorphisms-concrete-group-actions funext ```
diff --git a/src/group-theory/equivalences-concrete-groups.lagda.md b/src/group-theory/equivalences-concrete-groups.lagda.md index 52676af8d8..41b0a46531 100644 --- a/src/group-theory/equivalences-concrete-groups.lagda.md +++ b/src/group-theory/equivalences-concrete-groups.lagda.md @@ -1,25 +1,30 @@ # Equivalences of concrete groups ```agda -module group-theory.equivalences-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.equivalences-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.concrete-groups +open import group-theory.concrete-groups funext -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.equivalences-higher-groups funext +open import higher-group-theory.higher-groups funext ```
diff --git a/src/group-theory/equivalences-group-actions.lagda.md b/src/group-theory/equivalences-group-actions.lagda.md index cabae428b7..03d4a21532 100644 --- a/src/group-theory/equivalences-group-actions.lagda.md +++ b/src/group-theory/equivalences-group-actions.lagda.md @@ -1,34 +1,39 @@ # Equivalences of group actions ```agda -module group-theory.equivalences-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.equivalences-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.homomorphisms-groups -open import group-theory.symmetric-groups +open import group-theory.group-actions funext +open import group-theory.groups funext +open import group-theory.homomorphisms-group-actions funext +open import group-theory.homomorphisms-groups funext +open import group-theory.symmetric-groups funext ```
diff --git a/src/group-theory/equivalences-semigroups.lagda.md b/src/group-theory/equivalences-semigroups.lagda.md index b0ec4a907d..0928e3a427 100644 --- a/src/group-theory/equivalences-semigroups.lagda.md +++ b/src/group-theory/equivalences-semigroups.lagda.md @@ -1,28 +1,34 @@ # Equivalences between semigroups ```agda -module group-theory.equivalences-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.equivalences-semigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups +open import group-theory.homomorphisms-semigroups funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/exponents-abelian-groups.lagda.md b/src/group-theory/exponents-abelian-groups.lagda.md index 1f2bfdd78f..920d194193 100644 --- a/src/group-theory/exponents-abelian-groups.lagda.md +++ b/src/group-theory/exponents-abelian-groups.lagda.md @@ -1,19 +1,24 @@ # Exponents of abelian groups ```agda -module group-theory.exponents-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.exponents-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.exponents-groups -open import group-theory.subgroups-abelian-groups +open import group-theory.abelian-groups funext +open import group-theory.exponents-groups funext +open import group-theory.subgroups-abelian-groups funext ```
diff --git a/src/group-theory/exponents-groups.lagda.md b/src/group-theory/exponents-groups.lagda.md index 4df222fea0..e266800ed5 100644 --- a/src/group-theory/exponents-groups.lagda.md +++ b/src/group-theory/exponents-groups.lagda.md @@ -1,21 +1,26 @@ # Exponents of groups ```agda -module group-theory.exponents-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.exponents-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator -open import group-theory.groups -open import group-theory.intersections-subgroups-groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.subgroups +open import group-theory.free-groups-with-one-generator funext +open import group-theory.groups funext +open import group-theory.intersections-subgroups-groups funext +open import group-theory.kernels-homomorphisms-groups funext +open import group-theory.subgroups funext ```
diff --git a/src/group-theory/free-concrete-group-actions.lagda.md b/src/group-theory/free-concrete-group-actions.lagda.md index 7eb0462d9f..9f76b2fb9b 100644 --- a/src/group-theory/free-concrete-group-actions.lagda.md +++ b/src/group-theory/free-concrete-group-actions.lagda.md @@ -1,22 +1,27 @@ # Free concrete group actions ```agda -module group-theory.free-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.free-concrete-group-actions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions -open import foundation.sets +open import foundation.function-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext -open import higher-group-theory.free-higher-group-actions +open import higher-group-theory.free-higher-group-actions funext ```
diff --git a/src/group-theory/free-groups-with-one-generator.lagda.md b/src/group-theory/free-groups-with-one-generator.lagda.md index e66fdcf4d7..0d8a3204ff 100644 --- a/src/group-theory/free-groups-with-one-generator.lagda.md +++ b/src/group-theory/free-groups-with-one-generator.lagda.md @@ -1,31 +1,36 @@ # Free groups with one generator ```agda -module group-theory.free-groups-with-one-generator where +open import foundation.function-extensionality-axiom + +module + group-theory.free-groups-with-one-generator + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.group-of-integers funext open import elementary-number-theory.integers open import foundation.action-on-identifications-functions -open import foundation.contractible-maps +open import foundation.contractible-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.integer-powers-of-elements-groups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.integer-powers-of-elements-groups funext -open import structured-types.initial-pointed-type-equipped-with-automorphism +open import structured-types.initial-pointed-type-equipped-with-automorphism funext ```
diff --git a/src/group-theory/full-subgroups.lagda.md b/src/group-theory/full-subgroups.lagda.md index 5200efc0f3..3649a9fe91 100644 --- a/src/group-theory/full-subgroups.lagda.md +++ b/src/group-theory/full-subgroups.lagda.md @@ -1,23 +1,28 @@ # The full subgroup of a group ```agda -module group-theory.full-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.full-subgroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.full-subtypes funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext ```
diff --git a/src/group-theory/full-subsemigroups.lagda.md b/src/group-theory/full-subsemigroups.lagda.md index 507941cd28..5f028b21b6 100644 --- a/src/group-theory/full-subsemigroups.lagda.md +++ b/src/group-theory/full-subsemigroups.lagda.md @@ -1,24 +1,29 @@ # The full subsemigroup of a semigroup ```agda -module group-theory.full-subsemigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.full-subsemigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.full-subtypes funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.equivalences-semigroups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-semigroups -open import group-theory.semigroups -open import group-theory.subsemigroups -open import group-theory.subsets-semigroups +open import group-theory.equivalences-semigroups funext +open import group-theory.homomorphisms-semigroups funext +open import group-theory.isomorphisms-semigroups funext +open import group-theory.semigroups funext +open import group-theory.subsemigroups funext +open import group-theory.subsets-semigroups funext ```
diff --git a/src/group-theory/function-abelian-groups.lagda.md b/src/group-theory/function-abelian-groups.lagda.md index 6836e3eed4..517e058567 100644 --- a/src/group-theory/function-abelian-groups.lagda.md +++ b/src/group-theory/function-abelian-groups.lagda.md @@ -1,21 +1,26 @@ # Function groups of abelian groups ```agda -module group-theory.function-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.function-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.dependent-products-abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.dependent-products-abelian-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/function-commutative-monoids.lagda.md b/src/group-theory/function-commutative-monoids.lagda.md index 57b44087dc..09ffccec4c 100644 --- a/src/group-theory/function-commutative-monoids.lagda.md +++ b/src/group-theory/function-commutative-monoids.lagda.md @@ -1,19 +1,24 @@ # Function commutative monoids ```agda -module group-theory.function-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.function-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.dependent-products-commutative-monoids -open import group-theory.monoids +open import group-theory.commutative-monoids funext +open import group-theory.dependent-products-commutative-monoids funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/function-groups.lagda.md b/src/group-theory/function-groups.lagda.md index b9d8cff7aa..23dbecd6aa 100644 --- a/src/group-theory/function-groups.lagda.md +++ b/src/group-theory/function-groups.lagda.md @@ -1,21 +1,26 @@ # Function groups ```agda -module group-theory.function-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.function-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.dependent-products-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.dependent-products-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/function-monoids.lagda.md b/src/group-theory/function-monoids.lagda.md index bef75c807a..59a4b5bc6a 100644 --- a/src/group-theory/function-monoids.lagda.md +++ b/src/group-theory/function-monoids.lagda.md @@ -1,19 +1,24 @@ # Function monoids ```agda -module group-theory.function-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.function-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.dependent-products-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.dependent-products-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/function-semigroups.lagda.md b/src/group-theory/function-semigroups.lagda.md index 06605fc58c..e0a4e6c046 100644 --- a/src/group-theory/function-semigroups.lagda.md +++ b/src/group-theory/function-semigroups.lagda.md @@ -1,18 +1,23 @@ # Function semigroups ```agda -module group-theory.function-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.function-semigroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.dependent-products-semigroups -open import group-theory.semigroups +open import group-theory.dependent-products-semigroups funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/functoriality-quotient-groups.lagda.md b/src/group-theory/functoriality-quotient-groups.lagda.md index 6b48fc225f..e843537518 100644 --- a/src/group-theory/functoriality-quotient-groups.lagda.md +++ b/src/group-theory/functoriality-quotient-groups.lagda.md @@ -3,27 +3,32 @@ ```agda {-# OPTIONS --lossy-unification #-} -module group-theory.functoriality-quotient-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.functoriality-quotient-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commuting-squares-of-group-homomorphisms -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups -open import group-theory.normal-subgroups -open import group-theory.nullifying-group-homomorphisms -open import group-theory.quotient-groups +open import group-theory.commuting-squares-of-group-homomorphisms funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-groups funext-equipped-with-normal-subgroups +open import group-theory.normal-subgroups funext +open import group-theory.nullifying-group-homomorphisms funext +open import group-theory.quotient-groups funext ```
diff --git a/src/group-theory/furstenberg-groups.lagda.md b/src/group-theory/furstenberg-groups.lagda.md index a9e760780e..695a53a430 100644 --- a/src/group-theory/furstenberg-groups.lagda.md +++ b/src/group-theory/furstenberg-groups.lagda.md @@ -1,17 +1,22 @@ # Furstenberg groups ```agda -module group-theory.furstenberg-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.furstenberg-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/group-theory/generating-elements-groups.lagda.md b/src/group-theory/generating-elements-groups.lagda.md index f0b26019b2..db998672e7 100644 --- a/src/group-theory/generating-elements-groups.lagda.md +++ b/src/group-theory/generating-elements-groups.lagda.md @@ -1,54 +1,59 @@ # Generating elements of groups ```agda -module group-theory.generating-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.generating-elements-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.images -open import foundation.injective-maps -open import foundation.propositional-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.injective-maps funext +open import foundation.propositional-maps funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.addition-homomorphisms-abelian-groups -open import group-theory.commuting-elements-groups -open import group-theory.conjugation -open import group-theory.endomorphism-rings-abelian-groups -open import group-theory.free-groups-with-one-generator -open import group-theory.full-subgroups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.integer-multiples-of-elements-abelian-groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.isomorphisms-abelian-groups -open import group-theory.normal-subgroups -open import group-theory.quotient-groups -open import group-theory.subgroups-generated-by-elements-groups -open import group-theory.subsets-groups -open import group-theory.trivial-group-homomorphisms - -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings -open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups +open import group-theory.abelian-groups funext +open import group-theory.addition-homomorphisms-abelian-groups funext +open import group-theory.commuting-elements-groups funext +open import group-theory.conjugation funext +open import group-theory.endomorphism-rings-abelian-groups funext +open import group-theory.free-groups-with-one-generator funext +open import group-theory.full-subgroups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.integer-multiples-of-elements-abelian-groups funext +open import group-theory.integer-powers-of-elements-groups funext +open import group-theory.isomorphisms-abelian-groups funext +open import group-theory.normal-subgroups funext +open import group-theory.quotient-groups funext +open import group-theory.subgroups-generated-by-elements-groups funext +open import group-theory.subsets-groups funext +open import group-theory.trivial-group-homomorphisms funext + +open import ring-theory.integer-multiples-of-elements-rings funext +open import ring-theory.rings funext +open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups funext ```
diff --git a/src/group-theory/generating-sets-groups.lagda.md b/src/group-theory/generating-sets-groups.lagda.md index 513c92471a..dc386022fb 100644 --- a/src/group-theory/generating-sets-groups.lagda.md +++ b/src/group-theory/generating-sets-groups.lagda.md @@ -1,7 +1,12 @@ # Generating sets of groups ```agda -module group-theory.generating-sets-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.generating-sets-groups + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module group-theory.generating-sets-groups where ```agda open import foundation.universe-levels -open import group-theory.full-subgroups -open import group-theory.groups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups +open import group-theory.full-subgroups funext +open import group-theory.groups funext +open import group-theory.subgroups-generated-by-subsets-groups funext +open import group-theory.subsets-groups funext ```
diff --git a/src/group-theory/group-actions.lagda.md b/src/group-theory/group-actions.lagda.md index ae7b61578f..27cbac2328 100644 --- a/src/group-theory/group-actions.lagda.md +++ b/src/group-theory/group-actions.lagda.md @@ -1,7 +1,12 @@ # Group actions ```agda -module group-theory.group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.group-actions + (funext : function-extensionality) + where ```
Imports @@ -9,18 +14,17 @@ module group-theory.group-actions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.symmetric-groups -open import group-theory.trivial-group-homomorphisms +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.symmetric-groups funext +open import group-theory.trivial-group-homomorphisms funext ```
diff --git a/src/group-theory/groups.lagda.md b/src/group-theory/groups.lagda.md index ae04f5eb0d..3c936169c1 100644 --- a/src/group-theory/groups.lagda.md +++ b/src/group-theory/groups.lagda.md @@ -1,7 +1,12 @@ # Abstract groups ```agda -module group-theory.groups where +open import foundation.function-extensionality-axiom + +module + group-theory.groups + (funext : function-extensionality) + where ```
Imports @@ -9,34 +14,35 @@ module group-theory.groups where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.invertible-elements-monoids -open import group-theory.monoids -open import group-theory.products-of-elements-monoids -open import group-theory.semigroups +open import group-theory.invertible-elements-monoids funext +open import group-theory.monoids funext +open import group-theory.products-of-elements-monoids funext +open import group-theory.semigroups funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import structured-types.h-spaces +open import structured-types.h-spaces funext open import structured-types.pointed-types -open import structured-types.pointed-types-equipped-with-automorphisms +open import structured-types.pointed-types-equipped-with-automorphisms funext ```
diff --git a/src/group-theory/homomorphisms-abelian-groups.lagda.md b/src/group-theory/homomorphisms-abelian-groups.lagda.md index 172b824ed0..1930bf59c7 100644 --- a/src/group-theory/homomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/homomorphisms-abelian-groups.lagda.md @@ -1,27 +1,32 @@ # Homomorphisms of abelian groups ```agda -module group-theory.homomorphisms-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-categories +open import category-theory.large-categories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.category-of-abelian-groups -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups +open import group-theory.abelian-groups funext +open import group-theory.category-of-abelian-groups funext +open import group-theory.homomorphisms-commutative-monoids funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-semigroups funext ```
diff --git a/src/group-theory/homomorphisms-commutative-monoids.lagda.md b/src/group-theory/homomorphisms-commutative-monoids.lagda.md index b5783ad749..9bd3081a00 100644 --- a/src/group-theory/homomorphisms-commutative-monoids.lagda.md +++ b/src/group-theory/homomorphisms-commutative-monoids.lagda.md @@ -1,21 +1,26 @@ # Homomorphisms of commutative monoids ```agda -module group-theory.homomorphisms-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.homomorphisms-monoids -open import group-theory.homomorphisms-semigroups +open import group-theory.commutative-monoids funext +open import group-theory.homomorphisms-monoids funext +open import group-theory.homomorphisms-semigroups funext ```
diff --git a/src/group-theory/homomorphisms-concrete-group-actions.lagda.md b/src/group-theory/homomorphisms-concrete-group-actions.lagda.md index 62057b8e87..4244f46732 100644 --- a/src/group-theory/homomorphisms-concrete-group-actions.lagda.md +++ b/src/group-theory/homomorphisms-concrete-group-actions.lagda.md @@ -1,26 +1,32 @@ # Morphisms of concrete group actions ```agda -module group-theory.homomorphisms-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-concrete-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.0-connected-types funext +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext ```
diff --git a/src/group-theory/homomorphisms-concrete-groups.lagda.md b/src/group-theory/homomorphisms-concrete-groups.lagda.md index d61de489f6..f187ff3e1a 100644 --- a/src/group-theory/homomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/homomorphisms-concrete-groups.lagda.md @@ -1,24 +1,29 @@ # Homomorphisms of concrete groups ```agda -module group-theory.homomorphisms-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-groups +open import group-theory.concrete-groups funext +open import group-theory.homomorphisms-groups funext -open import higher-group-theory.homomorphisms-higher-groups +open import higher-group-theory.homomorphisms-higher-groups funext ```
diff --git a/src/group-theory/homomorphisms-generated-subgroups.lagda.md b/src/group-theory/homomorphisms-generated-subgroups.lagda.md index 4f2f8359a6..f7458d93e7 100644 --- a/src/group-theory/homomorphisms-generated-subgroups.lagda.md +++ b/src/group-theory/homomorphisms-generated-subgroups.lagda.md @@ -1,44 +1,49 @@ # Homomorphisms of generated subgroups ```agda -module group-theory.homomorphisms-generated-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-generated-subgroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.embeddings -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.truncated-types +open import foundation.dependent-products-truncated-types funext +open import foundation.embeddings funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.epimorphisms-groups -open import group-theory.full-subgroups -open import group-theory.generating-sets-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups +open import group-theory.epimorphisms-groups funext +open import group-theory.full-subgroups funext +open import group-theory.generating-sets-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.subgroups funext +open import group-theory.subgroups funext-generated-by-subsets-groups +open import group-theory.subsets-groups funext open import lists.lists -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/group-theory/homomorphisms-group-actions.lagda.md b/src/group-theory/homomorphisms-group-actions.lagda.md index 7c488f7072..113795f819 100644 --- a/src/group-theory/homomorphisms-group-actions.lagda.md +++ b/src/group-theory/homomorphisms-group-actions.lagda.md @@ -1,30 +1,35 @@ # Homomorphisms of group actions ```agda -module group-theory.homomorphisms-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle open import foundation.telescopes -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md b/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md index 824132ed84..70c0274522 100644 --- a/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md +++ b/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md @@ -1,23 +1,28 @@ # Homomorphisms of groups equipped with normal subgroups ```agda -module group-theory.homomorphisms-groups-equipped-with-normal-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-groups-equipped-with-normal-subgroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.pullbacks-subgroups -open import group-theory.subgroups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.normal-subgroups funext +open import group-theory.pullbacks-subgroups funext +open import group-theory.subgroups funext ```
diff --git a/src/group-theory/homomorphisms-groups.lagda.md b/src/group-theory/homomorphisms-groups.lagda.md index a4e286a07f..1d779ab78a 100644 --- a/src/group-theory/homomorphisms-groups.lagda.md +++ b/src/group-theory/homomorphisms-groups.lagda.md @@ -1,25 +1,30 @@ # Homomorphisms of groups ```agda -module group-theory.homomorphisms-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-monoids -open import group-theory.homomorphisms-semigroups +open import group-theory.groups funext +open import group-theory.homomorphisms-monoids funext +open import group-theory.homomorphisms-semigroups funext ```
diff --git a/src/group-theory/homomorphisms-monoids.lagda.md b/src/group-theory/homomorphisms-monoids.lagda.md index f8c37265bd..dae6f01976 100644 --- a/src/group-theory/homomorphisms-monoids.lagda.md +++ b/src/group-theory/homomorphisms-monoids.lagda.md @@ -1,7 +1,12 @@ # Homomorphisms of monoids ```agda -module group-theory.homomorphisms-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-monoids + (funext : function-extensionality) + where ```
Imports @@ -9,20 +14,20 @@ module group-theory.homomorphisms-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.invertible-elements-monoids -open import group-theory.monoids +open import group-theory.homomorphisms-semigroups funext +open import group-theory.invertible-elements-monoids funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/homomorphisms-semigroups.lagda.md b/src/group-theory/homomorphisms-semigroups.lagda.md index b00a30a3fa..562bfe04a6 100644 --- a/src/group-theory/homomorphisms-semigroups.lagda.md +++ b/src/group-theory/homomorphisms-semigroups.lagda.md @@ -1,7 +1,12 @@ # Homomorphisms of semigroups ```agda -module group-theory.homomorphisms-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.homomorphisms-semigroups + (funext : function-extensionality) + where ```
Imports @@ -9,19 +14,19 @@ module group-theory.homomorphisms-semigroups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/homotopy-automorphism-groups.lagda.md b/src/group-theory/homotopy-automorphism-groups.lagda.md index 0e344923e4..2cb60e575b 100644 --- a/src/group-theory/homotopy-automorphism-groups.lagda.md +++ b/src/group-theory/homotopy-automorphism-groups.lagda.md @@ -1,20 +1,25 @@ # Homotopy automorphism groups ```agda -module group-theory.homotopy-automorphism-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.homotopy-automorphism-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.truncation-levels -open import foundation.truncations +open import foundation.truncations funext open import foundation.universe-levels -open import group-theory.automorphism-groups -open import group-theory.concrete-groups +open import group-theory.automorphism-groups funext +open import group-theory.concrete-groups funext -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types ``` diff --git a/src/group-theory/images-of-group-homomorphisms.lagda.md b/src/group-theory/images-of-group-homomorphisms.lagda.md index 90366ef507..d45d2db35d 100644 --- a/src/group-theory/images-of-group-homomorphisms.lagda.md +++ b/src/group-theory/images-of-group-homomorphisms.lagda.md @@ -1,31 +1,36 @@ # Images of group homomorphisms ```agda -module group-theory.images-of-group-homomorphisms where +open import foundation.function-extensionality-axiom + +module + group-theory.images-of-group-homomorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.images -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.universal-property-image +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.images funext-subtypes +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext +open import foundation.universal-property-image funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.pullbacks-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.pullbacks-subgroups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.galois-connections-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext ```
diff --git a/src/group-theory/images-of-semigroup-homomorphisms.lagda.md b/src/group-theory/images-of-semigroup-homomorphisms.lagda.md index eced916451..7ab544ee1b 100644 --- a/src/group-theory/images-of-semigroup-homomorphisms.lagda.md +++ b/src/group-theory/images-of-semigroup-homomorphisms.lagda.md @@ -1,30 +1,35 @@ # Images of semigroup homomorphisms ```agda -module group-theory.images-of-semigroup-homomorphisms where +open import foundation.function-extensionality-axiom + +module + group-theory.images-of-semigroup-homomorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.images -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.universal-property-image +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.images funext-subtypes +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.universal-property-image funext open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.pullbacks-subsemigroups -open import group-theory.semigroups -open import group-theory.subsemigroups -open import group-theory.subsets-semigroups +open import group-theory.homomorphisms-semigroups funext +open import group-theory.pullbacks-subsemigroups funext +open import group-theory.semigroups funext +open import group-theory.subsemigroups funext +open import group-theory.subsets-semigroups funext -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.galois-connections-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext ```
diff --git a/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md b/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md index e592961eb4..a22caab59c 100644 --- a/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md +++ b/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md @@ -1,27 +1,32 @@ # Integer multiples of elements in abelian groups ```agda -module group-theory.integer-multiples-of-elements-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.integer-multiples-of-elements-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.multiples-of-elements-abelian-groups +open import group-theory.abelian-groups funext +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.integer-powers-of-elements-groups funext +open import group-theory.multiples-of-elements-abelian-groups funext ```
diff --git a/src/group-theory/integer-powers-of-elements-groups.lagda.md b/src/group-theory/integer-powers-of-elements-groups.lagda.md index 47de6edf13..3c9af34156 100644 --- a/src/group-theory/integer-powers-of-elements-groups.lagda.md +++ b/src/group-theory/integer-powers-of-elements-groups.lagda.md @@ -1,31 +1,36 @@ # Integer powers of elements of groups ```agda -module group-theory.integer-powers-of-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.integer-powers-of-elements-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.iterating-automorphisms -open import foundation.propositions +open import foundation.coproduct-types funext +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.iterating-automorphisms funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.commuting-elements-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.powers-of-elements-groups +open import group-theory.commuting-elements-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.powers-of-elements-groups funext -open import structured-types.initial-pointed-type-equipped-with-automorphism +open import structured-types.initial-pointed-type-equipped-with-automorphism funext ```
diff --git a/src/group-theory/intersections-subgroups-abelian-groups.lagda.md b/src/group-theory/intersections-subgroups-abelian-groups.lagda.md index fe6d807e06..bc42c927cb 100644 --- a/src/group-theory/intersections-subgroups-abelian-groups.lagda.md +++ b/src/group-theory/intersections-subgroups-abelian-groups.lagda.md @@ -1,18 +1,23 @@ # Intersections of subgroups of abelian groups ```agda -module group-theory.intersections-subgroups-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.intersections-subgroups-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.intersections-subgroups-groups -open import group-theory.subgroups-abelian-groups +open import group-theory.abelian-groups funext +open import group-theory.intersections-subgroups-groups funext +open import group-theory.subgroups-abelian-groups funext ```
diff --git a/src/group-theory/intersections-subgroups-groups.lagda.md b/src/group-theory/intersections-subgroups-groups.lagda.md index 485c7fe03b..3bf0d27920 100644 --- a/src/group-theory/intersections-subgroups-groups.lagda.md +++ b/src/group-theory/intersections-subgroups-groups.lagda.md @@ -1,22 +1,27 @@ # Intersections of subgroups of groups ```agda -module group-theory.intersections-subgroups-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.intersections-subgroups-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.intersections-subtypes -open import foundation.subtypes +open import foundation.intersections-subtypes funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.groups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext -open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext ```
diff --git a/src/group-theory/inverse-semigroups.lagda.md b/src/group-theory/inverse-semigroups.lagda.md index 983cf5a04e..c75d2b828a 100644 --- a/src/group-theory/inverse-semigroups.lagda.md +++ b/src/group-theory/inverse-semigroups.lagda.md @@ -1,20 +1,25 @@ # Inverse semigroups ```agda -module group-theory.inverse-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.inverse-semigroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/invertible-elements-monoids.lagda.md b/src/group-theory/invertible-elements-monoids.lagda.md index c50cf77558..5706614a84 100644 --- a/src/group-theory/invertible-elements-monoids.lagda.md +++ b/src/group-theory/invertible-elements-monoids.lagda.md @@ -1,27 +1,32 @@ # Invertible elements in monoids ```agda -module group-theory.invertible-elements-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.invertible-elements-monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext ```
diff --git a/src/group-theory/isomorphisms-abelian-groups.lagda.md b/src/group-theory/isomorphisms-abelian-groups.lagda.md index 9d7b07d36e..eed2b52f43 100644 --- a/src/group-theory/isomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/isomorphisms-abelian-groups.lagda.md @@ -1,29 +1,34 @@ # Isomorphisms of abelian groups ```agda -module group-theory.isomorphisms-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.isomorphisms-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.isomorphisms-groups +open import group-theory.abelian-groups funext +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.isomorphisms-groups funext ```
diff --git a/src/group-theory/isomorphisms-concrete-groups.lagda.md b/src/group-theory/isomorphisms-concrete-groups.lagda.md index 0815e62ecb..7e1143d51b 100644 --- a/src/group-theory/isomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/isomorphisms-concrete-groups.lagda.md @@ -1,18 +1,23 @@ # Isomorphisms of concrete groups ```agda -module group-theory.isomorphisms-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.isomorphisms-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.precategory-of-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.precategory-of-concrete-groups funext ```
diff --git a/src/group-theory/isomorphisms-group-actions.lagda.md b/src/group-theory/isomorphisms-group-actions.lagda.md index 49635eee09..82f4801b94 100644 --- a/src/group-theory/isomorphisms-group-actions.lagda.md +++ b/src/group-theory/isomorphisms-group-actions.lagda.md @@ -1,33 +1,39 @@ # Isomorphisms of group actions ```agda -module group-theory.isomorphisms-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.isomorphisms-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.equivalences-group-actions -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.precategory-of-group-actions +open import group-theory.equivalences-group-actions funext +open import group-theory.group-actions funext +open import group-theory.groups funext +open import group-theory.homomorphisms-group-actions funext +open import group-theory.precategory-of-group-actions funext ```
diff --git a/src/group-theory/isomorphisms-groups.lagda.md b/src/group-theory/isomorphisms-groups.lagda.md index 0ab46ae767..531aecb4c5 100644 --- a/src/group-theory/isomorphisms-groups.lagda.md +++ b/src/group-theory/isomorphisms-groups.lagda.md @@ -1,32 +1,37 @@ # Isomorphisms of groups ```agda -module group-theory.isomorphisms-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.isomorphisms-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.category-of-semigroups -open import group-theory.equivalences-semigroups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-semigroups -open import group-theory.precategory-of-groups +open import group-theory.category-of-semigroups funext +open import group-theory.equivalences-semigroups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.isomorphisms-semigroups funext +open import group-theory.precategory-of-groups funext ```
diff --git a/src/group-theory/isomorphisms-monoids.lagda.md b/src/group-theory/isomorphisms-monoids.lagda.md index 5ed4766a19..acfa2dac4c 100644 --- a/src/group-theory/isomorphisms-monoids.lagda.md +++ b/src/group-theory/isomorphisms-monoids.lagda.md @@ -1,26 +1,31 @@ # Isomorphisms of monoids ```agda -module group-theory.isomorphisms-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.isomorphisms-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.invertible-elements-monoids -open import group-theory.monoids -open import group-theory.precategory-of-monoids +open import group-theory.homomorphisms-monoids funext +open import group-theory.invertible-elements-monoids funext +open import group-theory.monoids funext +open import group-theory.precategory-of-monoids funext ```
diff --git a/src/group-theory/isomorphisms-semigroups.lagda.md b/src/group-theory/isomorphisms-semigroups.lagda.md index c6f29143b3..c537d21d8d 100644 --- a/src/group-theory/isomorphisms-semigroups.lagda.md +++ b/src/group-theory/isomorphisms-semigroups.lagda.md @@ -1,33 +1,37 @@ # Isomorphisms of semigroups ```agda -module group-theory.isomorphisms-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.isomorphisms-semigroups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.equivalences-semigroups -open import group-theory.homomorphisms-semigroups -open import group-theory.precategory-of-semigroups -open import group-theory.semigroups +open import group-theory.equivalences-semigroups funext +open import group-theory.homomorphisms-semigroups funext +open import group-theory.precategory-of-semigroups funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md index d189124e89..c530b22e44 100644 --- a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md +++ b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md @@ -1,7 +1,12 @@ # Iterated cartesian products of concrete groups ```agda -module group-theory.iterated-cartesian-products-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.iterated-cartesian-products-concrete-groups + (funext : function-extensionality) + where ```
Imports @@ -9,36 +14,36 @@ module group-theory.iterated-cartesian-products-concrete-groups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.1-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.0-connected-types funext +open import foundation.1-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.iterated-cartesian-product-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.sets -open import foundation.truncated-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.iterated-cartesian-product-types funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sets funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.cartesian-products-concrete-groups -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.trivial-concrete-groups +open import group-theory.cartesian-products-concrete-groups funext +open import group-theory.concrete-groups funext +open import group-theory.groups funext +open import group-theory.trivial-concrete-groups funext -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md b/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md index 9772e78e5d..79cd40d735 100644 --- a/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md @@ -1,7 +1,12 @@ # Kernels of homomorphisms between abelian groups ```agda -module group-theory.kernels-homomorphisms-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.kernels-homomorphisms-abelian-groups + (funext : function-extensionality) + where ```
Imports @@ -9,12 +14,12 @@ module group-theory.kernels-homomorphisms-abelian-groups where ```agda open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.embeddings-abelian-groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.subgroups-abelian-groups -open import group-theory.subsets-abelian-groups +open import group-theory.abelian-groups funext +open import group-theory.embeddings-abelian-groups funext +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.kernels-homomorphisms-groups funext +open import group-theory.subgroups-abelian-groups funext +open import group-theory.subsets-abelian-groups funext ```
diff --git a/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md b/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md index fa5ce10e8c..f5fb11db12 100644 --- a/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md @@ -1,26 +1,31 @@ # Kernels of homomorphisms of concrete groups ```agda -module group-theory.kernels-homomorphisms-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.kernels-homomorphisms-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.1-types -open import foundation.connected-components +open import foundation.0-connected-types funext +open import foundation.1-types funext +open import foundation.connected-components funext open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.sets -open import foundation.truncated-maps +open import foundation.fibers-of-maps funext +open import foundation.sets funext +open import foundation.truncated-maps funext open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.homomorphisms-concrete-groups funext -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types ``` diff --git a/src/group-theory/kernels-homomorphisms-groups.lagda.md b/src/group-theory/kernels-homomorphisms-groups.lagda.md index ba177596f8..6419141f21 100644 --- a/src/group-theory/kernels-homomorphisms-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-groups.lagda.md @@ -1,7 +1,12 @@ # Kernels of homomorphisms of groups ```agda -module group-theory.kernels-homomorphisms-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.kernels-homomorphisms-groups + (funext : function-extensionality) + where ```
Imports @@ -10,17 +15,17 @@ module group-theory.kernels-homomorphisms-groups where open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.embeddings-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.embeddings-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.normal-subgroups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext ```
diff --git a/src/group-theory/large-semigroups.lagda.md b/src/group-theory/large-semigroups.lagda.md index b4d82ec9cb..73a82f7e53 100644 --- a/src/group-theory/large-semigroups.lagda.md +++ b/src/group-theory/large-semigroups.lagda.md @@ -1,18 +1,23 @@ # Large semigroups ```agda -module group-theory.large-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.large-semigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/loop-groups-sets.lagda.md b/src/group-theory/loop-groups-sets.lagda.md index 15fdf92516..d9d5e08354 100644 --- a/src/group-theory/loop-groups-sets.lagda.md +++ b/src/group-theory/loop-groups-sets.lagda.md @@ -1,7 +1,12 @@ # Concrete automorphism groups on sets ```agda -module group-theory.loop-groups-sets where +open import foundation.function-extensionality-axiom + +module + group-theory.loop-groups-sets + (funext : function-extensionality) + where ```
Imports @@ -9,29 +14,30 @@ module group-theory.loop-groups-sets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-truncated-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.truncated-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.identity-truncated-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.truncated-types funext open import foundation.truncation-levels -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import group-theory.automorphism-groups -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-groups -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.symmetric-groups +open import group-theory.automorphism-groups funext +open import group-theory.concrete-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-semigroups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext +open import group-theory.symmetric-groups funext ```
diff --git a/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md b/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md index 5e895381eb..2ad2aa2bd4 100644 --- a/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md +++ b/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md @@ -1,21 +1,26 @@ # Mere equivalences of concrete group actions ```agda -module group-theory.mere-equivalences-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.mere-equivalences-concrete-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.functoriality-propositional-truncation -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.functoriality-propositional-truncation funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-group-actions +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext +open import group-theory.equivalences-concrete-group-actions funext ```
diff --git a/src/group-theory/mere-equivalences-group-actions.lagda.md b/src/group-theory/mere-equivalences-group-actions.lagda.md index 72c1412d12..7436e2f743 100644 --- a/src/group-theory/mere-equivalences-group-actions.lagda.md +++ b/src/group-theory/mere-equivalences-group-actions.lagda.md @@ -1,19 +1,24 @@ # Mere equivalences of group actions ```agda -module group-theory.mere-equivalences-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.mere-equivalences-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.equivalences-group-actions -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.equivalences-group-actions funext +open import group-theory.group-actions funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md b/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md index 6433e5bbad..6d31d54595 100644 --- a/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md +++ b/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md @@ -1,24 +1,29 @@ # Minkowski multiplication of subsets of a commutative monoid ```agda -module group-theory.minkowski-multiplication-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.minkowski-multiplication-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.powersets -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext +open import foundation.powersets funext +open import foundation.subtypes funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.minkowski-multiplication-monoids -open import group-theory.subsets-commutative-monoids +open import group-theory.commutative-monoids funext +open import group-theory.minkowski-multiplication-monoids funext +open import group-theory.subsets-commutative-monoids funext ```
diff --git a/src/group-theory/minkowski-multiplication-monoids.lagda.md b/src/group-theory/minkowski-multiplication-monoids.lagda.md index 8ce30adb8f..ebbd8b00f3 100644 --- a/src/group-theory/minkowski-multiplication-monoids.lagda.md +++ b/src/group-theory/minkowski-multiplication-monoids.lagda.md @@ -1,7 +1,12 @@ # Minkowski multiplication on subsets of a monoid ```agda -module group-theory.minkowski-multiplication-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.minkowski-multiplication-monoids + (funext : function-extensionality) + where ```
Imports @@ -9,18 +14,18 @@ module group-theory.minkowski-multiplication-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.powersets -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext +open import foundation.powersets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.minkowski-multiplication-semigroups -open import group-theory.monoids -open import group-theory.subsets-monoids +open import group-theory.minkowski-multiplication-semigroups funext +open import group-theory.monoids funext +open import group-theory.subsets-monoids funext ```
diff --git a/src/group-theory/minkowski-multiplication-semigroups.lagda.md b/src/group-theory/minkowski-multiplication-semigroups.lagda.md index 0fea876135..ab3cb551af 100644 --- a/src/group-theory/minkowski-multiplication-semigroups.lagda.md +++ b/src/group-theory/minkowski-multiplication-semigroups.lagda.md @@ -1,30 +1,35 @@ # Minkowski multiplication on subsets of a semigroup ```agda -module group-theory.minkowski-multiplication-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.minkowski-multiplication-semigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.powersets -open import foundation.sets -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext +open import foundation.powersets funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.semigroups -open import group-theory.subsets-semigroups +open import group-theory.semigroups funext +open import group-theory.subsets-semigroups funext -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext ```
diff --git a/src/group-theory/monoid-actions.lagda.md b/src/group-theory/monoid-actions.lagda.md index e195c009af..d504e9f202 100644 --- a/src/group-theory/monoid-actions.lagda.md +++ b/src/group-theory/monoid-actions.lagda.md @@ -1,7 +1,12 @@ # Monoid actions ```agda -module group-theory.monoid-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.monoid-actions + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,13 @@ module group-theory.monoid-actions where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.endomorphisms -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.sets +open import foundation.endomorphisms funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.monoids +open import group-theory.homomorphisms-monoids funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/monoids.lagda.md b/src/group-theory/monoids.lagda.md index 6a0c542cfc..50b0075ea2 100644 --- a/src/group-theory/monoids.lagda.md +++ b/src/group-theory/monoids.lagda.md @@ -1,25 +1,30 @@ # Monoids ```agda -module group-theory.monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.unit-type open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext -open import structured-types.h-spaces -open import structured-types.wild-monoids +open import structured-types.h-spaces funext +open import structured-types.wild-monoids funext ```
diff --git a/src/group-theory/monomorphisms-concrete-groups.lagda.md b/src/group-theory/monomorphisms-concrete-groups.lagda.md index 243579c974..1756c1ac04 100644 --- a/src/group-theory/monomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/monomorphisms-concrete-groups.lagda.md @@ -1,19 +1,24 @@ # Monomorphisms of concrete groups ```agda -module group-theory.monomorphisms-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.monomorphisms-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.homomorphisms-concrete-groups funext ```
diff --git a/src/group-theory/monomorphisms-groups.lagda.md b/src/group-theory/monomorphisms-groups.lagda.md index eeebe4fb6c..14e478ba69 100644 --- a/src/group-theory/monomorphisms-groups.lagda.md +++ b/src/group-theory/monomorphisms-groups.lagda.md @@ -1,21 +1,26 @@ # Monomorphisms in the category of groups ```agda -module group-theory.monomorphisms-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.monomorphisms-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.monomorphisms-in-large-precategories +open import category-theory.monomorphisms-in-large-precategories funext -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.precategory-of-groups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.precategory-of-groups funext ```
diff --git a/src/group-theory/multiples-of-elements-abelian-groups.lagda.md b/src/group-theory/multiples-of-elements-abelian-groups.lagda.md index 475f609270..c155942fb6 100644 --- a/src/group-theory/multiples-of-elements-abelian-groups.lagda.md +++ b/src/group-theory/multiples-of-elements-abelian-groups.lagda.md @@ -1,7 +1,12 @@ # Multiples of elements in abelian groups ```agda -module group-theory.multiples-of-elements-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.multiples-of-elements-abelian-groups + (funext : function-extensionality) + where ```
Imports @@ -11,12 +16,12 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.powers-of-elements-groups +open import group-theory.abelian-groups funext +open import group-theory.powers-of-elements-groups funext ```
diff --git a/src/group-theory/nontrivial-groups.lagda.md b/src/group-theory/nontrivial-groups.lagda.md index 725296c895..94edd22c3d 100644 --- a/src/group-theory/nontrivial-groups.lagda.md +++ b/src/group-theory/nontrivial-groups.lagda.md @@ -1,34 +1,39 @@ # Nontrivial groups ```agda -module group-theory.nontrivial-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.nontrivial-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.embeddings -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.disjunction funext +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.trivial-groups +open import group-theory.groups funext +open import group-theory.subgroups funext +open import group-theory.trivial-groups funext ```
diff --git a/src/group-theory/normal-closures-subgroups.lagda.md b/src/group-theory/normal-closures-subgroups.lagda.md index 704d72a7b2..cbd8238c61 100644 --- a/src/group-theory/normal-closures-subgroups.lagda.md +++ b/src/group-theory/normal-closures-subgroups.lagda.md @@ -1,32 +1,37 @@ # Normal closures of subgroups ```agda -module group-theory.normal-closures-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.normal-closures-subgroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.normal-subgroups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.normal-subgroups funext +open import group-theory.subgroups funext +open import group-theory.subgroups funext-generated-by-subsets-groups +open import group-theory.subsets-groups funext -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.galois-connections-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext ```
diff --git a/src/group-theory/normal-cores-subgroups.lagda.md b/src/group-theory/normal-cores-subgroups.lagda.md index 0e7447ffd7..73dd8d195c 100644 --- a/src/group-theory/normal-cores-subgroups.lagda.md +++ b/src/group-theory/normal-cores-subgroups.lagda.md @@ -1,7 +1,12 @@ # Normal cores of subgroups ```agda -module group-theory.normal-cores-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.normal-cores-subgroups + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,24 @@ module group-theory.normal-cores-subgroups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.identity-types -open import foundation.intersections-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.intersections-subtypes funext +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.normal-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.normal-subgroups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.galois-connections-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext ```
diff --git a/src/group-theory/normal-subgroups-concrete-groups.lagda.md b/src/group-theory/normal-subgroups-concrete-groups.lagda.md index 5e095bd183..890bccc91d 100644 --- a/src/group-theory/normal-subgroups-concrete-groups.lagda.md +++ b/src/group-theory/normal-subgroups-concrete-groups.lagda.md @@ -1,7 +1,12 @@ # Normal subgroups of concrete groups ```agda -module group-theory.normal-subgroups-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.normal-subgroups-concrete-groups + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module group-theory.normal-subgroups-concrete-groups where ```agda open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.subgroups-concrete-groups -open import group-theory.transitive-concrete-group-actions +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext +open import group-theory.subgroups-concrete-groups funext +open import group-theory.transitive-concrete-group-actions funext ```
diff --git a/src/group-theory/normal-subgroups.lagda.md b/src/group-theory/normal-subgroups.lagda.md index 1691141439..9fd10db5e7 100644 --- a/src/group-theory/normal-subgroups.lagda.md +++ b/src/group-theory/normal-subgroups.lagda.md @@ -1,40 +1,45 @@ # Normal subgroups ```agda -module group-theory.normal-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.normal-subgroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.congruence-relations-groups -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.subsets-groups - -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.posets -open import order-theory.preorders +open import group-theory.congruence-relations-groups funext +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext + +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/group-theory/normal-submonoids-commutative-monoids.lagda.md b/src/group-theory/normal-submonoids-commutative-monoids.lagda.md index 64d971f8b0..7734e0b99c 100644 --- a/src/group-theory/normal-submonoids-commutative-monoids.lagda.md +++ b/src/group-theory/normal-submonoids-commutative-monoids.lagda.md @@ -1,33 +1,38 @@ # Normal submonoids of commutative monoids ```agda -module group-theory.normal-submonoids-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.normal-submonoids-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.sets +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.retracts-of-types funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.congruence-relations-commutative-monoids -open import group-theory.monoids -open import group-theory.saturated-congruence-relations-commutative-monoids -open import group-theory.semigroups -open import group-theory.submonoids-commutative-monoids -open import group-theory.subsets-commutative-monoids +open import group-theory.commutative-monoids funext +open import group-theory.congruence-relations-commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.saturated-congruence-relations-commutative-monoids funext +open import group-theory.semigroups funext +open import group-theory.submonoids-commutative-monoids funext +open import group-theory.subsets-commutative-monoids funext ```
diff --git a/src/group-theory/normal-submonoids.lagda.md b/src/group-theory/normal-submonoids.lagda.md index 45aaa58a2c..7f9c773cf0 100644 --- a/src/group-theory/normal-submonoids.lagda.md +++ b/src/group-theory/normal-submonoids.lagda.md @@ -1,33 +1,38 @@ # Normal submonoids ```agda -module group-theory.normal-submonoids where +open import foundation.function-extensionality-axiom + +module + group-theory.normal-submonoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.sets +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.retracts-of-types funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.congruence-relations-monoids -open import group-theory.monoids -open import group-theory.saturated-congruence-relations-monoids -open import group-theory.semigroups -open import group-theory.submonoids -open import group-theory.subsets-monoids +open import group-theory.congruence-relations-monoids funext +open import group-theory.monoids funext +open import group-theory.saturated-congruence-relations-monoids funext +open import group-theory.semigroups funext +open import group-theory.submonoids funext +open import group-theory.subsets-monoids funext ```
diff --git a/src/group-theory/normalizer-subgroups.lagda.md b/src/group-theory/normalizer-subgroups.lagda.md index dfdbbcae1a..9ffaea0c0e 100644 --- a/src/group-theory/normalizer-subgroups.lagda.md +++ b/src/group-theory/normalizer-subgroups.lagda.md @@ -1,26 +1,31 @@ # Normalizer subgroups ```agda -module group-theory.normalizer-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.normalizer-subgroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.equality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext ```
diff --git a/src/group-theory/nullifying-group-homomorphisms.lagda.md b/src/group-theory/nullifying-group-homomorphisms.lagda.md index 92dfe9bbae..0f324b0e80 100644 --- a/src/group-theory/nullifying-group-homomorphisms.lagda.md +++ b/src/group-theory/nullifying-group-homomorphisms.lagda.md @@ -1,26 +1,31 @@ # Nullifying group homomorphisms ```agda -module group-theory.nullifying-group-homomorphisms where +open import foundation.function-extensionality-axiom + +module + group-theory.nullifying-group-homomorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.subtypes funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.normal-subgroups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-groups funext-equipped-with-normal-subgroups +open import group-theory.kernels-homomorphisms-groups funext +open import group-theory.normal-subgroups funext ```
diff --git a/src/group-theory/opposite-groups.lagda.md b/src/group-theory/opposite-groups.lagda.md index 1b8b84aac2..2b767bdc11 100644 --- a/src/group-theory/opposite-groups.lagda.md +++ b/src/group-theory/opposite-groups.lagda.md @@ -1,7 +1,12 @@ # The opposite of a group ```agda -module group-theory.opposite-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.opposite-groups + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module group-theory.opposite-groups where open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.groups -open import group-theory.isomorphisms-groups -open import group-theory.monoids -open import group-theory.opposite-semigroups +open import group-theory.groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.monoids funext +open import group-theory.opposite-semigroups funext ```
diff --git a/src/group-theory/opposite-semigroups.lagda.md b/src/group-theory/opposite-semigroups.lagda.md index 860ad6a7de..5ba26384b2 100644 --- a/src/group-theory/opposite-semigroups.lagda.md +++ b/src/group-theory/opposite-semigroups.lagda.md @@ -1,18 +1,23 @@ # The opposite of a semigroup ```agda -module group-theory.opposite-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.opposite-semigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md b/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md index d9cc6ffa5b..9f94459dd5 100644 --- a/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md +++ b/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md @@ -1,7 +1,12 @@ # The orbit-stabilizer theorem for concrete groups ```agda -module group-theory.orbit-stabilizer-theorem-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.orbit-stabilizer-theorem-concrete-groups + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module group-theory.orbit-stabilizer-theorem-concrete-groups where open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.mere-equivalences-concrete-group-actions -open import group-theory.stabilizer-groups-concrete-group-actions +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext +open import group-theory.mere-equivalences-concrete-group-actions funext +open import group-theory.stabilizer-groups-concrete-group-actions funext open import structured-types.pointed-types ``` diff --git a/src/group-theory/orbits-concrete-group-actions.lagda.md b/src/group-theory/orbits-concrete-group-actions.lagda.md index 1217af68ab..7c3012abf1 100644 --- a/src/group-theory/orbits-concrete-group-actions.lagda.md +++ b/src/group-theory/orbits-concrete-group-actions.lagda.md @@ -1,19 +1,24 @@ # Orbits of concrete group actions ```agda -module group-theory.orbits-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.orbits-concrete-group-actions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext ```
diff --git a/src/group-theory/orbits-group-actions.lagda.md b/src/group-theory/orbits-group-actions.lagda.md index 6cacd944fa..b3c0489c13 100644 --- a/src/group-theory/orbits-group-actions.lagda.md +++ b/src/group-theory/orbits-group-actions.lagda.md @@ -1,18 +1,23 @@ # Orbits of group actions ```agda -module group-theory.orbits-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.orbits-group-actions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/orders-of-elements-groups.lagda.md b/src/group-theory/orders-of-elements-groups.lagda.md index 78115f630b..61462134f3 100644 --- a/src/group-theory/orders-of-elements-groups.lagda.md +++ b/src/group-theory/orders-of-elements-groups.lagda.md @@ -1,23 +1,28 @@ # The order of an element in a group ```agda -module group-theory.orders-of-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.orders-of-elements-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext open import elementary-number-theory.integers open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator -open import group-theory.groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.free-groups-with-one-generator funext +open import group-theory.groups funext +open import group-theory.kernels-homomorphisms-groups funext +open import group-theory.normal-subgroups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext ```
diff --git a/src/group-theory/perfect-cores.lagda.md b/src/group-theory/perfect-cores.lagda.md index cb10247ebe..f5eb7f729c 100644 --- a/src/group-theory/perfect-cores.lagda.md +++ b/src/group-theory/perfect-cores.lagda.md @@ -1,18 +1,23 @@ # Perfect cores ```agda -module group-theory.perfect-cores where +open import foundation.function-extensionality-axiom + +module + group-theory.perfect-cores + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.logical-equivalences +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.perfect-subgroups -open import group-theory.subgroups +open import group-theory.groups funext +open import group-theory.perfect-subgroups funext +open import group-theory.subgroups funext ```
diff --git a/src/group-theory/perfect-groups.lagda.md b/src/group-theory/perfect-groups.lagda.md index 830d29efab..8494c47b8a 100644 --- a/src/group-theory/perfect-groups.lagda.md +++ b/src/group-theory/perfect-groups.lagda.md @@ -1,18 +1,23 @@ # Perfect groups ```agda -module group-theory.perfect-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.perfect-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.commutator-subgroups -open import group-theory.full-subgroups -open import group-theory.groups +open import group-theory.commutator-subgroups funext +open import group-theory.full-subgroups funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/perfect-subgroups.lagda.md b/src/group-theory/perfect-subgroups.lagda.md index 9e4dac3fc1..e4d9c5c03a 100644 --- a/src/group-theory/perfect-subgroups.lagda.md +++ b/src/group-theory/perfect-subgroups.lagda.md @@ -1,18 +1,23 @@ # Perfect subgroups ```agda -module group-theory.perfect-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.perfect-subgroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.perfect-groups -open import group-theory.subgroups +open import group-theory.groups funext +open import group-theory.perfect-groups funext +open import group-theory.subgroups funext ```
diff --git a/src/group-theory/powers-of-elements-commutative-monoids.lagda.md b/src/group-theory/powers-of-elements-commutative-monoids.lagda.md index 344471dcb0..303bfe280a 100644 --- a/src/group-theory/powers-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/powers-of-elements-commutative-monoids.lagda.md @@ -1,7 +1,12 @@ # Powers of elements in commutative monoids ```agda -module group-theory.powers-of-elements-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.powers-of-elements-commutative-monoids + (funext : function-extensionality) + where ```
Imports @@ -11,13 +16,13 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.powers-of-elements-monoids +open import group-theory.commutative-monoids funext +open import group-theory.homomorphisms-commutative-monoids funext +open import group-theory.powers-of-elements-monoids funext ```
diff --git a/src/group-theory/powers-of-elements-groups.lagda.md b/src/group-theory/powers-of-elements-groups.lagda.md index 745ee9159a..4085f7f059 100644 --- a/src/group-theory/powers-of-elements-groups.lagda.md +++ b/src/group-theory/powers-of-elements-groups.lagda.md @@ -1,7 +1,12 @@ # Powers of elements in groups ```agda -module group-theory.powers-of-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.powers-of-elements-groups + (funext : function-extensionality) + where ```
Imports @@ -11,14 +16,14 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.commuting-elements-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.powers-of-elements-monoids +open import group-theory.commuting-elements-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.powers-of-elements-monoids funext ```
diff --git a/src/group-theory/powers-of-elements-monoids.lagda.md b/src/group-theory/powers-of-elements-monoids.lagda.md index 66c4e4f41b..a9bc415e26 100644 --- a/src/group-theory/powers-of-elements-monoids.lagda.md +++ b/src/group-theory/powers-of-elements-monoids.lagda.md @@ -1,7 +1,12 @@ # Powers of elements in monoids ```agda -module group-theory.powers-of-elements-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.powers-of-elements-monoids + (funext : function-extensionality) + where ```
Imports @@ -12,13 +17,13 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositions +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.monoids +open import group-theory.homomorphisms-monoids funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/precategory-of-commutative-monoids.lagda.md b/src/group-theory/precategory-of-commutative-monoids.lagda.md index f3d5757c93..b86a74eae7 100644 --- a/src/group-theory/precategory-of-commutative-monoids.lagda.md +++ b/src/group-theory/precategory-of-commutative-monoids.lagda.md @@ -1,20 +1,25 @@ # The precategory of commutative monoids ```agda -module group-theory.precategory-of-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.precategory-of-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.precategory-of-monoids +open import group-theory.commutative-monoids funext +open import group-theory.precategory-of-monoids funext ```
diff --git a/src/group-theory/precategory-of-concrete-groups.lagda.md b/src/group-theory/precategory-of-concrete-groups.lagda.md index 43b955bd5d..5429bd563b 100644 --- a/src/group-theory/precategory-of-concrete-groups.lagda.md +++ b/src/group-theory/precategory-of-concrete-groups.lagda.md @@ -1,18 +1,23 @@ # The precategory of concrete groups ```agda -module group-theory.precategory-of-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.precategory-of-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.homomorphisms-concrete-groups funext ```
diff --git a/src/group-theory/precategory-of-group-actions.lagda.md b/src/group-theory/precategory-of-group-actions.lagda.md index d8fc00a1c5..7251001268 100644 --- a/src/group-theory/precategory-of-group-actions.lagda.md +++ b/src/group-theory/precategory-of-group-actions.lagda.md @@ -1,20 +1,25 @@ # The precategory of group actions ```agda -module group-theory.precategory-of-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.precategory-of-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions +open import group-theory.group-actions funext +open import group-theory.groups funext +open import group-theory.homomorphisms-group-actions funext ```
diff --git a/src/group-theory/precategory-of-groups.lagda.md b/src/group-theory/precategory-of-groups.lagda.md index 10f8be5a09..58987a13e0 100644 --- a/src/group-theory/precategory-of-groups.lagda.md +++ b/src/group-theory/precategory-of-groups.lagda.md @@ -1,20 +1,25 @@ # The precategory of groups ```agda -module group-theory.precategory-of-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.precategory-of-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.precategory-of-semigroups +open import group-theory.groups funext +open import group-theory.precategory-of-semigroups funext ```
diff --git a/src/group-theory/precategory-of-monoids.lagda.md b/src/group-theory/precategory-of-monoids.lagda.md index a16650574c..9ca444fa42 100644 --- a/src/group-theory/precategory-of-monoids.lagda.md +++ b/src/group-theory/precategory-of-monoids.lagda.md @@ -1,22 +1,27 @@ # The precategory of monoids ```agda -module group-theory.precategory-of-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.precategory-of-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.large-subprecategories -open import category-theory.precategories +open import category-theory.large-precategories funext +open import category-theory.large-subprecategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.precategory-of-semigroups +open import group-theory.homomorphisms-monoids funext +open import group-theory.monoids funext +open import group-theory.precategory-of-semigroups funext ```
diff --git a/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md b/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md index 5a51488a0e..0645388abf 100644 --- a/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md +++ b/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md @@ -1,27 +1,32 @@ # The precategory of orbits of a monoid action ```agda -module group-theory.precategory-of-orbits-monoid-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.precategory-of-orbits-monoid-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.monoid-actions -open import group-theory.monoids +open import group-theory.monoid-actions funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/precategory-of-semigroups.lagda.md b/src/group-theory/precategory-of-semigroups.lagda.md index 264d32e6b7..25507ba6d1 100644 --- a/src/group-theory/precategory-of-semigroups.lagda.md +++ b/src/group-theory/precategory-of-semigroups.lagda.md @@ -1,18 +1,23 @@ # The precategory of semigroups ```agda -module group-theory.precategory-of-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.precategory-of-semigroups + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups +open import group-theory.homomorphisms-semigroups funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/principal-group-actions.lagda.md b/src/group-theory/principal-group-actions.lagda.md index 18aaf88ca9..4d19a8506a 100644 --- a/src/group-theory/principal-group-actions.lagda.md +++ b/src/group-theory/principal-group-actions.lagda.md @@ -1,18 +1,23 @@ # Principal group actions ```agda -module group-theory.principal-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.principal-group-actions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality +open import foundation.equivalence-extensionality funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/principal-torsors-concrete-groups.lagda.md b/src/group-theory/principal-torsors-concrete-groups.lagda.md index d90716ffd3..30c416d128 100644 --- a/src/group-theory/principal-torsors-concrete-groups.lagda.md +++ b/src/group-theory/principal-torsors-concrete-groups.lagda.md @@ -1,7 +1,12 @@ # Principal torsors of concrete groups ```agda -module group-theory.principal-torsors-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.principal-torsors-concrete-groups + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module group-theory.principal-torsors-concrete-groups where ```agda open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext ```
diff --git a/src/group-theory/products-of-elements-monoids.lagda.md b/src/group-theory/products-of-elements-monoids.lagda.md index a4712a4f13..aaf2cafbad 100644 --- a/src/group-theory/products-of-elements-monoids.lagda.md +++ b/src/group-theory/products-of-elements-monoids.lagda.md @@ -1,19 +1,24 @@ # Products of elements in a monoid ```agda -module group-theory.products-of-elements-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.products-of-elements-monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists ``` diff --git a/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md b/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md index 120ca6b54c..b3cdcaeddb 100644 --- a/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md @@ -1,7 +1,12 @@ # Products of tuples of elements in commutative monoids ```agda -module group-theory.products-of-tuples-of-elements-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.products-of-tuples-of-elements-commutative-monoids + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module group-theory.products-of-tuples-of-elements-commutative-monoids where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.function-types +open import foundation.coproduct-types funext +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.commutative-monoids +open import group-theory.commutative-monoids funext -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/group-theory/pullbacks-subgroups.lagda.md b/src/group-theory/pullbacks-subgroups.lagda.md index 8ac1c10168..123a31645f 100644 --- a/src/group-theory/pullbacks-subgroups.lagda.md +++ b/src/group-theory/pullbacks-subgroups.lagda.md @@ -1,31 +1,36 @@ # Pullbacks of subgroups ```agda -module group-theory.pullbacks-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.pullbacks-subgroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.pullbacks-subtypes +open import foundation.identity-types funext +open import foundation.powersets funext +open import foundation.pullbacks-subtypes funext open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.pullbacks-subsemigroups -open import group-theory.subgroups -open import group-theory.subsemigroups -open import group-theory.subsets-groups - -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.normal-subgroups funext +open import group-theory.pullbacks-subsemigroups funext +open import group-theory.subgroups funext +open import group-theory.subsemigroups funext +open import group-theory.subsets-groups funext + +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.similarity-of-order-preserving-maps-large-posets funext ```
diff --git a/src/group-theory/pullbacks-subsemigroups.lagda.md b/src/group-theory/pullbacks-subsemigroups.lagda.md index cfefc2061d..1013c64069 100644 --- a/src/group-theory/pullbacks-subsemigroups.lagda.md +++ b/src/group-theory/pullbacks-subsemigroups.lagda.md @@ -1,28 +1,33 @@ # Pullbacks of subsemigroups ```agda -module group-theory.pullbacks-subsemigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.pullbacks-subsemigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.pullbacks-subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.powersets funext +open import foundation.pullbacks-subtypes funext open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups -open import group-theory.subsemigroups -open import group-theory.subsets-semigroups +open import group-theory.homomorphisms-semigroups funext +open import group-theory.semigroups funext +open import group-theory.subsemigroups funext +open import group-theory.subsets-semigroups funext -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.similarity-of-order-preserving-maps-large-posets funext ```
diff --git a/src/group-theory/quotient-groups-concrete-groups.lagda.md b/src/group-theory/quotient-groups-concrete-groups.lagda.md index f23e72c900..4f8afde78f 100644 --- a/src/group-theory/quotient-groups-concrete-groups.lagda.md +++ b/src/group-theory/quotient-groups-concrete-groups.lagda.md @@ -1,36 +1,41 @@ # Quotient groups of concrete groups ```agda -module group-theory.quotient-groups-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.quotient-groups-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.0-images-of-maps -open import foundation.1-types +open import foundation.0-connected-types funext +open import foundation.0-images-of-maps funext +open import foundation.1-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-group-actions -open import group-theory.mere-equivalences-concrete-group-actions -open import group-theory.normal-subgroups-concrete-groups -open import group-theory.transitive-concrete-group-actions +open import group-theory.concrete-groups funext +open import group-theory.equivalences-concrete-group-actions funext +open import group-theory.mere-equivalences-concrete-group-actions funext +open import group-theory.normal-subgroups-concrete-groups funext +open import group-theory.transitive-concrete-group-actions funext -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/group-theory/quotient-groups.lagda.md b/src/group-theory/quotient-groups.lagda.md index d109a8292d..272a8392ca 100644 --- a/src/group-theory/quotient-groups.lagda.md +++ b/src/group-theory/quotient-groups.lagda.md @@ -1,40 +1,45 @@ # Quotient groups ```agda -module group-theory.quotient-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.quotient-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-functoriality-set-quotients -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.binary-functoriality-set-quotients funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-set-quotients -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps -open import foundation.universal-property-set-quotients +open import foundation.effective-maps-equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-set-quotients funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.set-quotients funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.kernels-homomorphisms-groups -open import group-theory.normal-subgroups -open import group-theory.nullifying-group-homomorphisms -open import group-theory.semigroups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.kernels-homomorphisms-groups funext +open import group-theory.normal-subgroups funext +open import group-theory.nullifying-group-homomorphisms funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/quotients-abelian-groups.lagda.md b/src/group-theory/quotients-abelian-groups.lagda.md index 51ce7f9b4a..65f86ed3f1 100644 --- a/src/group-theory/quotients-abelian-groups.lagda.md +++ b/src/group-theory/quotients-abelian-groups.lagda.md @@ -3,34 +3,39 @@ ```agda {-# OPTIONS --lossy-unification #-} -module group-theory.quotients-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.quotients-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-functoriality-set-quotients +open import foundation.binary-functoriality-set-quotients funext open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations -open import foundation.equivalences -open import foundation.functoriality-set-quotients -open import foundation.identity-types -open import foundation.propositions -open import foundation.reflecting-maps-equivalence-relations -open import foundation.set-quotients -open import foundation.sets -open import foundation.surjective-maps -open import foundation.universal-property-set-quotients +open import foundation.effective-maps-equivalence-relations funext +open import foundation.equivalences funext +open import foundation.functoriality-set-quotients funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.set-quotients funext +open import foundation.sets funext +open import foundation.surjective-maps funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.nullifying-group-homomorphisms -open import group-theory.quotient-groups -open import group-theory.semigroups -open import group-theory.subgroups-abelian-groups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.nullifying-group-homomorphisms funext +open import group-theory.quotient-groups funext +open import group-theory.semigroups funext +open import group-theory.subgroups-abelian-groups funext ```
diff --git a/src/group-theory/rational-commutative-monoids.lagda.md b/src/group-theory/rational-commutative-monoids.lagda.md index 2c036f47fe..1785c5a04e 100644 --- a/src/group-theory/rational-commutative-monoids.lagda.md +++ b/src/group-theory/rational-commutative-monoids.lagda.md @@ -1,7 +1,12 @@ # Rational commutative monoids ```agda -module group-theory.rational-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.rational-commutative-monoids + (funext : function-extensionality) + where ```
Imports @@ -10,14 +15,14 @@ module group-theory.rational-commutative-monoids where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.powers-of-elements-commutative-monoids +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.powers-of-elements-commutative-monoids funext ```
diff --git a/src/group-theory/representations-monoids-precategories.lagda.md b/src/group-theory/representations-monoids-precategories.lagda.md index 934a1e2362..086c4099f1 100644 --- a/src/group-theory/representations-monoids-precategories.lagda.md +++ b/src/group-theory/representations-monoids-precategories.lagda.md @@ -1,23 +1,28 @@ # Representations of monoids in precategories ```agda -module group-theory.representations-monoids-precategories where +open import foundation.function-extensionality-axiom + +module + group-theory.representations-monoids-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.endomorphisms-in-precategories -open import category-theory.functors-precategories -open import category-theory.one-object-precategories -open import category-theory.precategories +open import category-theory.endomorphisms-in-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.one-object-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext ```
diff --git a/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md b/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md index 52a270e3cb..3a2f48b02f 100644 --- a/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md +++ b/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md @@ -1,26 +1,31 @@ # Saturated congruence relations on commutative monoids ```agda -module group-theory.saturated-congruence-relations-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.saturated-congruence-relations-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences +open import foundation.equivalence-relations funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.congruence-relations-commutative-monoids +open import group-theory.commutative-monoids funext +open import group-theory.congruence-relations-commutative-monoids funext ```
diff --git a/src/group-theory/saturated-congruence-relations-monoids.lagda.md b/src/group-theory/saturated-congruence-relations-monoids.lagda.md index fe77217ff6..4e3d71eeb4 100644 --- a/src/group-theory/saturated-congruence-relations-monoids.lagda.md +++ b/src/group-theory/saturated-congruence-relations-monoids.lagda.md @@ -1,26 +1,31 @@ # Saturated congruence relations on monoids ```agda -module group-theory.saturated-congruence-relations-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.saturated-congruence-relations-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences +open import foundation.equivalence-relations funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.congruence-relations-monoids -open import group-theory.monoids +open import group-theory.congruence-relations-monoids funext +open import group-theory.monoids funext ```
diff --git a/src/group-theory/semigroups.lagda.md b/src/group-theory/semigroups.lagda.md index 4709573fcf..a078dfb8f2 100644 --- a/src/group-theory/semigroups.lagda.md +++ b/src/group-theory/semigroups.lagda.md @@ -1,7 +1,12 @@ # Semigroups ```agda -module group-theory.semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.semigroups + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module group-theory.semigroups where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/group-theory/sheargroups.lagda.md b/src/group-theory/sheargroups.lagda.md index 42becd5b2b..0c48f9f41c 100644 --- a/src/group-theory/sheargroups.lagda.md +++ b/src/group-theory/sheargroups.lagda.md @@ -1,16 +1,21 @@ # Sheargroups ```agda -module group-theory.sheargroups where +open import foundation.function-extensionality-axiom + +module + group-theory.sheargroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/group-theory/shriek-concrete-group-actions.lagda.md b/src/group-theory/shriek-concrete-group-actions.lagda.md index 6e5364e97f..077d3dbd4d 100644 --- a/src/group-theory/shriek-concrete-group-actions.lagda.md +++ b/src/group-theory/shriek-concrete-group-actions.lagda.md @@ -1,22 +1,27 @@ # Shriek of concrete group homomorphisms ```agda -module group-theory.shriek-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.shriek-concrete-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.set-truncations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext +open import group-theory.homomorphisms-concrete-groups funext ```
diff --git a/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md b/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md index fccff9b2a3..8531ba783d 100644 --- a/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md +++ b/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md @@ -1,26 +1,31 @@ # Stabilizers of concrete group actions ```agda -module group-theory.stabilizer-groups-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.stabilizer-groups-concrete-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.subgroups-concrete-groups -open import group-theory.transitive-concrete-group-actions +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext +open import group-theory.subgroups-concrete-groups funext +open import group-theory.transitive-concrete-group-actions funext ```
diff --git a/src/group-theory/stabilizer-groups.lagda.md b/src/group-theory/stabilizer-groups.lagda.md index 6786bf463a..ac0a6b7282 100644 --- a/src/group-theory/stabilizer-groups.lagda.md +++ b/src/group-theory/stabilizer-groups.lagda.md @@ -1,18 +1,23 @@ # Stabilizer groups ```agda -module group-theory.stabilizer-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.stabilizer-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/subgroups-abelian-groups.lagda.md b/src/group-theory/subgroups-abelian-groups.lagda.md index 61238aa5c7..2729ca79d1 100644 --- a/src/group-theory/subgroups-abelian-groups.lagda.md +++ b/src/group-theory/subgroups-abelian-groups.lagda.md @@ -1,37 +1,42 @@ # Subgroups of abelian groups ```agda -module group-theory.subgroups-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.subgroups-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.congruence-relations-abelian-groups -open import group-theory.congruence-relations-groups -open import group-theory.groups -open import group-theory.homomorphisms-abelian-groups -open import group-theory.normal-subgroups -open import group-theory.semigroups -open import group-theory.subgroups -open import group-theory.subsets-abelian-groups - -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.posets -open import order-theory.preorders +open import group-theory.abelian-groups funext +open import group-theory.congruence-relations-abelian-groups funext +open import group-theory.congruence-relations-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.normal-subgroups funext +open import group-theory.semigroups funext +open import group-theory.subgroups funext +open import group-theory.subsets-abelian-groups funext + +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/group-theory/subgroups-concrete-groups.lagda.md b/src/group-theory/subgroups-concrete-groups.lagda.md index eb86e36730..275e88ba57 100644 --- a/src/group-theory/subgroups-concrete-groups.lagda.md +++ b/src/group-theory/subgroups-concrete-groups.lagda.md @@ -1,37 +1,42 @@ # Subgroups of concrete groups ```agda -module group-theory.subgroups-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.subgroups-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.0-maps +open import foundation.0-connected-types funext +open import foundation.0-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.faithful-maps -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.faithful-maps funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.structure-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-group-actions -open import group-theory.homomorphisms-concrete-groups -open import group-theory.orbits-concrete-group-actions -open import group-theory.transitive-concrete-group-actions +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext +open import group-theory.equivalences-concrete-group-actions funext +open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.orbits-concrete-group-actions funext +open import group-theory.transitive-concrete-group-actions funext -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/group-theory/subgroups-generated-by-elements-groups.lagda.md b/src/group-theory/subgroups-generated-by-elements-groups.lagda.md index fe9afdb421..76613f3386 100644 --- a/src/group-theory/subgroups-generated-by-elements-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-elements-groups.lagda.md @@ -1,33 +1,38 @@ # Subgroups generated by elements of a group ```agda -module group-theory.subgroups-generated-by-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.subgroups-generated-by-elements-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext open import elementary-number-theory.integers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.singleton-subtypes -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.images-subtypes funext +open import foundation.logical-equivalences funext +open import foundation.singleton-subtypes funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.integer-powers-of-elements-groups -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups -open import group-theory.trivial-subgroups +open import group-theory.free-groups-with-one-generator funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.images-of-group-homomorphisms funext +open import group-theory.integer-powers-of-elements-groups funext +open import group-theory.subgroups funext +open import group-theory.subgroups funext-generated-by-subsets-groups +open import group-theory.subsets-groups funext +open import group-theory.trivial-subgroups funext ```
diff --git a/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md b/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md index 34c8ab61bf..997a2cb12f 100644 --- a/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md @@ -1,30 +1,35 @@ # Subgroups generated by families of elements ```agda -module group-theory.subgroups-generated-by-families-of-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.subgroups-generated-by-families-of-elements-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.images -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.universal-property-image +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.images funext-subtypes +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext +open import foundation.universal-property-image funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.subgroups -open import group-theory.subgroups-generated-by-subsets-groups -open import group-theory.subsets-groups -open import group-theory.trivial-subgroups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.images-of-group-homomorphisms funext +open import group-theory.subgroups funext +open import group-theory.subgroups funext-generated-by-subsets-groups +open import group-theory.subsets-groups funext +open import group-theory.trivial-subgroups funext ```
diff --git a/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md b/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md index bdcb3c854f..25aab31f29 100644 --- a/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md @@ -1,52 +1,57 @@ # Subgroups generated by subsets of groups ```agda -module group-theory.subgroups-generated-by-subsets-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.subgroups-generated-by-subsets-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types -open import foundation.images-subtypes -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.pullbacks-subtypes -open import foundation.singleton-subtypes -open import foundation.subtypes +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.images-subtypes funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.pullbacks-subtypes funext +open import foundation.singleton-subtypes funext +open import foundation.subtypes funext open import foundation.unit-type open import foundation.universe-levels -open import group-theory.conjugation -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.normal-subgroups -open import group-theory.pullbacks-subgroups -open import group-theory.subgroups -open import group-theory.subsets-groups -open import group-theory.trivial-subgroups - -open import lists.concatenation-lists +open import group-theory.conjugation funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.images-of-group-homomorphisms funext +open import group-theory.normal-subgroups funext +open import group-theory.pullbacks-subgroups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext +open import group-theory.trivial-subgroups funext + +open import lists.concatenation-lists funext open import lists.lists -open import order-theory.commuting-squares-of-galois-connections-large-posets -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets -open import order-theory.galois-connections-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.commuting-squares-of-galois-connections-large-posets funext +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext +open import order-theory.galois-connections-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.similarity-of-order-preserving-maps-large-posets funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/group-theory/subgroups.lagda.md b/src/group-theory/subgroups.lagda.md index 98631e94e6..071aad55eb 100644 --- a/src/group-theory/subgroups.lagda.md +++ b/src/group-theory/subgroups.lagda.md @@ -1,7 +1,12 @@ # Subgroups ```agda -module group-theory.subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.subgroups + (funext : function-extensionality) + where ```
Imports @@ -10,41 +15,41 @@ module group-theory.subgroups where open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.coproduct-types +open import foundation.binary-relations funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.embeddings -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.disjunction funext +open import foundation.embeddings funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.large-binary-relations funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.semigroups -open import group-theory.subsemigroups -open import group-theory.subsets-groups - -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.posets -open import order-theory.preorders -open import order-theory.similarity-of-elements-large-posets +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.integer-powers-of-elements-groups funext +open import group-theory.semigroups funext +open import group-theory.subsemigroups funext +open import group-theory.subsets-groups funext + +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.similarity-of-elements-large-posets funext ```
diff --git a/src/group-theory/submonoids-commutative-monoids.lagda.md b/src/group-theory/submonoids-commutative-monoids.lagda.md index 1b93a31af2..2bc32fe8cf 100644 --- a/src/group-theory/submonoids-commutative-monoids.lagda.md +++ b/src/group-theory/submonoids-commutative-monoids.lagda.md @@ -1,26 +1,31 @@ # Submonoids of commutative monoids ```agda -module group-theory.submonoids-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.submonoids-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.submonoids -open import group-theory.subsets-commutative-monoids +open import group-theory.commutative-monoids funext +open import group-theory.homomorphisms-commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext +open import group-theory.submonoids funext +open import group-theory.subsets-commutative-monoids funext ```
diff --git a/src/group-theory/submonoids.lagda.md b/src/group-theory/submonoids.lagda.md index 4245b22e10..6da7d43b49 100644 --- a/src/group-theory/submonoids.lagda.md +++ b/src/group-theory/submonoids.lagda.md @@ -1,26 +1,31 @@ # Submonoids ```agda -module group-theory.submonoids where +open import foundation.function-extensionality-axiom + +module + group-theory.submonoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.semigroups -open import group-theory.subsets-monoids +open import group-theory.homomorphisms-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext +open import group-theory.subsets-monoids funext ```
diff --git a/src/group-theory/subsemigroups.lagda.md b/src/group-theory/subsemigroups.lagda.md index f283a68db3..78903abd03 100644 --- a/src/group-theory/subsemigroups.lagda.md +++ b/src/group-theory/subsemigroups.lagda.md @@ -1,34 +1,39 @@ # Subsemigroups ```agda -module group-theory.subsemigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.subsemigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.powersets -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.powersets funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups -open import group-theory.semigroups -open import group-theory.subsets-semigroups +open import group-theory.homomorphisms-semigroups funext +open import group-theory.semigroups funext +open import group-theory.subsets-semigroups funext -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/group-theory/subsets-abelian-groups.lagda.md b/src/group-theory/subsets-abelian-groups.lagda.md index 98fe503199..0802611e6c 100644 --- a/src/group-theory/subsets-abelian-groups.lagda.md +++ b/src/group-theory/subsets-abelian-groups.lagda.md @@ -1,22 +1,27 @@ # Subsets of abelian groups ```agda -module group-theory.subsets-abelian-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.subsets-abelian-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.large-locale-of-subtypes -open import foundation.powersets -open import foundation.sets +open import foundation.large-locale-of-subtypes funext +open import foundation.powersets funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.subsets-groups +open import group-theory.abelian-groups funext +open import group-theory.subsets-groups funext -open import order-theory.large-locales -open import order-theory.large-posets +open import order-theory.large-locales funext +open import order-theory.large-posets funext ```
diff --git a/src/group-theory/subsets-commutative-monoids.lagda.md b/src/group-theory/subsets-commutative-monoids.lagda.md index be1275afe2..ab7a48756b 100644 --- a/src/group-theory/subsets-commutative-monoids.lagda.md +++ b/src/group-theory/subsets-commutative-monoids.lagda.md @@ -1,19 +1,24 @@ # Subsets of commutative monoids ```agda -module group-theory.subsets-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.subsets-commutative-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.subsets-monoids +open import group-theory.commutative-monoids funext +open import group-theory.subsets-monoids funext ```
diff --git a/src/group-theory/subsets-groups.lagda.md b/src/group-theory/subsets-groups.lagda.md index 7eab7bced3..617a4b4edc 100644 --- a/src/group-theory/subsets-groups.lagda.md +++ b/src/group-theory/subsets-groups.lagda.md @@ -1,20 +1,25 @@ # Subsets of groups ```agda -module group-theory.subsets-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.subsets-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.large-locale-of-subtypes -open import foundation.sets +open import foundation.large-locale-of-subtypes funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.groups +open import group-theory.groups funext -open import order-theory.large-locales -open import order-theory.large-posets +open import order-theory.large-locales funext +open import order-theory.large-posets funext ```
diff --git a/src/group-theory/subsets-monoids.lagda.md b/src/group-theory/subsets-monoids.lagda.md index 97bb8b9059..8312af5e92 100644 --- a/src/group-theory/subsets-monoids.lagda.md +++ b/src/group-theory/subsets-monoids.lagda.md @@ -1,19 +1,24 @@ # Subsets of monoids ```agda -module group-theory.subsets-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.subsets-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext ```
diff --git a/src/group-theory/subsets-semigroups.lagda.md b/src/group-theory/subsets-semigroups.lagda.md index ddfdf50d40..af75cb9b55 100644 --- a/src/group-theory/subsets-semigroups.lagda.md +++ b/src/group-theory/subsets-semigroups.lagda.md @@ -1,24 +1,29 @@ # Subsets of semigroups ```agda -module group-theory.subsets-semigroups where +open import foundation.function-extensionality-axiom + +module + group-theory.subsets-semigroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-locale-of-subtypes -open import foundation.powersets -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.large-locale-of-subtypes funext +open import foundation.powersets funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext -open import order-theory.large-locales -open import order-theory.large-posets +open import order-theory.large-locales funext +open import order-theory.large-posets funext ```
diff --git a/src/group-theory/substitution-functor-concrete-group-actions.lagda.md b/src/group-theory/substitution-functor-concrete-group-actions.lagda.md index 80b294ad6c..7469055db2 100644 --- a/src/group-theory/substitution-functor-concrete-group-actions.lagda.md +++ b/src/group-theory/substitution-functor-concrete-group-actions.lagda.md @@ -1,7 +1,12 @@ # The substitution functor of concrete group actions ```agda -module group-theory.substitution-functor-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.substitution-functor-concrete-group-actions + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module group-theory.substitution-functor-concrete-group-actions where ```agda open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.homomorphisms-concrete-groups +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext +open import group-theory.homomorphisms-concrete-groups funext ```
diff --git a/src/group-theory/substitution-functor-group-actions.lagda.md b/src/group-theory/substitution-functor-group-actions.lagda.md index d8d73e7e03..e744fab386 100644 --- a/src/group-theory/substitution-functor-group-actions.lagda.md +++ b/src/group-theory/substitution-functor-group-actions.lagda.md @@ -1,31 +1,36 @@ # The substitution functor of group actions ```agda -module group-theory.substitution-functor-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.substitution-functor-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories +open import category-theory.functors-large-precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-relations -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.equivalence-classes funext +open import foundation.equivalence-relations funext +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-group-actions -open import group-theory.homomorphisms-groups -open import group-theory.precategory-of-group-actions -open import group-theory.symmetric-groups +open import group-theory.group-actions funext +open import group-theory.groups funext +open import group-theory.homomorphisms-group-actions funext +open import group-theory.homomorphisms-groups funext +open import group-theory.precategory-of-group-actions funext +open import group-theory.symmetric-groups funext ```
diff --git a/src/group-theory/surjective-group-homomorphisms.lagda.md b/src/group-theory/surjective-group-homomorphisms.lagda.md index c482bc5e50..5e9dd1691c 100644 --- a/src/group-theory/surjective-group-homomorphisms.lagda.md +++ b/src/group-theory/surjective-group-homomorphisms.lagda.md @@ -1,21 +1,26 @@ # Surjective group homomorphisms ```agda -module group-theory.surjective-group-homomorphisms where +open import foundation.function-extensionality-axiom + +module + group-theory.surjective-group-homomorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.propositions funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import group-theory.full-subgroups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.images-of-group-homomorphisms -open import group-theory.surjective-semigroup-homomorphisms +open import group-theory.full-subgroups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.images-of-group-homomorphisms funext +open import group-theory.surjective-semigroup-homomorphisms funext ```
diff --git a/src/group-theory/surjective-semigroup-homomorphisms.lagda.md b/src/group-theory/surjective-semigroup-homomorphisms.lagda.md index e112844df8..131c05bf24 100644 --- a/src/group-theory/surjective-semigroup-homomorphisms.lagda.md +++ b/src/group-theory/surjective-semigroup-homomorphisms.lagda.md @@ -1,20 +1,25 @@ # Surjective semigroup homomorphisms ```agda -module group-theory.surjective-semigroup-homomorphisms where +open import foundation.function-extensionality-axiom + +module + group-theory.surjective-semigroup-homomorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.propositions funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import group-theory.full-subsemigroups -open import group-theory.homomorphisms-semigroups -open import group-theory.images-of-semigroup-homomorphisms -open import group-theory.semigroups +open import group-theory.full-subsemigroups funext +open import group-theory.homomorphisms-semigroups funext +open import group-theory.images-of-semigroup-homomorphisms funext +open import group-theory.semigroups funext ```
diff --git a/src/group-theory/symmetric-concrete-groups.lagda.md b/src/group-theory/symmetric-concrete-groups.lagda.md index 006ef44e03..aa4d03f779 100644 --- a/src/group-theory/symmetric-concrete-groups.lagda.md +++ b/src/group-theory/symmetric-concrete-groups.lagda.md @@ -1,22 +1,27 @@ # Symmetric concrete groups ```agda -module group-theory.symmetric-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.symmetric-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.sets funext open import foundation.subtype-identity-principle open import foundation.universe-levels -open import group-theory.automorphism-groups -open import group-theory.concrete-groups +open import group-theory.automorphism-groups funext +open import group-theory.concrete-groups funext ```
diff --git a/src/group-theory/symmetric-groups.lagda.md b/src/group-theory/symmetric-groups.lagda.md index bb5b38be9e..d0dbabcfb6 100644 --- a/src/group-theory/symmetric-groups.lagda.md +++ b/src/group-theory/symmetric-groups.lagda.md @@ -1,31 +1,37 @@ # Symmetric groups ```agda -module group-theory.symmetric-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.symmetric-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.automorphisms +open import foundation.automorphisms funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-semigroups -open import group-theory.isomorphisms-groups -open import group-theory.monoids -open import group-theory.opposite-groups -open import group-theory.semigroups -open import group-theory.symmetric-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-semigroups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.monoids funext +open import group-theory.opposite-groups funext +open import group-theory.semigroups funext +open import group-theory.symmetric-concrete-groups funext ```
diff --git a/src/group-theory/torsion-elements-groups.lagda.md b/src/group-theory/torsion-elements-groups.lagda.md index 9b7a129185..45e2e658ba 100644 --- a/src/group-theory/torsion-elements-groups.lagda.md +++ b/src/group-theory/torsion-elements-groups.lagda.md @@ -1,24 +1,29 @@ # Torsion elements of groups ```agda -module group-theory.torsion-elements-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.torsion-elements-groups + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.integers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.nonzero-integers funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.integer-powers-of-elements-groups +open import group-theory.groups funext +open import group-theory.integer-powers-of-elements-groups funext ```
diff --git a/src/group-theory/torsion-free-groups.lagda.md b/src/group-theory/torsion-free-groups.lagda.md index d7e4ed6170..01a8150b3d 100644 --- a/src/group-theory/torsion-free-groups.lagda.md +++ b/src/group-theory/torsion-free-groups.lagda.md @@ -1,34 +1,39 @@ # Torsion-free groups ```agda -module group-theory.torsion-free-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.torsion-free-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers -open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.nonzero-integers funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification +open import foundation.equivalences funext +open import foundation.existential-quantification funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.singleton-subtypes -open import foundation.standard-pullbacks +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.singleton-subtypes funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.integer-powers-of-elements-groups -open import group-theory.orders-of-elements-groups -open import group-theory.subgroups -open import group-theory.torsion-elements-groups +open import group-theory.groups funext +open import group-theory.integer-powers-of-elements-groups funext +open import group-theory.orders-of-elements-groups funext +open import group-theory.subgroups funext +open import group-theory.torsion-elements-groups funext ```
diff --git a/src/group-theory/torsors.lagda.md b/src/group-theory/torsors.lagda.md index 0e1b1d1375..feb12a47c6 100644 --- a/src/group-theory/torsors.lagda.md +++ b/src/group-theory/torsors.lagda.md @@ -1,42 +1,47 @@ # Torsors of abstract groups ```agda -module group-theory.torsors where +open import foundation.function-extensionality-axiom + +module + group-theory.torsors + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.equivalences-group-actions -open import group-theory.group-actions -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.isomorphisms-groups -open import group-theory.mere-equivalences-group-actions -open import group-theory.principal-group-actions -open import group-theory.symmetric-groups - -open import higher-group-theory.higher-groups +open import group-theory.concrete-groups funext +open import group-theory.equivalences-group-actions funext +open import group-theory.group-actions funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.isomorphisms-groups funext +open import group-theory.mere-equivalences-group-actions funext +open import group-theory.principal-group-actions funext +open import group-theory.symmetric-groups funext + +open import higher-group-theory.higher-groups funext ```
diff --git a/src/group-theory/transitive-concrete-group-actions.lagda.md b/src/group-theory/transitive-concrete-group-actions.lagda.md index f6af5d47b3..ff360cb51c 100644 --- a/src/group-theory/transitive-concrete-group-actions.lagda.md +++ b/src/group-theory/transitive-concrete-group-actions.lagda.md @@ -1,32 +1,37 @@ # Transitive concrete group actions ```agda -module group-theory.transitive-concrete-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.transitive-concrete-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.1-types +open import foundation.1-types funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import group-theory.concrete-group-actions -open import group-theory.concrete-groups -open import group-theory.equivalences-concrete-group-actions +open import group-theory.concrete-group-actions funext +open import group-theory.concrete-groups funext +open import group-theory.equivalences-concrete-group-actions funext -open import higher-group-theory.transitive-higher-group-actions +open import higher-group-theory.transitive-higher-group-actions funext ```
diff --git a/src/group-theory/transitive-group-actions.lagda.md b/src/group-theory/transitive-group-actions.lagda.md index c8513a1bf5..662c6efd2d 100644 --- a/src/group-theory/transitive-group-actions.lagda.md +++ b/src/group-theory/transitive-group-actions.lagda.md @@ -1,20 +1,25 @@ # Transitive group actions ```agda -module group-theory.transitive-group-actions where +open import foundation.function-extensionality-axiom + +module + group-theory.transitive-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import group-theory.group-actions -open import group-theory.groups +open import group-theory.group-actions funext +open import group-theory.groups funext ```
diff --git a/src/group-theory/trivial-concrete-groups.lagda.md b/src/group-theory/trivial-concrete-groups.lagda.md index 5c20a531f4..b138f2f6ca 100644 --- a/src/group-theory/trivial-concrete-groups.lagda.md +++ b/src/group-theory/trivial-concrete-groups.lagda.md @@ -1,23 +1,28 @@ # Trivial concrete groups ```agda -module group-theory.trivial-concrete-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.trivial-concrete-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.concrete-groups +open import group-theory.concrete-groups funext -open import higher-group-theory.trivial-higher-groups +open import higher-group-theory.trivial-higher-groups funext ```
diff --git a/src/group-theory/trivial-group-homomorphisms.lagda.md b/src/group-theory/trivial-group-homomorphisms.lagda.md index 3cc3b50278..40ce202e9a 100644 --- a/src/group-theory/trivial-group-homomorphisms.lagda.md +++ b/src/group-theory/trivial-group-homomorphisms.lagda.md @@ -1,20 +1,25 @@ # Trivial group homomorphisms ```agda -module group-theory.trivial-group-homomorphisms where +open import foundation.function-extensionality-axiom + +module + group-theory.trivial-group-homomorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.homomorphisms-groups +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext ```
diff --git a/src/group-theory/trivial-groups.lagda.md b/src/group-theory/trivial-groups.lagda.md index a018e83b69..c1170859b4 100644 --- a/src/group-theory/trivial-groups.lagda.md +++ b/src/group-theory/trivial-groups.lagda.md @@ -1,28 +1,33 @@ # Trivial groups ```agda -module group-theory.trivial-groups where +open import foundation.function-extensionality-axiom + +module + group-theory.trivial-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext open import foundation.structure-identity-principle open import foundation.unit-type open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.full-subgroups -open import group-theory.groups -open import group-theory.subgroups -open import group-theory.trivial-subgroups +open import group-theory.abelian-groups funext +open import group-theory.full-subgroups funext +open import group-theory.groups funext +open import group-theory.subgroups funext +open import group-theory.trivial-subgroups funext ```
diff --git a/src/group-theory/trivial-subgroups.lagda.md b/src/group-theory/trivial-subgroups.lagda.md index e26bfde47b..035cfcf327 100644 --- a/src/group-theory/trivial-subgroups.lagda.md +++ b/src/group-theory/trivial-subgroups.lagda.md @@ -1,18 +1,23 @@ # Trivial subgroups ```agda -module group-theory.trivial-subgroups where +open import foundation.function-extensionality-axiom + +module + group-theory.trivial-subgroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.subgroups +open import group-theory.groups funext +open import group-theory.subgroups funext ```
diff --git a/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md b/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md index 55ccfa28c6..76e345d173 100644 --- a/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md @@ -1,7 +1,12 @@ # Unordered tuples of elements in commutative monoids ```agda -module group-theory.unordered-tuples-of-elements-commutative-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.unordered-tuples-of-elements-commutative-monoids + (funext : function-extensionality) + where ```
Imports @@ -10,9 +15,9 @@ module group-theory.unordered-tuples-of-elements-commutative-monoids where open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import foundation.unordered-tuples +open import foundation.unordered-tuples funext -open import group-theory.commutative-monoids +open import group-theory.commutative-monoids funext ```
diff --git a/src/group-theory/wild-representations-monoids.lagda.md b/src/group-theory/wild-representations-monoids.lagda.md index 153d5c80a5..e61a3803d0 100644 --- a/src/group-theory/wild-representations-monoids.lagda.md +++ b/src/group-theory/wild-representations-monoids.lagda.md @@ -1,21 +1,26 @@ # Wild representations of monoids ```agda -module group-theory.wild-representations-monoids where +open import foundation.function-extensionality-axiom + +module + group-theory.wild-representations-monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.endomorphisms -open import foundation.function-types -open import foundation.identity-types +open import foundation.endomorphisms funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext -open import structured-types.morphisms-wild-monoids +open import structured-types.morphisms-wild-monoids funext ```
diff --git a/src/higher-group-theory.lagda.md b/src/higher-group-theory.lagda.md index 14d69b791a..23d3cb9fdc 100644 --- a/src/higher-group-theory.lagda.md +++ b/src/higher-group-theory.lagda.md @@ -3,31 +3,36 @@ ## Modules in the higher group theory namespace ```agda -module higher-group-theory where +open import foundation.function-extensionality-axiom -open import higher-group-theory.abelian-higher-groups public -open import higher-group-theory.automorphism-groups public -open import higher-group-theory.cartesian-products-higher-groups public -open import higher-group-theory.conjugation public -open import higher-group-theory.cyclic-higher-groups public -open import higher-group-theory.deloopable-groups public -open import higher-group-theory.deloopable-h-spaces public -open import higher-group-theory.deloopable-types public -open import higher-group-theory.eilenberg-mac-lane-spaces public -open import higher-group-theory.equivalences-higher-groups public -open import higher-group-theory.fixed-points-higher-group-actions public -open import higher-group-theory.free-higher-group-actions public -open import higher-group-theory.higher-group-actions public -open import higher-group-theory.higher-groups public -open import higher-group-theory.homomorphisms-higher-group-actions public -open import higher-group-theory.homomorphisms-higher-groups public -open import higher-group-theory.integers-higher-group public -open import higher-group-theory.iterated-cartesian-products-higher-groups public -open import higher-group-theory.iterated-deloopings-of-pointed-types public -open import higher-group-theory.orbits-higher-group-actions public -open import higher-group-theory.small-higher-groups public -open import higher-group-theory.subgroups-higher-groups public -open import higher-group-theory.symmetric-higher-groups public -open import higher-group-theory.transitive-higher-group-actions public -open import higher-group-theory.trivial-higher-groups public +module + higher-group-theory + (funext : function-extensionality) + where + +open import higher-group-theory.abelian-higher-groups funext public +open import higher-group-theory.automorphism-groups funext public +open import higher-group-theory.cartesian-products-higher-groups funext public +open import higher-group-theory.conjugation funext public +open import higher-group-theory.cyclic-higher-groups funext public +open import higher-group-theory.deloopable-groups funext public +open import higher-group-theory.deloopable-h-spaces funext public +open import higher-group-theory.deloopable-types funext public +open import higher-group-theory.eilenberg-mac-lane-spaces funext public +open import higher-group-theory.equivalences-higher-groups funext public +open import higher-group-theory.fixed-points-higher-group-actions funext public +open import higher-group-theory.free-higher-group-actions funext public +open import higher-group-theory.higher-group-actions funext public +open import higher-group-theory.higher-groups funext public +open import higher-group-theory.homomorphisms-higher-group-actions funext public +open import higher-group-theory.homomorphisms-higher-groups funext public +open import higher-group-theory.integers-higher-group funext public +open import higher-group-theory.iterated-cartesian-products-higher-groups funext public +open import higher-group-theory.iterated-deloopings-of-pointed-types funext public +open import higher-group-theory.orbits-higher-group-actions funext public +open import higher-group-theory.small-higher-groups funext public +open import higher-group-theory.subgroups-higher-groups funext public +open import higher-group-theory.symmetric-higher-groups funext public +open import higher-group-theory.transitive-higher-group-actions funext public +open import higher-group-theory.trivial-higher-groups funext public ``` diff --git a/src/higher-group-theory/abelian-higher-groups.lagda.md b/src/higher-group-theory/abelian-higher-groups.lagda.md index cdfe3e08ba..78a688d1fc 100644 --- a/src/higher-group-theory/abelian-higher-groups.lagda.md +++ b/src/higher-group-theory/abelian-higher-groups.lagda.md @@ -1,26 +1,31 @@ # Abelian higher groups ```agda -module higher-group-theory.abelian-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.abelian-higher-groups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.small-types funext open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups -open import higher-group-theory.small-higher-groups +open import higher-group-theory.equivalences-higher-groups funext +open import higher-group-theory.higher-groups funext +open import higher-group-theory.small-higher-groups funext -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext open import structured-types.pointed-types -open import structured-types.small-pointed-types +open import structured-types.small-pointed-types funext -open import synthetic-homotopy-theory.connective-spectra +open import synthetic-homotopy-theory.connective-spectra funext ```
diff --git a/src/higher-group-theory/automorphism-groups.lagda.md b/src/higher-group-theory/automorphism-groups.lagda.md index 3c2e64a205..c94fe7ae18 100644 --- a/src/higher-group-theory/automorphism-groups.lagda.md +++ b/src/higher-group-theory/automorphism-groups.lagda.md @@ -1,26 +1,31 @@ # Automorphism groups ```agda -module higher-group-theory.automorphism-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.automorphism-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.connected-components -open import foundation.contractible-types +open import foundation.0-connected-types funext +open import foundation.connected-components funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.equivalences-higher-groups funext +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types ``` diff --git a/src/higher-group-theory/cartesian-products-higher-groups.lagda.md b/src/higher-group-theory/cartesian-products-higher-groups.lagda.md index 2183bb2862..9903fc84a6 100644 --- a/src/higher-group-theory/cartesian-products-higher-groups.lagda.md +++ b/src/higher-group-theory/cartesian-products-higher-groups.lagda.md @@ -1,28 +1,33 @@ # Cartesian products of higher groups ```agda -module higher-group-theory.cartesian-products-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.cartesian-products-higher-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.cartesian-product-types +open import foundation.0-connected-types funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.propositions funext open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext -open import structured-types.pointed-cartesian-product-types +open import structured-types.pointed-cartesian-product-types funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/higher-group-theory/conjugation.lagda.md b/src/higher-group-theory/conjugation.lagda.md index 66e53af615..00540064f2 100644 --- a/src/higher-group-theory/conjugation.lagda.md +++ b/src/higher-group-theory/conjugation.lagda.md @@ -1,22 +1,27 @@ # Conjugation in higher groups ```agda -module higher-group-theory.conjugation where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.conjugation + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import higher-group-theory.higher-groups -open import higher-group-theory.homomorphisms-higher-groups +open import higher-group-theory.higher-groups funext +open import higher-group-theory.homomorphisms-higher-groups funext -open import structured-types.conjugation-pointed-types +open import structured-types.conjugation-pointed-types funext -open import synthetic-homotopy-theory.conjugation-loops +open import synthetic-homotopy-theory.conjugation-loops funext ```
diff --git a/src/higher-group-theory/cyclic-higher-groups.lagda.md b/src/higher-group-theory/cyclic-higher-groups.lagda.md index d9067fb971..4a3dfc4861 100644 --- a/src/higher-group-theory/cyclic-higher-groups.lagda.md +++ b/src/higher-group-theory/cyclic-higher-groups.lagda.md @@ -1,19 +1,24 @@ # Cyclic higher groups ```agda -module higher-group-theory.cyclic-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.cyclic-higher-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.embeddings -open import foundation.existential-quantification -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.existential-quantification funext +open import foundation.propositions funext open import foundation.universe-levels -open import higher-group-theory.higher-groups -open import higher-group-theory.homomorphisms-higher-groups +open import higher-group-theory.higher-groups funext +open import higher-group-theory.homomorphisms-higher-groups funext ```
diff --git a/src/higher-group-theory/deloopable-groups.lagda.md b/src/higher-group-theory/deloopable-groups.lagda.md index 45c31edf78..65447fd5ac 100644 --- a/src/higher-group-theory/deloopable-groups.lagda.md +++ b/src/higher-group-theory/deloopable-groups.lagda.md @@ -1,7 +1,12 @@ # Deloopable groups ```agda -module higher-group-theory.deloopable-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.deloopable-groups + (funext : function-extensionality) + where ```
Imports @@ -10,9 +15,9 @@ module higher-group-theory.deloopable-groups where open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.groups +open import group-theory.groups funext -open import higher-group-theory.deloopable-h-spaces +open import higher-group-theory.deloopable-h-spaces funext ```
diff --git a/src/higher-group-theory/deloopable-h-spaces.lagda.md b/src/higher-group-theory/deloopable-h-spaces.lagda.md index 90b0d90e0c..24138fd502 100644 --- a/src/higher-group-theory/deloopable-h-spaces.lagda.md +++ b/src/higher-group-theory/deloopable-h-spaces.lagda.md @@ -1,7 +1,12 @@ # Deloopable H-spaces ```agda -module higher-group-theory.deloopable-h-spaces where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.deloopable-h-spaces + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module higher-group-theory.deloopable-h-spaces where open import foundation.dependent-pair-types open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext -open import structured-types.equivalences-h-spaces -open import structured-types.h-spaces +open import structured-types.equivalences-h-spaces funext +open import structured-types.h-spaces funext ```
diff --git a/src/higher-group-theory/deloopable-types.lagda.md b/src/higher-group-theory/deloopable-types.lagda.md index 23e7bac773..5b090c33f6 100644 --- a/src/higher-group-theory/deloopable-types.lagda.md +++ b/src/higher-group-theory/deloopable-types.lagda.md @@ -1,24 +1,29 @@ # Deloopable types ```agda -module higher-group-theory.deloopable-types where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.deloopable-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.small-types funext open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups -open import higher-group-theory.small-higher-groups +open import higher-group-theory.equivalences-higher-groups funext +open import higher-group-theory.higher-groups funext +open import higher-group-theory.small-higher-groups funext -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext open import structured-types.pointed-types -open import structured-types.small-pointed-types +open import structured-types.small-pointed-types funext ```
diff --git a/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md b/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md index 13a8cf9fab..574ce2d003 100644 --- a/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md +++ b/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md @@ -1,7 +1,12 @@ # Eilenberg-Mac Lane spaces ```agda -module higher-group-theory.eilenberg-mac-lane-spaces where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.eilenberg-mac-lane-spaces + (funext : function-extensionality) + where ```
Imports @@ -9,22 +14,22 @@ module higher-group-theory.eilenberg-mac-lane-spaces where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.cartesian-product-types -open import foundation.connected-types -open import foundation.truncated-types +open import foundation.0-connected-types funext +open import foundation.cartesian-product-types funext +open import foundation.connected-types funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups +open import group-theory.abelian-groups funext +open import group-theory.groups funext -open import structured-types.equivalences-h-spaces -open import structured-types.pointed-equivalences +open import structured-types.equivalences-h-spaces funext +open import structured-types.pointed-equivalences funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.iterated-loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/higher-group-theory/equivalences-higher-groups.lagda.md b/src/higher-group-theory/equivalences-higher-groups.lagda.md index c494c345cf..cc73889557 100644 --- a/src/higher-group-theory/equivalences-higher-groups.lagda.md +++ b/src/higher-group-theory/equivalences-higher-groups.lagda.md @@ -1,30 +1,35 @@ # Equivalences of higher groups ```agda -module higher-group-theory.equivalences-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.equivalences-higher-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import higher-group-theory.higher-groups -open import higher-group-theory.homomorphisms-higher-groups +open import higher-group-theory.higher-groups funext +open import higher-group-theory.homomorphisms-higher-groups funext -open import structured-types.pointed-equivalences -open import structured-types.pointed-isomorphisms +open import structured-types.pointed-equivalences funext +open import structured-types.pointed-isomorphisms funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext ```
diff --git a/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md b/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md index 4dfdc5fb40..befb47ba5b 100644 --- a/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md +++ b/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md @@ -1,7 +1,12 @@ # Fixed points of higher group actions ```agda -module higher-group-theory.fixed-points-higher-group-actions where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.fixed-points-higher-group-actions + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module higher-group-theory.fixed-points-higher-group-actions where ```agda open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-group-actions funext +open import higher-group-theory.higher-groups funext ```
diff --git a/src/higher-group-theory/free-higher-group-actions.lagda.md b/src/higher-group-theory/free-higher-group-actions.lagda.md index ea43e3e1b2..b0bae655f6 100644 --- a/src/higher-group-theory/free-higher-group-actions.lagda.md +++ b/src/higher-group-theory/free-higher-group-actions.lagda.md @@ -1,27 +1,32 @@ # Free higher group actions ```agda -module higher-group-theory.free-higher-group-actions where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.free-higher-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.embeddings -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.regensburg-extension-fundamental-theorem-of-identity-types -open import foundation.sets -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.regensburg-extension-fundamental-theorem-of-identity-types funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.truncation-levels open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups -open import higher-group-theory.orbits-higher-group-actions +open import higher-group-theory.higher-group-actions funext +open import higher-group-theory.higher-groups funext +open import higher-group-theory.orbits-higher-group-actions funext ```
diff --git a/src/higher-group-theory/higher-group-actions.lagda.md b/src/higher-group-theory/higher-group-actions.lagda.md index 67119d09c0..a08fbae8eb 100644 --- a/src/higher-group-theory/higher-group-actions.lagda.md +++ b/src/higher-group-theory/higher-group-actions.lagda.md @@ -1,17 +1,22 @@ # Higher group actions ```agda -module higher-group-theory.higher-group-actions where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.higher-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext ```
diff --git a/src/higher-group-theory/higher-groups.lagda.md b/src/higher-group-theory/higher-groups.lagda.md index 6102d85536..c2f464f64e 100644 --- a/src/higher-group-theory/higher-groups.lagda.md +++ b/src/higher-group-theory/higher-groups.lagda.md @@ -1,28 +1,33 @@ # Higher groups ```agda -module higher-group-theory.higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.higher-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.identity-types -open import foundation.images -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.full-subtypes funext +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.h-spaces +open import structured-types.h-spaces funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md b/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md index 5929ab0dbc..d522aa80ca 100644 --- a/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md +++ b/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md @@ -1,22 +1,28 @@ # Homomorphisms of higher group actions ```agda -module higher-group-theory.homomorphisms-higher-group-actions where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.homomorphisms-higher-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-group-actions funext +open import higher-group-theory.higher-groups funext ```
diff --git a/src/higher-group-theory/homomorphisms-higher-groups.lagda.md b/src/higher-group-theory/homomorphisms-higher-groups.lagda.md index cd94013ef2..2b2aae3694 100644 --- a/src/higher-group-theory/homomorphisms-higher-groups.lagda.md +++ b/src/higher-group-theory/homomorphisms-higher-groups.lagda.md @@ -1,22 +1,27 @@ # Homomorphisms of higher groups ```agda -module higher-group-theory.homomorphisms-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.homomorphisms-higher-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext -open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext ```
diff --git a/src/higher-group-theory/integers-higher-group.lagda.md b/src/higher-group-theory/integers-higher-group.lagda.md index 7220677f16..15af00e242 100644 --- a/src/higher-group-theory/integers-higher-group.lagda.md +++ b/src/higher-group-theory/integers-higher-group.lagda.md @@ -1,7 +1,12 @@ # The higher group of integers ```agda -module higher-group-theory.integers-higher-group where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.integers-higher-group + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module higher-group-theory.integers-higher-group where open import foundation.dependent-pair-types open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.circle funext ```
diff --git a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md index d8ae507260..261d2a7c94 100644 --- a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md +++ b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md @@ -1,7 +1,12 @@ # Iterated cartesian products of higher groups ```agda -module higher-group-theory.iterated-cartesian-products-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.iterated-cartesian-products-higher-groups + (funext : function-extensionality) + where ```
Imports @@ -9,31 +14,31 @@ module higher-group-theory.iterated-cartesian-products-higher-groups where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.0-connected-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.iterated-cartesian-product-types -open import foundation.mere-equality -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.iterated-cartesian-product-types funext +open import foundation.mere-equality funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import higher-group-theory.cartesian-products-higher-groups -open import higher-group-theory.higher-groups -open import higher-group-theory.trivial-higher-groups +open import higher-group-theory.cartesian-products-higher-groups funext +open import higher-group-theory.higher-groups funext +open import higher-group-theory.trivial-higher-groups funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md b/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md index d5f051b7fd..b854b63b88 100644 --- a/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md +++ b/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md @@ -1,7 +1,12 @@ # Iterated deloopings of pointed types ```agda -module higher-group-theory.iterated-deloopings-of-pointed-types where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.iterated-deloopings-of-pointed-types + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module higher-group-theory.iterated-deloopings-of-pointed-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.connected-types +open import foundation.cartesian-product-types funext +open import foundation.connected-types funext open import foundation.dependent-pair-types open import foundation.truncation-levels open import foundation.universe-levels -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-loop-spaces +open import synthetic-homotopy-theory.iterated-loop-spaces funext ```
diff --git a/src/higher-group-theory/orbits-higher-group-actions.lagda.md b/src/higher-group-theory/orbits-higher-group-actions.lagda.md index 69003ac59b..68e9932188 100644 --- a/src/higher-group-theory/orbits-higher-group-actions.lagda.md +++ b/src/higher-group-theory/orbits-higher-group-actions.lagda.md @@ -1,7 +1,12 @@ # Orbits of higher group actions ```agda -module higher-group-theory.orbits-higher-group-actions where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.orbits-higher-group-actions + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module higher-group-theory.orbits-higher-group-actions where open import foundation.dependent-pair-types open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-group-actions funext +open import higher-group-theory.higher-groups funext ```
diff --git a/src/higher-group-theory/small-higher-groups.lagda.md b/src/higher-group-theory/small-higher-groups.lagda.md index 0252d1093d..9443afbd5f 100644 --- a/src/higher-group-theory/small-higher-groups.lagda.md +++ b/src/higher-group-theory/small-higher-groups.lagda.md @@ -1,32 +1,37 @@ # Small ∞-groups ```agda -module higher-group-theory.small-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.small-higher-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.images -open import foundation.locally-small-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.replacement -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.locally-small-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.replacement funext +open import foundation.small-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups -open import higher-group-theory.higher-groups +open import higher-group-theory.equivalences-higher-groups funext +open import higher-group-theory.higher-groups funext -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext open import structured-types.pointed-types -open import structured-types.small-pointed-types +open import structured-types.small-pointed-types funext ```
diff --git a/src/higher-group-theory/subgroups-higher-groups.lagda.md b/src/higher-group-theory/subgroups-higher-groups.lagda.md index 14e6b1ebce..f0a3239346 100644 --- a/src/higher-group-theory/subgroups-higher-groups.lagda.md +++ b/src/higher-group-theory/subgroups-higher-groups.lagda.md @@ -1,20 +1,25 @@ # Subgroups of higher groups ```agda -module higher-group-theory.subgroups-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.subgroups-higher-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.cartesian-product-types +open import foundation.0-connected-types funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.sets funext open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types ``` diff --git a/src/higher-group-theory/symmetric-higher-groups.lagda.md b/src/higher-group-theory/symmetric-higher-groups.lagda.md index 9af7adc4fe..0dcec903bf 100644 --- a/src/higher-group-theory/symmetric-higher-groups.lagda.md +++ b/src/higher-group-theory/symmetric-higher-groups.lagda.md @@ -1,19 +1,24 @@ # Symmetric higher groups ```agda -module higher-group-theory.symmetric-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.symmetric-higher-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.connected-components-universes +open import foundation.0-connected-types funext +open import foundation.connected-components-universes funext open import foundation.dependent-pair-types -open import foundation.mere-equivalences +open import foundation.mere-equivalences funext open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types ``` diff --git a/src/higher-group-theory/transitive-higher-group-actions.lagda.md b/src/higher-group-theory/transitive-higher-group-actions.lagda.md index a6a4b3f711..9592ad6059 100644 --- a/src/higher-group-theory/transitive-higher-group-actions.lagda.md +++ b/src/higher-group-theory/transitive-higher-group-actions.lagda.md @@ -1,26 +1,31 @@ # Transitive higher group actions ```agda -module higher-group-theory.transitive-higher-group-actions where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.transitive-higher-group-actions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.regensburg-extension-fundamental-theorem-of-identity-types -open import foundation.surjective-maps +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.regensburg-extension-fundamental-theorem-of-identity-types funext +open import foundation.surjective-maps funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.higher-group-actions -open import higher-group-theory.higher-groups -open import higher-group-theory.orbits-higher-group-actions +open import higher-group-theory.higher-group-actions funext +open import higher-group-theory.higher-groups funext +open import higher-group-theory.orbits-higher-group-actions funext ```
diff --git a/src/higher-group-theory/trivial-higher-groups.lagda.md b/src/higher-group-theory/trivial-higher-groups.lagda.md index 32e453fac8..7ec887a0f5 100644 --- a/src/higher-group-theory/trivial-higher-groups.lagda.md +++ b/src/higher-group-theory/trivial-higher-groups.lagda.md @@ -1,21 +1,26 @@ # Trivial higher groups ```agda -module higher-group-theory.trivial-higher-groups where +open import foundation.function-extensionality-axiom + +module + higher-group-theory.trivial-higher-groups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.contractible-types +open import foundation.0-connected-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext ```
diff --git a/src/linear-algebra.lagda.md b/src/linear-algebra.lagda.md index 883be1c3fa..55f66bbd51 100644 --- a/src/linear-algebra.lagda.md +++ b/src/linear-algebra.lagda.md @@ -3,24 +3,29 @@ ## Modules in the linear algebra namespace ```agda -module linear-algebra where +open import foundation.function-extensionality-axiom -open import linear-algebra.constant-matrices public -open import linear-algebra.constant-vectors public -open import linear-algebra.diagonal-matrices-on-rings public -open import linear-algebra.functoriality-matrices public -open import linear-algebra.functoriality-vectors public -open import linear-algebra.matrices public -open import linear-algebra.matrices-on-rings public +module + linear-algebra + (funext : function-extensionality) + where + +open import linear-algebra.constant-matrices funext public +open import linear-algebra.constant-vectors funext public +open import linear-algebra.diagonal-matrices-on-rings funext public +open import linear-algebra.functoriality-matrices funext public +open import linear-algebra.functoriality-vectors funext public +open import linear-algebra.matrices funext public +open import linear-algebra.matrices-on-rings funext public open import linear-algebra.multiplication-matrices public -open import linear-algebra.scalar-multiplication-matrices public -open import linear-algebra.scalar-multiplication-vectors public -open import linear-algebra.scalar-multiplication-vectors-on-rings public -open import linear-algebra.transposition-matrices public -open import linear-algebra.vectors public -open import linear-algebra.vectors-on-commutative-rings public -open import linear-algebra.vectors-on-commutative-semirings public -open import linear-algebra.vectors-on-euclidean-domains public -open import linear-algebra.vectors-on-rings public -open import linear-algebra.vectors-on-semirings public +open import linear-algebra.scalar-multiplication-matrices funext public +open import linear-algebra.scalar-multiplication-vectors funext public +open import linear-algebra.scalar-multiplication-vectors-on-rings funext public +open import linear-algebra.transposition-matrices funext public +open import linear-algebra.vectors funext public +open import linear-algebra.vectors-on-commutative-rings funext public +open import linear-algebra.vectors-on-commutative-semirings funext public +open import linear-algebra.vectors-on-euclidean-domains funext public +open import linear-algebra.vectors-on-rings funext public +open import linear-algebra.vectors-on-semirings funext public ``` diff --git a/src/linear-algebra/constant-matrices.lagda.md b/src/linear-algebra/constant-matrices.lagda.md index 03b95489d8..0025604aa4 100644 --- a/src/linear-algebra/constant-matrices.lagda.md +++ b/src/linear-algebra/constant-matrices.lagda.md @@ -1,7 +1,12 @@ # Constant matrices ```agda -module linear-algebra.constant-matrices where +open import foundation.function-extensionality-axiom + +module + linear-algebra.constant-matrices + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.constant-vectors -open import linear-algebra.matrices +open import linear-algebra.constant-vectors funext +open import linear-algebra.matrices funext ```
diff --git a/src/linear-algebra/constant-vectors.lagda.md b/src/linear-algebra/constant-vectors.lagda.md index 11b8372bc9..e55194a3f4 100644 --- a/src/linear-algebra/constant-vectors.lagda.md +++ b/src/linear-algebra/constant-vectors.lagda.md @@ -1,7 +1,12 @@ # Diagonal vectors ```agda -module linear-algebra.constant-vectors where +open import foundation.function-extensionality-axiom + +module + linear-algebra.constant-vectors + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext ```
diff --git a/src/linear-algebra/diagonal-matrices-on-rings.lagda.md b/src/linear-algebra/diagonal-matrices-on-rings.lagda.md index c15d89761a..5983c684dd 100644 --- a/src/linear-algebra/diagonal-matrices-on-rings.lagda.md +++ b/src/linear-algebra/diagonal-matrices-on-rings.lagda.md @@ -1,7 +1,12 @@ # Diagonal matrices on rings ```agda -module linear-algebra.diagonal-matrices-on-rings where +open import foundation.function-extensionality-axiom + +module + linear-algebra.diagonal-matrices-on-rings + (funext : function-extensionality) + where ```
Imports @@ -11,13 +16,13 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.constant-vectors -open import linear-algebra.functoriality-vectors -open import linear-algebra.matrices-on-rings -open import linear-algebra.vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.constant-vectors funext +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.matrices-on-rings funext +open import linear-algebra.vectors funext +open import linear-algebra.vectors funext-on-rings -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/linear-algebra/functoriality-matrices.lagda.md b/src/linear-algebra/functoriality-matrices.lagda.md index 1c0b419bd0..88f49cc229 100644 --- a/src/linear-algebra/functoriality-matrices.lagda.md +++ b/src/linear-algebra/functoriality-matrices.lagda.md @@ -1,7 +1,12 @@ # Functoriality of the type of matrices ```agda -module linear-algebra.functoriality-matrices where +open import foundation.function-extensionality-axiom + +module + linear-algebra.functoriality-matrices + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.matrices +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.matrices funext ```
diff --git a/src/linear-algebra/functoriality-vectors.lagda.md b/src/linear-algebra/functoriality-vectors.lagda.md index 021cff9837..1c89cf7c4f 100644 --- a/src/linear-algebra/functoriality-vectors.lagda.md +++ b/src/linear-algebra/functoriality-vectors.lagda.md @@ -1,7 +1,12 @@ # Functoriality of the type of vectors ```agda -module linear-algebra.functoriality-vectors where +open import foundation.function-extensionality-axiom + +module + linear-algebra.functoriality-vectors + (funext : function-extensionality) + where ```
Imports @@ -11,15 +16,15 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/linear-algebra/matrices-on-rings.lagda.md b/src/linear-algebra/matrices-on-rings.lagda.md index e14bfa5210..606dc31e5e 100644 --- a/src/linear-algebra/matrices-on-rings.lagda.md +++ b/src/linear-algebra/matrices-on-rings.lagda.md @@ -1,7 +1,12 @@ # Matrices on rings ```agda -module linear-algebra.matrices-on-rings where +open import foundation.function-extensionality-axiom + +module + linear-algebra.matrices-on-rings + (funext : function-extensionality) + where ```
Imports @@ -10,16 +15,16 @@ module linear-algebra.matrices-on-rings where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.constant-matrices -open import linear-algebra.functoriality-matrices -open import linear-algebra.matrices -open import linear-algebra.vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.constant-matrices funext +open import linear-algebra.functoriality-matrices funext +open import linear-algebra.matrices funext +open import linear-algebra.vectors funext +open import linear-algebra.vectors funext-on-rings -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/linear-algebra/matrices.lagda.md b/src/linear-algebra/matrices.lagda.md index f95efc19d8..48e1ccd5a7 100644 --- a/src/linear-algebra/matrices.lagda.md +++ b/src/linear-algebra/matrices.lagda.md @@ -1,7 +1,12 @@ # Matrices ```agda -module linear-algebra.matrices where +open import foundation.function-extensionality-axiom + +module + linear-algebra.matrices + (funext : function-extensionality) + where ```
Imports @@ -10,13 +15,13 @@ module linear-algebra.matrices where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext ```
diff --git a/src/linear-algebra/scalar-multiplication-matrices.lagda.md b/src/linear-algebra/scalar-multiplication-matrices.lagda.md index 460f312973..ffc8eaa057 100644 --- a/src/linear-algebra/scalar-multiplication-matrices.lagda.md +++ b/src/linear-algebra/scalar-multiplication-matrices.lagda.md @@ -1,7 +1,12 @@ # Scalar multiplication on matrices ```agda -module linear-algebra.scalar-multiplication-matrices where +open import foundation.function-extensionality-axiom + +module + linear-algebra.scalar-multiplication-matrices + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.matrices -open import linear-algebra.scalar-multiplication-vectors +open import linear-algebra.matrices funext +open import linear-algebra.scalar-multiplication-vectors funext ```
diff --git a/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md b/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md index b4d616f839..795bd5e2a7 100644 --- a/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md +++ b/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md @@ -1,7 +1,12 @@ # Scalar multiplication of vectors on rings ```agda -module linear-algebra.scalar-multiplication-vectors-on-rings where +open import foundation.function-extensionality-axiom + +module + linear-algebra.scalar-multiplication-vectors-on-rings + (funext : function-extensionality) + where ```
Imports @@ -11,18 +16,18 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.endomorphism-rings-abelian-groups -open import group-theory.homomorphisms-abelian-groups +open import group-theory.endomorphism-rings-abelian-groups funext +open import group-theory.homomorphisms-abelian-groups funext -open import linear-algebra.vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.vectors funext +open import linear-algebra.vectors funext-on-rings -open import ring-theory.homomorphisms-rings -open import ring-theory.modules-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.modules-rings funext +open import ring-theory.rings funext ```
diff --git a/src/linear-algebra/scalar-multiplication-vectors.lagda.md b/src/linear-algebra/scalar-multiplication-vectors.lagda.md index b6f55dd1cd..e86ec48a77 100644 --- a/src/linear-algebra/scalar-multiplication-vectors.lagda.md +++ b/src/linear-algebra/scalar-multiplication-vectors.lagda.md @@ -1,7 +1,12 @@ # Scalar multiplication of vectors ```agda -module linear-algebra.scalar-multiplication-vectors where +open import foundation.function-extensionality-axiom + +module + linear-algebra.scalar-multiplication-vectors + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext ```
diff --git a/src/linear-algebra/transposition-matrices.lagda.md b/src/linear-algebra/transposition-matrices.lagda.md index c46fe91ff2..c391e5f214 100644 --- a/src/linear-algebra/transposition-matrices.lagda.md +++ b/src/linear-algebra/transposition-matrices.lagda.md @@ -1,7 +1,12 @@ # Transposition of matrices ```agda -module linear-algebra.transposition-matrices where +open import foundation.function-extensionality-axiom + +module + linear-algebra.transposition-matrices + (funext : function-extensionality) + where ```
Imports @@ -11,12 +16,12 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.matrices -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.matrices funext +open import linear-algebra.vectors funext ```
diff --git a/src/linear-algebra/vectors-on-commutative-rings.lagda.md b/src/linear-algebra/vectors-on-commutative-rings.lagda.md index 83724fd171..1c3e1e2eee 100644 --- a/src/linear-algebra/vectors-on-commutative-rings.lagda.md +++ b/src/linear-algebra/vectors-on-commutative-rings.lagda.md @@ -1,25 +1,30 @@ # Vectors on commutative rings ```agda -module linear-algebra.vectors-on-commutative-rings where +open import foundation.function-extensionality-axiom + +module + linear-algebra.vectors-on-commutative-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import linear-algebra.constant-vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.constant-vectors funext +open import linear-algebra.vectors-on-rings funext ```
diff --git a/src/linear-algebra/vectors-on-commutative-semirings.lagda.md b/src/linear-algebra/vectors-on-commutative-semirings.lagda.md index 37cfe9c5b2..63053b91d4 100644 --- a/src/linear-algebra/vectors-on-commutative-semirings.lagda.md +++ b/src/linear-algebra/vectors-on-commutative-semirings.lagda.md @@ -1,25 +1,30 @@ # Vectors on commutative semirings ```agda -module linear-algebra.vectors-on-commutative-semirings where +open import foundation.function-extensionality-axiom + +module + linear-algebra.vectors-on-commutative-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-semirings +open import commutative-algebra.commutative-semirings funext open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import linear-algebra.constant-vectors -open import linear-algebra.vectors-on-semirings +open import linear-algebra.constant-vectors funext +open import linear-algebra.vectors-on-semirings funext ```
diff --git a/src/linear-algebra/vectors-on-euclidean-domains.lagda.md b/src/linear-algebra/vectors-on-euclidean-domains.lagda.md index 63019ac835..39fad1bf18 100644 --- a/src/linear-algebra/vectors-on-euclidean-domains.lagda.md +++ b/src/linear-algebra/vectors-on-euclidean-domains.lagda.md @@ -1,32 +1,38 @@ # Vectors on euclidean domains ```agda -module linear-algebra.vectors-on-euclidean-domains where +open import foundation.function-extensionality-axiom + +module + linear-algebra.vectors-on-euclidean-domains + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.euclidean-domains +open import commutative-algebra.euclidean-domains funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext + +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import linear-algebra.constant-vectors -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.constant-vectors funext +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext ```
diff --git a/src/linear-algebra/vectors-on-rings.lagda.md b/src/linear-algebra/vectors-on-rings.lagda.md index fbeb4ee829..1cd2806ae8 100644 --- a/src/linear-algebra/vectors-on-rings.lagda.md +++ b/src/linear-algebra/vectors-on-rings.lagda.md @@ -1,7 +1,12 @@ # Vectors on rings ```agda -module linear-algebra.vectors-on-rings where +open import foundation.function-extensionality-axiom + +module + linear-algebra.vectors-on-rings + (funext : function-extensionality) + where ```
Imports @@ -11,22 +16,23 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext + +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import linear-algebra.constant-vectors -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.constant-vectors funext +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/linear-algebra/vectors-on-semirings.lagda.md b/src/linear-algebra/vectors-on-semirings.lagda.md index c66387088a..9736c97e98 100644 --- a/src/linear-algebra/vectors-on-semirings.lagda.md +++ b/src/linear-algebra/vectors-on-semirings.lagda.md @@ -1,7 +1,12 @@ # Vectors on semirings ```agda -module linear-algebra.vectors-on-semirings where +open import foundation.function-extensionality-axiom + +module + linear-algebra.vectors-on-semirings + (funext : function-extensionality) + where ```
Imports @@ -11,19 +16,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext + +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import linear-algebra.constant-vectors -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.constant-vectors funext +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/linear-algebra/vectors.lagda.md b/src/linear-algebra/vectors.lagda.md index 4a6be035b9..4d7ecc8350 100644 --- a/src/linear-algebra/vectors.lagda.md +++ b/src/linear-algebra/vectors.lagda.md @@ -1,7 +1,12 @@ # Vectors ```agda -module linear-algebra.vectors where +open import foundation.function-extensionality-axiom + +module + linear-algebra.vectors + (funext : function-extensionality) + where ```
Imports @@ -10,30 +15,30 @@ module linear-algebra.vectors where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type -open import foundation.sets +open import foundation.dependent-products-truncated-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type +open import foundation.sets funext open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import univalent-combinatorics.involution-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.involution-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/lists.lagda.md b/src/lists.lagda.md index 612d0e6270..14cd2e5402 100644 --- a/src/lists.lagda.md +++ b/src/lists.lagda.md @@ -3,25 +3,30 @@ ## Modules in the lists namespace ```agda -module lists where +open import foundation.function-extensionality-axiom -open import lists.arrays public -open import lists.concatenation-lists public -open import lists.equality-lists public -open import lists.flattening-lists public -open import lists.functoriality-lists public +module + lists + (funext : function-extensionality) + where + +open import lists.arrays funext public +open import lists.concatenation-lists funext public +open import lists.equality-lists funext public +open import lists.flattening-lists funext public +open import lists.functoriality-lists funext public open import lists.lists public -open import lists.lists-discrete-types public -open import lists.permutation-lists public -open import lists.permutation-vectors public -open import lists.predicates-on-lists public -open import lists.quicksort-lists public -open import lists.reversing-lists public -open import lists.sort-by-insertion-lists public -open import lists.sort-by-insertion-vectors public -open import lists.sorted-lists public -open import lists.sorted-vectors public -open import lists.sorting-algorithms-lists public -open import lists.sorting-algorithms-vectors public -open import lists.universal-property-lists-wild-monoids public +open import lists.lists-discrete-types funext public +open import lists.permutation-lists funext public +open import lists.permutation-vectors funext public +open import lists.predicates-on-lists funext public +open import lists.quicksort-lists funext public +open import lists.reversing-lists funext public +open import lists.sort-by-insertion-lists funext public +open import lists.sort-by-insertion-vectors funext public +open import lists.sorted-lists funext public +open import lists.sorted-vectors funext public +open import lists.sorting-algorithms-lists funext public +open import lists.sorting-algorithms-vectors funext public +open import lists.universal-property-lists-wild-monoids funext public ``` diff --git a/src/lists/arrays.lagda.md b/src/lists/arrays.lagda.md index 054ea39af4..573d6784f1 100644 --- a/src/lists/arrays.lagda.md +++ b/src/lists/arrays.lagda.md @@ -1,7 +1,12 @@ # Arrays ```agda -module lists.arrays where +open import foundation.function-extensionality-axiom + +module + lists.arrays + (funext : function-extensionality) + where ```
Imports @@ -10,24 +15,24 @@ module lists.arrays where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext open import lists.lists -open import univalent-combinatorics.involution-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.involution-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/lists/concatenation-lists.lagda.md b/src/lists/concatenation-lists.lagda.md index 3471f3bcc5..a093dd4793 100644 --- a/src/lists/concatenation-lists.lagda.md +++ b/src/lists/concatenation-lists.lagda.md @@ -1,7 +1,12 @@ # Concatenation of lists ```agda -module lists.concatenation-lists where +open import foundation.function-extensionality-axiom + +module + lists.concatenation-lists + (funext : function-extensionality) + where ```
Imports @@ -12,14 +17,14 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.monoids +open import group-theory.monoids funext -open import lists.equality-lists +open import lists.equality-lists funext open import lists.lists ``` diff --git a/src/lists/equality-lists.lagda.md b/src/lists/equality-lists.lagda.md index b2345f4801..ff2997e650 100644 --- a/src/lists/equality-lists.lagda.md +++ b/src/lists/equality-lists.lagda.md @@ -1,7 +1,12 @@ # Equality of lists ```agda -module lists.equality-lists where +open import foundation.function-extensionality-axiom + +module + lists.equality-lists + (funext : function-extensionality) + where ```
Imports @@ -9,23 +14,23 @@ module lists.equality-lists where ```agda open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.negation -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type -open import foundation.sets -open import foundation.torsorial-type-families -open import foundation.truncated-types +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.negation funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type +open import foundation.sets funext +open import foundation.torsorial-type-families funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels diff --git a/src/lists/flattening-lists.lagda.md b/src/lists/flattening-lists.lagda.md index 3534e0b657..2e28302871 100644 --- a/src/lists/flattening-lists.lagda.md +++ b/src/lists/flattening-lists.lagda.md @@ -1,21 +1,26 @@ # Flattening of lists ```agda -module lists.flattening-lists where +open import foundation.function-extensionality-axiom + +module + lists.flattening-lists + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.sums-of-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext +open import lists.functoriality-lists funext open import lists.lists ``` diff --git a/src/lists/functoriality-lists.lagda.md b/src/lists/functoriality-lists.lagda.md index 233992c6a0..a4e7f0ee73 100644 --- a/src/lists/functoriality-lists.lagda.md +++ b/src/lists/functoriality-lists.lagda.md @@ -1,31 +1,36 @@ # Functoriality of the list operation ```agda -module lists.functoriality-lists where +open import foundation.function-extensionality-axiom + +module + lists.functoriality-lists + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.equality-dependent-pair-types funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext -open import lists.arrays -open import lists.concatenation-lists -open import lists.equality-lists +open import lists.arrays funext +open import lists.concatenation-lists funext +open import lists.equality-lists funext open import lists.lists ``` diff --git a/src/lists/lists-discrete-types.lagda.md b/src/lists/lists-discrete-types.lagda.md index 64cecc520a..ca6bc9d44e 100644 --- a/src/lists/lists-discrete-types.lagda.md +++ b/src/lists/lists-discrete-types.lagda.md @@ -1,27 +1,32 @@ # Lists of elements in discrete types ```agda -module lists.lists-discrete-types where +open import foundation.function-extensionality-axiom + +module + lists.lists-discrete-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.booleans -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.booleans funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type open import foundation.unit-type open import foundation.universe-levels -open import lists.equality-lists +open import lists.equality-lists funext open import lists.lists ``` diff --git a/src/lists/permutation-lists.lagda.md b/src/lists/permutation-lists.lagda.md index 26ca630086..f9ed68f56f 100644 --- a/src/lists/permutation-lists.lagda.md +++ b/src/lists/permutation-lists.lagda.md @@ -1,32 +1,37 @@ # Permutations of lists ```agda -module lists.permutation-lists where +open import foundation.function-extensionality-axiom + +module + lists.permutation-lists + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.equality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext -open import lists.arrays -open import lists.functoriality-lists +open import lists.arrays funext +open import lists.functoriality-lists funext open import lists.lists -open import lists.permutation-vectors +open import lists.permutation-vectors funext ```
diff --git a/src/lists/permutation-vectors.lagda.md b/src/lists/permutation-vectors.lagda.md index 4099f1bfe0..ab3e646a0c 100644 --- a/src/lists/permutation-vectors.lagda.md +++ b/src/lists/permutation-vectors.lagda.md @@ -1,7 +1,12 @@ # Permutations of vectors ```agda -module lists.permutation-vectors where +open import foundation.function-extensionality-axiom + +module + lists.permutation-vectors + (funext : function-extensionality) + where ```
Imports @@ -9,29 +14,29 @@ module lists.permutation-vectors where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types -open import finite-group-theory.transpositions-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.transpositions-standard-finite-types funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.negated-equality +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext -open import lists.arrays +open import lists.arrays funext open import lists.lists -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/lists/predicates-on-lists.lagda.md b/src/lists/predicates-on-lists.lagda.md index 69fb45c9a5..9b30b6df8f 100644 --- a/src/lists/predicates-on-lists.lagda.md +++ b/src/lists/predicates-on-lists.lagda.md @@ -1,14 +1,19 @@ # Predicates on lists ```agda -module lists.predicates-on-lists where +open import foundation.function-extensionality-axiom + +module + lists.predicates-on-lists + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels diff --git a/src/lists/quicksort-lists.lagda.md b/src/lists/quicksort-lists.lagda.md index 0acbdc4224..55b3c13ade 100644 --- a/src/lists/quicksort-lists.lagda.md +++ b/src/lists/quicksort-lists.lagda.md @@ -1,25 +1,30 @@ # Quicksort for lists ```agda -module lists.quicksort-lists where +open import foundation.function-extensionality-axiom + +module + lists.quicksort-lists + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.strong-induction-natural-numbers funext -open import foundation.coproduct-types -open import foundation.identity-types +open import foundation.coproduct-types funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext ```
diff --git a/src/lists/reversing-lists.lagda.md b/src/lists/reversing-lists.lagda.md index 551bed29c5..cd09f824b3 100644 --- a/src/lists/reversing-lists.lagda.md +++ b/src/lists/reversing-lists.lagda.md @@ -1,7 +1,12 @@ # Reversing lists ```agda -module lists.reversing-lists where +open import foundation.function-extensionality-axiom + +module + lists.reversing-lists + (funext : function-extensionality) + where ```
Imports @@ -10,13 +15,13 @@ module lists.reversing-lists where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.flattening-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext +open import lists.flattening-lists funext +open import lists.functoriality-lists funext open import lists.lists ``` diff --git a/src/lists/sort-by-insertion-lists.lagda.md b/src/lists/sort-by-insertion-lists.lagda.md index c14433df58..2882f9f99a 100644 --- a/src/lists/sort-by-insertion-lists.lagda.md +++ b/src/lists/sort-by-insertion-lists.lagda.md @@ -1,26 +1,31 @@ # Sort by insertion for lists ```agda -module lists.sort-by-insertion-lists where +open import foundation.function-extensionality-axiom + +module + lists.sort-by-insertion-lists + (funext : function-extensionality) + where ```
Imports ```agda -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import lists.arrays +open import lists.arrays funext open import lists.lists -open import lists.permutation-lists -open import lists.sort-by-insertion-vectors -open import lists.sorted-lists -open import lists.sorting-algorithms-lists +open import lists.permutation-lists funext +open import lists.sort-by-insertion-vectors funext +open import lists.sorted-lists funext +open import lists.sorting-algorithms-lists funext -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext ```
diff --git a/src/lists/sort-by-insertion-vectors.lagda.md b/src/lists/sort-by-insertion-vectors.lagda.md index 0624942846..968c5cfc0c 100644 --- a/src/lists/sort-by-insertion-vectors.lagda.md +++ b/src/lists/sort-by-insertion-vectors.lagda.md @@ -1,7 +1,12 @@ # Sort by insertion for vectors ```agda -module lists.sort-by-insertion-vectors where +open import foundation.function-extensionality-axiom + +module + lists.sort-by-insertion-vectors + (funext : function-extensionality) + where ```
Imports @@ -9,27 +14,27 @@ module lists.sort-by-insertion-vectors where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types -open import finite-group-theory.transpositions-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.transpositions-standard-finite-types funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.raising-universe-levels-unit-type +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import lists.permutation-vectors -open import lists.sorted-vectors -open import lists.sorting-algorithms-vectors +open import lists.permutation-vectors funext +open import lists.sorted-vectors funext +open import lists.sorting-algorithms-vectors funext -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext ```
diff --git a/src/lists/sorted-lists.lagda.md b/src/lists/sorted-lists.lagda.md index fb82aebedd..9b78e228d3 100644 --- a/src/lists/sorted-lists.lagda.md +++ b/src/lists/sorted-lists.lagda.md @@ -1,7 +1,12 @@ # Sorted lists ```agda -module lists.sorted-lists where +open import foundation.function-extensionality-axiom + +module + lists.sorted-lists + (funext : function-extensionality) + where ```
Imports @@ -10,18 +15,18 @@ module lists.sorted-lists where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import lists.arrays +open import lists.arrays funext open import lists.lists -open import lists.sorted-vectors +open import lists.sorted-vectors funext -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext ```
diff --git a/src/lists/sorted-vectors.lagda.md b/src/lists/sorted-vectors.lagda.md index 0aeb41d303..50783db037 100644 --- a/src/lists/sorted-vectors.lagda.md +++ b/src/lists/sorted-vectors.lagda.md @@ -1,7 +1,12 @@ # Sorted vectors ```agda -module lists.sorted-vectors where +open import foundation.function-extensionality-axiom + +module + lists.sorted-vectors + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,24 @@ module lists.sorted-vectors where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import lists.permutation-vectors +open import lists.permutation-vectors funext -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/lists/sorting-algorithms-lists.lagda.md b/src/lists/sorting-algorithms-lists.lagda.md index 14b5f6541e..72c6fb4ecc 100644 --- a/src/lists/sorting-algorithms-lists.lagda.md +++ b/src/lists/sorting-algorithms-lists.lagda.md @@ -1,7 +1,12 @@ # Sorting algorithms for lists ```agda -module lists.sorting-algorithms-lists where +open import foundation.function-extensionality-axiom + +module + lists.sorting-algorithms-lists + (funext : function-extensionality) + where ```
Imports @@ -9,22 +14,22 @@ module lists.sorting-algorithms-lists where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import lists.arrays +open import lists.arrays funext open import lists.lists -open import lists.permutation-lists -open import lists.sorted-lists -open import lists.sorting-algorithms-vectors +open import lists.permutation-lists funext +open import lists.sorted-lists funext +open import lists.sorting-algorithms-vectors funext -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext ```
diff --git a/src/lists/sorting-algorithms-vectors.lagda.md b/src/lists/sorting-algorithms-vectors.lagda.md index 029591d5fb..2126ed7c65 100644 --- a/src/lists/sorting-algorithms-vectors.lagda.md +++ b/src/lists/sorting-algorithms-vectors.lagda.md @@ -1,7 +1,12 @@ # Sorting algorithms for vectors ```agda -module lists.sorting-algorithms-vectors where +open import foundation.function-extensionality-axiom + +module + lists.sorting-algorithms-vectors + (funext : function-extensionality) + where ```
Imports @@ -9,19 +14,19 @@ module lists.sorting-algorithms-vectors where ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import lists.permutation-vectors -open import lists.sorted-vectors +open import lists.permutation-vectors funext +open import lists.sorted-vectors funext -open import order-theory.decidable-total-orders +open import order-theory.decidable-total-orders funext ```
diff --git a/src/lists/universal-property-lists-wild-monoids.lagda.md b/src/lists/universal-property-lists-wild-monoids.lagda.md index 67c4735fec..37cd520af5 100644 --- a/src/lists/universal-property-lists-wild-monoids.lagda.md +++ b/src/lists/universal-property-lists-wild-monoids.lagda.md @@ -1,7 +1,12 @@ # The universal property of lists with respect to wild monoids ```agda -module lists.universal-property-lists-wild-monoids where +open import foundation.function-extensionality-axiom + +module + lists.universal-property-lists-wild-monoids + (funext : function-extensionality) + where ```
Imports @@ -9,22 +14,22 @@ module lists.universal-property-lists-wild-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import structured-types.h-spaces -open import structured-types.morphisms-h-spaces -open import structured-types.morphisms-wild-monoids -open import structured-types.pointed-maps +open import structured-types.h-spaces funext +open import structured-types.morphisms-h-spaces funext +open import structured-types.morphisms-wild-monoids funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext ```
diff --git a/src/literature.lagda.md b/src/literature.lagda.md index 97fa876ae4..3d35112637 100644 --- a/src/literature.lagda.md +++ b/src/literature.lagda.md @@ -7,14 +7,19 @@ ## Modules in the literature namespace ```agda -module literature where +open import foundation.function-extensionality-axiom -open import literature.100-theorems public -open import literature.1000plus-theorems public -open import literature.idempotents-in-intensional-type-theory public -open import literature.introduction-to-homotopy-type-theory public -open import literature.oeis public -open import literature.sequential-colimits-in-homotopy-type-theory public +module + literature + (funext : function-extensionality) + where + +open import literature.100-theorems funext public +open import literature.1000plus-theorems funext public +open import literature.idempotents-in-intensional-type-theory funext public +open import literature.introduction-to-homotopy-type-theory funext public +open import literature.oeis funext public +open import literature.sequential-colimits-in-homotopy-type-theory funext public ``` ## References diff --git a/src/literature/100-theorems.lagda.md b/src/literature/100-theorems.lagda.md index a7891c065f..e7bf258f14 100644 --- a/src/literature/100-theorems.lagda.md +++ b/src/literature/100-theorems.lagda.md @@ -6,7 +6,12 @@ This file records formalized results from {{#cite 100theorems}} ```agda -module literature.100-theorems where +open import foundation.function-extensionality-axiom + +module + literature.100-theorems + (funext : function-extensionality) + where ``` ## The list @@ -16,7 +21,7 @@ module literature.100-theorems where **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import elementary-number-theory.rational-numbers using +open import elementary-number-theory.rational-numbers funext using ( is-countable-ℚ) ``` @@ -25,7 +30,7 @@ open import elementary-number-theory.rational-numbers using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import elementary-number-theory.infinitude-of-primes using +open import elementary-number-theory.infinitude-of-primes funext using ( infinitude-of-primes-ℕ) ``` @@ -40,7 +45,7 @@ hence we refer to the generalization as the Cantor-Schröder-Bernstein-Escardó theorem. ```agda -open import foundation.cantor-schroder-bernstein-escardo using +open import foundation.cantor-schroder-bernstein-escardo funext using ( Cantor-Schröder-Bernstein-Escardó ; Cantor-Schröder-Bernstein) ``` @@ -50,17 +55,17 @@ open import foundation.cantor-schroder-bernstein-escardo using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import commutative-algebra.binomial-theorem-commutative-rings using +open import commutative-algebra.binomial-theorem-commutative-rings funext using ( binomial-theorem-Commutative-Ring) -open import commutative-algebra.binomial-theorem-commutative-semirings using +open import commutative-algebra.binomial-theorem-commutative-semirings funext using ( binomial-theorem-Commutative-Semiring) -open import ring-theory.binomial-theorem-rings using +open import ring-theory.binomial-theorem-rings funext using ( binomial-theorem-Ring) -open import ring-theory.binomial-theorem-semirings using +open import ring-theory.binomial-theorem-semirings funext using ( binomial-theorem-Semiring) -open import elementary-number-theory.binomial-theorem-integers using +open import elementary-number-theory.binomial-theorem-integers funext using ( binomial-theorem-ℤ) -open import elementary-number-theory.binomial-theorem-natural-numbers using +open import elementary-number-theory.binomial-theorem-natural-numbers funext using ( binomial-theorem-ℕ) ``` @@ -69,7 +74,7 @@ open import elementary-number-theory.binomial-theorem-natural-numbers using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import univalent-combinatorics.decidable-subtypes using +open import univalent-combinatorics.decidable-subtypes funext using ( number-of-elements-decidable-subtype-is-finite) ``` @@ -78,7 +83,7 @@ open import univalent-combinatorics.decidable-subtypes using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import univalent-combinatorics.binomial-types using +open import univalent-combinatorics.binomial-types funext using ( has-cardinality-binomial-type) ``` @@ -91,9 +96,9 @@ while the linked theorems are formalizations of Bezout's lemma, even though these are different statements. ```agda -open import elementary-number-theory.bezouts-lemma-integers using +open import elementary-number-theory.bezouts-lemma-integers funext using ( bezouts-lemma-ℤ) -open import elementary-number-theory.bezouts-lemma-natural-numbers using +open import elementary-number-theory.bezouts-lemma-natural-numbers funext using ( bezouts-lemma-ℕ) ``` @@ -102,7 +107,7 @@ open import elementary-number-theory.bezouts-lemma-natural-numbers using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.cantors-theorem using +open import foundation.cantors-theorem funext using ( theorem-Cantor) ``` @@ -112,7 +117,7 @@ open import foundation.cantors-theorem using ```agda open import - elementary-number-theory.greatest-common-divisor-natural-numbers using + elementary-number-theory.greatest-common-divisor-natural-numbers funext using ( GCD-ℕ) ``` @@ -130,7 +135,7 @@ open import elementary-number-theory.natural-numbers using **Author:** [Victor Blanchi](https://github.com/VictorBlanchi) ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic using +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext using ( fundamental-theorem-arithmetic-list-ℕ) ``` @@ -139,7 +144,7 @@ open import elementary-number-theory.fundamental-theorem-of-arithmetic using **Author:** [malarbol](https://github.com/malarbol) ```agda -open import real-numbers.metric-space-of-real-numbers using +open import real-numbers.metric-space-of-real-numbers funext using ( is-triangular-premetric-leq-ℝ) ``` diff --git a/src/literature/1000plus-theorems.lagda.md b/src/literature/1000plus-theorems.lagda.md index 2257a9effc..a8d7e1e978 100644 --- a/src/literature/1000plus-theorems.lagda.md +++ b/src/literature/1000plus-theorems.lagda.md @@ -9,7 +9,12 @@ theorems in mathematics that have their own Wikipedia entry. We welcome any contribution to this list! ```agda -module literature.1000plus-theorems where +open import foundation.function-extensionality-axiom + +module + literature.1000plus-theorems + (funext : function-extensionality) + where ``` ## Formalized theorems @@ -21,9 +26,9 @@ The theorems are ordered alphabetically, omitting definite articles ("the"). **Author:** [Bryan Lu](https://blu-bird.github.io) ```agda -open import elementary-number-theory.bezouts-lemma-integers using +open import elementary-number-theory.bezouts-lemma-integers funext using ( bezouts-lemma-ℤ) -open import elementary-number-theory.bezouts-lemma-natural-numbers using +open import elementary-number-theory.bezouts-lemma-natural-numbers funext using ( bezouts-lemma-ℕ) ``` @@ -32,17 +37,17 @@ open import elementary-number-theory.bezouts-lemma-natural-numbers using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import commutative-algebra.binomial-theorem-commutative-rings using +open import commutative-algebra.binomial-theorem-commutative-rings funext using ( binomial-theorem-Commutative-Ring) -open import commutative-algebra.binomial-theorem-commutative-semirings using +open import commutative-algebra.binomial-theorem-commutative-semirings funext using ( binomial-theorem-Commutative-Semiring) -open import ring-theory.binomial-theorem-rings using +open import ring-theory.binomial-theorem-rings funext using ( binomial-theorem-Ring) -open import ring-theory.binomial-theorem-semirings using +open import ring-theory.binomial-theorem-semirings funext using ( binomial-theorem-Semiring) -open import elementary-number-theory.binomial-theorem-integers using +open import elementary-number-theory.binomial-theorem-integers funext using ( binomial-theorem-ℤ) -open import elementary-number-theory.binomial-theorem-natural-numbers using +open import elementary-number-theory.binomial-theorem-natural-numbers funext using ( binomial-theorem-ℕ) ``` @@ -57,7 +62,7 @@ hence we refer to the generalization as the Cantor-Schröder-Bernstein-Escardó theorem. ```agda -open import foundation.cantor-schroder-bernstein-escardo using +open import foundation.cantor-schroder-bernstein-escardo funext using ( Cantor-Schröder-Bernstein-Escardó ; Cantor-Schröder-Bernstein) ``` @@ -67,7 +72,7 @@ open import foundation.cantor-schroder-bernstein-escardo using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.cantors-theorem using +open import foundation.cantors-theorem funext using ( theorem-Cantor) ``` @@ -76,7 +81,7 @@ open import foundation.cantors-theorem using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import group-theory.cayleys-theorem using +open import group-theory.cayleys-theorem funext using ( Cayleys-theorem) ``` @@ -85,7 +90,7 @@ open import group-theory.cayleys-theorem using **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import foundation.diaconescus-theorem using +open import foundation.diaconescus-theorem funext using ( theorem-Diaconescu) ``` @@ -94,7 +99,7 @@ open import foundation.diaconescus-theorem using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import elementary-number-theory.infinitude-of-primes using +open import elementary-number-theory.infinitude-of-primes funext using ( infinitude-of-primes-ℕ) ``` @@ -103,7 +108,7 @@ open import elementary-number-theory.infinitude-of-primes using **Author:** [Victor Blanchi](https://github.com/VictorBlanchi) ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic using +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext using ( fundamental-theorem-arithmetic-list-ℕ) ``` @@ -112,7 +117,7 @@ open import elementary-number-theory.fundamental-theorem-of-arithmetic using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.fundamental-theorem-of-equivalence-relations using +open import foundation.fundamental-theorem-of-equivalence-relations funext using ( equiv-equivalence-relation-partition) ``` @@ -121,10 +126,10 @@ open import foundation.fundamental-theorem-of-equivalence-relations using **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import domain-theory.kleenes-fixed-point-theorem-posets using +open import domain-theory.kleenes-fixed-point-theorem-posets funext using ( is-least-fixed-point-theorem-kleene-hom-Poset ; is-least-fixed-point-theorem-kleene-Poset) -open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets using +open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets funext using ( is-least-fixed-point-theorem-kleene-hom-ω-Complete-Poset ; is-least-fixed-point-theorem-kleene-ω-Complete-Poset) ``` @@ -134,7 +139,7 @@ open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets usin **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import order-theory.knaster-tarski-fixed-point-theorem using +open import order-theory.knaster-tarski-fixed-point-theorem funext using ( least-fixed-point-knaster-tarski-Inflattice ; greatest-fixed-point-knaster-tarski-Suplattice) ``` @@ -144,7 +149,7 @@ open import order-theory.knaster-tarski-fixed-point-theorem using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.lawveres-fixed-point-theorem using +open import foundation.lawveres-fixed-point-theorem funext using ( fixed-point-theorem-Lawvere) ``` @@ -153,9 +158,9 @@ open import foundation.lawveres-fixed-point-theorem using **Author:** [Emily Riehl](https://emilyriehl.github.io/) ```agda -open import category-theory.yoneda-lemma-categories using +open import category-theory.yoneda-lemma-categories funext using ( lemma-yoneda-Category) -open import category-theory.yoneda-lemma-precategories using +open import category-theory.yoneda-lemma-precategories funext using ( lemma-yoneda-Precategory) ``` diff --git a/src/literature/idempotents-in-intensional-type-theory.lagda.md b/src/literature/idempotents-in-intensional-type-theory.lagda.md index 448cd6e695..fe8f2d81d7 100644 --- a/src/literature/idempotents-in-intensional-type-theory.lagda.md +++ b/src/literature/idempotents-in-intensional-type-theory.lagda.md @@ -4,7 +4,12 @@ This file collects references to formalization of constructions and theorems from {{#cite Shu17}}. ```agda -module literature.idempotents-in-intensional-type-theory where +open import foundation.function-extensionality-axiom + +module + literature.idempotents-in-intensional-type-theory + (funext : function-extensionality) + where ``` ## 1 Introduction @@ -13,11 +18,11 @@ The introduction section gives an introduction to the problem at hand and motivates its study in univalent foundations. ```agda -open import group-theory.groups using +open import group-theory.groups funext using ( Group ) -open import higher-group-theory.higher-groups using +open import higher-group-theory.higher-groups funext using ( ∞-Group ) ``` @@ -27,11 +32,11 @@ open import higher-group-theory.higher-groups using The second section introduces basic notions from homotopy type theory. ```agda -open import foundation.dependent-function-types -- "dependent products" +open import foundation.dependent-function-types funext -- "dependent products" open import foundation.dependent-pair-types -- "dependent sums" -open import foundation.identity-types using +open import foundation.identity-types funext using ( _＝_ -- "identity type, its elements are paths" ; refl -- "the canonical elements of the identity types" ; concat -- "transitivity of paths" @@ -67,7 +72,7 @@ open import foundation-core.sets using ; is-set -- all identity types are propositions ) -open import foundation.homotopies using +open import foundation.homotopies funext using ( _~_ -- "homotopy" ; nat-htpy -- "naturality of homotopies" ) @@ -78,32 +83,33 @@ given in the article: an equivalence is a function equipped with a left inverse and a right inverse. ```agda -open import foundation.equivalences using +open import foundation.equivalences funext using ( is-equiv -- "type of equivalence proofs" ; equiv -- "type of equivalences" ; is-property-is-equiv -- "the type of equivalence proofs is a mere proposition" ) -open import foundation.function-extensionality using +open import foundation.function-extensionality funext + using ( funext -- "the function extensionality axiom" ) -open import foundation.univalence using +open import foundation.univalence funext using ( equiv-eq -- "the canonical map `(A ＝ B) → (A ≃ B)`" ; univalence -- "the univalence axiom" ) -open import foundation.propositional-truncations using +open import foundation.propositional-truncations funext using ( ║_║₋₁ -- "propositional truncation" ; unit-trunc-Prop -- "the map `A → ║ A ║₋₁`" ; universal-property-trunc-Prop -- "the universal property of propositional truncation" ) -open import foundation.mere-equivalences using +open import foundation.mere-equivalences funext using ( mere-equiv -- "merely equivalent" ) -open import foundation.univalence-implies-function-extensionality using +open import foundation.univalence-implies-function-extensionality funext using ( funext-univalence -- "univalence implies function extensionality" ) @@ -127,11 +133,11 @@ We reserve the terminology "a coherent idempotent" for what in the article is referred to as "a (fully coherent) idempotent". ```agda -open import foundation.endomorphisms using +open import foundation.endomorphisms funext using ( endo -- "endofunction" ) -open import foundation.idempotent-maps using +open import foundation.idempotent-maps funext using ( is-idempotent -- "idempotency witness" ; idempotent-map -- "pre-idempotent (map)" ) @@ -140,29 +146,27 @@ open import foundation.idempotent-maps using **Definition 3.2.** Retracts and splittings. ```agda -open import foundation.retracts-of-types using +open import foundation.retracts-of-types funext using ( retracts -- "retracts of a type" ; retract -- "type of retracts between two types" ) -open import foundation.split-idempotent-maps using +open import foundation.split-idempotent-maps funext using ( is-split-idempotent -- "splitting of an endofunction" ) ``` **Lemma 3.3.** If $f$ has a splitting, then it is pre-idempotent. -```agda -open import foundation.split-idempotent-maps using +`open import foundation.split-idempotent-maps funext using + using ( is-idempotent-is-split-idempotent ) ``` **Lemma 3.4.** The type associated to a splitting of a map is unique up to -equivalence. - -```agda -open import foundation.split-idempotent-maps using +equivaleopen import foundation.split-idempotent-maps funext using +nt-maps using ( essentially-unique-splitting-type-is-split-idempotent ) ``` @@ -173,25 +177,20 @@ The library's preferred terminology for "a quasi-idempotent" is "a quasicoherent idempotent". ```agda -open import foundation.quasicoherently-idempotent-maps using +open import foundation.quasicoherently-idempotent-maps funext using ( is-quasicoherently-idempotent -- "the type of witnesses of quasi-idempotence" ; quasicoherently-idempotent-map -- "the type of quasi-idempotents" ) ``` -**Lemma 3.6.** If $f$ has a splitting, then it is a quasi-idempotent. - -```agda -open import foundation.split-idempotent-maps using +**Lemma 3.6.** If $f$ has a splitting, then it is a quasi-open import foundation.split-idempotent-maps funext using +dempotent-maps using ( is-quasicoherently-idempotent-is-split-idempotent ) ``` -**Theorem 3.7.** If $X$ is a set, then any pre-idempotent on $X$ has a -splitting. - -```agda -open import foundation.split-idempotent-maps using +**Theorem 3.7.** If $X$ is a set, then any pre-idempotent on $Xopen import foundation.split-idempotent-maps funext using +split-idempotent-maps using ( is-split-idempotent-is-idempotent-is-set ) ``` @@ -204,12 +203,10 @@ open import foundation.split-idempotent-maps using splitting. ```agda -open import foundation.weakly-constant-maps using +open import foundation.weakly-constant-maps funext using ( is-weakly-constant -- "the type of witnesses that a map is weakly constant" - ; weakly-constant-map -- "the type of weakly constant maps" - ) - -open import foundation.split-idempotent-maps using + ; weakly-constant-map -- "the open import foundation.split-idempotent-maps funext using +dation.split-idempotent-maps using ( is-split-idempotent-is-weakly-constant-is-idempotent ) ``` @@ -219,12 +216,12 @@ is an embedding if and only if it is pre-idempotent and the type $f(x) = x$ admits a weakly constant endofunction for all $x$. ```agda -open import foundation.sections using +open import foundation.sections funext using ( is-section -- "the type of witnesses that a map is a section to a map" ; section -- "the type of sections of a map" ) -open import foundation.embeddings using +open import foundation.embeddings funext using ( is-emb -- "the type of witnesses that a map is an embedding" ; _↪_ -- "the type of embeddings between two types" ) @@ -254,7 +251,7 @@ a coherent system of idempotence data. **Definition 4.2.** The Cantor space. ```agda -open import set-theory.cantor-space using +open import set-theory.cantor-space funext using ( cantor-space -- "C" ) ``` @@ -268,7 +265,7 @@ open import set-theory.cantor-space using **Definition 4.5.** $B\operatorname{Aut}({-})$. ```agda -open import foundation.connected-components-universes using +open import foundation.connected-components-universes funext using ( component-UU -- "BAut(-)" ) ``` @@ -300,11 +297,11 @@ quasi-idempotent map splits. Sequential colimits of types. ```agda -open import synthetic-homotopy-theory.sequential-diagrams using +open import synthetic-homotopy-theory.sequential-diagrams funext using ( sequential-diagram ) -open import synthetic-homotopy-theory.sequential-colimits using +open import synthetic-homotopy-theory.sequential-colimits funext using ( standard-sequential-colimit ) ``` @@ -312,11 +309,11 @@ open import synthetic-homotopy-theory.sequential-colimits using Sequential limits of types. ```agda -open import foundation.inverse-sequential-diagrams using +open import foundation.inverse-sequential-diagrams funext using ( inverse-sequential-diagram ) -open import foundation.sequential-limits using +open import foundation.sequential-limits funext using ( standard-sequential-limit ) ``` @@ -328,25 +325,21 @@ The formalization generalizes the result of the paper by considering general inverse sequential diagrams rather than those that are constantly $f$. Also note that compared to the paper, the coherences in the formalization are transposed. -```agda -open import foundation.sequential-limits using +`open import foundation.sequential-limits funext using + using ( Eq-standard-sequential-limit -- observational equality on standard sequential limits ; extensionality-standard-sequential-limit ) ``` -**Theorem 5.3.** Assuming function extensionality, any quasi-idempotent splits. - -```agda -open import foundation.split-idempotent-maps using +**Theorem 5.3.** Assuming function extensionaliopen import foundation.split-idempotent-maps funext using +rt foundation.split-idempotent-maps using ( is-split-idempotent-is-quasicoherently-idempotent ) ``` -**Remark 5.4.** Components of the construction. - -```agda -open import foundation.split-idempotent-maps using +**Remarkopen import foundation.split-idempotent-maps funext using +en import foundation.split-idempotent-maps using ( inverse-sequential-diagram-splitting-type-is-quasicoherently-idempotent' ; splitting-type-is-quasicoherently-idempotent' ; inclusion-splitting-type-is-quasicoherently-idempotent' @@ -366,8 +359,8 @@ quasi-idempotence. **Lemma 6.3.** Characterization of the identity types of retract formation. -```agda -open import foundation.retracts-of-types using +`open import foundation.retracts-of-types funext using + using ( equiv-retracts -- observational equality on retracts ; extensionality-retracts ) @@ -398,7 +391,7 @@ definition of coherently idempotent maps is given. **Definition 9.1.** (Fully coherent) idempotents. ```agda -open import foundation.coherently-idempotent-maps using +open import foundation.coherently-idempotent-maps funext using ( is-coherently-idempotent -- "type of (fully coherent) idempotence witnesses" ) ``` diff --git a/src/literature/introduction-to-homotopy-type-theory.lagda.md b/src/literature/introduction-to-homotopy-type-theory.lagda.md index 73694d20ac..b12f99d148 100644 --- a/src/literature/introduction-to-homotopy-type-theory.lagda.md +++ b/src/literature/introduction-to-homotopy-type-theory.lagda.md @@ -4,7 +4,12 @@ This file collects references to formalization of constructions, propositions, theorems and exercises from {{#cite Rij22}}. ```agda -module literature.introduction-to-homotopy-type-theory where +open import foundation.function-extensionality-axiom + +module + literature.introduction-to-homotopy-type-theory + (funext : function-extensionality) + where open import foundation.universe-levels ``` @@ -37,7 +42,7 @@ open import elementary-number-theory.addition-natural-numbers using ### 3.3 Pattern matching ```agda -open import elementary-number-theory.fibonacci-sequence using +open import elementary-number-theory.fibonacci-sequence funext using ( Fibonacci-ℕ) ``` @@ -51,16 +56,16 @@ open import elementary-number-theory.multiplication-natural-numbers using ( mul-ℕ ; _*ℕ_) -- (b) -open import elementary-number-theory.exponentiation-natural-numbers using +open import elementary-number-theory.exponentiation-natural-numbers funext using ( exp-ℕ) ``` **Exercise 3.2.** Minimum and maximum. ```agda -open import elementary-number-theory.minimum-natural-numbers using +open import elementary-number-theory.minimum-natural-numbers funext using ( min-ℕ) -open import elementary-number-theory.maximum-natural-numbers using +open import elementary-number-theory.maximum-natural-numbers funext using ( max-ℕ) ``` @@ -72,14 +77,14 @@ open import elementary-number-theory.triangular-numbers using ( triangular-number-ℕ) -- (b) -open import elementary-number-theory.factorials using +open import elementary-number-theory.factorials funext using ( factorial-ℕ) ``` **Exercise 3.4.** Binomial coefficients. ```agda -open import elementary-number-theory.binomial-coefficients using +open import elementary-number-theory.binomial-coefficients funext using ( binomial-coefficient-ℕ ; is-zero-binomial-coefficient-ℕ) ``` @@ -87,8 +92,8 @@ open import elementary-number-theory.binomial-coefficients using **Exercise 3.5.** Fibonacci sequence using the induction principle of natural numbers. -```agda -open import elementary-number-theory.fibonacci-sequence using +`open import elementary-number-theory.fibonacci-sequence funext using + using ( Fibo) ``` @@ -103,10 +108,8 @@ div-two-pattern-match (succ-ℕ (succ-ℕ n)) = succ-ℕ (div-two-pattern-match For the definition using the induction principle, we think of iterating the swapping operation `(m, 0) ↦ (m, 1) ; (m, 1) ↦ (m + 1, 0)`, using the same -encoding of pairs with functions as the definition of the Fibonacci sequence. - -```agda -open import elementary-number-theory.fibonacci-sequence using +encoding of pairs with functions as the definition of the Fibonacci sequeopen import elementary-number-theory.fibonacci-sequence funext using +equence using ( shift-one ; shift-two) div-two-induction-step : (ℕ → ℕ) → (ℕ → ℕ) @@ -154,7 +157,7 @@ open import foundation.unit-type using **Definition 4.3.1.** The empty type. ```agda -open import foundation.empty-types using +open import foundation.empty-types funext using ( empty -- ∅ ; ind-empty ; ex-falso) @@ -163,16 +166,16 @@ open import foundation.empty-types using **Definition 4.3.2.** Negation of types. ```agda -open import foundation.negation using - ( ¬_) -open import foundation.empty-types using +open import foundation.negation funext using + open import foundation.empty-types funext using + using ( is-empty) ``` **Proposition 4.3.4** Contrapositives. -```agda -open import foundation.negation using +`open import foundation.negation funext using + using ( map-neg) ``` @@ -181,7 +184,7 @@ open import foundation.negation using **Definition 4.4.1.** Coproducts of types. ```agda -open import foundation.coproduct-types using +open import foundation.coproduct-types funext using ( _+_ ; inl ; inr @@ -192,7 +195,7 @@ open import foundation.coproduct-types using **Remark 4.4.2.** Coproducts of functions. ```agda -open import foundation.functoriality-coproduct-types using +open import foundation.functoriality-coproduct-types funext using ( map-coproduct -- f + g : A + B → A' + B' ) ``` @@ -200,7 +203,7 @@ open import foundation.functoriality-coproduct-types using **Proposition 4.4.3.** Projections from coproducts with an empty type. ```agda -open import foundation.type-arithmetic-empty-type using +open import foundation.type-arithmetic-empty-type funext using ( map-right-unit-law-coproduct-is-empty -- is-empty B → (A + B) → A ) ``` @@ -266,7 +269,7 @@ open import foundation.dependent-pair-types using **Definition 4.6.4.** The cartesian product. ```agda -open import foundation.cartesian-product-types using +open import foundation.cartesian-product-types funext using ( _×_ ; ind-product) ``` @@ -282,35 +285,31 @@ open import elementary-number-theory.integers using ( pred-ℤ) -- (b) -open import elementary-number-theory.addition-integers using +open import elementary-number-theory.addition-integers funext using ( add-ℤ) open import elementary-number-theory.integers using ( neg-ℤ) -- (c) -open import elementary-number-theory.multiplication-integers using +open import elementary-number-theory.multiplication-integers funext using ( mul-ℤ) ``` **Exercise 4.2.** Boolean negation, conjunction and disjunction. ```agda -open import foundation.booleans using +open import foundation.booleans funext using ( bool ; false ; true ; ind-bool) --- (a) -open import foundation.booleans using - ( neg-bool) - --- (b) -open import foundation.booleans using - ( conjunction-bool) - --- (c) -open import foundation.booleans using +open import foundation.booleans funext using + using + ( neg-open import foundation.booleans funext using +ooleans using + ( conjuopen import foundation.booleans funext using +ation.booleans using ( disjunction-bool) ``` @@ -321,36 +320,36 @@ Note that we call bi-implications _logical equivalences_ in the library. A type `X` for which we can show `¬¬X` is called _irrefutable_. ```agda -open import foundation.logical-equivalences using +open import foundation.logical-equivalences funext using ( _↔_) -- (a) _ : {l : Level} (P : UU l) → ¬ (P × ¬ P) -_ = λ P (p , np) → np p -open import foundation.negation using +_ = λ P (popen import foundation.negation funext using +egation using ( no-fixed-points-neg -- ¬(P ↔ ¬P) ) -- (b) -open import foundation.double-negation using +open import foundation.double-negation funext using ( ¬¬_ ; intro-double-negation -- P → ¬¬P ; map-double-negation -- (P → Q) → (¬¬P → ¬¬Q) ; double-negation-extend -- (P → ¬¬Q) → (¬¬P → ¬¬Q) ) --- (c) -open import foundation.double-negation using +open import foundation.double-negation funext using + using ( double-negation-double-negation-elim -- ¬¬(¬¬P → P) ; double-negation-Peirces-law -- ¬¬(((P → Q) → P) → P) ; double-negation-linearity-implication -- ¬¬((P → Q) + (Q → P)) ) -open import foundation.irrefutable-propositions using +open import foundation.irrefutable-propositions funext using ( is-irrefutable-is-decidable -- ¬¬(P + ¬P) ) -- (d) -open import foundation.decidable-types using +open import foundation.decidable-types funext using ( double-negation-elim-is-decidable -- (P + ¬P) → (¬¬P → P) ) @@ -366,7 +365,7 @@ _ = ( λ (p : P) → nqp (λ _ → p)) -- (e) -open import logic.double-negation-elimination using +open import logic.double-negation-elimination funext using ( double-negation-elim-neg -- ¬¬(¬ P) → P ; double-negation-elim-exp-neg-neg -- ¬¬(P → ¬¬Q) → (P → ¬¬Q) ; double-negation-elim-product @@ -381,8 +380,8 @@ _ = ( double-negation-elim-neg (¬ P)) ( double-negation-elim-neg (¬ Q)) --- (f) -open import foundation.irrefutable-propositions using +open import foundation.irrefutable-propositions funext using + using ( is-irrefutable-product -- ¬¬A → ¬¬B → ¬¬(A × B) ) @@ -427,7 +426,7 @@ open import lists.lists using ( fold-list) -- (c) -open import lists.functoriality-lists using +open import lists.functoriality-lists funext using ( map-list) -- (d) @@ -435,21 +434,21 @@ open import lists.lists using ( length-list) -- (e) -open import elementary-number-theory.sums-of-natural-numbers using +open import elementary-number-theory.sums-of-natural-numbers funext using ( sum-list-ℕ) -open import elementary-number-theory.products-of-natural-numbers using +open import elementary-number-theory.products-of-natural-numbers funext using ( product-list-ℕ) -- (f) -open import lists.concatenation-lists using +open import lists.concatenation-lists funext using ( concat-list) -- (g) -open import lists.flattening-lists using +open import lists.flattening-lists funext using ( flatten-list) -- (h) -open import lists.reversing-lists using +open import lists.reversing-lists funext using ( reverse-list) ``` @@ -460,7 +459,7 @@ open import lists.reversing-lists using **Definition 5.1.1.** The identity type. ```agda -open import foundation.identity-types using +open import foundation.identity-types funext using ( _＝_ ; Id ; refl ; ind-Id) @@ -470,39 +469,31 @@ open import foundation.identity-types using **Definition 5.2.1.** Concatenation of identifications. -```agda -open import foundation.identity-types using +`open import foundation.identity-types funext using + using ( concat ; _∙_) ``` -**Definition 5.2.2.** Inverse operation. - -```agda -open import foundation.identity-types using +**Definition 5.2.2.** Inverse operatopen import foundation.identity-types funext using +y-types using ( inv) ``` -**Definition 5.2.4.** Associator. - -```agda -open import foundation.identity-types using +**Definition 5.2.4.** open import foundation.identity-types funext using +identity-types using ( assoc -- (p ∙ q) ∙ r = p ∙ (q ∙ r) ) ``` -**Definition 5.2.5.** Unit law operations. - -```agda -open import foundation.identity-types using +**Definition 5.2.5.** Unopen import foundation.identity-types funext using +dation.identity-types using ( left-unit -- refl ∙ p = p ; right-unit -- p ∙ refl = p ) ``` -**Definition 5.2.5.** Inverse law operations. - -```agda -open import foundation.identity-types using +**Definition 5.2.5.*open import foundation.identity-types funext using +rt foundation.identity-types using ( left-inv -- inv p ∙ p = refl ; right-inv -- p ∙ inv p = refl ) @@ -554,9 +545,9 @@ open import foundation.action-on-identifications-dependent-functions using **Proposition 5.5.1.** Contractibility of singletons. ```agda -open import foundation.torsorial-type-families using +open import foundation.torsorial-type-families funext using ( is-torsorial-Id) -open import foundation.contractible-types using +open import foundation.contractible-types funext using ( eq-is-contr') _ : {l : Level} {A : UU l} (a : A) (y : Σ A (λ x → a ＝ x)) → (a , refl) ＝ y @@ -601,18 +592,15 @@ open import elementary-number-theory.addition-natural-numbers using ### Exercises -**Exercise 5.1.** Distributivity of inversion over concatenation. - -```agda -open import foundation.identity-types using +**Exercise 5.1.** Distributivity open import foundation.identity-types funext using +en import foundation.identity-types using ( distributive-inv-concat -- inv (p ∙ q) = inv q ∙ inv p ) ``` -**Exercise 5.2.** Transposing concatenation. - -```agda -open import foundation.identity-types using +**Exeopen import foundation.identity-types funext using +agda +open import foundation.identity-types funext using ( left-transpose-eq-concat -- (p ∙ q = r) → (q = inv p ∙ r) ; right-transpose-eq-concat -- (p ∙ q = r) → (p = r ∙ inv q) ) @@ -621,14 +609,12 @@ open import foundation.identity-types using **Exercise 5.3.** Path lifting. ```agda -open import foundation.equality-dependent-pair-types using - ( eq-pair-eq-base) -``` - -**Exercise 5.4.** Mac Lane pentagon. +open import foundation.equality-dependent-pair-types funext using + ( eq-pair-eq-bopen import foundation.identity-types funext using +n. -```agda -open import foundation.identity-types using +`open import foundation.identity-types funext using + using ( mac-lane-pentagon) ``` @@ -676,28 +662,19 @@ open import elementary-number-theory.integers using **Exercise 5.7.** Abelian group laws for addition of integers. ```agda --- (a) -open import elementary-number-theory.addition-integers using +open import elementary-number-theory.addition-integers funext using + using ( left-unit-law-add-ℤ -- 0 + x = x - ; right-unit-law-add-ℤ -- x + 0 = x - ) - --- (b) -open import elementary-number-theory.addition-integers using + ; right-unit-law-add-ℤ -- x + 0 = open import elementary-number-theory.addition-integers funext using +ntegers using ( left-predecessor-law-add-ℤ -- pred x + y = pred (x + y) ; right-predecessor-law-add-ℤ -- x + pred y = pred (x + y) ; left-successor-law-add-ℤ -- succ x + y = succ (x + y) - ; right-successor-law-add-ℤ -- x + succ y = succ (x + y) - ) - --- (c) -open import elementary-number-theory.addition-integers using + ; right-successor-law-add-ℤ -- x + succ y = succopen import elementary-number-theory.addition-integers funext using +ition-integers using ( associative-add-ℤ -- (x + y) + z = x + (y + z) - ; commutative-add-ℤ -- x + y = y + x - ) - --- (d) -open import elementary-number-theory.addition-integers using + ; commutative-add-ℤ -open import elementary-number-theory.addition-integers funext using +ory.addition-integers using ( left-inverse-law-add-ℤ -- (-x) + x = 0 ; right-inverse-law-add-ℤ -- x + (-x) = 0 ) @@ -706,30 +683,21 @@ open import elementary-number-theory.addition-integers using **Exercise 5.8.** Ring laws for multiplication of integers. ```agda --- (a) -open import elementary-number-theory.multiplication-integers using +open import elementary-number-theory.multiplication-integers funext using + using ( left-zero-law-mul-ℤ -- 0 * x = x ; right-zero-law-mul-ℤ -- x * 0 = x ; left-unit-law-mul-ℤ -- 1 * x = x - ; right-unit-law-mul-ℤ -- x * 1 = x - ) - --- (b) -open import elementary-number-theory.multiplication-integers using + ; right-unit-law-mul-ℤ -- x * 1 = open import elementary-number-theory.multiplication-integers funext using +ntegers using ( left-predecessor-law-mul-ℤ' -- pred x * y = x * y - y ; right-predecessor-law-mul-ℤ' -- x * pred y = x * y - x ; left-successor-law-mul-ℤ' -- succ x * y = x * y + y - ; right-successor-law-mul-ℤ' -- x * succ y = x * y + x - ) - --- (c) -open import elementary-number-theory.multiplication-integers using + ; right-successor-law-mul-ℤ' -- x * succ y = xopen import elementary-number-theory.multiplication-integers funext using +ation-integers using ( left-distributive-mul-add-ℤ -- x * (y + z) = x * y + x * z - ; right-distributive-mul-add-ℤ -- (x + y) * z = x * z + y * z - ) - --- (d) -open import elementary-number-theory.multiplication-integers using + ; right-distributive-mul-add-ℤ -- (x + y) * z open import elementary-number-theory.multiplication-integers funext using +ltiplication-integers using ( associative-mul-ℤ -- (x * y) * z = x * (y * z) ; commutative-mul-ℤ -- x * y = y * x ) @@ -786,7 +754,7 @@ open import foundation.universe-levels using **Remark 6.2.4.** Inclusions into the successor universe. ```agda -open import foundation.raising-universe-levels using +open import foundation.raising-universe-levels funext using ( raise) _ : (l : Level) → UU l → UU (lsuc l) @@ -811,22 +779,20 @@ unrelated, Agda considers them equal. Other universe equalities may be found in **Definition 6.3.1.** Observational equality of ℕ. ```agda -open import elementary-number-theory.equality-natural-numbers using +open import elementary-number-theory.equality-natural-numbers funext using ( Eq-ℕ) ``` **Lemma 6.3.2.** Observational equality of ℕ is reflexive. -```agda -open import elementary-number-theory.equality-natural-numbers using +`open import elementary-number-theory.equality-natural-numbers funext using + using ( refl-Eq-ℕ) ``` **Proposition 6.3.3.** Logical equivalence of observational equality of ℕ and -identifications. - -```agda -open import elementary-number-theory.equality-natural-numbers using +identificatiopen import elementary-number-theory.equality-natural-numbers funext using +numbers using ( Eq-eq-ℕ ; eq-Eq-ℕ) @@ -919,23 +885,16 @@ open import elementary-number-theory.multiplication-natural-numbers using ) ``` -**Exercise 6.2.** Observational equality of booleans. - -```agda --- (a) -open import foundation.booleans using - ( Eq-bool) - --- (b) -open import foundation.booleans using +**Exercise 6.2.** Observational equality oopen import foundation.booleans funext using +t foundation.bopen import foundation.booleans funext using +n import foundation.booleans using ( Eq-eq-bool ; eq-Eq-bool) _ : (x y : bool) → (x ＝ y) ↔ Eq-bool x y -_ = λ x y → (Eq-eq-bool , eq-Eq-bool) - --- (c) -open import foundation.booleans using +_ = open import foundation.booleans funext using +(c) +open import foundation.booleans funext using ( neq-neg-bool -- b ≠ neg-bool b ) _ : ¬ (false ＝ true) @@ -945,31 +904,24 @@ _ = neq-neg-bool false **Exercise 6.3.** Standard linear order on ℕ. ```agda -open import elementary-number-theory.inequality-natural-numbers using +open import elementary-number-theory.inequality-natural-numbers funext using ( _≤-ℕ_) --- (a) -open import elementary-number-theory.inequality-natural-numbers using +open import elementary-number-theory.inequality-natural-numbers funext using + using ( refl-leq-ℕ ; antisymmetric-leq-ℕ - ; transitive-leq-ℕ) - --- (b) -open import elementary-number-theory.inequality-natural-numbers using - ( linear-leq-ℕ -- (m ≤ n) + (n ≤ m) - ) - --- (c) -open import elementary-number-theory.inequality-natural-numbers using + ; transitive-lopen import elementary-number-theory.inequality-natural-numbers funext using +numbers using + ( linear-leq-ℕ -- (m ≤ n) +open import elementary-number-theory.inequality-natural-numbers funext using +atural-numbers using ( preserves-leq-left-add-ℕ ; reflects-leq-left-add-ℕ) _ : (m n k : ℕ) → (m ≤-ℕ n) ↔ (m +ℕ k ≤-ℕ n +ℕ k) _ = - λ m n k → (preserves-leq-left-add-ℕ k m n , reflects-leq-left-add-ℕ k m n) - --- (d) -open import elementary-number-theory.inequality-natural-numbers using + λ m n k → (preserves-leq-left-add-ℕ k m n , reflects-leopen import elementary-number-theory.inequality-natural-numbers funext using +ality-natural-numbers using ( preserves-leq-left-mul-ℕ ; reflects-order-mul-ℕ) @@ -978,11 +930,10 @@ _ = λ m n k → (preserves-leq-left-mul-ℕ (succ-ℕ k) m n , reflects-order-mul-ℕ k m n) --- (e) -open import elementary-number-theory.minimum-natural-numbers using - ( is-greatest-lower-bound-min-ℕ -- (k ≤ min m n) ↔ (k ≤ m) × (k ≤ n) - ) -open import elementary-number-theory.maximum-natural-numbers using +open import elementary-number-theory.minimum-natural-numbers funext using + using + ( is-greatest-lower-bound-min-ℕ -- (k ≤ min m n) ↔ (k ≤ m) × (k ≤ open import elementary-number-theory.maximum-natural-numbers funext using + using ( is-least-upper-bound-max-ℕ -- (max m n ≤ k) ↔ (m ≤ k) × (n ≤ k) ) ``` @@ -990,23 +941,18 @@ open import elementary-number-theory.maximum-natural-numbers using **Exercise 6.4.** Standard strict order on ℕ. ```agda -open import elementary-number-theory.strict-inequality-natural-numbers using +open import elementary-number-theory.strict-inequality-natural-numbers funext using ( _<-ℕ_) --- (a) -open import elementary-number-theory.strict-inequality-natural-numbers using +open import elementary-number-theory.strict-inequality-natural-numbers funext using + using ( anti-reflexive-le-ℕ ; antisymmetric-le-ℕ - ; transitive-le-ℕ) - --- (b) -open import elementary-number-theory.strict-inequality-natural-numbers using + ; transitive-open import elementary-number-theory.strict-inequality-natural-numbers funext using +numbers using ( succ-le-ℕ -- n < n + 1 - ; preserves-le-succ-ℕ -- m < n → m < n + 1 - ) - --- (c) -open import elementary-number-theory.strict-inequality-natural-numbers using + ; preserves-le-succ-ℕ -- m < n → mopen import elementary-number-theory.strict-inequality-natural-numbers funext using +atural-numbers using ( leq-succ-le-ℕ ; le-leq-succ-ℕ ; contradiction-le-ℕ @@ -1022,11 +968,11 @@ _ = λ m n → contradiction-le-ℕ m n , le-not-leq-ℕ m n **Exercise 6.5.** Distance function on ℕ. ```agda -open import elementary-number-theory.distance-natural-numbers using +open import elementary-number-theory.distance-natural-numbers funext using ( dist-ℕ) --- (a) -open import elementary-number-theory.distance-natural-numbers using +open import elementary-number-theory.distance-natural-numbers funext using + using ( dist-eq-ℕ ; eq-dist-ℕ ; symmetric-dist-ℕ -- dist m n = dist n m @@ -1036,16 +982,11 @@ open import elementary-number-theory.distance-natural-numbers using _ : (m n : ℕ) → (m ＝ n) ↔ (dist-ℕ m n ＝ 0) _ = λ m n → (dist-eq-ℕ m n , eq-dist-ℕ m n) --- TODO: b - --- (c) -open import elementary-number-theory.distance-natural-numbers using +-- TOopen import elementary-number-theory.distance-natural-numbers funext using +numbers using ( translation-invariant-dist-ℕ -- dist (a + m) (a + n) = dist m n - ; left-distributive-mul-dist-ℕ' -- dist (k * m) (k * n) = k * (dist m n) - ) - --- (d) -open import elementary-number-theory.distance-natural-numbers using + ; left-distributive-mul-dist-ℕ' -- dist (k * m) (k * n) = k * (dopen import elementary-number-theory.distance-natural-numbers funext using +atural-numbers using ( is-additive-right-inverse-dist-ℕ -- x + dist x y = y for x ≤ y ) ``` @@ -1053,7 +994,7 @@ open import elementary-number-theory.distance-natural-numbers using **Exercise 6.6.** The absolute value function. ```agda -open import elementary-number-theory.absolute-value-integers using +open import elementary-number-theory.absolute-value-integers funext using ( abs-ℤ ; eq-abs-ℤ ; abs-eq-ℤ @@ -1075,23 +1016,21 @@ Note that the library's division relation uses the property `k * d = n`, as opposed to the book's `d * k = n`. ```agda -open import elementary-number-theory.divisibility-natural-numbers using +open import elementary-number-theory.divisibility-natural-numbers funext using ( div-ℕ) ``` **Example 7.1.4.** Divisibility by one. -```agda -open import elementary-number-theory.divisibility-natural-numbers using +`open import elementary-number-theory.divisibility-natural-numbers funext using + using ( div-one-ℕ -- 1 | x ) ``` **Proposition 7.1.5.** A 3-for-2 property of division. - - -```agda -open import elementary-number-theory.divisibility-natural-numbers using +open import elementary-number-theory.divisibility-natural-numbers funext using +numbers using ( div-add-ℕ -- d | x → d | y → d | (x + y) ) ``` @@ -1103,7 +1042,7 @@ The other other two claims are shown in Exercise [7.1](#exercise-7.1). **Definition 7.2.1.** Typal binary relations. ```agda -open import foundation.binary-relations using +open import foundation.binary-relations funext using ( Relation ; is-reflexive ; is-symmetric @@ -1114,22 +1053,20 @@ open import foundation.binary-relations using **Definition 7.2.2.** Congruence relations on ℕ. ```agda -open import elementary-number-theory.congruence-natural-numbers using +open import elementary-number-theory.congruence-natural-numbers funext using ( _≡_mod_) ``` **Example 7.2.3.** The modulus is congruent to zero. -```agda -open import elementary-number-theory.congruence-natural-numbers using +`open import elementary-number-theory.congruence-natural-numbers funext using + using ( cong-zero-ℕ -- k ≡ 0 mod k ) ``` -**Proposition 7.2.4.** Congruence modulo `k` is an equivalence relation. - -```agda -open import elementary-number-theory.congruence-natural-numbers using +**Proposition 7.2.4.** Congruence modulo `k` is an equivalence relatopen import elementary-number-theory.congruence-natural-numbers funext using +numbers using ( refl-cong-ℕ ; symmetric-cong-ℕ ; transitive-cong-ℕ) @@ -1143,7 +1080,7 @@ The point `⋆` is called `neg-one-Fin` because it represents the element `k - 1 under the inclusion into ℕ. ```agda -open import univalent-combinatorics.standard-finite-types using +open import univalent-combinatorics.standard-finite-types funext using ( Fin ; inl-Fin -- inclusion Fin k → Fin (k + 1) ; neg-one-Fin -- point Fin (k + 1) @@ -1152,23 +1089,19 @@ open import univalent-combinatorics.standard-finite-types using **Definition 7.3.4.** Inclusion into ℕ. -```agda -open import univalent-combinatorics.standard-finite-types using +`open import univalent-combinatorics.standard-finite-types funext using + using ( nat-Fin) ``` -**Lemma 7.3.5.** The inclusion into ℕ is bounded. - -```agda -open import univalent-combinatorics.standard-finite-types using +**Lemma 7.3.5.** The inclusion into ℕ is bounopen import univalent-combinatorics.standard-finite-types funext using +e-types using ( strict-upper-bound-nat-Fin -- ι x < k ) ``` -**Proposition 7.3.6.** The inclusion into ℕ is injective. - -```agda -open import univalent-combinatorics.standard-finite-types using +**Proposition 7.3.6.** The inclusion into ℕ isopen import univalent-combinatorics.standard-finite-types funext using +d-finite-types using ( is-injective-nat-Fin) ``` @@ -1181,10 +1114,8 @@ open import foundation.split-surjective-maps using ( is-split-surjective) ``` -**Definition 7.4.2.** Zero and successor on standard finite types. - -```agda -open import univalent-combinatorics.standard-finite-types using +**Definition 7.4.2.** Zero and successor on stanopen import univalent-combinatorics.standard-finite-types funext using +standard-finite-types using ( zero-Fin ; skip-zero-Fin ; succ-Fin) @@ -1193,42 +1124,34 @@ open import univalent-combinatorics.standard-finite-types using **Definition 7.4.3.** The surjection from ℕ into standard finite types. ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext using ( mod-succ-ℕ -- [-]ₖ₊₁ ) ``` -**Lemma 7.4.4.** Preservation of zero and successor `mod k`. - -```agda -open import univalent-combinatorics.standard-finite-types using +**Lemma 7.4.4.** Preservation of zeopen import univalent-combinatorics.standard-finite-types funext using +torics.standard-finite-types using ( is-zero-nat-zero-Fin -- ι(zero) = 0 - ; nat-skip-zero-Fin -- ι(skip-zero x) = ι(x) + 1 - ) -open import elementary-number-theory.modular-arithmetic-standard-finite-types using + ; nat-skip-zero-Fin -- ι(skip-zero x) = ι(x) +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext using + using ( cong-nat-succ-Fin -- ι(succ x) ≡ ι(x) + 1 mod k ) ``` -**Proposition 7.4.5.** - -```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types using +**Proposition 7.4.open import elementary-number-theory.modular-arithmetic-standard-finite-types funext using +e-types using ( cong-nat-mod-succ-ℕ -- ι[x]ₖ₊₁ ≡ x mod (k + 1) ) ``` -**Proposition 7.4.6.** - -```agda -open import elementary-number-theory.divisibility-natural-numbers using +**Propositiopen import elementary-number-theory.divisibility-natural-numbers funext using +atural-numbers using ( is-zero-div-ℕ ; div-is-zero-ℕ) _ : (d x : ℕ) → x <-ℕ d → div-ℕ d x ↔ (x ＝ 0) -_ = λ d x x - -```agda -open import elementary-number-theory.divisibility-natural-numbers using +Imports ```agda -open import foundation.complements-subtypes -open import foundation.decidable-subtypes +open import foundation.complements-subtypes funext +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.full-subtypes -open import foundation.involutions -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.double-negation funext +open import foundation.full-subtypes funext +open import foundation.involutions funext +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext +open import foundation.unions-subtypes funext open import foundation.universe-levels open import foundation-core.function-types -open import logic.complements-decidable-subtypes -open import logic.de-morgan-propositions -open import logic.de-morgan-subtypes +open import logic.complements-decidable-subtypes funext +open import logic.de-morgan-propositions funext +open import logic.de-morgan-subtypes funext ```
diff --git a/src/logic/complements-decidable-subtypes.lagda.md b/src/logic/complements-decidable-subtypes.lagda.md index ae2a775f33..59a094daab 100644 --- a/src/logic/complements-decidable-subtypes.lagda.md +++ b/src/logic/complements-decidable-subtypes.lagda.md @@ -1,33 +1,38 @@ # Complements of decidable subtypes ```agda -module logic.complements-decidable-subtypes where +open import foundation.function-extensionality-axiom + +module + logic.complements-decidable-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.complements-subtypes -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.complements-subtypes funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions +open import foundation.double-negation-stable-propositions funext open import foundation.evaluation-functions -open import foundation.full-subtypes -open import foundation.involutions -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.unions-subtypes +open import foundation.full-subtypes funext +open import foundation.involutions funext +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.unions-subtypes funext open import foundation.universe-levels open import foundation-core.function-types -open import foundation-core.subtypes +open import foundation-core.subtypes funext -open import logic.double-negation-stable-subtypes +open import logic.double-negation-stable-subtypes funext ```
diff --git a/src/logic/complements-double-negation-stable-subtypes.lagda.md b/src/logic/complements-double-negation-stable-subtypes.lagda.md index e4ba546190..2b574ab615 100644 --- a/src/logic/complements-double-negation-stable-subtypes.lagda.md +++ b/src/logic/complements-double-negation-stable-subtypes.lagda.md @@ -1,28 +1,33 @@ # Complements of double negation stable subtypes ```agda -module logic.complements-double-negation-stable-subtypes where +open import foundation.function-extensionality-axiom + +module + logic.complements-double-negation-stable-subtypes + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.double-negation-stable-propositions -open import foundation.full-subtypes -open import foundation.involutions -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.double-negation funext +open import foundation.double-negation funext-stable-propositions +open import foundation.full-subtypes funext +open import foundation.involutions funext +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext +open import foundation.unions-subtypes funext open import foundation.universe-levels open import foundation-core.function-types -open import logic.double-negation-stable-subtypes +open import logic.double-negation-stable-subtypes funext ```
diff --git a/src/logic/de-morgan-embeddings.lagda.md b/src/logic/de-morgan-embeddings.lagda.md index 3391dea43b..0a24ef774b 100644 --- a/src/logic/de-morgan-embeddings.lagda.md +++ b/src/logic/de-morgan-embeddings.lagda.md @@ -1,35 +1,40 @@ # De Morgan embeddings ```agda -module logic.de-morgan-embeddings where +open import foundation.function-extensionality-axiom + +module + logic.de-morgan-embeddings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.decidable-embeddings -open import foundation.decidable-maps -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext +open import foundation.decidable-embeddings funext +open import foundation.decidable-maps funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.fibers-of-maps -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types +open import foundation.embeddings funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.retracts-of-maps +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-maps funext +open import foundation.propositions funext +open import foundation.retracts-of-maps funext open import foundation.subtype-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -42,11 +47,11 @@ open import foundation-core.homotopies open import foundation-core.injective-maps open import foundation-core.torsorial-type-families -open import logic.de-morgan-maps -open import logic.de-morgan-propositions -open import logic.de-morgan-types -open import logic.double-negation-eliminating-maps -open import logic.double-negation-elimination +open import logic.de-morgan-maps funext +open import logic.de-morgan-propositions funext +open import logic.de-morgan-types funext +open import logic.double-negation-eliminating-maps funext +open import logic.double-negation-elimination funext ```
diff --git a/src/logic/de-morgan-maps.lagda.md b/src/logic/de-morgan-maps.lagda.md index 17b5a68d6e..9850f05d95 100644 --- a/src/logic/de-morgan-maps.lagda.md +++ b/src/logic/de-morgan-maps.lagda.md @@ -1,7 +1,12 @@ # De Morgan maps ```agda -module logic.de-morgan-maps where +open import foundation.function-extensionality-axiom + +module + logic.de-morgan-maps + (funext : function-extensionality) + where ```
Imports @@ -10,28 +15,28 @@ module logic.de-morgan-maps where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-maps -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-maps funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.embeddings -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negation -open import foundation.propositions -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types +open import foundation.double-negation funext +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext +open import foundation.retracts-of-types funext open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-maps @@ -41,10 +46,10 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import logic.de-morgan-types -open import logic.de-morgans-law -open import logic.double-negation-eliminating-maps -open import logic.double-negation-elimination +open import logic.de-morgan-types funext +open import logic.de-morgans-law funext +open import logic.double-negation-eliminating-maps funext +open import logic.double-negation-elimination funext ```
diff --git a/src/logic/de-morgan-propositions.lagda.md b/src/logic/de-morgan-propositions.lagda.md index 5ca81ba117..c779611211 100644 --- a/src/logic/de-morgan-propositions.lagda.md +++ b/src/logic/de-morgan-propositions.lagda.md @@ -1,43 +1,48 @@ # De Morgan propositions ```agda -module logic.de-morgan-propositions where +open import foundation.function-extensionality-axiom + +module + logic.de-morgan-propositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.double-negation -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences +open import foundation.disjunction funext +open import foundation.double-negation funext +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.irrefutable-propositions -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.irrefutable-propositions funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.retracts-of-types funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext -open import logic.de-morgan-types -open import logic.de-morgans-law +open import logic.de-morgan-types funext +open import logic.de-morgans-law funext ```
diff --git a/src/logic/de-morgan-subtypes.lagda.md b/src/logic/de-morgan-subtypes.lagda.md index b01a79ab1f..1fd8ac5b63 100644 --- a/src/logic/de-morgan-subtypes.lagda.md +++ b/src/logic/de-morgan-subtypes.lagda.md @@ -1,25 +1,30 @@ # De Morgan subtypes ```agda -module logic.de-morgan-subtypes where +open import foundation.function-extensionality-axiom + +module + logic.de-morgan-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.1-types -open import foundation.coproduct-types +open import foundation.1-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.equality-dependent-function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.sets -open import foundation.structured-type-duality -open import foundation.subtypes -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.sets funext +open import foundation.structured-type-duality funext +open import foundation.subtypes funext +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation-core.embeddings @@ -32,10 +37,10 @@ open import foundation-core.propositions open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import logic.de-morgan-embeddings -open import logic.de-morgan-maps -open import logic.de-morgan-propositions -open import logic.de-morgan-types +open import logic.de-morgan-embeddings funext +open import logic.de-morgan-maps funext +open import logic.de-morgan-propositions funext +open import logic.de-morgan-types funext ```
diff --git a/src/logic/de-morgan-types.lagda.md b/src/logic/de-morgan-types.lagda.md index 749e83645f..108a756610 100644 --- a/src/logic/de-morgan-types.lagda.md +++ b/src/logic/de-morgan-types.lagda.md @@ -1,41 +1,46 @@ # De Morgan types ```agda -module logic.de-morgan-types where +open import foundation.function-extensionality-axiom + +module + logic.de-morgan-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.disjunction -open import foundation.double-negation -open import foundation.empty-types +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext +open import foundation.double-negation funext +open import foundation.empty-types funext open import foundation.evaluation-functions -open import foundation.function-types -open import foundation.identity-types -open import foundation.irrefutable-propositions -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.retracts-of-types +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.irrefutable-propositions funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext +open import foundation.retracts-of-types funext open import foundation.truncation-levels -open import foundation.truncations +open import foundation.truncations funext open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.equivalences open import foundation-core.propositions -open import logic.de-morgans-law +open import logic.de-morgans-law funext ```
diff --git a/src/logic/de-morgans-law.lagda.md b/src/logic/de-morgans-law.lagda.md index 670b532a88..ea1a05566f 100644 --- a/src/logic/de-morgans-law.lagda.md +++ b/src/logic/de-morgans-law.lagda.md @@ -1,31 +1,36 @@ # De Morgan's law ```agda -module logic.de-morgans-law where +open import foundation.function-extensionality-axiom + +module + logic.de-morgans-law + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.disjunction -open import foundation.double-negation -open import foundation.empty-types +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext +open import foundation.double-negation funext +open import foundation.empty-types funext open import foundation.evaluation-functions -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.negation +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.propositions -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext ```
diff --git a/src/logic/double-negation-eliminating-maps.lagda.md b/src/logic/double-negation-eliminating-maps.lagda.md index 836e3191e1..c4c043f1ce 100644 --- a/src/logic/double-negation-eliminating-maps.lagda.md +++ b/src/logic/double-negation-eliminating-maps.lagda.md @@ -1,28 +1,33 @@ # Double negation eliminating maps ```agda -module logic.double-negation-eliminating-maps where +open import foundation.function-extensionality-axiom + +module + logic.double-negation-eliminating-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-maps -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-maps funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types +open import foundation.double-negation funext +open import foundation.empty-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext +open import foundation.retracts-of-types funext open import foundation.transport-along-identifications open import foundation.universe-levels @@ -33,7 +38,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import logic.double-negation-elimination +open import logic.double-negation-elimination funext ```
diff --git a/src/logic/double-negation-elimination.lagda.md b/src/logic/double-negation-elimination.lagda.md index cdc299f056..37fefe6cad 100644 --- a/src/logic/double-negation-elimination.lagda.md +++ b/src/logic/double-negation-elimination.lagda.md @@ -1,28 +1,33 @@ # Double negation elimination ```agda -module logic.double-negation-elimination where +open import foundation.function-extensionality-axiom + +module + logic.double-negation-elimination + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.double-negation +open import foundation.dependent-products-propositions funext +open import foundation.double-negation funext open import foundation.evaluation-functions -open import foundation.hilberts-epsilon-operators -open import foundation.logical-equivalences -open import foundation.retracts-of-types +open import foundation.hilberts-epsilon-operators funext +open import foundation.logical-equivalences funext +open import foundation.retracts-of-types funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-types -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/logic/double-negation-stable-embeddings.lagda.md b/src/logic/double-negation-stable-embeddings.lagda.md index 4e6a207085..7686f9eb4d 100644 --- a/src/logic/double-negation-stable-embeddings.lagda.md +++ b/src/logic/double-negation-stable-embeddings.lagda.md @@ -1,36 +1,41 @@ # Double negation stable embeddings ```agda -module logic.double-negation-stable-embeddings where +open import foundation.function-extensionality-axiom + +module + logic.double-negation-stable-embeddings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.decidable-embeddings -open import foundation.decidable-maps -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-morphisms-arrows funext +open import foundation.decidable-embeddings funext +open import foundation.decidable-maps funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions -open import foundation.embeddings -open import foundation.fibers-of-maps -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types +open import foundation.double-negation-stable-propositions funext +open import foundation.embeddings funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-maps -open import foundation.propositions -open import foundation.retracts-of-maps +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-maps funext +open import foundation.propositions funext +open import foundation.retracts-of-maps funext open import foundation.subtype-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -43,8 +48,8 @@ open import foundation-core.homotopies open import foundation-core.injective-maps open import foundation-core.torsorial-type-families -open import logic.double-negation-eliminating-maps -open import logic.double-negation-elimination +open import logic.double-negation-eliminating-maps funext +open import logic.double-negation-elimination funext ```
diff --git a/src/logic/double-negation-stable-subtypes.lagda.md b/src/logic/double-negation-stable-subtypes.lagda.md index 5780836046..4833b34673 100644 --- a/src/logic/double-negation-stable-subtypes.lagda.md +++ b/src/logic/double-negation-stable-subtypes.lagda.md @@ -1,27 +1,32 @@ # Double negation stable subtypes ```agda -module logic.double-negation-stable-subtypes where +open import foundation.function-extensionality-axiom + +module + logic.double-negation-stable-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.1-types -open import foundation.coproduct-types +open import foundation.1-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.double-negation-stable-propositions -open import foundation.equality-dependent-function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositional-maps -open import foundation.sets -open import foundation.structured-type-duality -open import foundation.subtypes -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-propositions funext +open import foundation.double-negation-stable-propositions funext +open import foundation.equality-dependent-function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-maps funext +open import foundation.sets funext +open import foundation.structured-type-duality funext +open import foundation.subtypes funext +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation-core.embeddings @@ -35,9 +40,9 @@ open import foundation-core.transport-along-identifications open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import logic.double-negation-eliminating-maps -open import logic.double-negation-elimination -open import logic.double-negation-stable-embeddings +open import logic.double-negation-eliminating-maps funext +open import logic.double-negation-elimination funext +open import logic.double-negation-stable-embeddings funext ```
diff --git a/src/logic/functoriality-existential-quantification.lagda.md b/src/logic/functoriality-existential-quantification.lagda.md index 30953b6729..baf5f5ac62 100644 --- a/src/logic/functoriality-existential-quantification.lagda.md +++ b/src/logic/functoriality-existential-quantification.lagda.md @@ -1,13 +1,18 @@ # Functoriality of existential quantification ```agda -module logic.functoriality-existential-quantification where +open import foundation.function-extensionality-axiom + +module + logic.functoriality-existential-quantification + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.existential-quantification +open import foundation.existential-quantification funext open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/logic/markovian-types.lagda.md b/src/logic/markovian-types.lagda.md index 4add56697f..0327bc37f4 100644 --- a/src/logic/markovian-types.lagda.md +++ b/src/logic/markovian-types.lagda.md @@ -1,7 +1,12 @@ # Markovian types ```agda -module logic.markovian-types where +open import foundation.function-extensionality-axiom + +module + logic.markovian-types + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module logic.markovian-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-subtypes +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.inhabited-types -open import foundation.negation -open import foundation.universal-quantification +open import foundation.dependent-products-propositions funext +open import foundation.disjunction funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.inhabited-types funext +open import foundation.negation funext +open import foundation.universal-quantification funext open import foundation.universe-levels open import foundation-core.booleans @@ -25,7 +30,7 @@ open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/logic/markovs-principle.lagda.md b/src/logic/markovs-principle.lagda.md index 66eeefbf91..64312c7b02 100644 --- a/src/logic/markovs-principle.lagda.md +++ b/src/logic/markovs-principle.lagda.md @@ -1,7 +1,12 @@ # Markov's principle ```agda -module logic.markovs-principle where +open import foundation.function-extensionality-axiom + +module + logic.markovs-principle + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module logic.markovs-principle where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-subtypes +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.inhabited-types -open import foundation.negation -open import foundation.universal-quantification +open import foundation.disjunction funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.inhabited-types funext +open import foundation.negation funext +open import foundation.universal-quantification funext open import foundation.universe-levels open import foundation-core.booleans @@ -24,9 +29,9 @@ open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import logic.markovian-types +open import logic.markovian-types funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/metric-spaces.lagda.md b/src/metric-spaces.lagda.md index 24e7a77fbe..bbfdcf4620 100644 --- a/src/metric-spaces.lagda.md +++ b/src/metric-spaces.lagda.md @@ -43,50 +43,55 @@ property of **indistinguishability of identicals** ## Modules in the metric spaces namespace ```agda -module metric-spaces where - -open import metric-spaces.category-of-metric-spaces-and-isometries public -open import metric-spaces.category-of-metric-spaces-and-short-functions public -open import metric-spaces.cauchy-approximations-metric-spaces public -open import metric-spaces.cauchy-approximations-premetric-spaces public -open import metric-spaces.closed-premetric-structures public -open import metric-spaces.complete-metric-spaces public -open import metric-spaces.convergent-cauchy-approximations-metric-spaces public -open import metric-spaces.dependent-products-metric-spaces public -open import metric-spaces.discrete-premetric-structures public -open import metric-spaces.equality-of-metric-spaces public -open import metric-spaces.equality-of-premetric-spaces public -open import metric-spaces.extensional-premetric-structures public -open import metric-spaces.functions-metric-spaces public -open import metric-spaces.functor-category-set-functions-isometry-metric-spaces public -open import metric-spaces.functor-category-short-isometry-metric-spaces public -open import metric-spaces.induced-premetric-structures-on-preimages public -open import metric-spaces.isometric-equivalences-premetric-spaces public -open import metric-spaces.isometries-metric-spaces public -open import metric-spaces.isometries-premetric-spaces public -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces public -open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space public -open import metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space public -open import metric-spaces.metric-space-of-rational-numbers public -open import metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods public -open import metric-spaces.metric-spaces public -open import metric-spaces.metric-structures public -open import metric-spaces.monotonic-premetric-structures public -open import metric-spaces.ordering-premetric-structures public -open import metric-spaces.precategory-of-metric-spaces-and-functions public -open import metric-spaces.precategory-of-metric-spaces-and-isometries public -open import metric-spaces.precategory-of-metric-spaces-and-short-functions public -open import metric-spaces.premetric-spaces public -open import metric-spaces.premetric-structures public -open import metric-spaces.pseudometric-spaces public -open import metric-spaces.pseudometric-structures public -open import metric-spaces.reflexive-premetric-structures public -open import metric-spaces.saturated-metric-spaces public -open import metric-spaces.short-functions-metric-spaces public -open import metric-spaces.short-functions-premetric-spaces public -open import metric-spaces.subspaces-metric-spaces public -open import metric-spaces.symmetric-premetric-structures public -open import metric-spaces.triangular-premetric-structures public +open import foundation.function-extensionality-axiom + +module + metric-spaces + (funext : function-extensionality) + where + +open import metric-spaces.category-of-metric-spaces-and-isometries funext public +open import metric-spaces.category-of-metric-spaces-and-short-functions funext public +open import metric-spaces.cauchy-approximations-metric-spaces funext public +open import metric-spaces.cauchy-approximations-premetric-spaces funext public +open import metric-spaces.closed-premetric-structures funext public +open import metric-spaces.complete-metric-spaces funext public +open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext public +open import metric-spaces.dependent-products-metric-spaces funext public +open import metric-spaces.discrete-premetric-structures funext public +open import metric-spaces.equality-of-metric-spaces funext public +open import metric-spaces.equality-of-premetric-spaces funext public +open import metric-spaces.extensional-premetric-structures funext public +open import metric-spaces.functions-metric-spaces funext public +open import metric-spaces.functor-category-set-functions-isometry-metric-spaces funext public +open import metric-spaces.functor-category-short-isometry-metric-spaces funext public +open import metric-spaces.induced-premetric-structures-on-preimages funext public +open import metric-spaces.isometric-equivalences-premetric-spaces funext public +open import metric-spaces.isometries-metric-spaces funext public +open import metric-spaces.isometries-premetric-spaces funext public +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext public +open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space funext public +open import metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space funext public +open import metric-spaces.metric-space-of-rational-numbers funext public +open import metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods funext public +open import metric-spaces.metric-spaces funext public +open import metric-spaces.metric-structures funext public +open import metric-spaces.monotonic-premetric-structures funext public +open import metric-spaces.ordering-premetric-structures funext public +open import metric-spaces.precategory-of-metric-spaces-and-functions funext public +open import metric-spaces.precategory-of-metric-spaces-and-isometries funext public +open import metric-spaces.precategory-of-metric-spaces-and-short-functions funext public +open import metric-spaces.premetric-spaces funext public +open import metric-spaces.premetric-structures funext public +open import metric-spaces.pseudometric-spaces funext public +open import metric-spaces.pseudometric-structures funext public +open import metric-spaces.reflexive-premetric-structures funext public +open import metric-spaces.saturated-metric-spaces funext public +open import metric-spaces.short-functions-metric-spaces funext public +open import metric-spaces.short-functions-premetric-spaces funext public +open import metric-spaces.subspaces-metric-spaces funext public +open import metric-spaces.symmetric-premetric-structures funext public +open import metric-spaces.triangular-premetric-structures funext public ``` ## References diff --git a/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md index 33740c7c95..3d5ba921b6 100644 --- a/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md @@ -1,25 +1,30 @@ # The category of metric spaces and isometries ```agda -module metric-spaces.category-of-metric-spaces-and-isometries where +open import foundation.function-extensionality-axiom + +module + metric-spaces.category-of-metric-spaces-and-isometries + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories +open import category-theory.categories funext +open import category-theory.isomorphisms-in-precategories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.precategory-of-metric-spaces-and-isometries +open import metric-spaces.equality-of-metric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.precategory-of-metric-spaces-and-isometries funext ```
diff --git a/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md index 64d510500c..e3646ffe3e 100644 --- a/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md @@ -1,25 +1,30 @@ # The category of metric spaces and short maps ```agda -module metric-spaces.category-of-metric-spaces-and-short-functions where +open import foundation.function-extensionality-axiom + +module + metric-spaces.category-of-metric-spaces-and-short-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories +open import category-theory.categories funext +open import category-theory.isomorphisms-in-precategories funext -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.precategory-of-metric-spaces-and-short-functions +open import metric-spaces.equality-of-metric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.precategory-of-metric-spaces-and-short-functions funext ```
diff --git a/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md index 1b5a1f41c2..b530112c5f 100644 --- a/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md @@ -1,26 +1,31 @@ # Cauchy approximations in metric spaces ```agda -module metric-spaces.cauchy-approximations-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.cauchy-approximations-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-premetric-spaces -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.cauchy-approximations-premetric-spaces funext +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext +open import metric-spaces.metric-spaces funext ```
diff --git a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md index 55627ce6e3..07df9fb1c1 100644 --- a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md @@ -1,23 +1,28 @@ # Cauchy approximations in premetric spaces ```agda -module metric-spaces.cauchy-approximations-premetric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.cauchy-approximations-premetric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.premetric-spaces -open import metric-spaces.short-functions-premetric-spaces +open import metric-spaces.premetric-spaces funext +open import metric-spaces.short-functions-premetric-spaces funext ```
diff --git a/src/metric-spaces/closed-premetric-structures.lagda.md b/src/metric-spaces/closed-premetric-structures.lagda.md index 8bf46dea34..877ecb766d 100644 --- a/src/metric-spaces/closed-premetric-structures.lagda.md +++ b/src/metric-spaces/closed-premetric-structures.lagda.md @@ -1,41 +1,47 @@ # Closed premetric structures ```agda -module metric-spaces.closed-premetric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.closed-premetric-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.ordering-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.ordering-premetric-structures funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/complete-metric-spaces.lagda.md b/src/metric-spaces/complete-metric-spaces.lagda.md index 1cb1c38a3a..66ed58c7df 100644 --- a/src/metric-spaces/complete-metric-spaces.lagda.md +++ b/src/metric-spaces/complete-metric-spaces.lagda.md @@ -1,22 +1,27 @@ # Complete metric spaces ```agda -module metric-spaces.complete-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.complete-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.convergent-cauchy-approximations-metric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.cauchy-approximations-metric-spaces funext +open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext +open import metric-spaces.metric-spaces funext ```
diff --git a/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md b/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md index f8ade7ad4b..a6748e121a 100644 --- a/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md +++ b/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md @@ -1,22 +1,27 @@ # Convergent Cauchy approximations in metric spaces ```agda -module metric-spaces.convergent-cauchy-approximations-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.convergent-cauchy-approximations-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.cauchy-approximations-metric-spaces funext +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext +open import metric-spaces.metric-spaces funext ```
diff --git a/src/metric-spaces/dependent-products-metric-spaces.lagda.md b/src/metric-spaces/dependent-products-metric-spaces.lagda.md index 9114877759..ff0cc56e35 100644 --- a/src/metric-spaces/dependent-products-metric-spaces.lagda.md +++ b/src/metric-spaces/dependent-products-metric-spaces.lagda.md @@ -1,28 +1,34 @@ # Dependent products of metric spaces ```agda -module metric-spaces.dependent-products-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.dependent-products-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.propositions -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.short-functions-metric-spaces -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.metric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.pseudometric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.short-functions-metric-spaces funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/discrete-premetric-structures.lagda.md b/src/metric-spaces/discrete-premetric-structures.lagda.md index 7dfae22799..3bf776ea51 100644 --- a/src/metric-spaces/discrete-premetric-structures.lagda.md +++ b/src/metric-spaces/discrete-premetric-structures.lagda.md @@ -1,29 +1,34 @@ # Discrete premetric structures ```agda -module metric-spaces.discrete-premetric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.discrete-premetric-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/equality-of-metric-spaces.lagda.md b/src/metric-spaces/equality-of-metric-spaces.lagda.md index 9e6b49a73c..472ffa7569 100644 --- a/src/metric-spaces/equality-of-metric-spaces.lagda.md +++ b/src/metric-spaces/equality-of-metric-spaces.lagda.md @@ -1,27 +1,32 @@ # Equality of metric spaces ```agda -module metric-spaces.equality-of-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.equality-of-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import metric-spaces.equality-of-premetric-spaces -open import metric-spaces.isometric-equivalences-premetric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.premetric-spaces +open import metric-spaces.equality-of-premetric-spaces funext +open import metric-spaces.isometric-equivalences-premetric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.premetric-spaces funext ```
diff --git a/src/metric-spaces/equality-of-premetric-spaces.lagda.md b/src/metric-spaces/equality-of-premetric-spaces.lagda.md index bf75c6dad0..55888aa93f 100644 --- a/src/metric-spaces/equality-of-premetric-spaces.lagda.md +++ b/src/metric-spaces/equality-of-premetric-spaces.lagda.md @@ -1,7 +1,12 @@ # Equality of premetric spaces ```agda -module metric-spaces.equality-of-premetric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.equality-of-premetric-spaces + (funext : function-extensionality) + where ```
Imports @@ -9,23 +14,23 @@ module metric-spaces.equality-of-premetric-spaces where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import metric-spaces.isometries-premetric-spaces -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures +open import metric-spaces.isometries-premetric-spaces funext +open import metric-spaces.premetric-spaces funext +open import metric-spaces.premetric-structures funext ```
diff --git a/src/metric-spaces/extensional-premetric-structures.lagda.md b/src/metric-spaces/extensional-premetric-structures.lagda.md index 0e614ca440..52f1bf0412 100644 --- a/src/metric-spaces/extensional-premetric-structures.lagda.md +++ b/src/metric-spaces/extensional-premetric-structures.lagda.md @@ -1,28 +1,33 @@ # Extensional premetric structures on types ```agda -module metric-spaces.extensional-premetric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.extensional-premetric-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.premetric-structures funext +open import metric-spaces.reflexive-premetric-structures funext ```
diff --git a/src/metric-spaces/functions-metric-spaces.lagda.md b/src/metric-spaces/functions-metric-spaces.lagda.md index 2c95ab35af..fc758b51e0 100644 --- a/src/metric-spaces/functions-metric-spaces.lagda.md +++ b/src/metric-spaces/functions-metric-spaces.lagda.md @@ -1,19 +1,24 @@ # Functions between metric spaces ```agda -module metric-spaces.functions-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.functions-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.sets funext open import foundation.universe-levels -open import metric-spaces.metric-spaces -open import metric-spaces.premetric-spaces +open import metric-spaces.metric-spaces funext +open import metric-spaces.premetric-spaces funext ```
diff --git a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md index e825f25eff..e7938e25bf 100644 --- a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md @@ -1,27 +1,32 @@ # The functor from the precategory of metric spaces and isometries to the precategory of sets ```agda -module metric-spaces.functor-category-set-functions-isometry-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.functor-category-set-functions-isometry-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.conservative-functors-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories +open import category-theory.conservative-functors-precategories funext +open import category-theory.faithful-functors-precategories funext +open import category-theory.functors-precategories funext -open import foundation.category-of-sets +open import foundation.category-of-sets funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.isomorphisms-of-sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.isomorphisms-of-sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.precategory-of-metric-spaces-and-isometries +open import metric-spaces.isometries-metric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.precategory-of-metric-spaces-and-isometries funext ```
diff --git a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md index 9e55f22584..89d9412938 100644 --- a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md @@ -1,24 +1,29 @@ # The inclusion of isometries into the category of metric spaces and short maps ```agda -module metric-spaces.functor-category-short-isometry-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.functor-category-short-isometry-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.conservative-functors-precategories -open import category-theory.faithful-functors-precategories -open import category-theory.functors-precategories +open import category-theory.conservative-functors-precategories funext +open import category-theory.faithful-functors-precategories funext +open import category-theory.functors-precategories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import metric-spaces.precategory-of-metric-spaces-and-isometries -open import metric-spaces.precategory-of-metric-spaces-and-short-functions -open import metric-spaces.short-functions-metric-spaces +open import metric-spaces.precategory-of-metric-spaces-and-isometries funext +open import metric-spaces.precategory-of-metric-spaces-and-short-functions funext +open import metric-spaces.short-functions-metric-spaces funext ```
diff --git a/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md b/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md index 880bd2efd8..cd57a57411 100644 --- a/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md +++ b/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md @@ -1,25 +1,30 @@ # Induced premetric structures on preimages ```agda -module metric-spaces.induced-premetric-structures-on-preimages where +open import foundation.function-extensionality-axiom + +module + metric-spaces.induced-premetric-structures-on-preimages + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md b/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md index 34c143ce20..2e9b722b02 100644 --- a/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md +++ b/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md @@ -1,31 +1,37 @@ # Isometric equivalences between premetric spaces ```agda -module metric-spaces.isometric-equivalences-premetric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.isometric-equivalences-premetric-spaces + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import metric-spaces.equality-of-premetric-spaces -open import metric-spaces.isometries-premetric-spaces -open import metric-spaces.premetric-spaces +open import metric-spaces.equality-of-premetric-spaces funext +open import metric-spaces.isometries-premetric-spaces funext +open import metric-spaces.premetric-spaces funext ```
diff --git a/src/metric-spaces/isometries-metric-spaces.lagda.md b/src/metric-spaces/isometries-metric-spaces.lagda.md index 5078244b1f..7bdd0581d1 100644 --- a/src/metric-spaces/isometries-metric-spaces.lagda.md +++ b/src/metric-spaces/isometries-metric-spaces.lagda.md @@ -1,35 +1,41 @@ # Isometries between metric spaces ```agda -module metric-spaces.isometries-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.isometries-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.sequences -open import foundation.sets -open import foundation.subtypes -open import foundation.univalence +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.univalence funext open import foundation.universe-levels -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometries-premetric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.functions-metric-spaces funext +open import metric-spaces.isometries-premetric-spaces funext +open import metric-spaces.metric-spaces funext ```
diff --git a/src/metric-spaces/isometries-premetric-spaces.lagda.md b/src/metric-spaces/isometries-premetric-spaces.lagda.md index 6b3812351b..96b0f1beb8 100644 --- a/src/metric-spaces/isometries-premetric-spaces.lagda.md +++ b/src/metric-spaces/isometries-premetric-spaces.lagda.md @@ -1,30 +1,36 @@ # Isometries between premetric spaces ```agda -module metric-spaces.isometries-premetric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.isometries-premetric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.premetric-spaces +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.premetric-spaces funext ```
diff --git a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md index a3390d3a52..370b61f10b 100644 --- a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md +++ b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md @@ -1,24 +1,29 @@ # Limits of Cauchy approximations in premetric spaces ```agda -module metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-premetric-spaces -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.cauchy-approximations-premetric-spaces funext +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.premetric-spaces funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md b/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md index dc0c9c9e53..d5b8b6abaf 100644 --- a/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md +++ b/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md @@ -1,20 +1,25 @@ # The metric space of cauchy approximations in a metric space ```agda -module metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space where +open import foundation.function-extensionality-axiom + +module + metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.dependent-products-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.subspaces-metric-spaces +open import metric-spaces.cauchy-approximations-metric-spaces funext +open import metric-spaces.dependent-products-metric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.subspaces-metric-spaces funext ```
diff --git a/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md b/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md index 07c23b1fdf..5782851d81 100644 --- a/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md +++ b/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md @@ -1,7 +1,12 @@ # The metric space of convergent cauchy approximations in a metric space ```agda -module metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space where +open import foundation.function-extensionality-axiom + +module + metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metri ```agda open import foundation.universe-levels -open import metric-spaces.convergent-cauchy-approximations-metric-spaces -open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space -open import metric-spaces.metric-spaces -open import metric-spaces.subspaces-metric-spaces +open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext +open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.subspaces-metric-spaces funext ```
diff --git a/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md b/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md index 5f2525fef2..0046388c48 100644 --- a/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md +++ b/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md @@ -3,40 +3,45 @@ ```agda {-# OPTIONS --lossy-unification #-} -module metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods where +open import foundation.function-extensionality-axiom + +module + metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.difference-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.metric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-spaces funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.pseudometric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/metric-space-of-rational-numbers.lagda.md b/src/metric-spaces/metric-space-of-rational-numbers.lagda.md index 8ad75841c4..c643b02bac 100644 --- a/src/metric-spaces/metric-space-of-rational-numbers.lagda.md +++ b/src/metric-spaces/metric-space-of-rational-numbers.lagda.md @@ -3,49 +3,54 @@ ```agda {-# OPTIONS --lossy-unification #-} -module metric-spaces.metric-space-of-rational-numbers where +open import foundation.function-extensionality-axiom + +module + metric-spaces.metric-space-of-rational-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.difference-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.diagonal-maps-cartesian-products-of-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.diagonal-maps-cartesian-products-of-types funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces -open import metric-spaces.convergent-cauchy-approximations-metric-spaces -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.saturated-metric-spaces -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.cauchy-approximations-metric-spaces funext +open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.isometries-metric-spaces funext +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.metric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-spaces funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.pseudometric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.saturated-metric-spaces funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/metric-spaces.lagda.md b/src/metric-spaces/metric-spaces.lagda.md index 27701dbe35..ab46d4e6a9 100644 --- a/src/metric-spaces/metric-spaces.lagda.md +++ b/src/metric-spaces/metric-spaces.lagda.md @@ -1,36 +1,41 @@ # Metric spaces ```agda -module metric-spaces.metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-spaces -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.metric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-spaces funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.pseudometric-spaces funext +open import metric-spaces.pseudometric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/metric-structures.lagda.md b/src/metric-spaces/metric-structures.lagda.md index 0839f2efae..a67b035f6b 100644 --- a/src/metric-spaces/metric-structures.lagda.md +++ b/src/metric-spaces/metric-structures.lagda.md @@ -1,27 +1,32 @@ # Metric structures ```agda -module metric-spaces.metric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.metric-structures + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.universe-levels -open import metric-spaces.closed-premetric-structures -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.ordering-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.closed-premetric-structures funext +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.ordering-premetric-structures funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.pseudometric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/monotonic-premetric-structures.lagda.md b/src/metric-spaces/monotonic-premetric-structures.lagda.md index d495f3087d..c7caede9ab 100644 --- a/src/metric-spaces/monotonic-premetric-structures.lagda.md +++ b/src/metric-spaces/monotonic-premetric-structures.lagda.md @@ -1,18 +1,23 @@ # Monotonic premetric structures on types ```agda -module metric-spaces.monotonic-premetric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.monotonic-premetric-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import metric-spaces.premetric-structures +open import metric-spaces.premetric-structures funext ```
diff --git a/src/metric-spaces/ordering-premetric-structures.lagda.md b/src/metric-spaces/ordering-premetric-structures.lagda.md index 9d31996995..646ebe12c8 100644 --- a/src/metric-spaces/ordering-premetric-structures.lagda.md +++ b/src/metric-spaces/ordering-premetric-structures.lagda.md @@ -1,25 +1,30 @@ # The poset of premetric structures on a type ```agda -module metric-spaces.ordering-premetric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.ordering-premetric-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import metric-spaces.premetric-structures +open import metric-spaces.premetric-structures funext -open import order-theory.posets -open import order-theory.preorders +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md index 0ad621c3a1..b959e04df2 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md @@ -1,20 +1,25 @@ # The precategory of metric spaces and functions ```agda -module metric-spaces.precategory-of-metric-spaces-and-functions where +open import foundation.function-extensionality-axiom + +module + metric-spaces.precategory-of-metric-spaces-and-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import metric-spaces.functions-metric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.functions-metric-spaces funext +open import metric-spaces.metric-spaces funext ```
diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md index aceb047872..8ec36ffd11 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md @@ -1,30 +1,34 @@ # The precategory of metric spaces and isometries ```agda -module metric-spaces.precategory-of-metric-spaces-and-isometries where +open import foundation.function-extensionality-axiom + +module + metric-spaces.precategory-of-metric-spaces-and-isometries + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.logical-equivalences +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces +open import metric-spaces.equality-of-metric-spaces funext +open import metric-spaces.functions-metric-spaces funext +open import metric-spaces.isometries-metric-spaces funext +open import metric-spaces.metric-spaces funext ```
diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md index bc3ca88ffe..ba40e55f4f 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md @@ -1,32 +1,36 @@ # The precategory of metric spaces and short functions ```agda -module metric-spaces.precategory-of-metric-spaces-and-short-functions where +open import foundation.function-extensionality-axiom + +module + metric-spaces.precategory-of-metric-spaces-and-short-functions + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.functoriality-dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometric-equivalences-premetric-spaces -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.short-functions-metric-spaces +open import metric-spaces.equality-of-metric-spaces funext +open import metric-spaces.functions-metric-spaces funext +open import metric-spaces.isometric-equivalences-premetric-spaces funext +open import metric-spaces.isometries-metric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.short-functions-metric-spaces funext ```
diff --git a/src/metric-spaces/premetric-spaces.lagda.md b/src/metric-spaces/premetric-spaces.lagda.md index edc68f4a20..9ee09c5365 100644 --- a/src/metric-spaces/premetric-spaces.lagda.md +++ b/src/metric-spaces/premetric-spaces.lagda.md @@ -1,26 +1,31 @@ # Premetric spaces ```agda -module metric-spaces.premetric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.premetric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import metric-spaces.discrete-premetric-structures -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.discrete-premetric-structures funext +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/premetric-structures.lagda.md b/src/metric-spaces/premetric-structures.lagda.md index 1efac73fa8..8b0066b45a 100644 --- a/src/metric-spaces/premetric-structures.lagda.md +++ b/src/metric-spaces/premetric-structures.lagda.md @@ -1,32 +1,38 @@ # Premetric structures on types ```agda -module metric-spaces.premetric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.premetric-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-types +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels ``` diff --git a/src/metric-spaces/pseudometric-spaces.lagda.md b/src/metric-spaces/pseudometric-spaces.lagda.md index 1504bef0ae..7537bab100 100644 --- a/src/metric-spaces/pseudometric-spaces.lagda.md +++ b/src/metric-spaces/pseudometric-spaces.lagda.md @@ -1,30 +1,35 @@ # Pseudometric spaces ```agda -module metric-spaces.pseudometric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.pseudometric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalence-relations funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.discrete-premetric-structures -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.discrete-premetric-structures funext +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-spaces funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.pseudometric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/pseudometric-structures.lagda.md b/src/metric-spaces/pseudometric-structures.lagda.md index fb0476457b..a7ee1b258c 100644 --- a/src/metric-spaces/pseudometric-structures.lagda.md +++ b/src/metric-spaces/pseudometric-structures.lagda.md @@ -1,25 +1,30 @@ # Pseudometric structures on a type ```agda -module metric-spaces.pseudometric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.pseudometric-structures + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import metric-spaces.closed-premetric-structures -open import metric-spaces.discrete-premetric-structures -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.closed-premetric-structures funext +open import metric-spaces.discrete-premetric-structures funext +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/reflexive-premetric-structures.lagda.md b/src/metric-spaces/reflexive-premetric-structures.lagda.md index 5bb77664f7..26a2f94f85 100644 --- a/src/metric-spaces/reflexive-premetric-structures.lagda.md +++ b/src/metric-spaces/reflexive-premetric-structures.lagda.md @@ -1,28 +1,33 @@ # Reflexive premetric structures on types ```agda -module metric-spaces.reflexive-premetric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.reflexive-premetric-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.premetric-structures +open import metric-spaces.premetric-structures funext ```
diff --git a/src/metric-spaces/saturated-metric-spaces.lagda.md b/src/metric-spaces/saturated-metric-spaces.lagda.md index f4d759453b..b0101f8cd1 100644 --- a/src/metric-spaces/saturated-metric-spaces.lagda.md +++ b/src/metric-spaces/saturated-metric-spaces.lagda.md @@ -1,33 +1,38 @@ # Saturated metric spaces ```agda -module metric-spaces.saturated-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.saturated-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.closed-premetric-structures -open import metric-spaces.functions-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.short-functions-metric-spaces +open import metric-spaces.closed-premetric-structures funext +open import metric-spaces.functions-metric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.metric-structures funext +open import metric-spaces.premetric-spaces funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.short-functions-metric-spaces funext ```
diff --git a/src/metric-spaces/short-functions-metric-spaces.lagda.md b/src/metric-spaces/short-functions-metric-spaces.lagda.md index bab344ebbb..37f418dfb9 100644 --- a/src/metric-spaces/short-functions-metric-spaces.lagda.md +++ b/src/metric-spaces/short-functions-metric-spaces.lagda.md @@ -1,32 +1,38 @@ # Short functions between metric spaces ```agda -module metric-spaces.short-functions-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.short-functions-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.sequences -open import foundation.sets -open import foundation.subtypes +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.short-functions-premetric-spaces +open import metric-spaces.functions-metric-spaces funext +open import metric-spaces.isometries-metric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.short-functions-premetric-spaces funext ```
diff --git a/src/metric-spaces/short-functions-premetric-spaces.lagda.md b/src/metric-spaces/short-functions-premetric-spaces.lagda.md index f719e1acfc..6afcde009f 100644 --- a/src/metric-spaces/short-functions-premetric-spaces.lagda.md +++ b/src/metric-spaces/short-functions-premetric-spaces.lagda.md @@ -1,31 +1,37 @@ # Short functions between premetric spaces ```agda -module metric-spaces.short-functions-premetric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.short-functions-premetric-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.sequences -open import foundation.sets -open import foundation.subtypes +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.isometries-premetric-spaces -open import metric-spaces.premetric-spaces +open import metric-spaces.isometries-premetric-spaces funext +open import metric-spaces.premetric-spaces funext ```
diff --git a/src/metric-spaces/subspaces-metric-spaces.lagda.md b/src/metric-spaces/subspaces-metric-spaces.lagda.md index 0b5765b507..3753d76e4f 100644 --- a/src/metric-spaces/subspaces-metric-spaces.lagda.md +++ b/src/metric-spaces/subspaces-metric-spaces.lagda.md @@ -1,28 +1,33 @@ # Subspaces of metric spaces ```agda -module metric-spaces.subspaces-metric-spaces where +open import foundation.function-extensionality-axiom + +module + metric-spaces.subspaces-metric-spaces + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.subtypes +open import foundation.logical-equivalences funext +open import foundation.subtypes funext open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.functions-metric-spaces -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.functions-metric-spaces funext +open import metric-spaces.isometries-metric-spaces funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.metric-structures funext +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.pseudometric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext ```
diff --git a/src/metric-spaces/symmetric-premetric-structures.lagda.md b/src/metric-spaces/symmetric-premetric-structures.lagda.md index 86d360e6a2..b4df549191 100644 --- a/src/metric-spaces/symmetric-premetric-structures.lagda.md +++ b/src/metric-spaces/symmetric-premetric-structures.lagda.md @@ -1,22 +1,27 @@ # Symmetric premetric structures on types ```agda -module metric-spaces.symmetric-premetric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.symmetric-premetric-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.binary-relations -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.binary-relations funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import metric-spaces.premetric-structures +open import metric-spaces.premetric-structures funext ```
diff --git a/src/metric-spaces/triangular-premetric-structures.lagda.md b/src/metric-spaces/triangular-premetric-structures.lagda.md index 98b2b7c42a..de181e5683 100644 --- a/src/metric-spaces/triangular-premetric-structures.lagda.md +++ b/src/metric-spaces/triangular-premetric-structures.lagda.md @@ -1,24 +1,29 @@ # Triangular premetric structures on types ```agda -module metric-spaces.triangular-premetric-structures where +open import foundation.function-extensionality-axiom + +module + metric-spaces.triangular-premetric-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.positive-rational-numbers funext -open import foundation.binary-relations -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.binary-relations funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.monotonic-premetric-structures -open import metric-spaces.premetric-structures -open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.monotonic-premetric-structures funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.reflexive-premetric-structures funext ```
diff --git a/src/modal-type-theory.lagda.md b/src/modal-type-theory.lagda.md index e9f60ad038..e278c1e9b9 100644 --- a/src/modal-type-theory.lagda.md +++ b/src/modal-type-theory.lagda.md @@ -20,29 +20,34 @@ _cohesive_ structure. ## Modules in the modal type theory namespace ```agda -module modal-type-theory where - -open import modal-type-theory.action-on-homotopies-flat-modality public -open import modal-type-theory.action-on-identifications-crisp-functions public -open import modal-type-theory.action-on-identifications-flat-modality public -open import modal-type-theory.crisp-cartesian-product-types public -open import modal-type-theory.crisp-coproduct-types public -open import modal-type-theory.crisp-dependent-function-types public -open import modal-type-theory.crisp-dependent-pair-types public -open import modal-type-theory.crisp-function-types public -open import modal-type-theory.crisp-identity-types public -open import modal-type-theory.crisp-law-of-excluded-middle public -open import modal-type-theory.crisp-pullbacks public +open import foundation.function-extensionality-axiom + +module + modal-type-theory + (funext : function-extensionality) + where + +open import modal-type-theory.action-on-homotopies-flat-modality funext public +open import modal-type-theory.action-on-identifications-crisp-functions funext public +open import modal-type-theory.action-on-identifications-flat-modality funext public +open import modal-type-theory.crisp-cartesian-product-types funext public +open import modal-type-theory.crisp-coproduct-types funext public +open import modal-type-theory.crisp-dependent-function-types funext public +open import modal-type-theory.crisp-dependent-pair-types funext public +open import modal-type-theory.crisp-function-types funext public +open import modal-type-theory.crisp-identity-types funext public +open import modal-type-theory.crisp-law-of-excluded-middle funext public +open import modal-type-theory.crisp-pullbacks funext public open import modal-type-theory.crisp-types public -open import modal-type-theory.dependent-universal-property-flat-discrete-crisp-types public -open import modal-type-theory.flat-discrete-crisp-types public -open import modal-type-theory.flat-modality public -open import modal-type-theory.flat-sharp-adjunction public -open import modal-type-theory.functoriality-flat-modality public -open import modal-type-theory.functoriality-sharp-modality public -open import modal-type-theory.sharp-codiscrete-maps public -open import modal-type-theory.sharp-codiscrete-types public -open import modal-type-theory.sharp-modality public -open import modal-type-theory.transport-along-crisp-identifications public -open import modal-type-theory.universal-property-flat-discrete-crisp-types public +open import modal-type-theory.dependent-universal-property-flat-discrete-crisp-types funext public +open import modal-type-theory.flat-discrete-crisp-types funext public +open import modal-type-theory.flat-modality funext public +open import modal-type-theory.flat-sharp-adjunction funext public +open import modal-type-theory.functoriality-flat-modality funext public +open import modal-type-theory.functoriality-sharp-modality funext public +open import modal-type-theory.sharp-codiscrete-maps funext public +open import modal-type-theory.sharp-codiscrete-types funext public +open import modal-type-theory.sharp-modality funext public +open import modal-type-theory.transport-along-crisp-identifications funext public +open import modal-type-theory.universal-property-flat-discrete-crisp-types funext public ``` diff --git a/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md b/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md index 248652177b..f9768264b9 100644 --- a/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md +++ b/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.action-on-homotopies-flat-modality where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.action-on-homotopies-flat-modality + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-flat-modality funext +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext ```
diff --git a/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md b/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md index 085fda16e2..f1824ee303 100644 --- a/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md +++ b/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.action-on-identifications-crisp-functions where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.action-on-identifications-crisp-functions + (funext : function-extensionality) + where ```
Imports @@ -13,7 +18,7 @@ open import foundation.universe-levels open import foundation-core.identity-types -open import modal-type-theory.crisp-identity-types +open import modal-type-theory.crisp-identity-types funext ```
diff --git a/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md b/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md index 4f878208a8..ef1612fb19 100644 --- a/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md +++ b/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.action-on-identifications-flat-modality where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.action-on-identifications-flat-modality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-crisp-functions -open import modal-type-theory.crisp-identity-types -open import modal-type-theory.flat-modality +open import modal-type-theory.action-on-identifications-crisp-functions funext +open import modal-type-theory.crisp-identity-types funext +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-cartesian-product-types.lagda.md b/src/modal-type-theory/crisp-cartesian-product-types.lagda.md index 000d78c746..01a8bc6fd2 100644 --- a/src/modal-type-theory/crisp-cartesian-product-types.lagda.md +++ b/src/modal-type-theory/crisp-cartesian-product-types.lagda.md @@ -3,27 +3,32 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.crisp-cartesian-product-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.crisp-cartesian-product-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality +open import modal-type-theory.flat-discrete-crisp-types funext +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-coproduct-types.lagda.md b/src/modal-type-theory/crisp-coproduct-types.lagda.md index 1fc84587d7..41bc6c326b 100644 --- a/src/modal-type-theory/crisp-coproduct-types.lagda.md +++ b/src/modal-type-theory/crisp-coproduct-types.lagda.md @@ -3,25 +3,30 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.crisp-coproduct-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.crisp-coproduct-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality +open import modal-type-theory.flat-discrete-crisp-types funext +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-dependent-function-types.lagda.md b/src/modal-type-theory/crisp-dependent-function-types.lagda.md index a5034fb664..3f438c2db7 100644 --- a/src/modal-type-theory/crisp-dependent-function-types.lagda.md +++ b/src/modal-type-theory/crisp-dependent-function-types.lagda.md @@ -3,23 +3,29 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.crisp-dependent-function-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.crisp-dependent-function-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-flat-modality funext +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-dependent-pair-types.lagda.md b/src/modal-type-theory/crisp-dependent-pair-types.lagda.md index 962a9f0762..c1c0612e10 100644 --- a/src/modal-type-theory/crisp-dependent-pair-types.lagda.md +++ b/src/modal-type-theory/crisp-dependent-pair-types.lagda.md @@ -3,25 +3,30 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.crisp-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.crisp-dependent-pair-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.flat-discrete-crisp-types funext +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-function-types.lagda.md b/src/modal-type-theory/crisp-function-types.lagda.md index 57b0ed3e46..78b625299f 100644 --- a/src/modal-type-theory/crisp-function-types.lagda.md +++ b/src/modal-type-theory/crisp-function-types.lagda.md @@ -3,25 +3,31 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.crisp-function-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.crisp-function-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.crisp-dependent-function-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-flat-modality funext +open import modal-type-theory.crisp-dependent-function-types funext +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-identity-types.lagda.md b/src/modal-type-theory/crisp-identity-types.lagda.md index adffea8d96..a17e0ba7a4 100644 --- a/src/modal-type-theory/crisp-identity-types.lagda.md +++ b/src/modal-type-theory/crisp-identity-types.lagda.md @@ -3,22 +3,27 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.crisp-identity-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.crisp-identity-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.flat-modality +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md b/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md index 52f9b9c10f..3651c68d44 100644 --- a/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md +++ b/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md @@ -3,17 +3,22 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.crisp-law-of-excluded-middle where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.crisp-law-of-excluded-middle + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext open import foundation-core.propositions ``` diff --git a/src/modal-type-theory/crisp-pullbacks.lagda.md b/src/modal-type-theory/crisp-pullbacks.lagda.md index d0e87ca486..30a578b33a 100644 --- a/src/modal-type-theory/crisp-pullbacks.lagda.md +++ b/src/modal-type-theory/crisp-pullbacks.lagda.md @@ -3,33 +3,38 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.crisp-pullbacks where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.crisp-pullbacks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-pullbacks -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-pullbacks funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.morphisms-cospan-diagrams -open import foundation.pullbacks -open import foundation.standard-pullbacks +open import foundation.pullbacks funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-crisp-functions -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.crisp-dependent-pair-types -open import modal-type-theory.crisp-identity-types -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-crisp-functions funext +open import modal-type-theory.action-on-identifications-flat-modality funext +open import modal-type-theory.crisp-dependent-pair-types funext +open import modal-type-theory.crisp-identity-types funext +open import modal-type-theory.flat-discrete-crisp-types funext +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext ```
diff --git a/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md index 1754d487ba..1e107b20da 100644 --- a/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md @@ -3,16 +3,21 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.dependent-universal-property-flat-discrete-crisp-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.dependent-universal-property-flat-discrete-crisp-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import modal-type-theory.flat-modality +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/flat-discrete-crisp-types.lagda.md index 5bf37687fc..d587bee7bc 100644 --- a/src/modal-type-theory/flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/flat-discrete-crisp-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.flat-discrete-crisp-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.flat-discrete-crisp-types + (funext : function-extensionality) + where ```
Imports @@ -12,24 +17,24 @@ module modal-type-theory.flat-discrete-crisp-types where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.booleans +open import foundation.booleans funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.unit-type open import foundation.universe-levels -open import modal-type-theory.action-on-homotopies-flat-modality -open import modal-type-theory.crisp-identity-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-homotopies-flat-modality funext +open import modal-type-theory.crisp-identity-types funext +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext ```
diff --git a/src/modal-type-theory/flat-modality.lagda.md b/src/modal-type-theory/flat-modality.lagda.md index 10318f9d11..d3e917659d 100644 --- a/src/modal-type-theory/flat-modality.lagda.md +++ b/src/modal-type-theory/flat-modality.lagda.md @@ -3,17 +3,22 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.flat-modality where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.flat-modality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels ``` diff --git a/src/modal-type-theory/flat-sharp-adjunction.lagda.md b/src/modal-type-theory/flat-sharp-adjunction.lagda.md index f3cd07d5ef..be552aa494 100644 --- a/src/modal-type-theory/flat-sharp-adjunction.lagda.md +++ b/src/modal-type-theory/flat-sharp-adjunction.lagda.md @@ -3,26 +3,31 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.flat-sharp-adjunction where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.flat-sharp-adjunction + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality -open import modal-type-theory.sharp-codiscrete-types -open import modal-type-theory.sharp-modality +open import modal-type-theory.action-on-identifications-flat-modality funext +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext +open import modal-type-theory.sharp-codiscrete-types funext +open import modal-type-theory.sharp-modality funext ```
diff --git a/src/modal-type-theory/functoriality-flat-modality.lagda.md b/src/modal-type-theory/functoriality-flat-modality.lagda.md index 150a1c469e..9e238b8219 100644 --- a/src/modal-type-theory/functoriality-flat-modality.lagda.md +++ b/src/modal-type-theory/functoriality-flat-modality.lagda.md @@ -3,24 +3,29 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.functoriality-flat-modality where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.functoriality-flat-modality + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext +open import foundation.sections funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality -open import modal-type-theory.flat-modality +open import modal-type-theory.action-on-identifications-flat-modality funext +open import modal-type-theory.flat-modality funext ```
diff --git a/src/modal-type-theory/functoriality-sharp-modality.lagda.md b/src/modal-type-theory/functoriality-sharp-modality.lagda.md index 673562dad9..14a7e2c95a 100644 --- a/src/modal-type-theory/functoriality-sharp-modality.lagda.md +++ b/src/modal-type-theory/functoriality-sharp-modality.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.functoriality-sharp-modality where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.functoriality-sharp-modality + (funext : function-extensionality) + where ```
Imports @@ -11,17 +16,17 @@ module modal-type-theory.functoriality-sharp-modality where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.locally-small-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.locally-small-types funext open import foundation.universe-levels -open import modal-type-theory.sharp-modality +open import modal-type-theory.sharp-modality funext -open import orthogonal-factorization-systems.locally-small-modal-operators -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-subuniverse-induction +open import orthogonal-factorization-systems.locally-small-modal-operators funext +open import orthogonal-factorization-systems.modal-induction funext +open import orthogonal-factorization-systems.modal-subuniverse-induction funext ```
diff --git a/src/modal-type-theory/sharp-codiscrete-maps.lagda.md b/src/modal-type-theory/sharp-codiscrete-maps.lagda.md index b6f62e6748..bed39825a8 100644 --- a/src/modal-type-theory/sharp-codiscrete-maps.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-maps.lagda.md @@ -3,17 +3,22 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.sharp-codiscrete-maps where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.sharp-codiscrete-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.fibers-of-maps -open import foundation.propositions +open import foundation.fibers-of-maps funext +open import foundation.propositions funext open import foundation.universe-levels -open import modal-type-theory.sharp-codiscrete-types +open import modal-type-theory.sharp-codiscrete-types funext ```
diff --git a/src/modal-type-theory/sharp-codiscrete-types.lagda.md b/src/modal-type-theory/sharp-codiscrete-types.lagda.md index 7b570a8aa2..94caf20a69 100644 --- a/src/modal-type-theory/sharp-codiscrete-types.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.sharp-codiscrete-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.sharp-codiscrete-types + (funext : function-extensionality) + where ```
Imports @@ -11,19 +16,18 @@ module modal-type-theory.sharp-codiscrete-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.transport-along-equivalences +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.transport-along-equivalences funext open import foundation.universe-levels -open import modal-type-theory.sharp-modality +open import modal-type-theory.sharp-modality funext -open import orthogonal-factorization-systems.higher-modalities -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.higher-modalities funext +open import orthogonal-factorization-systems.modal-operators funext ```
diff --git a/src/modal-type-theory/sharp-modality.lagda.md b/src/modal-type-theory/sharp-modality.lagda.md index 3dba911431..779b136c63 100644 --- a/src/modal-type-theory/sharp-modality.lagda.md +++ b/src/modal-type-theory/sharp-modality.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.sharp-modality where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.sharp-modality + (funext : function-extensionality) + where ```
Imports @@ -11,15 +16,15 @@ module modal-type-theory.sharp-modality where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.locally-small-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.locally-small-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.locally-small-modal-operators -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-subuniverse-induction +open import orthogonal-factorization-systems.locally-small-modal-operators funext +open import orthogonal-factorization-systems.modal-induction funext +open import orthogonal-factorization-systems.modal-subuniverse-induction funext ```
diff --git a/src/modal-type-theory/transport-along-crisp-identifications.lagda.md b/src/modal-type-theory/transport-along-crisp-identifications.lagda.md index 3405430500..233d03b939 100644 --- a/src/modal-type-theory/transport-along-crisp-identifications.lagda.md +++ b/src/modal-type-theory/transport-along-crisp-identifications.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.transport-along-crisp-identifications where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.transport-along-crisp-identifications + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import modal-type-theory.crisp-identity-types +open import modal-type-theory.crisp-identity-types funext ```
diff --git a/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md index 63e293c714..759461fb7e 100644 --- a/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -module modal-type-theory.universal-property-flat-discrete-crisp-types where +open import foundation.function-extensionality-axiom + +module + modal-type-theory.universal-property-flat-discrete-crisp-types + (funext : function-extensionality) + where ```
Imports @@ -11,19 +16,20 @@ module modal-type-theory.universal-property-flat-discrete-crisp-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.universal-property-equivalences +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-crisp-functions -open import modal-type-theory.crisp-function-types -open import modal-type-theory.flat-discrete-crisp-types -open import modal-type-theory.flat-modality -open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.action-on-identifications-crisp-functions funext +open import modal-type-theory.crisp-function-types funext +open import modal-type-theory.flat-discrete-crisp-types funext +open import modal-type-theory.flat-modality funext +open import modal-type-theory.functoriality-flat-modality funext ```
diff --git a/src/order-theory.lagda.md b/src/order-theory.lagda.md index 349f62993a..c38720517a 100644 --- a/src/order-theory.lagda.md +++ b/src/order-theory.lagda.md @@ -3,139 +3,144 @@ ## Modules in the order theory namespace ```agda -module order-theory where +open import foundation.function-extensionality-axiom -open import order-theory.accessible-elements-relations public -open import order-theory.bottom-elements-large-posets public -open import order-theory.bottom-elements-posets public -open import order-theory.bottom-elements-preorders public -open import order-theory.chains-posets public -open import order-theory.chains-preorders public -open import order-theory.closure-operators-large-locales public -open import order-theory.closure-operators-large-posets public -open import order-theory.commuting-squares-of-galois-connections-large-posets public -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets public -open import order-theory.coverings-locales public -open import order-theory.decidable-posets public -open import order-theory.decidable-preorders public -open import order-theory.decidable-subposets public -open import order-theory.decidable-subpreorders public -open import order-theory.decidable-total-orders public -open import order-theory.decidable-total-preorders public -open import order-theory.deflationary-maps-posets public -open import order-theory.deflationary-maps-preorders public -open import order-theory.dependent-products-large-frames public -open import order-theory.dependent-products-large-inflattices public -open import order-theory.dependent-products-large-locales public -open import order-theory.dependent-products-large-meet-semilattices public -open import order-theory.dependent-products-large-posets public -open import order-theory.dependent-products-large-preorders public -open import order-theory.dependent-products-large-suplattices public -open import order-theory.distributive-lattices public -open import order-theory.finite-coverings-locales public -open import order-theory.finite-posets public -open import order-theory.finite-preorders public -open import order-theory.finite-total-orders public -open import order-theory.finitely-graded-posets public -open import order-theory.frames public -open import order-theory.galois-connections public -open import order-theory.galois-connections-large-posets public -open import order-theory.greatest-lower-bounds-large-posets public -open import order-theory.greatest-lower-bounds-posets public -open import order-theory.homomorphisms-frames public -open import order-theory.homomorphisms-large-frames public -open import order-theory.homomorphisms-large-locales public -open import order-theory.homomorphisms-large-meet-semilattices public -open import order-theory.homomorphisms-large-suplattices public -open import order-theory.homomorphisms-meet-semilattices public -open import order-theory.homomorphisms-meet-suplattices public -open import order-theory.homomorphisms-suplattices public -open import order-theory.ideals-preorders public -open import order-theory.incidence-algebras public -open import order-theory.inflationary-maps-posets public -open import order-theory.inflationary-maps-preorders public -open import order-theory.inflattices public -open import order-theory.inhabited-chains-posets public -open import order-theory.inhabited-chains-preorders public -open import order-theory.inhabited-finite-total-orders public -open import order-theory.interval-subposets public -open import order-theory.join-preserving-maps-posets public -open import order-theory.join-semilattices public -open import order-theory.knaster-tarski-fixed-point-theorem public -open import order-theory.large-frames public -open import order-theory.large-inflattices public -open import order-theory.large-join-semilattices public -open import order-theory.large-locales public -open import order-theory.large-meet-semilattices public -open import order-theory.large-meet-subsemilattices public -open import order-theory.large-posets public -open import order-theory.large-preorders public -open import order-theory.large-quotient-locales public -open import order-theory.large-subframes public -open import order-theory.large-subposets public -open import order-theory.large-subpreorders public -open import order-theory.large-subsuplattices public -open import order-theory.large-suplattices public -open import order-theory.lattices public -open import order-theory.least-upper-bounds-large-posets public -open import order-theory.least-upper-bounds-posets public -open import order-theory.locales public -open import order-theory.locally-finite-posets public -open import order-theory.lower-bounds-large-posets public -open import order-theory.lower-bounds-posets public -open import order-theory.lower-sets-large-posets public -open import order-theory.lower-types-preorders public -open import order-theory.maximal-chains-posets public -open import order-theory.maximal-chains-preorders public -open import order-theory.meet-semilattices public -open import order-theory.meet-suplattices public -open import order-theory.nuclei-large-locales public -open import order-theory.opposite-large-posets public -open import order-theory.opposite-large-preorders public -open import order-theory.opposite-posets public -open import order-theory.opposite-preorders public -open import order-theory.order-preserving-maps-large-posets public -open import order-theory.order-preserving-maps-large-preorders public -open import order-theory.order-preserving-maps-posets public -open import order-theory.order-preserving-maps-preorders public -open import order-theory.ordinals public -open import order-theory.posets public -open import order-theory.powers-of-large-locales public -open import order-theory.precategory-of-decidable-total-orders public -open import order-theory.precategory-of-finite-posets public -open import order-theory.precategory-of-finite-total-orders public -open import order-theory.precategory-of-inhabited-finite-total-orders public -open import order-theory.precategory-of-posets public -open import order-theory.precategory-of-total-orders public -open import order-theory.preorders public -open import order-theory.principal-lower-sets-large-posets public -open import order-theory.principal-upper-sets-large-posets public -open import order-theory.reflective-galois-connections-large-posets public -open import order-theory.resizing-posets public -open import order-theory.resizing-preorders public -open import order-theory.resizing-suplattices public -open import order-theory.similarity-of-elements-large-posets public -open import order-theory.similarity-of-elements-large-preorders public -open import order-theory.similarity-of-order-preserving-maps-large-posets public -open import order-theory.similarity-of-order-preserving-maps-large-preorders public -open import order-theory.strict-order-preserving-maps public -open import order-theory.strict-preorders public -open import order-theory.strictly-inflationary-maps-strict-preorders public -open import order-theory.strictly-preordered-sets public -open import order-theory.subposets public -open import order-theory.subpreorders public -open import order-theory.suplattices public -open import order-theory.supremum-preserving-maps-posets public -open import order-theory.top-elements-large-posets public -open import order-theory.top-elements-posets public -open import order-theory.top-elements-preorders public -open import order-theory.total-orders public -open import order-theory.total-preorders public -open import order-theory.transitive-well-founded-relations public -open import order-theory.upper-bounds-chains-posets public -open import order-theory.upper-bounds-large-posets public -open import order-theory.upper-bounds-posets public -open import order-theory.upper-sets-large-posets public -open import order-theory.well-founded-relations public -open import order-theory.zorns-lemma public +module + order-theory + (funext : function-extensionality) + where + +open import order-theory.accessible-elements-relations funext public +open import order-theory.bottom-elements-large-posets funext public +open import order-theory.bottom-elements-posets funext public +open import order-theory.bottom-elements-preorders funext public +open import order-theory.chains-posets funext public +open import order-theory.chains-preorders funext public +open import order-theory.closure-operators-large-locales funext public +open import order-theory.closure-operators-large-posets funext public +open import order-theory.commuting-squares-of-galois-connections-large-posets funext public +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext public +open import order-theory.coverings-locales funext public +open import order-theory.decidable-posets funext public +open import order-theory.decidable-preorders funext public +open import order-theory.decidable-subposets funext public +open import order-theory.decidable-subpreorders funext public +open import order-theory.decidable-total-orders funext public +open import order-theory.decidable-total-preorders funext public +open import order-theory.deflationary-maps-posets funext public +open import order-theory.deflationary-maps-preorders funext public +open import order-theory.dependent-products-large-frames funext public +open import order-theory.dependent-products-large-inflattices funext public +open import order-theory.dependent-products-large-locales funext public +open import order-theory.dependent-products-large-meet-semilattices funext public +open import order-theory.dependent-products-large-posets funext public +open import order-theory.dependent-products-large-preorders funext public +open import order-theory.dependent-products-large-suplattices funext public +open import order-theory.distributive-lattices funext public +open import order-theory.finite-coverings-locales funext public +open import order-theory.finite-posets funext public +open import order-theory.finite-preorders funext public +open import order-theory.finite-total-orders funext public +open import order-theory.finitely-graded-posets funext public +open import order-theory.frames funext public +open import order-theory.galois-connections funext public +open import order-theory.galois-connections-large-posets funext public +open import order-theory.greatest-lower-bounds-large-posets funext public +open import order-theory.greatest-lower-bounds-posets funext public +open import order-theory.homomorphisms-frames funext public +open import order-theory.homomorphisms-large-frames funext public +open import order-theory.homomorphisms-large-locales funext public +open import order-theory.homomorphisms-large-meet-semilattices funext public +open import order-theory.homomorphisms-large-suplattices funext public +open import order-theory.homomorphisms-meet-semilattices funext public +open import order-theory.homomorphisms-meet-suplattices funext public +open import order-theory.homomorphisms-suplattices funext public +open import order-theory.ideals-preorders funext public +open import order-theory.incidence-algebras funext public +open import order-theory.inflationary-maps-posets funext public +open import order-theory.inflationary-maps-preorders funext public +open import order-theory.inflattices funext public +open import order-theory.inhabited-chains-posets funext public +open import order-theory.inhabited-chains-preorders funext public +open import order-theory.inhabited-finite-total-orders funext public +open import order-theory.interval-subposets funext public +open import order-theory.join-preserving-maps-posets funext public +open import order-theory.join-semilattices funext public +open import order-theory.knaster-tarski-fixed-point-theorem funext public +open import order-theory.large-frames funext public +open import order-theory.large-inflattices funext public +open import order-theory.large-join-semilattices funext public +open import order-theory.large-locales funext public +open import order-theory.large-meet-semilattices funext public +open import order-theory.large-meet-subsemilattices funext public +open import order-theory.large-posets funext public +open import order-theory.large-preorders funext public +open import order-theory.large-quotient-locales funext public +open import order-theory.large-subframes funext public +open import order-theory.large-subposets funext public +open import order-theory.large-subpreorders funext public +open import order-theory.large-subsuplattices funext public +open import order-theory.large-suplattices funext public +open import order-theory.lattices funext public +open import order-theory.least-upper-bounds-large-posets funext public +open import order-theory.least-upper-bounds-posets funext public +open import order-theory.locales funext public +open import order-theory.locally-finite-posets funext public +open import order-theory.lower-bounds-large-posets funext public +open import order-theory.lower-bounds-posets funext public +open import order-theory.lower-sets-large-posets funext public +open import order-theory.lower-types-preorders funext public +open import order-theory.maximal-chains-posets funext public +open import order-theory.maximal-chains-preorders funext public +open import order-theory.meet-semilattices funext public +open import order-theory.meet-suplattices funext public +open import order-theory.nuclei-large-locales funext public +open import order-theory.opposite-large-posets funext public +open import order-theory.opposite-large-preorders funext public +open import order-theory.opposite-posets funext public +open import order-theory.opposite-preorders funext public +open import order-theory.order-preserving-maps-large-posets funext public +open import order-theory.order-preserving-maps-large-preorders funext public +open import order-theory.order-preserving-maps-posets funext public +open import order-theory.order-preserving-maps-preorders funext public +open import order-theory.ordinals funext public +open import order-theory.posets funext public +open import order-theory.powers-of-large-locales funext public +open import order-theory.precategory-of-decidable-total-orders funext public +open import order-theory.precategory-of-finite-posets funext public +open import order-theory.precategory-of-finite-total-orders funext public +open import order-theory.precategory-of-inhabited-finite-total-orders funext public +open import order-theory.precategory-of-posets funext public +open import order-theory.precategory-of-total-orders funext public +open import order-theory.preorders funext public +open import order-theory.principal-lower-sets-large-posets funext public +open import order-theory.principal-upper-sets-large-posets funext public +open import order-theory.reflective-galois-connections-large-posets funext public +open import order-theory.resizing-posets funext public +open import order-theory.resizing-preorders funext public +open import order-theory.resizing-suplattices funext public +open import order-theory.similarity-of-elements-large-posets funext public +open import order-theory.similarity-of-elements-large-preorders funext public +open import order-theory.similarity-of-order-preserving-maps-large-posets funext public +open import order-theory.similarity-of-order-preserving-maps-large-preorders funext public +open import order-theory.strict-order-preserving-maps funext public +open import order-theory.strict-preorders funext public +open import order-theory.strictly-inflationary-maps-strict-preorders funext public +open import order-theory.strictly-preordered-sets funext public +open import order-theory.subposets funext public +open import order-theory.subpreorders funext public +open import order-theory.suplattices funext public +open import order-theory.supremum-preserving-maps-posets funext public +open import order-theory.top-elements-large-posets funext public +open import order-theory.top-elements-posets funext public +open import order-theory.top-elements-preorders funext public +open import order-theory.total-orders funext public +open import order-theory.total-preorders funext public +open import order-theory.transitive-well-founded-relations funext public +open import order-theory.upper-bounds-chains-posets funext public +open import order-theory.upper-bounds-large-posets funext public +open import order-theory.upper-bounds-posets funext public +open import order-theory.upper-sets-large-posets funext public +open import order-theory.well-founded-relations funext public +open import order-theory.zorns-lemma funext public ``` diff --git a/src/order-theory/accessible-elements-relations.lagda.md b/src/order-theory/accessible-elements-relations.lagda.md index a6b6863dca..523ff37fd9 100644 --- a/src/order-theory/accessible-elements-relations.lagda.md +++ b/src/order-theory/accessible-elements-relations.lagda.md @@ -1,16 +1,22 @@ # Accessible elements with respect to relations ```agda -module order-theory.accessible-elements-relations where +open import foundation.function-extensionality-axiom + +module + order-theory.accessible-elements-relations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.universe-levels open import foundation-core.negation diff --git a/src/order-theory/bottom-elements-large-posets.lagda.md b/src/order-theory/bottom-elements-large-posets.lagda.md index 76262a6702..2906b54ffc 100644 --- a/src/order-theory/bottom-elements-large-posets.lagda.md +++ b/src/order-theory/bottom-elements-large-posets.lagda.md @@ -1,7 +1,12 @@ # Bottom elements in large posets ```agda -module order-theory.bottom-elements-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.bottom-elements-large-posets + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module order-theory.bottom-elements-large-posets where ```agda open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext +open import order-theory.large-posets funext ```
diff --git a/src/order-theory/bottom-elements-posets.lagda.md b/src/order-theory/bottom-elements-posets.lagda.md index 19f835b65c..60fa8dae52 100644 --- a/src/order-theory/bottom-elements-posets.lagda.md +++ b/src/order-theory/bottom-elements-posets.lagda.md @@ -1,19 +1,24 @@ # Bottom elements in posets ```agda -module order-theory.bottom-elements-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.bottom-elements-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.bottom-elements-preorders -open import order-theory.posets +open import order-theory.bottom-elements-preorders funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/bottom-elements-preorders.lagda.md b/src/order-theory/bottom-elements-preorders.lagda.md index 5d5c0f1b8b..04c1dfb0d0 100644 --- a/src/order-theory/bottom-elements-preorders.lagda.md +++ b/src/order-theory/bottom-elements-preorders.lagda.md @@ -1,17 +1,22 @@ # Bottom elements in preorders ```agda -module order-theory.bottom-elements-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.bottom-elements-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext ```
diff --git a/src/order-theory/chains-posets.lagda.md b/src/order-theory/chains-posets.lagda.md index 404b506ee9..48b47da535 100644 --- a/src/order-theory/chains-posets.lagda.md +++ b/src/order-theory/chains-posets.lagda.md @@ -1,29 +1,34 @@ # Chains in posets ```agda -module order-theory.chains-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.chains-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.images -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.disjunction funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.images funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.chains-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.subposets -open import order-theory.total-orders +open import order-theory.chains-preorders funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext +open import order-theory.subposets funext +open import order-theory.total-orders funext ```
diff --git a/src/order-theory/chains-preorders.lagda.md b/src/order-theory/chains-preorders.lagda.md index 65c1ad4c19..13ef627d97 100644 --- a/src/order-theory/chains-preorders.lagda.md +++ b/src/order-theory/chains-preorders.lagda.md @@ -1,20 +1,25 @@ # Chains in preorders ```agda -module order-theory.chains-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.chains-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.preorders -open import order-theory.subpreorders -open import order-theory.total-preorders +open import order-theory.preorders funext +open import order-theory.subpreorders funext +open import order-theory.total-preorders funext ```
diff --git a/src/order-theory/closure-operators-large-locales.lagda.md b/src/order-theory/closure-operators-large-locales.lagda.md index 3bc839becd..9e8b6172e8 100644 --- a/src/order-theory/closure-operators-large-locales.lagda.md +++ b/src/order-theory/closure-operators-large-locales.lagda.md @@ -1,7 +1,12 @@ # Closure operators on large locales ```agda -module order-theory.closure-operators-large-locales where +open import foundation.function-extensionality-axiom + +module + order-theory.closure-operators-large-locales + (funext : function-extensionality) + where ```
Imports @@ -9,26 +14,26 @@ module order-theory.closure-operators-large-locales where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.closure-operators-large-posets -open import order-theory.large-frames -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-meet-subsemilattices -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets +open import order-theory.closure-operators-large-posets funext +open import order-theory.large-frames funext +open import order-theory.large-locales funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-meet-subsemilattices funext +open import order-theory.large-posets funext +open import order-theory.large-subposets funext +open import order-theory.large-subpreorders funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext ```
diff --git a/src/order-theory/closure-operators-large-posets.lagda.md b/src/order-theory/closure-operators-large-posets.lagda.md index edc0a558e9..0b0359c810 100644 --- a/src/order-theory/closure-operators-large-posets.lagda.md +++ b/src/order-theory/closure-operators-large-posets.lagda.md @@ -1,22 +1,27 @@ # Closure operators on large posets ```agda -module order-theory.closure-operators-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.closure-operators-large-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.order-preserving-maps-large-posets +open import order-theory.large-posets funext +open import order-theory.large-subposets funext +open import order-theory.large-subpreorders funext +open import order-theory.order-preserving-maps-large-posets funext ```
diff --git a/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md b/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md index ff9bfb86c1..68101ec457 100644 --- a/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md +++ b/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md @@ -1,7 +1,12 @@ # Commuting squares of Galois connections between large posets ```agda -module order-theory.commuting-squares-of-galois-connections-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.commuting-squares-of-galois-connections-large-posets + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module order-theory.commuting-squares-of-galois-connections-large-posets where ```agda open import foundation.universe-levels -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets -open import order-theory.galois-connections-large-posets -open import order-theory.large-posets +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext +open import order-theory.galois-connections-large-posets funext +open import order-theory.large-posets funext ```
diff --git a/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md b/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md index 42b32bdb2f..a233ea711b 100644 --- a/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md +++ b/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md @@ -11,11 +11,11 @@ module ```agda open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext -open import order-theory.large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.similarity-of-order-preserving-maps-large-posets funext ```
@@ -51,7 +51,12 @@ words, we say that the square above commutes if the composites `j ∘ f` and ## Definitions ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {αP αQ αU αV γi γf γg γj : Level → Level} {βP βQ βU βV : Level → Level → Level} (P : Large-Poset αP βP) diff --git a/src/order-theory/coverings-locales.lagda.md b/src/order-theory/coverings-locales.lagda.md index 70165cf95e..bc63072dfc 100644 --- a/src/order-theory/coverings-locales.lagda.md +++ b/src/order-theory/coverings-locales.lagda.md @@ -1,17 +1,22 @@ # Coverings in locales ```agda -module order-theory.coverings-locales where +open import foundation.function-extensionality-axiom + +module + order-theory.coverings-locales + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.locales +open import order-theory.locales funext ```
diff --git a/src/order-theory/decidable-posets.lagda.md b/src/order-theory/decidable-posets.lagda.md index b02c21afbf..a6697faaa9 100644 --- a/src/order-theory/decidable-posets.lagda.md +++ b/src/order-theory/decidable-posets.lagda.md @@ -1,23 +1,28 @@ # Decidable posets ```agda -module order-theory.decidable-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.decidable-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-propositions +open import foundation.binary-relations funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.decidable-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.decidable-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/decidable-preorders.lagda.md b/src/order-theory/decidable-preorders.lagda.md index b752e33a13..02adf9422b 100644 --- a/src/order-theory/decidable-preorders.lagda.md +++ b/src/order-theory/decidable-preorders.lagda.md @@ -1,19 +1,24 @@ # Decidable preorders ```agda -module order-theory.decidable-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.decidable-preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-propositions +open import foundation.binary-relations funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext ```
diff --git a/src/order-theory/decidable-subposets.lagda.md b/src/order-theory/decidable-subposets.lagda.md index d57463aa0b..2216b42708 100644 --- a/src/order-theory/decidable-subposets.lagda.md +++ b/src/order-theory/decidable-subposets.lagda.md @@ -1,21 +1,26 @@ # Decidable subposets ```agda -module order-theory.decidable-subposets where +open import foundation.function-extensionality-axiom + +module + order-theory.decidable-subposets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-subtypes +open import foundation.binary-relations funext +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.posets -open import order-theory.subposets +open import order-theory.posets funext +open import order-theory.subposets funext ```
diff --git a/src/order-theory/decidable-subpreorders.lagda.md b/src/order-theory/decidable-subpreorders.lagda.md index 57e290edc2..720d13a3fc 100644 --- a/src/order-theory/decidable-subpreorders.lagda.md +++ b/src/order-theory/decidable-subpreorders.lagda.md @@ -1,21 +1,26 @@ # Decidable subpreorders ```agda -module order-theory.decidable-subpreorders where +open import foundation.function-extensionality-axiom + +module + order-theory.decidable-subpreorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.decidable-subtypes +open import foundation.binary-relations funext +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.preorders -open import order-theory.subpreorders +open import order-theory.preorders funext +open import order-theory.subpreorders funext ```
diff --git a/src/order-theory/decidable-total-orders.lagda.md b/src/order-theory/decidable-total-orders.lagda.md index 1b3086e12d..8725952740 100644 --- a/src/order-theory/decidable-total-orders.lagda.md +++ b/src/order-theory/decidable-total-orders.lagda.md @@ -1,31 +1,36 @@ # Decidable total orders ```agda -module order-theory.decidable-total-orders where +open import foundation.function-extensionality-axiom + +module + order-theory.decidable-total-orders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.coproduct-types -open import foundation.decidable-propositions +open import foundation.binary-relations funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.decidable-posets -open import order-theory.decidable-total-preorders -open import order-theory.greatest-lower-bounds-posets -open import order-theory.join-semilattices -open import order-theory.least-upper-bounds-posets -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.preorders -open import order-theory.total-orders +open import order-theory.decidable-posets funext +open import order-theory.decidable-total-preorders funext +open import order-theory.greatest-lower-bounds-posets funext +open import order-theory.join-semilattices funext +open import order-theory.least-upper-bounds-posets funext +open import order-theory.meet-semilattices funext +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.total-orders funext ```
diff --git a/src/order-theory/decidable-total-preorders.lagda.md b/src/order-theory/decidable-total-preorders.lagda.md index c3385ce7ae..f0e25d8bdb 100644 --- a/src/order-theory/decidable-total-preorders.lagda.md +++ b/src/order-theory/decidable-total-preorders.lagda.md @@ -1,28 +1,33 @@ # Decidable total preorders ```agda -module order-theory.decidable-total-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.decidable-total-preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.decidable-preorders -open import order-theory.preorders -open import order-theory.total-preorders +open import order-theory.decidable-preorders funext +open import order-theory.preorders funext +open import order-theory.total-preorders funext ```
diff --git a/src/order-theory/deflationary-maps-posets.lagda.md b/src/order-theory/deflationary-maps-posets.lagda.md index ffeb8f4da5..555331ec25 100644 --- a/src/order-theory/deflationary-maps-posets.lagda.md +++ b/src/order-theory/deflationary-maps-posets.lagda.md @@ -1,20 +1,25 @@ # Deflationary maps on a poset ```agda -module order-theory.deflationary-maps-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.deflationary-maps-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.deflationary-maps-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.deflationary-maps-preorders funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/deflationary-maps-preorders.lagda.md b/src/order-theory/deflationary-maps-preorders.lagda.md index 508b702878..3206a6d1a3 100644 --- a/src/order-theory/deflationary-maps-preorders.lagda.md +++ b/src/order-theory/deflationary-maps-preorders.lagda.md @@ -1,19 +1,24 @@ # Deflationary maps on a preorder ```agda -module order-theory.deflationary-maps-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.deflationary-maps-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.preorders +open import order-theory.order-preserving-maps-preorders funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/dependent-products-large-frames.lagda.md b/src/order-theory/dependent-products-large-frames.lagda.md index 8766e231c0..3002829f36 100644 --- a/src/order-theory/dependent-products-large-frames.lagda.md +++ b/src/order-theory/dependent-products-large-frames.lagda.md @@ -1,28 +1,34 @@ # Dependent products of large frames ```agda -module order-theory.dependent-products-large-frames where +open import foundation.function-extensionality-axiom + +module + order-theory.dependent-products-large-frames + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.dependent-products-large-meet-semilattices -open import order-theory.dependent-products-large-posets -open import order-theory.dependent-products-large-suplattices -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-frames -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.dependent-products-large-meet-semilattices funext +open import order-theory.dependent-products-large-posets funext +open import order-theory.dependent-products-large-suplattices funext +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-frames funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/order-theory/dependent-products-large-inflattices.lagda.md b/src/order-theory/dependent-products-large-inflattices.lagda.md index 7078f31b85..1672173eb0 100644 --- a/src/order-theory/dependent-products-large-inflattices.lagda.md +++ b/src/order-theory/dependent-products-large-inflattices.lagda.md @@ -1,20 +1,25 @@ # Dependent products of large inflattices ```agda -module order-theory.dependent-products-large-inflattices where +open import foundation.function-extensionality-axiom + +module + order-theory.dependent-products-large-inflattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-inflattices -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-inflattices funext +open import order-theory.large-posets funext ```
diff --git a/src/order-theory/dependent-products-large-locales.lagda.md b/src/order-theory/dependent-products-large-locales.lagda.md index 07f9743e81..0c5a8eaab1 100644 --- a/src/order-theory/dependent-products-large-locales.lagda.md +++ b/src/order-theory/dependent-products-large-locales.lagda.md @@ -1,25 +1,30 @@ # Dependent products of large locales ```agda -module order-theory.dependent-products-large-locales where +open import foundation.function-extensionality-axiom + +module + order-theory.dependent-products-large-locales + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.dependent-products-large-frames -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.dependent-products-large-frames funext +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-locales funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/order-theory/dependent-products-large-meet-semilattices.lagda.md b/src/order-theory/dependent-products-large-meet-semilattices.lagda.md index 5d235a6767..a2c44bf15c 100644 --- a/src/order-theory/dependent-products-large-meet-semilattices.lagda.md +++ b/src/order-theory/dependent-products-large-meet-semilattices.lagda.md @@ -1,21 +1,26 @@ # Dependent products of large meet-semilattices ```agda -module order-theory.dependent-products-large-meet-semilattices where +open import foundation.function-extensionality-axiom + +module + order-theory.dependent-products-large-meet-semilattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.top-elements-large-posets +open import order-theory.dependent-products-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/order-theory/dependent-products-large-posets.lagda.md b/src/order-theory/dependent-products-large-posets.lagda.md index f445638b89..c73e4e4c69 100644 --- a/src/order-theory/dependent-products-large-posets.lagda.md +++ b/src/order-theory/dependent-products-large-posets.lagda.md @@ -1,19 +1,25 @@ # Dependent products of large posets ```agda -module order-theory.dependent-products-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.dependent-products-large-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.function-extensionality -open import foundation.large-binary-relations +open import foundation.function-extensionality funext + +open import foundation.large-binary-relations funext open import foundation.universe-levels -open import order-theory.dependent-products-large-preorders -open import order-theory.large-posets -open import order-theory.large-preorders +open import order-theory.dependent-products-large-preorders funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext ```
diff --git a/src/order-theory/dependent-products-large-preorders.lagda.md b/src/order-theory/dependent-products-large-preorders.lagda.md index fa7fafa61e..e6956c6c21 100644 --- a/src/order-theory/dependent-products-large-preorders.lagda.md +++ b/src/order-theory/dependent-products-large-preorders.lagda.md @@ -1,17 +1,22 @@ # Dependent products of large preorders ```agda -module order-theory.dependent-products-large-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.dependent-products-large-preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.propositions +open import foundation.large-binary-relations funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.large-preorders +open import order-theory.large-preorders funext ```
diff --git a/src/order-theory/dependent-products-large-suplattices.lagda.md b/src/order-theory/dependent-products-large-suplattices.lagda.md index 41fbf2ead1..b18ea1d500 100644 --- a/src/order-theory/dependent-products-large-suplattices.lagda.md +++ b/src/order-theory/dependent-products-large-suplattices.lagda.md @@ -1,20 +1,25 @@ # Dependent products of large suplattices ```agda -module order-theory.dependent-products-large-suplattices where +open import foundation.function-extensionality-axiom + +module + order-theory.dependent-products-large-suplattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets +open import order-theory.dependent-products-large-posets funext +open import order-theory.large-posets funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext ```
diff --git a/src/order-theory/distributive-lattices.lagda.md b/src/order-theory/distributive-lattices.lagda.md index e2dff425a0..9b864b2b0b 100644 --- a/src/order-theory/distributive-lattices.lagda.md +++ b/src/order-theory/distributive-lattices.lagda.md @@ -1,23 +1,28 @@ # Distributive lattices ```agda -module order-theory.distributive-lattices where +open import foundation.function-extensionality-axiom + +module + order-theory.distributive-lattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.join-semilattices -open import order-theory.lattices -open import order-theory.meet-semilattices -open import order-theory.posets +open import order-theory.join-semilattices funext +open import order-theory.lattices funext +open import order-theory.meet-semilattices funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/finite-coverings-locales.lagda.md b/src/order-theory/finite-coverings-locales.lagda.md index 94b7b34648..fffe499e6e 100644 --- a/src/order-theory/finite-coverings-locales.lagda.md +++ b/src/order-theory/finite-coverings-locales.lagda.md @@ -1,7 +1,12 @@ # Finite coverings in locales ```agda -module order-theory.finite-coverings-locales where +open import foundation.function-extensionality-axiom + +module + order-theory.finite-coverings-locales + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module order-theory.finite-coverings-locales where open import foundation.dependent-pair-types open import foundation.universe-levels -open import order-theory.coverings-locales -open import order-theory.locales +open import order-theory.coverings-locales funext +open import order-theory.locales funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/order-theory/finite-posets.lagda.md b/src/order-theory/finite-posets.lagda.md index 597af98d12..7fa14856f5 100644 --- a/src/order-theory/finite-posets.lagda.md +++ b/src/order-theory/finite-posets.lagda.md @@ -1,23 +1,28 @@ # Finite posets ```agda -module order-theory.finite-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.finite-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.finite-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.finite-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/order-theory/finite-preorders.lagda.md b/src/order-theory/finite-preorders.lagda.md index b7a2511b49..2905166f62 100644 --- a/src/order-theory/finite-preorders.lagda.md +++ b/src/order-theory/finite-preorders.lagda.md @@ -1,7 +1,12 @@ # Finite preorders ```agda -module order-theory.finite-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.finite-preorders + (funext : function-extensionality) + where ```
Imports @@ -9,26 +14,26 @@ module order-theory.finite-preorders where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.mere-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.decidable-preorders -open import order-theory.decidable-subpreorders -open import order-theory.preorders +open import order-theory.decidable-preorders funext +open import order-theory.decidable-subpreorders funext +open import order-theory.preorders funext -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.decidable-subtypes funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/order-theory/finite-total-orders.lagda.md b/src/order-theory/finite-total-orders.lagda.md index 4bfb6edcd4..7b734d440c 100644 --- a/src/order-theory/finite-total-orders.lagda.md +++ b/src/order-theory/finite-total-orders.lagda.md @@ -1,23 +1,28 @@ # Finite total orders ```agda -module order-theory.finite-total-orders where +open import foundation.function-extensionality-axiom + +module + order-theory.finite-total-orders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.finite-posets -open import order-theory.posets -open import order-theory.total-orders +open import order-theory.finite-posets funext +open import order-theory.posets funext +open import order-theory.total-orders funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/order-theory/finitely-graded-posets.lagda.md b/src/order-theory/finitely-graded-posets.lagda.md index b4fb4a404b..332e3a237a 100644 --- a/src/order-theory/finitely-graded-posets.lagda.md +++ b/src/order-theory/finitely-graded-posets.lagda.md @@ -1,40 +1,45 @@ # Finitely graded posets ```agda -module order-theory.finitely-graded-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.finitely-graded-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types -open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic funext open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.coproduct-types +open import foundation.binary-relations funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import order-theory.bottom-elements-posets -open import order-theory.posets -open import order-theory.preorders -open import order-theory.top-elements-posets -open import order-theory.total-orders +open import order-theory.bottom-elements-posets funext +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.top-elements-posets funext +open import order-theory.total-orders funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/order-theory/frames.lagda.md b/src/order-theory/frames.lagda.md index 96d2f47cec..034be27e22 100644 --- a/src/order-theory/frames.lagda.md +++ b/src/order-theory/frames.lagda.md @@ -1,25 +1,30 @@ # Frames ```agda -module order-theory.frames where +open import foundation.function-extensionality-axiom + +module + order-theory.frames + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.meet-semilattices -open import order-theory.meet-suplattices -open import order-theory.posets -open import order-theory.suplattices +open import order-theory.greatest-lower-bounds-posets funext +open import order-theory.least-upper-bounds-posets funext +open import order-theory.meet-semilattices funext +open import order-theory.meet-suplattices funext +open import order-theory.posets funext +open import order-theory.suplattices funext ```
diff --git a/src/order-theory/galois-connections-large-posets.lagda.md b/src/order-theory/galois-connections-large-posets.lagda.md index eee2b9a4da..8c05372f9e 100644 --- a/src/order-theory/galois-connections-large-posets.lagda.md +++ b/src/order-theory/galois-connections-large-posets.lagda.md @@ -1,7 +1,12 @@ # Galois connections between large posets ```agda -module order-theory.galois-connections-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.galois-connections-large-posets + (funext : function-extensionality) + where ```
Imports @@ -9,18 +14,18 @@ module order-theory.galois-connections-large-posets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.logical-equivalences +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.principal-lower-sets-large-posets -open import order-theory.principal-upper-sets-large-posets -open import order-theory.similarity-of-elements-large-posets -open import order-theory.similarity-of-order-preserving-maps-large-posets +open import order-theory.large-posets funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.principal-lower-sets-large-posets funext +open import order-theory.principal-upper-sets-large-posets funext +open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.similarity-of-order-preserving-maps-large-posets funext ```
diff --git a/src/order-theory/galois-connections.lagda.md b/src/order-theory/galois-connections.lagda.md index e0ac6170c7..3657f75826 100644 --- a/src/order-theory/galois-connections.lagda.md +++ b/src/order-theory/galois-connections.lagda.md @@ -1,7 +1,12 @@ # Galois connections ```agda -module order-theory.galois-connections where +open import foundation.function-extensionality-axiom + +module + order-theory.galois-connections + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module order-theory.galois-connections where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/greatest-lower-bounds-large-posets.lagda.md b/src/order-theory/greatest-lower-bounds-large-posets.lagda.md index c7a54580f2..f44de6e120 100644 --- a/src/order-theory/greatest-lower-bounds-large-posets.lagda.md +++ b/src/order-theory/greatest-lower-bounds-large-posets.lagda.md @@ -1,18 +1,23 @@ # Greatest lower bounds in large posets ```agda -module order-theory.greatest-lower-bounds-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.greatest-lower-bounds-large-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.logical-equivalences +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets -open import order-theory.lower-bounds-large-posets +open import order-theory.dependent-products-large-posets funext +open import order-theory.large-posets funext +open import order-theory.lower-bounds-large-posets funext ```
diff --git a/src/order-theory/greatest-lower-bounds-posets.lagda.md b/src/order-theory/greatest-lower-bounds-posets.lagda.md index 9a1430a0c4..dc1c5f0142 100644 --- a/src/order-theory/greatest-lower-bounds-posets.lagda.md +++ b/src/order-theory/greatest-lower-bounds-posets.lagda.md @@ -1,7 +1,12 @@ # Greatest lower bounds in posets ```agda -module order-theory.greatest-lower-bounds-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.greatest-lower-bounds-posets + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module order-theory.greatest-lower-bounds-posets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.lower-bounds-posets -open import order-theory.posets +open import order-theory.lower-bounds-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/homomorphisms-frames.lagda.md b/src/order-theory/homomorphisms-frames.lagda.md index 2af1ac44de..78864fb775 100644 --- a/src/order-theory/homomorphisms-frames.lagda.md +++ b/src/order-theory/homomorphisms-frames.lagda.md @@ -1,22 +1,27 @@ # Homomorphisms of frames ```agda -module order-theory.homomorphisms-frames where +open import foundation.function-extensionality-axiom + +module + order-theory.homomorphisms-frames + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import order-theory.frames -open import order-theory.homomorphisms-meet-semilattices -open import order-theory.homomorphisms-meet-suplattices -open import order-theory.homomorphisms-suplattices -open import order-theory.order-preserving-maps-posets +open import order-theory.frames funext +open import order-theory.homomorphisms-meet-semilattices funext +open import order-theory.homomorphisms-meet-suplattices funext +open import order-theory.homomorphisms-suplattices funext +open import order-theory.order-preserving-maps-posets funext ```
diff --git a/src/order-theory/homomorphisms-large-frames.lagda.md b/src/order-theory/homomorphisms-large-frames.lagda.md index 80de9de25d..6f223802fe 100644 --- a/src/order-theory/homomorphisms-large-frames.lagda.md +++ b/src/order-theory/homomorphisms-large-frames.lagda.md @@ -1,18 +1,23 @@ # Homomorphisms of large frames ```agda -module order-theory.homomorphisms-large-frames where +open import foundation.function-extensionality-axiom + +module + order-theory.homomorphisms-large-frames + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.homomorphisms-large-meet-semilattices -open import order-theory.homomorphisms-large-suplattices -open import order-theory.large-frames +open import order-theory.homomorphisms-large-meet-semilattices funext +open import order-theory.homomorphisms-large-suplattices funext +open import order-theory.large-frames funext ```
diff --git a/src/order-theory/homomorphisms-large-locales.lagda.md b/src/order-theory/homomorphisms-large-locales.lagda.md index ae621fd45d..f1331e5338 100644 --- a/src/order-theory/homomorphisms-large-locales.lagda.md +++ b/src/order-theory/homomorphisms-large-locales.lagda.md @@ -1,17 +1,22 @@ # Homomorphisms of large locales ```agda -module order-theory.homomorphisms-large-locales where +open import foundation.function-extensionality-axiom + +module + order-theory.homomorphisms-large-locales + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.homomorphisms-large-frames -open import order-theory.large-locales +open import order-theory.homomorphisms-large-frames funext +open import order-theory.large-locales funext ```
diff --git a/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md b/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md index c209e7d907..37d17a88f2 100644 --- a/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md +++ b/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md @@ -1,17 +1,22 @@ # Homomorphisms of large meet-semilattices ```agda -module order-theory.homomorphisms-large-meet-semilattices where +open import foundation.function-extensionality-axiom + +module + order-theory.homomorphisms-large-meet-semilattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.large-meet-semilattices -open import order-theory.order-preserving-maps-large-posets +open import order-theory.large-meet-semilattices funext +open import order-theory.order-preserving-maps-large-posets funext ```
diff --git a/src/order-theory/homomorphisms-large-suplattices.lagda.md b/src/order-theory/homomorphisms-large-suplattices.lagda.md index 181c422651..7ff77c91a7 100644 --- a/src/order-theory/homomorphisms-large-suplattices.lagda.md +++ b/src/order-theory/homomorphisms-large-suplattices.lagda.md @@ -1,17 +1,22 @@ # Homomorphisms of large suplattices ```agda -module order-theory.homomorphisms-large-suplattices where +open import foundation.function-extensionality-axiom + +module + order-theory.homomorphisms-large-suplattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.order-preserving-maps-large-posets +open import order-theory.large-suplattices funext +open import order-theory.order-preserving-maps-large-posets funext ```
diff --git a/src/order-theory/homomorphisms-meet-semilattices.lagda.md b/src/order-theory/homomorphisms-meet-semilattices.lagda.md index d22b55a690..6051dd310b 100644 --- a/src/order-theory/homomorphisms-meet-semilattices.lagda.md +++ b/src/order-theory/homomorphisms-meet-semilattices.lagda.md @@ -1,7 +1,12 @@ # Homomorphisms of meet-semilattices ```agda -module order-theory.homomorphisms-meet-semilattices where +open import foundation.function-extensionality-axiom + +module + order-theory.homomorphisms-meet-semilattices + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,17 @@ module order-theory.homomorphisms-meet-semilattices where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext -open import order-theory.greatest-lower-bounds-posets -open import order-theory.meet-semilattices -open import order-theory.order-preserving-maps-posets +open import order-theory.greatest-lower-bounds-posets funext +open import order-theory.meet-semilattices funext +open import order-theory.order-preserving-maps-posets funext ```
diff --git a/src/order-theory/homomorphisms-meet-suplattices.lagda.md b/src/order-theory/homomorphisms-meet-suplattices.lagda.md index ea4c27b234..54d3e0b5bd 100644 --- a/src/order-theory/homomorphisms-meet-suplattices.lagda.md +++ b/src/order-theory/homomorphisms-meet-suplattices.lagda.md @@ -1,21 +1,26 @@ # Homomorphisms of meet-suplattices ```agda -module order-theory.homomorphisms-meet-suplattices where +open import foundation.function-extensionality-axiom + +module + order-theory.homomorphisms-meet-suplattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import order-theory.homomorphisms-meet-semilattices -open import order-theory.homomorphisms-suplattices -open import order-theory.meet-suplattices -open import order-theory.order-preserving-maps-posets +open import order-theory.homomorphisms-meet-semilattices funext +open import order-theory.homomorphisms-suplattices funext +open import order-theory.meet-suplattices funext +open import order-theory.order-preserving-maps-posets funext ```
diff --git a/src/order-theory/homomorphisms-suplattices.lagda.md b/src/order-theory/homomorphisms-suplattices.lagda.md index 081cd8f204..b4437e0082 100644 --- a/src/order-theory/homomorphisms-suplattices.lagda.md +++ b/src/order-theory/homomorphisms-suplattices.lagda.md @@ -1,20 +1,25 @@ # Homomorphisms of suplattices ```agda -module order-theory.homomorphisms-suplattices where +open import foundation.function-extensionality-axiom + +module + order-theory.homomorphisms-suplattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.suplattices +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.suplattices funext ```
diff --git a/src/order-theory/ideals-preorders.lagda.md b/src/order-theory/ideals-preorders.lagda.md index 2994939994..8bb6460c0d 100644 --- a/src/order-theory/ideals-preorders.lagda.md +++ b/src/order-theory/ideals-preorders.lagda.md @@ -1,19 +1,24 @@ # Ideals in preorders ```agda -module order-theory.ideals-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.ideals-preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.inhabited-types +open import foundation.inhabited-types funext open import foundation.universe-levels -open import order-theory.lower-types-preorders -open import order-theory.preorders +open import order-theory.lower-types-preorders funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/incidence-algebras.lagda.md b/src/order-theory/incidence-algebras.lagda.md index f96b061659..66047c38f9 100644 --- a/src/order-theory/incidence-algebras.lagda.md +++ b/src/order-theory/incidence-algebras.lagda.md @@ -1,23 +1,28 @@ # Incidence algebras ```agda -module order-theory.incidence-algebras where +open import foundation.function-extensionality-axiom + +module + order-theory.incidence-algebras + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import foundation.dependent-pair-types -open import foundation.inhabited-types +open import foundation.inhabited-types funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import order-theory.interval-subposets -open import order-theory.locally-finite-posets -open import order-theory.posets +open import order-theory.interval-subposets funext +open import order-theory.locally-finite-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/inflationary-maps-posets.lagda.md b/src/order-theory/inflationary-maps-posets.lagda.md index 00c3374a3b..0985a10151 100644 --- a/src/order-theory/inflationary-maps-posets.lagda.md +++ b/src/order-theory/inflationary-maps-posets.lagda.md @@ -1,20 +1,25 @@ # Inflationary maps on a poset ```agda -module order-theory.inflationary-maps-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.inflationary-maps-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.inflationary-maps-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.inflationary-maps-preorders funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/inflationary-maps-preorders.lagda.md b/src/order-theory/inflationary-maps-preorders.lagda.md index aa2d482b97..35d6ee1697 100644 --- a/src/order-theory/inflationary-maps-preorders.lagda.md +++ b/src/order-theory/inflationary-maps-preorders.lagda.md @@ -1,19 +1,24 @@ # Inflationary maps on a preorder ```agda -module order-theory.inflationary-maps-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.inflationary-maps-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.preorders +open import order-theory.order-preserving-maps-preorders funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/inflattices.lagda.md b/src/order-theory/inflattices.lagda.md index 03b68b3db8..c79f8098f2 100644 --- a/src/order-theory/inflattices.lagda.md +++ b/src/order-theory/inflattices.lagda.md @@ -1,22 +1,27 @@ # Inflattices ```agda -module order-theory.inflattices where +open import foundation.function-extensionality-axiom + +module + order-theory.inflattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-posets -open import order-theory.lower-bounds-posets -open import order-theory.posets +open import order-theory.greatest-lower-bounds-posets funext +open import order-theory.lower-bounds-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/inhabited-chains-posets.lagda.md b/src/order-theory/inhabited-chains-posets.lagda.md index 8274e4af2a..f00966a114 100644 --- a/src/order-theory/inhabited-chains-posets.lagda.md +++ b/src/order-theory/inhabited-chains-posets.lagda.md @@ -1,28 +1,33 @@ # Inhabited chains in posets ```agda -module order-theory.inhabited-chains-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.inhabited-chains-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import domain-theory.directed-families-posets +open import domain-theory.directed-families-posets funext -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.inhabited-subtypes -open import foundation.inhabited-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.disjunction funext +open import foundation.existential-quantification funext +open import foundation.inhabited-subtypes funext +open import foundation.inhabited-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.chains-posets -open import order-theory.posets -open import order-theory.subposets -open import order-theory.total-preorders +open import order-theory.chains-posets funext +open import order-theory.posets funext +open import order-theory.subposets funext +open import order-theory.total-preorders funext ```
diff --git a/src/order-theory/inhabited-chains-preorders.lagda.md b/src/order-theory/inhabited-chains-preorders.lagda.md index 1722f40034..f1f79e175b 100644 --- a/src/order-theory/inhabited-chains-preorders.lagda.md +++ b/src/order-theory/inhabited-chains-preorders.lagda.md @@ -1,22 +1,27 @@ # Inhabited chains in preorders ```agda -module order-theory.inhabited-chains-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.inhabited-chains-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-subtypes -open import foundation.propositions -open import foundation.subtypes +open import foundation.inhabited-subtypes funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.chains-preorders -open import order-theory.preorders -open import order-theory.subpreorders -open import order-theory.total-preorders +open import order-theory.chains-preorders funext +open import order-theory.preorders funext +open import order-theory.subpreorders funext +open import order-theory.total-preorders funext ```
diff --git a/src/order-theory/inhabited-finite-total-orders.lagda.md b/src/order-theory/inhabited-finite-total-orders.lagda.md index a7a49e6404..ab12aafaa9 100644 --- a/src/order-theory/inhabited-finite-total-orders.lagda.md +++ b/src/order-theory/inhabited-finite-total-orders.lagda.md @@ -1,22 +1,27 @@ # Inhabited finite total orders ```agda -module order-theory.inhabited-finite-total-orders where +open import foundation.function-extensionality-axiom + +module + order-theory.inhabited-finite-total-orders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.inhabited-types -open import foundation.propositions +open import foundation.inhabited-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.finite-posets -open import order-theory.finite-total-orders -open import order-theory.posets -open import order-theory.total-orders +open import order-theory.finite-posets funext +open import order-theory.finite-total-orders funext +open import order-theory.posets funext +open import order-theory.total-orders funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/order-theory/interval-subposets.lagda.md b/src/order-theory/interval-subposets.lagda.md index 5f53725119..699cdaaae3 100644 --- a/src/order-theory/interval-subposets.lagda.md +++ b/src/order-theory/interval-subposets.lagda.md @@ -1,21 +1,26 @@ # Interval subposets ```agda -module order-theory.interval-subposets where +open import foundation.function-extensionality-axiom + +module + order-theory.interval-subposets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.propositions +open import foundation.inhabited-types funext +open import foundation.propositions funext open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import order-theory.posets -open import order-theory.subposets +open import order-theory.posets funext +open import order-theory.subposets funext ```
diff --git a/src/order-theory/join-preserving-maps-posets.lagda.md b/src/order-theory/join-preserving-maps-posets.lagda.md index 1da7506fa2..25aea8fb53 100644 --- a/src/order-theory/join-preserving-maps-posets.lagda.md +++ b/src/order-theory/join-preserving-maps-posets.lagda.md @@ -1,32 +1,37 @@ # Join preserving maps between posets ```agda -module order-theory.join-preserving-maps-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.join-preserving-maps-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.booleans +open import foundation.booleans funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.function-types +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.small-types funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/join-semilattices.lagda.md b/src/order-theory/join-semilattices.lagda.md index fe7f25a8cc..e127cd52f5 100644 --- a/src/order-theory/join-semilattices.lagda.md +++ b/src/order-theory/join-semilattices.lagda.md @@ -1,28 +1,33 @@ # Join-semilattices ```agda -module order-theory.join-semilattices where +open import foundation.function-extensionality-axiom + +module + order-theory.join-semilattices + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.semigroups +open import group-theory.semigroups funext -open import order-theory.least-upper-bounds-posets -open import order-theory.posets -open import order-theory.preorders -open import order-theory.upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.upper-bounds-posets funext ```
diff --git a/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md b/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md index fdc6bc2fc0..dff8080920 100644 --- a/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md +++ b/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md @@ -1,7 +1,12 @@ # The Knaster–Tarski fixed point theorem ```agda -module order-theory.knaster-tarski-fixed-point-theorem where +open import foundation.function-extensionality-axiom + +module + order-theory.knaster-tarski-fixed-point-theorem + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module order-theory.knaster-tarski-fixed-point-theorem where ```agda open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.inflattices -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.suplattices +open import order-theory.inflattices funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext +open import order-theory.suplattices funext ```
diff --git a/src/order-theory/large-frames.lagda.md b/src/order-theory/large-frames.lagda.md index dfd1287b72..00b795f64d 100644 --- a/src/order-theory/large-frames.lagda.md +++ b/src/order-theory/large-frames.lagda.md @@ -1,30 +1,35 @@ # Large frames ```agda -module order-theory.large-frames where +open import foundation.function-extensionality-axiom + +module + order-theory.large-frames + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.preorders -open import order-theory.suplattices -open import order-theory.top-elements-large-posets -open import order-theory.upper-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.meet-semilattices funext +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.suplattices funext +open import order-theory.top-elements-large-posets funext +open import order-theory.upper-bounds-large-posets funext ```
diff --git a/src/order-theory/large-inflattices.lagda.md b/src/order-theory/large-inflattices.lagda.md index 74860bf69e..a434a4d002 100644 --- a/src/order-theory/large-inflattices.lagda.md +++ b/src/order-theory/large-inflattices.lagda.md @@ -1,23 +1,28 @@ # Large inflattices ```agda -module order-theory.large-inflattices where +open import foundation.function-extensionality-axiom + +module + order-theory.large-inflattices + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.sets +open import foundation.large-binary-relations funext +open import foundation.logical-equivalences funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.inflattices -open import order-theory.large-posets -open import order-theory.lower-bounds-large-posets -open import order-theory.posets +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.inflattices funext +open import order-theory.large-posets funext +open import order-theory.lower-bounds-large-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/large-join-semilattices.lagda.md b/src/order-theory/large-join-semilattices.lagda.md index abd7e934e0..70b800058f 100644 --- a/src/order-theory/large-join-semilattices.lagda.md +++ b/src/order-theory/large-join-semilattices.lagda.md @@ -1,7 +1,12 @@ # Large join-semilattices ```agda -module order-theory.large-join-semilattices where +open import foundation.function-extensionality-axiom + +module + order-theory.large-join-semilattices + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module order-theory.large-join-semilattices where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.bottom-elements-large-posets -open import order-theory.join-semilattices -open import order-theory.large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.posets +open import order-theory.bottom-elements-large-posets funext +open import order-theory.join-semilattices funext +open import order-theory.large-posets funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/large-locales.lagda.md b/src/order-theory/large-locales.lagda.md index 9c6da1d97e..6e5322766d 100644 --- a/src/order-theory/large-locales.lagda.md +++ b/src/order-theory/large-locales.lagda.md @@ -1,30 +1,35 @@ # Large locales ```agda -module order-theory.large-locales where +open import foundation.function-extensionality-axiom + +module + order-theory.large-locales + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-frames -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.preorders -open import order-theory.suplattices -open import order-theory.top-elements-large-posets -open import order-theory.upper-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-frames funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.meet-semilattices funext +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.suplattices funext +open import order-theory.top-elements-large-posets funext +open import order-theory.upper-bounds-large-posets funext ```
diff --git a/src/order-theory/large-meet-semilattices.lagda.md b/src/order-theory/large-meet-semilattices.lagda.md index c9087cf742..f8cbdd9256 100644 --- a/src/order-theory/large-meet-semilattices.lagda.md +++ b/src/order-theory/large-meet-semilattices.lagda.md @@ -1,7 +1,12 @@ # Large meet-semilattices ```agda -module order-theory.large-meet-semilattices where +open import foundation.function-extensionality-axiom + +module + order-theory.large-meet-semilattices + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module order-theory.large-meet-semilattices where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-posets -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.top-elements-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-posets funext +open import order-theory.meet-semilattices funext +open import order-theory.posets funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/order-theory/large-meet-subsemilattices.lagda.md b/src/order-theory/large-meet-subsemilattices.lagda.md index 4c2bc6364c..5692ddedb5 100644 --- a/src/order-theory/large-meet-subsemilattices.lagda.md +++ b/src/order-theory/large-meet-subsemilattices.lagda.md @@ -1,22 +1,27 @@ # Large meet-subsemilattices ```agda -module order-theory.large-meet-subsemilattices where +open import foundation.function-extensionality-axiom + +module + order-theory.large-meet-subsemilattices + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations +open import foundation.large-binary-relations funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-subposets -open import order-theory.top-elements-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.large-subposets funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/order-theory/large-posets.lagda.md b/src/order-theory/large-posets.lagda.md index ebe0411daf..a5d73597cf 100644 --- a/src/order-theory/large-posets.lagda.md +++ b/src/order-theory/large-posets.lagda.md @@ -1,29 +1,34 @@ # Large posets ```agda -module order-theory.large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.large-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.large-categories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.isomorphisms-in-large-categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.large-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.large-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/large-preorders.lagda.md b/src/order-theory/large-preorders.lagda.md index 34c9170742..78aaaf4c78 100644 --- a/src/order-theory/large-preorders.lagda.md +++ b/src/order-theory/large-preorders.lagda.md @@ -1,23 +1,28 @@ # Large preorders ```agda -module order-theory.large-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.large-preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext ```
diff --git a/src/order-theory/large-quotient-locales.lagda.md b/src/order-theory/large-quotient-locales.lagda.md index 15e8cc8a46..0f9c31f0f0 100644 --- a/src/order-theory/large-quotient-locales.lagda.md +++ b/src/order-theory/large-quotient-locales.lagda.md @@ -1,29 +1,34 @@ # Large quotient locales ```agda -module order-theory.large-quotient-locales where +open import foundation.function-extensionality-axiom + +module + order-theory.large-quotient-locales + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations +open import foundation.identity-types funext +open import foundation.large-binary-relations funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-meet-subsemilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-subframes -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.large-subsuplattices -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-locales funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-meet-subsemilattices funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.large-subframes funext +open import order-theory.large-subposets funext +open import order-theory.large-subpreorders funext +open import order-theory.large-subsuplattices funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/order-theory/large-subframes.lagda.md b/src/order-theory/large-subframes.lagda.md index a425901336..aeb3387340 100644 --- a/src/order-theory/large-subframes.lagda.md +++ b/src/order-theory/large-subframes.lagda.md @@ -1,31 +1,36 @@ # Large subframes ```agda -module order-theory.large-subframes where +open import foundation.function-extensionality-axiom + +module + order-theory.large-subframes + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-frames -open import order-theory.large-meet-semilattices -open import order-theory.large-meet-subsemilattices -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.large-subsuplattices -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-frames funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-meet-subsemilattices funext +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.large-subposets funext +open import order-theory.large-subpreorders funext +open import order-theory.large-subsuplattices funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/order-theory/large-subposets.lagda.md b/src/order-theory/large-subposets.lagda.md index 6e2cefec16..f918d03f32 100644 --- a/src/order-theory/large-subposets.lagda.md +++ b/src/order-theory/large-subposets.lagda.md @@ -1,21 +1,26 @@ # Large subposets ```agda -module order-theory.large-subposets where +open import foundation.function-extensionality-axiom + +module + order-theory.large-subposets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.subtypes +open import foundation.large-binary-relations funext +open import foundation.logical-equivalences funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.large-subpreorders +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.large-subpreorders funext ```
diff --git a/src/order-theory/large-subpreorders.lagda.md b/src/order-theory/large-subpreorders.lagda.md index d69fca9bbe..9c96e79e14 100644 --- a/src/order-theory/large-subpreorders.lagda.md +++ b/src/order-theory/large-subpreorders.lagda.md @@ -1,19 +1,24 @@ # Large subpreorders ```agda -module order-theory.large-subpreorders where +open import foundation.function-extensionality-axiom + +module + order-theory.large-subpreorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.subtypes +open import foundation.large-binary-relations funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.large-preorders +open import order-theory.large-preorders funext ```
diff --git a/src/order-theory/large-subsuplattices.lagda.md b/src/order-theory/large-subsuplattices.lagda.md index c2a9126cba..550f7ffb0f 100644 --- a/src/order-theory/large-subsuplattices.lagda.md +++ b/src/order-theory/large-subsuplattices.lagda.md @@ -1,18 +1,23 @@ # Large subsuplattices ```agda -module order-theory.large-subsuplattices where +open import foundation.function-extensionality-axiom + +module + order-theory.large-subsuplattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.large-binary-relations +open import foundation.large-binary-relations funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-suplattices +open import order-theory.large-posets funext +open import order-theory.large-subposets funext +open import order-theory.large-suplattices funext ```
diff --git a/src/order-theory/large-suplattices.lagda.md b/src/order-theory/large-suplattices.lagda.md index 489330b18b..028337af4a 100644 --- a/src/order-theory/large-suplattices.lagda.md +++ b/src/order-theory/large-suplattices.lagda.md @@ -1,26 +1,31 @@ # Large suplattices ```agda -module order-theory.large-suplattices where +open import foundation.function-extensionality-axiom + +module + order-theory.large-suplattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.posets -open import order-theory.suplattices -open import order-theory.upper-bounds-large-posets +open import order-theory.large-posets funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.posets funext +open import order-theory.suplattices funext +open import order-theory.upper-bounds-large-posets funext ```
diff --git a/src/order-theory/lattices.lagda.md b/src/order-theory/lattices.lagda.md index bc9d9bc466..99e9a1821c 100644 --- a/src/order-theory/lattices.lagda.md +++ b/src/order-theory/lattices.lagda.md @@ -1,21 +1,26 @@ # Lattices ```agda -module order-theory.lattices where +open import foundation.function-extensionality-axiom + +module + order-theory.lattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.join-semilattices -open import order-theory.meet-semilattices -open import order-theory.posets +open import order-theory.join-semilattices funext +open import order-theory.meet-semilattices funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/least-upper-bounds-large-posets.lagda.md b/src/order-theory/least-upper-bounds-large-posets.lagda.md index a1ee5df25f..75972fe59a 100644 --- a/src/order-theory/least-upper-bounds-large-posets.lagda.md +++ b/src/order-theory/least-upper-bounds-large-posets.lagda.md @@ -1,21 +1,26 @@ # Least upper bounds in large posets ```agda -module order-theory.least-upper-bounds-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.least-upper-bounds-large-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.logical-equivalences +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.similarity-of-elements-large-posets -open import order-theory.upper-bounds-large-posets +open import order-theory.dependent-products-large-posets funext +open import order-theory.large-posets funext +open import order-theory.least-upper-bounds-posets funext +open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.upper-bounds-large-posets funext ```
diff --git a/src/order-theory/least-upper-bounds-posets.lagda.md b/src/order-theory/least-upper-bounds-posets.lagda.md index d0a5e74b02..c20eea66f0 100644 --- a/src/order-theory/least-upper-bounds-posets.lagda.md +++ b/src/order-theory/least-upper-bounds-posets.lagda.md @@ -1,23 +1,28 @@ # Least upper bounds in posets ```agda -module order-theory.least-upper-bounds-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.least-upper-bounds-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.booleans +open import foundation.booleans funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.posets -open import order-theory.upper-bounds-posets +open import order-theory.posets funext +open import order-theory.upper-bounds-posets funext ```
diff --git a/src/order-theory/locales.lagda.md b/src/order-theory/locales.lagda.md index 25983102a6..0ce60c3e25 100644 --- a/src/order-theory/locales.lagda.md +++ b/src/order-theory/locales.lagda.md @@ -1,25 +1,30 @@ # Locales ```agda -module order-theory.locales where +open import foundation.function-extensionality-axiom + +module + order-theory.locales + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.binary-relations funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.frames -open import order-theory.greatest-lower-bounds-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.meet-semilattices -open import order-theory.meet-suplattices -open import order-theory.posets -open import order-theory.suplattices +open import order-theory.frames funext +open import order-theory.greatest-lower-bounds-posets funext +open import order-theory.least-upper-bounds-posets funext +open import order-theory.meet-semilattices funext +open import order-theory.meet-suplattices funext +open import order-theory.posets funext +open import order-theory.suplattices funext ```
diff --git a/src/order-theory/locally-finite-posets.lagda.md b/src/order-theory/locally-finite-posets.lagda.md index 69a7c93beb..16dd993bc0 100644 --- a/src/order-theory/locally-finite-posets.lagda.md +++ b/src/order-theory/locally-finite-posets.lagda.md @@ -1,18 +1,23 @@ # Locally finite posets ```agda -module order-theory.locally-finite-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.locally-finite-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.finite-posets -open import order-theory.interval-subposets -open import order-theory.posets +open import order-theory.finite-posets funext +open import order-theory.interval-subposets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/lower-bounds-large-posets.lagda.md b/src/order-theory/lower-bounds-large-posets.lagda.md index 3f527ccddc..38a4ee7b42 100644 --- a/src/order-theory/lower-bounds-large-posets.lagda.md +++ b/src/order-theory/lower-bounds-large-posets.lagda.md @@ -1,20 +1,25 @@ # Lower bounds in large posets ```agda -module order-theory.lower-bounds-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.lower-bounds-large-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext +open import order-theory.large-posets funext ```
diff --git a/src/order-theory/lower-bounds-posets.lagda.md b/src/order-theory/lower-bounds-posets.lagda.md index 5ae8f55417..1db7547fc6 100644 --- a/src/order-theory/lower-bounds-posets.lagda.md +++ b/src/order-theory/lower-bounds-posets.lagda.md @@ -1,17 +1,22 @@ # Lower bounds in posets ```agda -module order-theory.lower-bounds-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.lower-bounds-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.posets +open import order-theory.posets funext ```
diff --git a/src/order-theory/lower-sets-large-posets.lagda.md b/src/order-theory/lower-sets-large-posets.lagda.md index bef92c55f0..7526a0bac3 100644 --- a/src/order-theory/lower-sets-large-posets.lagda.md +++ b/src/order-theory/lower-sets-large-posets.lagda.md @@ -1,7 +1,12 @@ # Lower sets in large posets ```agda -module order-theory.lower-sets-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.lower-sets-large-posets + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module order-theory.lower-sets-large-posets where ```agda open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets +open import order-theory.large-posets funext +open import order-theory.large-subposets funext ```
diff --git a/src/order-theory/lower-types-preorders.lagda.md b/src/order-theory/lower-types-preorders.lagda.md index 7967370856..03254048b8 100644 --- a/src/order-theory/lower-types-preorders.lagda.md +++ b/src/order-theory/lower-types-preorders.lagda.md @@ -1,17 +1,22 @@ # Lower types in preorders ```agda -module order-theory.lower-types-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.lower-types-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext ```
diff --git a/src/order-theory/maximal-chains-posets.lagda.md b/src/order-theory/maximal-chains-posets.lagda.md index e62dabcc6e..f3293d1432 100644 --- a/src/order-theory/maximal-chains-posets.lagda.md +++ b/src/order-theory/maximal-chains-posets.lagda.md @@ -1,18 +1,23 @@ # Maximal chains in posets ```agda -module order-theory.maximal-chains-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.maximal-chains-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.chains-posets -open import order-theory.maximal-chains-preorders -open import order-theory.posets +open import order-theory.chains-posets funext +open import order-theory.maximal-chains-preorders funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/maximal-chains-preorders.lagda.md b/src/order-theory/maximal-chains-preorders.lagda.md index 0cf6169f4f..86a66aad8f 100644 --- a/src/order-theory/maximal-chains-preorders.lagda.md +++ b/src/order-theory/maximal-chains-preorders.lagda.md @@ -1,18 +1,23 @@ # Maximal chains in preorders ```agda -module order-theory.maximal-chains-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.maximal-chains-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.chains-preorders -open import order-theory.preorders +open import order-theory.chains-preorders funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/meet-semilattices.lagda.md b/src/order-theory/meet-semilattices.lagda.md index 4a01ec4db8..b31f3f8c1b 100644 --- a/src/order-theory/meet-semilattices.lagda.md +++ b/src/order-theory/meet-semilattices.lagda.md @@ -1,29 +1,34 @@ # Meet-semilattices ```agda -module order-theory.meet-semilattices where +open import foundation.function-extensionality-axiom + +module + order-theory.meet-semilattices + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.isomorphisms-semigroups -open import group-theory.semigroups +open import group-theory.isomorphisms-semigroups funext +open import group-theory.semigroups funext -open import order-theory.greatest-lower-bounds-posets -open import order-theory.lower-bounds-posets -open import order-theory.posets -open import order-theory.preorders +open import order-theory.greatest-lower-bounds-posets funext +open import order-theory.lower-bounds-posets funext +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/meet-suplattices.lagda.md b/src/order-theory/meet-suplattices.lagda.md index 898eeb5f7a..2d67301fd1 100644 --- a/src/order-theory/meet-suplattices.lagda.md +++ b/src/order-theory/meet-suplattices.lagda.md @@ -1,21 +1,26 @@ # Meet-suplattices ```agda -module order-theory.meet-suplattices where +open import foundation.function-extensionality-axiom + +module + order-theory.meet-suplattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.meet-semilattices -open import order-theory.posets -open import order-theory.suplattices +open import order-theory.meet-semilattices funext +open import order-theory.posets funext +open import order-theory.suplattices funext ```
diff --git a/src/order-theory/nuclei-large-locales.lagda.md b/src/order-theory/nuclei-large-locales.lagda.md index b6d44973c9..a54ae4f7bc 100644 --- a/src/order-theory/nuclei-large-locales.lagda.md +++ b/src/order-theory/nuclei-large-locales.lagda.md @@ -1,7 +1,12 @@ # Nuclei on large locales ```agda -module order-theory.nuclei-large-locales where +open import foundation.function-extensionality-axiom + +module + order-theory.nuclei-large-locales + (funext : function-extensionality) + where ```
Imports @@ -9,25 +14,25 @@ module order-theory.nuclei-large-locales where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.homomorphisms-large-meet-semilattices -open import order-theory.large-frames -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-meet-subsemilattices -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets +open import order-theory.homomorphisms-large-meet-semilattices funext +open import order-theory.large-frames funext +open import order-theory.large-locales funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-meet-subsemilattices funext +open import order-theory.large-posets funext +open import order-theory.large-subposets funext +open import order-theory.large-subpreorders funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext ```
diff --git a/src/order-theory/opposite-large-posets.lagda.md b/src/order-theory/opposite-large-posets.lagda.md index cbb94d58f5..1566f395bd 100644 --- a/src/order-theory/opposite-large-posets.lagda.md +++ b/src/order-theory/opposite-large-posets.lagda.md @@ -1,25 +1,30 @@ # Opposite large posets ```agda -module order-theory.opposite-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.opposite-large-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.large-identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.opposite-large-preorders -open import order-theory.order-preserving-maps-large-posets +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.opposite-large-preorders funext +open import order-theory.order-preserving-maps-large-posets funext ```
diff --git a/src/order-theory/opposite-large-preorders.lagda.md b/src/order-theory/opposite-large-preorders.lagda.md index 5ecbfef3d7..39124b3a83 100644 --- a/src/order-theory/opposite-large-preorders.lagda.md +++ b/src/order-theory/opposite-large-preorders.lagda.md @@ -1,23 +1,28 @@ # Opposite large preorders ```agda -module order-theory.opposite-large-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.opposite-large-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.large-identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-preorders +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-large-preorders funext ```
diff --git a/src/order-theory/opposite-posets.lagda.md b/src/order-theory/opposite-posets.lagda.md index 45b842294c..ef5d17eb8e 100644 --- a/src/order-theory/opposite-posets.lagda.md +++ b/src/order-theory/opposite-posets.lagda.md @@ -1,24 +1,29 @@ # Opposite posets ```agda -module order-theory.opposite-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.opposite-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.opposite-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.preorders +open import order-theory.opposite-preorders funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/opposite-preorders.lagda.md b/src/order-theory/opposite-preorders.lagda.md index 2e6db98be2..39d960bd75 100644 --- a/src/order-theory/opposite-preorders.lagda.md +++ b/src/order-theory/opposite-preorders.lagda.md @@ -1,22 +1,27 @@ # Opposite preorders ```agda -module order-theory.opposite-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.opposite-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.preorders +open import order-theory.order-preserving-maps-preorders funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/order-preserving-maps-large-posets.lagda.md b/src/order-theory/order-preserving-maps-large-posets.lagda.md index 5c8636c874..556945e9fb 100644 --- a/src/order-theory/order-preserving-maps-large-posets.lagda.md +++ b/src/order-theory/order-preserving-maps-large-posets.lagda.md @@ -1,7 +1,12 @@ # Order preserving maps between large posets ```agda -module order-theory.order-preserving-maps-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.order-preserving-maps-large-posets + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module order-theory.order-preserving-maps-large-posets where ```agda open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.order-preserving-maps-posets -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.similarity-of-elements-large-posets funext ```
diff --git a/src/order-theory/order-preserving-maps-large-preorders.lagda.md b/src/order-theory/order-preserving-maps-large-preorders.lagda.md index d9150512e7..6a9088af23 100644 --- a/src/order-theory/order-preserving-maps-large-preorders.lagda.md +++ b/src/order-theory/order-preserving-maps-large-preorders.lagda.md @@ -1,7 +1,12 @@ # Order preserving maps between large preorders ```agda -module order-theory.order-preserving-maps-large-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.order-preserving-maps-large-preorders + (funext : function-extensionality) + where ```
Imports @@ -13,9 +18,9 @@ open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.homotopies -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-preorders -open import order-theory.similarity-of-elements-large-preorders +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-preorders funext +open import order-theory.similarity-of-elements-large-preorders funext ```
diff --git a/src/order-theory/order-preserving-maps-posets.lagda.md b/src/order-theory/order-preserving-maps-posets.lagda.md index 163aee3f3f..6bff92ab1b 100644 --- a/src/order-theory/order-preserving-maps-posets.lagda.md +++ b/src/order-theory/order-preserving-maps-posets.lagda.md @@ -1,24 +1,29 @@ # Order preserving maps between posets ```agda -module order-theory.order-preserving-maps-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.order-preserving-maps-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.strictly-involutive-identity-types -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.posets +open import order-theory.order-preserving-maps-preorders funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/order-preserving-maps-preorders.lagda.md b/src/order-theory/order-preserving-maps-preorders.lagda.md index a45df09656..fd518afef5 100644 --- a/src/order-theory/order-preserving-maps-preorders.lagda.md +++ b/src/order-theory/order-preserving-maps-preorders.lagda.md @@ -1,27 +1,32 @@ # Order preserving maps between preorders ```agda -module order-theory.order-preserving-maps-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.order-preserving-maps-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subtype-identity-principle open import foundation.universe-levels open import foundation-core.torsorial-type-families -open import order-theory.preorders +open import order-theory.preorders funext ```
diff --git a/src/order-theory/ordinals.lagda.md b/src/order-theory/ordinals.lagda.md index 7dc9994603..187a6a048f 100644 --- a/src/order-theory/ordinals.lagda.md +++ b/src/order-theory/ordinals.lagda.md @@ -1,25 +1,30 @@ # Ordinals ```agda -module order-theory.ordinals where +open import foundation.function-extensionality-axiom + +module + order-theory.ordinals + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders -open import order-theory.transitive-well-founded-relations -open import order-theory.well-founded-relations +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.transitive-well-founded-relations funext +open import order-theory.well-founded-relations funext ```
diff --git a/src/order-theory/posets.lagda.md b/src/order-theory/posets.lagda.md index f1875f86f2..3abd37fcfc 100644 --- a/src/order-theory/posets.lagda.md +++ b/src/order-theory/posets.lagda.md @@ -1,28 +1,33 @@ # Posets ```agda -module order-theory.posets where +open import foundation.function-extensionality-axiom + +module + order-theory.posets + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.isomorphisms-in-precategories -open import category-theory.precategories +open import category-theory.categories funext +open import category-theory.isomorphisms-in-precategories funext +open import category-theory.precategories funext -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext ```
diff --git a/src/order-theory/powers-of-large-locales.lagda.md b/src/order-theory/powers-of-large-locales.lagda.md index 1822320130..5480b824f2 100644 --- a/src/order-theory/powers-of-large-locales.lagda.md +++ b/src/order-theory/powers-of-large-locales.lagda.md @@ -1,25 +1,30 @@ # Powers of large locales ```agda -module order-theory.powers-of-large-locales where +open import foundation.function-extensionality-axiom + +module + order-theory.powers-of-large-locales + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.sets +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.dependent-products-large-locales -open import order-theory.greatest-lower-bounds-large-posets -open import order-theory.large-locales -open import order-theory.large-meet-semilattices -open import order-theory.large-posets -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.top-elements-large-posets +open import order-theory.dependent-products-large-locales funext +open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.large-locales funext +open import order-theory.large-meet-semilattices funext +open import order-theory.large-posets funext +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.top-elements-large-posets funext ```
diff --git a/src/order-theory/precategory-of-decidable-total-orders.lagda.md b/src/order-theory/precategory-of-decidable-total-orders.lagda.md index ee91924562..9186f19ba8 100644 --- a/src/order-theory/precategory-of-decidable-total-orders.lagda.md +++ b/src/order-theory/precategory-of-decidable-total-orders.lagda.md @@ -1,20 +1,25 @@ # The precategory of decidable total orders ```agda -module order-theory.precategory-of-decidable-total-orders where +open import foundation.function-extensionality-axiom + +module + order-theory.precategory-of-decidable-total-orders + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import order-theory.decidable-total-orders -open import order-theory.precategory-of-posets +open import order-theory.decidable-total-orders funext +open import order-theory.precategory-of-posets funext ```
diff --git a/src/order-theory/precategory-of-finite-posets.lagda.md b/src/order-theory/precategory-of-finite-posets.lagda.md index 87c506290f..0f5fe4aa5f 100644 --- a/src/order-theory/precategory-of-finite-posets.lagda.md +++ b/src/order-theory/precategory-of-finite-posets.lagda.md @@ -1,20 +1,25 @@ # The precategory of finite posets ```agda -module order-theory.precategory-of-finite-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.precategory-of-finite-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import order-theory.finite-posets -open import order-theory.precategory-of-posets +open import order-theory.finite-posets funext +open import order-theory.precategory-of-posets funext ```
diff --git a/src/order-theory/precategory-of-finite-total-orders.lagda.md b/src/order-theory/precategory-of-finite-total-orders.lagda.md index e5e28bf9c5..b91b516f29 100644 --- a/src/order-theory/precategory-of-finite-total-orders.lagda.md +++ b/src/order-theory/precategory-of-finite-total-orders.lagda.md @@ -1,20 +1,25 @@ # The precategory of finite total orders ```agda -module order-theory.precategory-of-finite-total-orders where +open import foundation.function-extensionality-axiom + +module + order-theory.precategory-of-finite-total-orders + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import order-theory.finite-total-orders -open import order-theory.precategory-of-posets +open import order-theory.finite-total-orders funext +open import order-theory.precategory-of-posets funext ```
diff --git a/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md b/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md index cbcc011d57..c59414f1a3 100644 --- a/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md +++ b/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md @@ -1,20 +1,25 @@ # The precategory of inhabited finite total orders ```agda -module order-theory.precategory-of-inhabited-finite-total-orders where +open import foundation.function-extensionality-axiom + +module + order-theory.precategory-of-inhabited-finite-total-orders + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import order-theory.inhabited-finite-total-orders -open import order-theory.precategory-of-posets +open import order-theory.inhabited-finite-total-orders funext +open import order-theory.precategory-of-posets funext ```
diff --git a/src/order-theory/precategory-of-posets.lagda.md b/src/order-theory/precategory-of-posets.lagda.md index 69a33a4c81..2af76d06ba 100644 --- a/src/order-theory/precategory-of-posets.lagda.md +++ b/src/order-theory/precategory-of-posets.lagda.md @@ -1,19 +1,24 @@ # The precategory of posets ```agda -module order-theory.precategory-of-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.precategory-of-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/precategory-of-total-orders.lagda.md b/src/order-theory/precategory-of-total-orders.lagda.md index aeb5d9ffd2..d6ae76dfdf 100644 --- a/src/order-theory/precategory-of-total-orders.lagda.md +++ b/src/order-theory/precategory-of-total-orders.lagda.md @@ -1,20 +1,25 @@ # The precategory of total orders ```agda -module order-theory.precategory-of-total-orders where +open import foundation.function-extensionality-axiom + +module + order-theory.precategory-of-total-orders + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subprecategories -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.full-large-subprecategories funext +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import order-theory.precategory-of-posets -open import order-theory.total-orders +open import order-theory.precategory-of-posets funext +open import order-theory.total-orders funext ```
diff --git a/src/order-theory/preorders.lagda.md b/src/order-theory/preorders.lagda.md index 37293a7863..0521e102ee 100644 --- a/src/order-theory/preorders.lagda.md +++ b/src/order-theory/preorders.lagda.md @@ -1,24 +1,29 @@ # Preorders ```agda -module order-theory.preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/order-theory/principal-lower-sets-large-posets.lagda.md b/src/order-theory/principal-lower-sets-large-posets.lagda.md index 6823e5413e..83c700f447 100644 --- a/src/order-theory/principal-lower-sets-large-posets.lagda.md +++ b/src/order-theory/principal-lower-sets-large-posets.lagda.md @@ -1,21 +1,26 @@ # Principal lower sets of large posets ```agda -module order-theory.principal-lower-sets-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.principal-lower-sets-large-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext +open import order-theory.large-subposets funext +open import order-theory.large-subpreorders funext +open import order-theory.similarity-of-elements-large-posets funext ```
diff --git a/src/order-theory/principal-upper-sets-large-posets.lagda.md b/src/order-theory/principal-upper-sets-large-posets.lagda.md index c66b312a07..981aa11bcc 100644 --- a/src/order-theory/principal-upper-sets-large-posets.lagda.md +++ b/src/order-theory/principal-upper-sets-large-posets.lagda.md @@ -1,21 +1,26 @@ # Principal upper sets of large posets ```agda -module order-theory.principal-upper-sets-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.principal-upper-sets-large-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences +open import foundation.identity-types funext +open import foundation.logical-equivalences funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets -open import order-theory.large-subpreorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext +open import order-theory.large-subposets funext +open import order-theory.large-subpreorders funext +open import order-theory.similarity-of-elements-large-posets funext ```
diff --git a/src/order-theory/reflective-galois-connections-large-posets.lagda.md b/src/order-theory/reflective-galois-connections-large-posets.lagda.md index bd27be52af..caec33de61 100644 --- a/src/order-theory/reflective-galois-connections-large-posets.lagda.md +++ b/src/order-theory/reflective-galois-connections-large-posets.lagda.md @@ -1,18 +1,23 @@ # Reflective Galois connections between large posets ```agda -module order-theory.reflective-galois-connections-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.reflective-galois-connections-large-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.universe-levels -open import order-theory.galois-connections-large-posets -open import order-theory.large-posets -open import order-theory.order-preserving-maps-large-posets +open import order-theory.galois-connections-large-posets funext +open import order-theory.large-posets funext +open import order-theory.order-preserving-maps-large-posets funext ```
diff --git a/src/order-theory/resizing-posets.lagda.md b/src/order-theory/resizing-posets.lagda.md index 4fcaf5e66f..9cd4a30eb3 100644 --- a/src/order-theory/resizing-posets.lagda.md +++ b/src/order-theory/resizing-posets.lagda.md @@ -1,33 +1,38 @@ # Resizing posets ```agda -module order-theory.resizing-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.resizing-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.small-types funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.precategory-of-posets -open import order-theory.preorders -open import order-theory.resizing-preorders +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext +open import order-theory.precategory-of-posets funext +open import order-theory.preorders funext +open import order-theory.resizing-preorders funext ```
diff --git a/src/order-theory/resizing-preorders.lagda.md b/src/order-theory/resizing-preorders.lagda.md index 26a17b7682..a73cacd1c6 100644 --- a/src/order-theory/resizing-preorders.lagda.md +++ b/src/order-theory/resizing-preorders.lagda.md @@ -1,27 +1,32 @@ # Resizing preorders ```agda -module order-theory.resizing-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.resizing-preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.small-types funext open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders -open import order-theory.preorders +open import order-theory.order-preserving-maps-preorders funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/resizing-suplattices.lagda.md b/src/order-theory/resizing-suplattices.lagda.md index 6c0cdeede8..06cb2d0284 100644 --- a/src/order-theory/resizing-suplattices.lagda.md +++ b/src/order-theory/resizing-suplattices.lagda.md @@ -1,31 +1,36 @@ # Resizing suplattices ```agda -module order-theory.resizing-suplattices where +open import foundation.function-extensionality-axiom + +module + order-theory.resizing-suplattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.small-types funext open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets -open import order-theory.resizing-posets -open import order-theory.suplattices +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext +open import order-theory.resizing-posets funext +open import order-theory.suplattices funext ```
diff --git a/src/order-theory/similarity-of-elements-large-posets.lagda.md b/src/order-theory/similarity-of-elements-large-posets.lagda.md index 5e2d8199ea..1878dbc0db 100644 --- a/src/order-theory/similarity-of-elements-large-posets.lagda.md +++ b/src/order-theory/similarity-of-elements-large-posets.lagda.md @@ -1,24 +1,29 @@ # Similarity of elements in large posets ```agda -module order-theory.similarity-of-elements-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.similarity-of-elements-large-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.similarity-of-elements-large-preorders +open import order-theory.large-posets funext +open import order-theory.similarity-of-elements-large-preorders funext ```
diff --git a/src/order-theory/similarity-of-elements-large-preorders.lagda.md b/src/order-theory/similarity-of-elements-large-preorders.lagda.md index c027bb56db..3e1633d49b 100644 --- a/src/order-theory/similarity-of-elements-large-preorders.lagda.md +++ b/src/order-theory/similarity-of-elements-large-preorders.lagda.md @@ -1,19 +1,24 @@ # Similarity of elements in large preorders ```agda -module order-theory.similarity-of-elements-large-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.similarity-of-elements-large-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.large-preorders +open import order-theory.large-preorders funext ```
diff --git a/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md b/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md index 663ec217c0..e75d8229a6 100644 --- a/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md +++ b/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md @@ -1,19 +1,24 @@ # Similarity of order preserving maps between large posets ```agda -module order-theory.similarity-of-order-preserving-maps-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.similarity-of-order-preserving-maps-large-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.similarity-of-elements-large-posets -open import order-theory.similarity-of-order-preserving-maps-large-preorders +open import order-theory.large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.similarity-of-order-preserving-maps-large-preorders funext ```
diff --git a/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md b/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md index 62ce3a3d85..4f34f8bcff 100644 --- a/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md +++ b/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md @@ -1,18 +1,23 @@ # Similarity of order preserving maps between large preorders ```agda -module order-theory.similarity-of-order-preserving-maps-large-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.similarity-of-order-preserving-maps-large-preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.universe-levels -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-preorders +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.similarity-of-elements-large-preorders funext ```
diff --git a/src/order-theory/strict-order-preserving-maps.lagda.md b/src/order-theory/strict-order-preserving-maps.lagda.md index 44b8225347..4bf0892ac6 100644 --- a/src/order-theory/strict-order-preserving-maps.lagda.md +++ b/src/order-theory/strict-order-preserving-maps.lagda.md @@ -1,20 +1,25 @@ # Strict order preserving maps ```agda -module order-theory.strict-order-preserving-maps where +open import foundation.function-extensionality-axiom + +module + order-theory.strict-order-preserving-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.strict-preorders -open import order-theory.strictly-preordered-sets +open import order-theory.strict-preorders funext +open import order-theory.strictly-preordered-sets funext ```
diff --git a/src/order-theory/strict-preorders.lagda.md b/src/order-theory/strict-preorders.lagda.md index 071d017b3d..65e3f23b7d 100644 --- a/src/order-theory/strict-preorders.lagda.md +++ b/src/order-theory/strict-preorders.lagda.md @@ -1,18 +1,23 @@ # Strict preorders ```agda -module order-theory.strict-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.strict-preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.negation -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.universe-levels ``` diff --git a/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md b/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md index d8a4672caa..2f63126c6d 100644 --- a/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md +++ b/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md @@ -1,19 +1,24 @@ # Strictly inflationary maps on a strictly preordered type ```agda -module order-theory.strictly-inflationary-maps-strict-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.strictly-inflationary-maps-strict-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.strict-order-preserving-maps -open import order-theory.strict-preorders +open import order-theory.strict-order-preserving-maps funext +open import order-theory.strict-preorders funext ```
diff --git a/src/order-theory/strictly-preordered-sets.lagda.md b/src/order-theory/strictly-preordered-sets.lagda.md index c639e6fe02..860efc968b 100644 --- a/src/order-theory/strictly-preordered-sets.lagda.md +++ b/src/order-theory/strictly-preordered-sets.lagda.md @@ -1,22 +1,27 @@ # Strictly preordered sets ```agda -module order-theory.strictly-preordered-sets where +open import foundation.function-extensionality-axiom + +module + order-theory.strictly-preordered-sets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.empty-types funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.strict-preorders +open import order-theory.strict-preorders funext ```
diff --git a/src/order-theory/subposets.lagda.md b/src/order-theory/subposets.lagda.md index d7cd52162e..38f8a05a95 100644 --- a/src/order-theory/subposets.lagda.md +++ b/src/order-theory/subposets.lagda.md @@ -1,21 +1,26 @@ # Subposets ```agda -module order-theory.subposets where +open import foundation.function-extensionality-axiom + +module + order-theory.subposets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders -open import order-theory.subpreorders +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.subpreorders funext ```
diff --git a/src/order-theory/subpreorders.lagda.md b/src/order-theory/subpreorders.lagda.md index 8ac0925ccd..fce45d7c7b 100644 --- a/src/order-theory/subpreorders.lagda.md +++ b/src/order-theory/subpreorders.lagda.md @@ -1,21 +1,26 @@ # Subpreorders ```agda -module order-theory.subpreorders where +open import foundation.function-extensionality-axiom + +module + order-theory.subpreorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext ```
diff --git a/src/order-theory/suplattices.lagda.md b/src/order-theory/suplattices.lagda.md index e2cac7a583..86a1563326 100644 --- a/src/order-theory/suplattices.lagda.md +++ b/src/order-theory/suplattices.lagda.md @@ -1,25 +1,30 @@ # Suplattices ```agda -module order-theory.suplattices where +open import foundation.function-extensionality-axiom + +module + order-theory.suplattices + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets -open import order-theory.posets -open import order-theory.upper-bounds-posets +open import order-theory.least-upper-bounds-posets funext +open import order-theory.posets funext +open import order-theory.upper-bounds-posets funext ```
diff --git a/src/order-theory/supremum-preserving-maps-posets.lagda.md b/src/order-theory/supremum-preserving-maps-posets.lagda.md index b5abca4ab4..c75c301030 100644 --- a/src/order-theory/supremum-preserving-maps-posets.lagda.md +++ b/src/order-theory/supremum-preserving-maps-posets.lagda.md @@ -1,33 +1,38 @@ # Supremum preserving maps between posets ```agda -module order-theory.supremum-preserving-maps-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.supremum-preserving-maps-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.booleans +open import foundation.booleans funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.function-types +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.strictly-involutive-identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.small-types funext +open import foundation.strictly-involutive-identity-types funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import order-theory.join-preserving-maps-posets -open import order-theory.least-upper-bounds-posets -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.join-preserving-maps-posets funext +open import order-theory.least-upper-bounds-posets funext +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext ```
diff --git a/src/order-theory/top-elements-large-posets.lagda.md b/src/order-theory/top-elements-large-posets.lagda.md index f861a1a336..8e760b8df5 100644 --- a/src/order-theory/top-elements-large-posets.lagda.md +++ b/src/order-theory/top-elements-large-posets.lagda.md @@ -1,7 +1,12 @@ # Top elements in large posets ```agda -module order-theory.top-elements-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.top-elements-large-posets + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module order-theory.top-elements-large-posets where ```agda open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext +open import order-theory.large-posets funext ```
diff --git a/src/order-theory/top-elements-posets.lagda.md b/src/order-theory/top-elements-posets.lagda.md index 658fc977cc..802fcfb581 100644 --- a/src/order-theory/top-elements-posets.lagda.md +++ b/src/order-theory/top-elements-posets.lagda.md @@ -1,19 +1,24 @@ # Top elements in posets ```agda -module order-theory.top-elements-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.top-elements-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.posets -open import order-theory.top-elements-preorders +open import order-theory.posets funext +open import order-theory.top-elements-preorders funext ```
diff --git a/src/order-theory/top-elements-preorders.lagda.md b/src/order-theory/top-elements-preorders.lagda.md index 1c9655f1de..94a3834174 100644 --- a/src/order-theory/top-elements-preorders.lagda.md +++ b/src/order-theory/top-elements-preorders.lagda.md @@ -1,17 +1,22 @@ # Top elements in preorders ```agda -module order-theory.top-elements-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.top-elements-preorders + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext ```
diff --git a/src/order-theory/total-orders.lagda.md b/src/order-theory/total-orders.lagda.md index 1f84d69e67..a0dd92af88 100644 --- a/src/order-theory/total-orders.lagda.md +++ b/src/order-theory/total-orders.lagda.md @@ -1,22 +1,27 @@ # Total orders ```agda -module order-theory.total-orders where +open import foundation.function-extensionality-axiom + +module + order-theory.total-orders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import order-theory.posets -open import order-theory.preorders -open import order-theory.total-preorders +open import order-theory.posets funext +open import order-theory.preorders funext +open import order-theory.total-preorders funext ```
diff --git a/src/order-theory/total-preorders.lagda.md b/src/order-theory/total-preorders.lagda.md index facdaddbd8..be203bcef2 100644 --- a/src/order-theory/total-preorders.lagda.md +++ b/src/order-theory/total-preorders.lagda.md @@ -1,19 +1,24 @@ # Total preorders ```agda -module order-theory.total-preorders where +open import foundation.function-extensionality-axiom + +module + order-theory.total-preorders + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.propositions +open import foundation.disjunction funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.preorders +open import order-theory.preorders funext ```
diff --git a/src/order-theory/transitive-well-founded-relations.lagda.md b/src/order-theory/transitive-well-founded-relations.lagda.md index f011a6666e..2a95571b4f 100644 --- a/src/order-theory/transitive-well-founded-relations.lagda.md +++ b/src/order-theory/transitive-well-founded-relations.lagda.md @@ -1,18 +1,23 @@ # Transitive well-founded relations ```agda -module order-theory.transitive-well-founded-relations where +open import foundation.function-extensionality-axiom + +module + order-theory.transitive-well-founded-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import order-theory.well-founded-relations +open import order-theory.well-founded-relations funext ```
diff --git a/src/order-theory/upper-bounds-chains-posets.lagda.md b/src/order-theory/upper-bounds-chains-posets.lagda.md index 3da859e4e1..4588a2df75 100644 --- a/src/order-theory/upper-bounds-chains-posets.lagda.md +++ b/src/order-theory/upper-bounds-chains-posets.lagda.md @@ -1,21 +1,26 @@ # Upper bounds of chains in posets ```agda -module order-theory.upper-bounds-chains-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.upper-bounds-chains-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.existential-quantification +open import foundation.existential-quantification funext open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.propositions -open import order-theory.chains-posets -open import order-theory.posets -open import order-theory.upper-bounds-posets +open import order-theory.chains-posets funext +open import order-theory.posets funext +open import order-theory.upper-bounds-posets funext ```
diff --git a/src/order-theory/upper-bounds-large-posets.lagda.md b/src/order-theory/upper-bounds-large-posets.lagda.md index bada6644c6..51321f7487 100644 --- a/src/order-theory/upper-bounds-large-posets.lagda.md +++ b/src/order-theory/upper-bounds-large-posets.lagda.md @@ -1,20 +1,25 @@ # Upper bounds in large posets ```agda -module order-theory.upper-bounds-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.upper-bounds-large-posets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.dependent-products-large-posets -open import order-theory.large-posets +open import order-theory.dependent-products-large-posets funext +open import order-theory.large-posets funext ```
diff --git a/src/order-theory/upper-bounds-posets.lagda.md b/src/order-theory/upper-bounds-posets.lagda.md index 0193ab6052..514a58283b 100644 --- a/src/order-theory/upper-bounds-posets.lagda.md +++ b/src/order-theory/upper-bounds-posets.lagda.md @@ -1,17 +1,22 @@ # Upper bounds in posets ```agda -module order-theory.upper-bounds-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.upper-bounds-posets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.posets +open import order-theory.posets funext ```
diff --git a/src/order-theory/upper-sets-large-posets.lagda.md b/src/order-theory/upper-sets-large-posets.lagda.md index f5c8d8ec1c..0dd83dbf8c 100644 --- a/src/order-theory/upper-sets-large-posets.lagda.md +++ b/src/order-theory/upper-sets-large-posets.lagda.md @@ -1,7 +1,12 @@ # Upper sets of large posets ```agda -module order-theory.upper-sets-large-posets where +open import foundation.function-extensionality-axiom + +module + order-theory.upper-sets-large-posets + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module order-theory.upper-sets-large-posets where ```agda open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-subposets +open import order-theory.large-posets funext +open import order-theory.large-subposets funext ```
diff --git a/src/order-theory/well-founded-relations.lagda.md b/src/order-theory/well-founded-relations.lagda.md index 7ae600f45c..05a5a53042 100644 --- a/src/order-theory/well-founded-relations.lagda.md +++ b/src/order-theory/well-founded-relations.lagda.md @@ -1,21 +1,26 @@ # Well-founded relations ```agda -module order-theory.well-founded-relations where +open import foundation.function-extensionality-axiom + +module + order-theory.well-founded-relations + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import order-theory.accessible-elements-relations -open import order-theory.preorders +open import order-theory.accessible-elements-relations funext +open import order-theory.preorders funext ```
diff --git a/src/order-theory/zorns-lemma.lagda.md b/src/order-theory/zorns-lemma.lagda.md index 8d1381868b..d13ce39247 100644 --- a/src/order-theory/zorns-lemma.lagda.md +++ b/src/order-theory/zorns-lemma.lagda.md @@ -1,29 +1,34 @@ # Zorn's lemma ```agda -module order-theory.zorns-lemma where +open import foundation.function-extensionality-axiom + +module + order-theory.zorns-lemma + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.inhabited-types -open import foundation.law-of-excluded-middle -open import foundation.logical-equivalences -open import foundation.propositional-truncations +open import foundation.dependent-products-propositions funext +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.inhabited-types funext +open import foundation.law-of-excluded-middle funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.propositions -open import order-theory.chains-posets -open import order-theory.posets -open import order-theory.top-elements-posets -open import order-theory.upper-bounds-chains-posets +open import order-theory.chains-posets funext +open import order-theory.posets funext +open import order-theory.top-elements-posets funext +open import order-theory.upper-bounds-chains-posets funext ```
diff --git a/src/organic-chemistry.lagda.md b/src/organic-chemistry.lagda.md index d4b75e9bc7..7d0fc2ed59 100644 --- a/src/organic-chemistry.lagda.md +++ b/src/organic-chemistry.lagda.md @@ -3,14 +3,19 @@ ## Modules in the organic chemistry namespace ```agda -module organic-chemistry where +open import foundation.function-extensionality-axiom -open import organic-chemistry.alcohols public -open import organic-chemistry.alkanes public -open import organic-chemistry.alkenes public -open import organic-chemistry.alkynes public -open import organic-chemistry.ethane public -open import organic-chemistry.hydrocarbons public -open import organic-chemistry.methane public -open import organic-chemistry.saturated-carbons public +module + organic-chemistry + (funext : function-extensionality) + where + +open import organic-chemistry.alcohols funext public +open import organic-chemistry.alkanes funext public +open import organic-chemistry.alkenes funext public +open import organic-chemistry.alkynes funext public +open import organic-chemistry.ethane funext public +open import organic-chemistry.hydrocarbons funext public +open import organic-chemistry.methane funext public +open import organic-chemistry.saturated-carbons funext public ``` diff --git a/src/organic-chemistry/alcohols.lagda.md b/src/organic-chemistry/alcohols.lagda.md index f28fc09806..cdc4500b3b 100644 --- a/src/organic-chemistry/alcohols.lagda.md +++ b/src/organic-chemistry/alcohols.lagda.md @@ -1,22 +1,27 @@ # Alcohols ```agda -module organic-chemistry.alcohols where +open import foundation.function-extensionality-axiom + +module + organic-chemistry.alcohols + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.decidable-subtypes +open import foundation.cartesian-product-types funext +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.negation -open import foundation.propositional-truncations +open import foundation.negation funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import organic-chemistry.hydrocarbons -open import organic-chemistry.saturated-carbons +open import organic-chemistry.hydrocarbons funext +open import organic-chemistry.saturated-carbons funext ```
diff --git a/src/organic-chemistry/alkanes.lagda.md b/src/organic-chemistry/alkanes.lagda.md index ae5bc42c05..328077f317 100644 --- a/src/organic-chemistry/alkanes.lagda.md +++ b/src/organic-chemistry/alkanes.lagda.md @@ -1,7 +1,12 @@ # Alkanes ```agda -module organic-chemistry.alkanes where +open import foundation.function-extensionality-axiom + +module + organic-chemistry.alkanes + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module organic-chemistry.alkanes where ```agda open import foundation.universe-levels -open import organic-chemistry.hydrocarbons -open import organic-chemistry.saturated-carbons +open import organic-chemistry.hydrocarbons funext +open import organic-chemistry.saturated-carbons funext ```
diff --git a/src/organic-chemistry/alkenes.lagda.md b/src/organic-chemistry/alkenes.lagda.md index 66a563f86e..9d7a7c7823 100644 --- a/src/organic-chemistry/alkenes.lagda.md +++ b/src/organic-chemistry/alkenes.lagda.md @@ -1,7 +1,12 @@ # Alkenes ```agda -module organic-chemistry.alkenes where +open import foundation.function-extensionality-axiom + +module + organic-chemistry.alkenes + (funext : function-extensionality) + where ```
Imports @@ -10,13 +15,13 @@ module organic-chemistry.alkenes where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import organic-chemistry.hydrocarbons -open import organic-chemistry.saturated-carbons +open import organic-chemistry.hydrocarbons funext +open import organic-chemistry.saturated-carbons funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/organic-chemistry/alkynes.lagda.md b/src/organic-chemistry/alkynes.lagda.md index 80956732ce..2f4eccad47 100644 --- a/src/organic-chemistry/alkynes.lagda.md +++ b/src/organic-chemistry/alkynes.lagda.md @@ -1,7 +1,12 @@ # Alkynes ```agda -module organic-chemistry.alkynes where +open import foundation.function-extensionality-axiom + +module + organic-chemistry.alkynes + (funext : function-extensionality) + where ```
Imports @@ -10,13 +15,13 @@ module organic-chemistry.alkynes where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.embeddings +open import foundation.embeddings funext open import foundation.universe-levels -open import organic-chemistry.hydrocarbons -open import organic-chemistry.saturated-carbons +open import organic-chemistry.hydrocarbons funext +open import organic-chemistry.saturated-carbons funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/organic-chemistry/ethane.lagda.md b/src/organic-chemistry/ethane.lagda.md index b20b3fe687..644f189b87 100644 --- a/src/organic-chemistry/ethane.lagda.md +++ b/src/organic-chemistry/ethane.lagda.md @@ -1,44 +1,49 @@ # Ethane ```agda -module organic-chemistry.ethane where +open import foundation.function-extensionality-axiom + +module + organic-chemistry.ethane + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext -open import finite-group-theory.tetrahedra-in-3-space +open import finite-group-theory.tetrahedra-in-3-space funext -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.finite-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.finite-graphs funext +open import graph-theory.walks-undirected-graphs funext -open import organic-chemistry.alkanes -open import organic-chemistry.hydrocarbons +open import organic-chemistry.alkanes funext +open import organic-chemistry.hydrocarbons funext -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/organic-chemistry/hydrocarbons.lagda.md b/src/organic-chemistry/hydrocarbons.lagda.md index 6012140cf2..7c2a4736df 100644 --- a/src/organic-chemistry/hydrocarbons.lagda.md +++ b/src/organic-chemistry/hydrocarbons.lagda.md @@ -1,27 +1,32 @@ # Hydrocarbons ```agda -module organic-chemistry.hydrocarbons where +open import foundation.function-extensionality-axiom + +module + organic-chemistry.hydrocarbons + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext -open import finite-group-theory.tetrahedra-in-3-space +open import finite-group-theory.tetrahedra-in-3-space funext -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.negation +open import foundation.embeddings funext +open import foundation.negation funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.connected-undirected-graphs -open import graph-theory.finite-graphs +open import graph-theory.connected-undirected-graphs funext +open import graph-theory.finite-graphs funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/organic-chemistry/methane.lagda.md b/src/organic-chemistry/methane.lagda.md index 806fb0cbc9..64cc068f95 100644 --- a/src/organic-chemistry/methane.lagda.md +++ b/src/organic-chemistry/methane.lagda.md @@ -1,30 +1,35 @@ # Methane ```agda -module organic-chemistry.methane where +open import foundation.function-extensionality-axiom + +module + organic-chemistry.methane + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext -open import finite-group-theory.tetrahedra-in-3-space +open import finite-group-theory.tetrahedra-in-3-space funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.walks-undirected-graphs +open import graph-theory.walks-undirected-graphs funext -open import organic-chemistry.alkanes -open import organic-chemistry.hydrocarbons +open import organic-chemistry.alkanes funext +open import organic-chemistry.hydrocarbons funext -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/organic-chemistry/saturated-carbons.lagda.md b/src/organic-chemistry/saturated-carbons.lagda.md index f214d5aa80..0754610b22 100644 --- a/src/organic-chemistry/saturated-carbons.lagda.md +++ b/src/organic-chemistry/saturated-carbons.lagda.md @@ -1,21 +1,26 @@ # Saturated carbons ```agda -module organic-chemistry.saturated-carbons where +open import foundation.function-extensionality-axiom + +module + organic-chemistry.saturated-carbons + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import organic-chemistry.hydrocarbons +open import organic-chemistry.hydrocarbons funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems.lagda.md index a167d57d4a..d621d09720 100644 --- a/src/orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems.lagda.md @@ -7,71 +7,76 @@ ## Modules in the orthogonal factorization systems namespace ```agda -module orthogonal-factorization-systems where +open import foundation.function-extensionality-axiom -open import orthogonal-factorization-systems.cd-structures public -open import orthogonal-factorization-systems.cellular-maps public -open import orthogonal-factorization-systems.closed-modalities public -open import orthogonal-factorization-systems.continuation-modalities public -open import orthogonal-factorization-systems.double-lifts-families-of-elements public -open import orthogonal-factorization-systems.double-negation-sheaves public -open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements public -open import orthogonal-factorization-systems.extensions-lifts-families-of-elements public -open import orthogonal-factorization-systems.extensions-maps public -open import orthogonal-factorization-systems.factorization-operations public -open import orthogonal-factorization-systems.factorization-operations-function-classes public -open import orthogonal-factorization-systems.factorization-operations-global-function-classes public -open import orthogonal-factorization-systems.factorizations-of-maps public -open import orthogonal-factorization-systems.factorizations-of-maps-function-classes public -open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes public -open import orthogonal-factorization-systems.families-of-types-local-at-maps public -open import orthogonal-factorization-systems.fiberwise-orthogonal-maps public -open import orthogonal-factorization-systems.function-classes public -open import orthogonal-factorization-systems.functoriality-higher-modalities public -open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses public -open import orthogonal-factorization-systems.functoriality-pullback-hom public -open import orthogonal-factorization-systems.functoriality-reflective-global-subuniverses public -open import orthogonal-factorization-systems.global-function-classes public -open import orthogonal-factorization-systems.higher-modalities public -open import orthogonal-factorization-systems.identity-modality public -open import orthogonal-factorization-systems.large-lawvere-tierney-topologies public -open import orthogonal-factorization-systems.lawvere-tierney-topologies public -open import orthogonal-factorization-systems.lifting-operations public -open import orthogonal-factorization-systems.lifting-structures-on-squares public -open import orthogonal-factorization-systems.lifts-families-of-elements public -open import orthogonal-factorization-systems.lifts-maps public -open import orthogonal-factorization-systems.localizations-at-global-subuniverses public -open import orthogonal-factorization-systems.localizations-at-maps public -open import orthogonal-factorization-systems.localizations-at-subuniverses public -open import orthogonal-factorization-systems.locally-small-modal-operators public -open import orthogonal-factorization-systems.maps-local-at-maps public -open import orthogonal-factorization-systems.mere-lifting-properties public -open import orthogonal-factorization-systems.modal-induction public -open import orthogonal-factorization-systems.modal-operators public -open import orthogonal-factorization-systems.modal-subuniverse-induction public -open import orthogonal-factorization-systems.null-families-of-types public -open import orthogonal-factorization-systems.null-maps public -open import orthogonal-factorization-systems.null-types public -open import orthogonal-factorization-systems.open-modalities public -open import orthogonal-factorization-systems.orthogonal-factorization-systems public -open import orthogonal-factorization-systems.orthogonal-maps public -open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements public -open import orthogonal-factorization-systems.pullback-hom public -open import orthogonal-factorization-systems.raise-modalities public -open import orthogonal-factorization-systems.reflective-global-subuniverses public -open import orthogonal-factorization-systems.reflective-modalities public -open import orthogonal-factorization-systems.reflective-subuniverses public +module + orthogonal-factorization-systems + (funext : function-extensionality) + where + +open import orthogonal-factorization-systems.cd-structures funext public +open import orthogonal-factorization-systems.cellular-maps funext public +open import orthogonal-factorization-systems.closed-modalities funext public +open import orthogonal-factorization-systems.continuation-modalities funext public +open import orthogonal-factorization-systems.double-lifts-families-of-elements funext public +open import orthogonal-factorization-systems.double-negation-sheaves funext public +open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements funext public +open import orthogonal-factorization-systems.extensions-lifts-families-of-elements funext public +open import orthogonal-factorization-systems.extensions-maps funext public +open import orthogonal-factorization-systems.factorization-operations funext public +open import orthogonal-factorization-systems.factorization-operations-function-classes funext public +open import orthogonal-factorization-systems.factorization-operations-global-function-classes funext public +open import orthogonal-factorization-systems.factorizations-of-maps funext public +open import orthogonal-factorization-systems.factorizations-of-maps-function-classes funext public +open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes funext public +open import orthogonal-factorization-systems.families-of-types-local-at-maps funext public +open import orthogonal-factorization-systems.fiberwise-orthogonal-maps funext public +open import orthogonal-factorization-systems.function-classes funext public +open import orthogonal-factorization-systems.functoriality-higher-modalities funext public +open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses funext public +open import orthogonal-factorization-systems.functoriality-pullback-hom funext public +open import orthogonal-factorization-systems.functoriality-reflective-global-subuniverses funext public +open import orthogonal-factorization-systems.global-function-classes funext public +open import orthogonal-factorization-systems.higher-modalities funext public +open import orthogonal-factorization-systems.identity-modality funext public +open import orthogonal-factorization-systems.large-lawvere-tierney-topologies funext public +open import orthogonal-factorization-systems.lawvere-tierney-topologies funext public +open import orthogonal-factorization-systems.lifting-operations funext public +open import orthogonal-factorization-systems.lifting-structures-on-squares funext public +open import orthogonal-factorization-systems.lifts-families-of-elements funext public +open import orthogonal-factorization-systems.lifts-maps funext public +open import orthogonal-factorization-systems.localizations-at-global-subuniverses funext public +open import orthogonal-factorization-systems.localizations-at-maps funext public +open import orthogonal-factorization-systems.localizations-at-subuniverses funext public +open import orthogonal-factorization-systems.locally-small-modal-operators funext public +open import orthogonal-factorization-systems.maps-local-at-maps funext public +open import orthogonal-factorization-systems.mere-lifting-properties funext public +open import orthogonal-factorization-systems.modal-induction funext public +open import orthogonal-factorization-systems.modal-operators funext public +open import orthogonal-factorization-systems.modal-subuniverse-induction funext public +open import orthogonal-factorization-systems.null-families-of-types funext public +open import orthogonal-factorization-systems.null-maps funext public +open import orthogonal-factorization-systems.null-types funext public +open import orthogonal-factorization-systems.open-modalities funext public +open import orthogonal-factorization-systems.orthogonal-factorization-systems funext public +open import orthogonal-factorization-systems.orthogonal-maps funext public +open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements funext public +open import orthogonal-factorization-systems.pullback-hom funext public +open import orthogonal-factorization-systems.raise-modalities funext public +open import orthogonal-factorization-systems.reflective-global-subuniverses funext public +open import orthogonal-factorization-systems.reflective-modalities funext public +open import orthogonal-factorization-systems.reflective-subuniverses funext public open import orthogonal-factorization-systems.regular-cd-structures public -open import orthogonal-factorization-systems.sigma-closed-modalities public -open import orthogonal-factorization-systems.sigma-closed-reflective-modalities public -open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses public -open import orthogonal-factorization-systems.stable-orthogonal-factorization-systems public -open import orthogonal-factorization-systems.types-colocal-at-maps public -open import orthogonal-factorization-systems.types-local-at-maps public -open import orthogonal-factorization-systems.types-separated-at-maps public -open import orthogonal-factorization-systems.uniquely-eliminating-modalities public -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses public -open import orthogonal-factorization-systems.wide-function-classes public -open import orthogonal-factorization-systems.wide-global-function-classes public -open import orthogonal-factorization-systems.zero-modality public +open import orthogonal-factorization-systems.sigma-closed-modalities funext public +open import orthogonal-factorization-systems.sigma-closed-reflective-modalities funext public +open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses funext public +open import orthogonal-factorization-systems.stable-orthogonal-factorization-systems funext public +open import orthogonal-factorization-systems.types-colocal-at-maps funext public +open import orthogonal-factorization-systems.types-local-at-maps funext public +open import orthogonal-factorization-systems.types-separated-at-maps funext public +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext public +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext public +open import orthogonal-factorization-systems.wide-function-classes funext public +open import orthogonal-factorization-systems.wide-global-function-classes funext public +open import orthogonal-factorization-systems.zero-modality funext public ``` diff --git a/src/orthogonal-factorization-systems/cd-structures.lagda.md b/src/orthogonal-factorization-systems/cd-structures.lagda.md index d33d5a3d4a..27013b19df 100644 --- a/src/orthogonal-factorization-systems/cd-structures.lagda.md +++ b/src/orthogonal-factorization-systems/cd-structures.lagda.md @@ -1,15 +1,20 @@ # Cd-structures ```agda -module orthogonal-factorization-systems.cd-structures where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.cd-structures + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.morphisms-arrows -open import foundation.propositions -open import foundation.subtypes +open import foundation.morphisms-arrows funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/cellular-maps.lagda.md b/src/orthogonal-factorization-systems/cellular-maps.lagda.md index 0bcd3a38aa..0544a9aac7 100644 --- a/src/orthogonal-factorization-systems/cellular-maps.lagda.md +++ b/src/orthogonal-factorization-systems/cellular-maps.lagda.md @@ -1,17 +1,22 @@ # Cellular maps ```agda -module orthogonal-factorization-systems.cellular-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.cellular-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.connected-maps +open import foundation.connected-maps funext open import foundation.truncation-levels open import foundation.universe-levels -open import orthogonal-factorization-systems.mere-lifting-properties +open import orthogonal-factorization-systems.mere-lifting-properties funext ```
diff --git a/src/orthogonal-factorization-systems/closed-modalities.lagda.md b/src/orthogonal-factorization-systems/closed-modalities.lagda.md index c42bfe9572..bf2bae353b 100644 --- a/src/orthogonal-factorization-systems/closed-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/closed-modalities.lagda.md @@ -1,29 +1,34 @@ # The closed modalities ```agda -module orthogonal-factorization-systems.closed-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.closed-modalities + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.reflective-subuniverses -open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.reflective-subuniverses funext +open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses funext -open import synthetic-homotopy-theory.joins-of-types +open import synthetic-homotopy-theory.joins-of-types funext ```
diff --git a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md index 37b7855617..ee6cf0a7e3 100644 --- a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md @@ -1,27 +1,32 @@ # Continuation modalities ```agda -module orthogonal-factorization-systems.continuation-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.continuation-modalities + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.continuations +open import foundation.cartesian-product-types funext +open import foundation.continuations funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.large-lawvere-tierney-topologies -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.large-lawvere-tierney-topologies funext +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext ```
diff --git a/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md index 4c248d4992..251388aacc 100644 --- a/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md @@ -1,7 +1,12 @@ # Double lifts of families of elements ```agda -module orthogonal-factorization-systems.double-lifts-families-of-elements where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.double-lifts-families-of-elements + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module orthogonal-factorization-systems.double-lifts-families-of-elements where ```agda open import foundation.universe-levels -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
diff --git a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md index d48dc64cdd..f91b2b0986 100644 --- a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md +++ b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md @@ -1,29 +1,34 @@ # Double negation sheaves ```agda -module orthogonal-factorization-systems.double-negation-sheaves where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.double-negation-sheaves + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions -open import foundation.double-negation-stable-propositions -open import foundation.empty-types -open import foundation.irrefutable-propositions -open import foundation.logical-equivalences -open import foundation.negation +open import foundation.dependent-products-propositions funext +open import foundation.double-negation-stable-propositions funext +open import foundation.empty-types funext +open import foundation.irrefutable-propositions funext +open import foundation.logical-equivalences funext +open import foundation.negation funext open import foundation.type-arithmetic-cartesian-product-types -open import foundation.universal-property-coproduct-types +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.propositions -open import orthogonal-factorization-systems.null-types +open import orthogonal-factorization-systems.null-types funext ```
diff --git a/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md index c590c46263..5eb86ba4d9 100644 --- a/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md @@ -17,8 +17,8 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import orthogonal-factorization-systems.double-lifts-families-of-elements -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.double-lifts-families-of-elements funext +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
@@ -60,7 +60,12 @@ elements `a : (i : I) → A i` induces an evaluation map given by `c ↦ (λ i → c i (a i) (b i))`. ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {l1 l2 l3 l4 : Level} {I : UU l1} {A : I → UU l2} {B : (i : I) → A i → UU l3} {C : (i : I) (x : A i) → B i x → UU l4} {a : (i : I) → A i} (b : dependent-lift-family-of-elements B a) diff --git a/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md index 8766921e92..ef201d3db3 100644 --- a/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md @@ -17,7 +17,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
@@ -66,7 +66,12 @@ Any family of elements `a : (i : I) → A i` induces an evaluation map defined by `b ↦ (λ i → b i (a i))`. ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {l1 l2 l3 : Level} {I : UU l1} {A : I → UU l2} {B : (i : I) → A i → UU l3} (a : (i : I) → A i) where diff --git a/src/orthogonal-factorization-systems/extensions-maps.lagda.md b/src/orthogonal-factorization-systems/extensions-maps.lagda.md index 1afb566035..438090583e 100644 --- a/src/orthogonal-factorization-systems/extensions-maps.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-maps.lagda.md @@ -1,7 +1,12 @@ # Extensions of maps ```agda -module orthogonal-factorization-systems.extensions-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.extensions-maps + (funext : function-extensionality) + where ```
Imports @@ -9,25 +14,25 @@ module orthogonal-factorization-systems.extensions-maps where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-products-truncated-types funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.monomorphisms -open import foundation.postcomposition-functions -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.monomorphisms funext +open import foundation.postcomposition-functions funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.structure-identity-principle open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md index 1d51743a99..1a5f24806b 100644 --- a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md @@ -1,37 +1,42 @@ # Factorization operations into function classes ```agda -module orthogonal-factorization-systems.factorization-operations-function-classes where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.factorization-operations-function-classes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.telescopes open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorizations-of-maps -open import orthogonal-factorization-systems.factorizations-of-maps-function-classes -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.lifting-structures-on-squares +open import orthogonal-factorization-systems.factorizations-of-maps funext +open import orthogonal-factorization-systems.factorizations-of-maps funext-function-classes +open import orthogonal-factorization-systems.function-classes funext +open import orthogonal-factorization-systems.lifting-structures-on-squares funext ```
diff --git a/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md index a372c14a56..708d067acb 100644 --- a/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md @@ -1,18 +1,23 @@ # Factorization operations into global function classes ```agda -module orthogonal-factorization-systems.factorization-operations-global-function-classes where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.factorization-operations-global-function-classes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import orthogonal-factorization-systems.factorization-operations-function-classes -open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes -open import orthogonal-factorization-systems.global-function-classes +open import orthogonal-factorization-systems.factorization-operations-function-classes funext +open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes funext +open import orthogonal-factorization-systems.global-function-classes funext ```
diff --git a/src/orthogonal-factorization-systems/factorization-operations.lagda.md b/src/orthogonal-factorization-systems/factorization-operations.lagda.md index 9262dfd081..c580cbce90 100644 --- a/src/orthogonal-factorization-systems/factorization-operations.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations.lagda.md @@ -1,7 +1,12 @@ # Factorization operations ```agda -module orthogonal-factorization-systems.factorization-operations where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.factorization-operations + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module orthogonal-factorization-systems.factorization-operations where ```agda open import foundation.universe-levels -open import orthogonal-factorization-systems.factorizations-of-maps +open import orthogonal-factorization-systems.factorizations-of-maps funext ```
diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md index f4eee03050..369674f700 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md @@ -1,34 +1,39 @@ # Factorizations of maps into function classes ```agda -module orthogonal-factorization-systems.factorizations-of-maps-function-classes where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.factorizations-of-maps-function-classes + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorizations-of-maps -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.global-function-classes +open import orthogonal-factorization-systems.factorizations-of-maps funext +open import orthogonal-factorization-systems.function-classes funext +open import orthogonal-factorization-systems.global-function-classes funext ```
diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md index 9945116577..b8190052e7 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md @@ -1,34 +1,39 @@ # Factorizations of maps into global function classes ```agda -module orthogonal-factorization-systems.factorizations-of-maps-global-function-classes where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.factorizations-of-maps-global-function-classes + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorizations-of-maps -open import orthogonal-factorization-systems.factorizations-of-maps-function-classes -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.global-function-classes +open import orthogonal-factorization-systems.factorizations-of-maps funext +open import orthogonal-factorization-systems.factorizations-of-maps funext-function-classes +open import orthogonal-factorization-systems.function-classes funext +open import orthogonal-factorization-systems.global-function-classes funext ```
diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md index a4266abdd5..ef5eb84631 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md @@ -1,24 +1,29 @@ # Factorizations of maps ```agda -module orthogonal-factorization-systems.factorizations-of-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.factorizations-of-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.retracts-of-types +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.retracts-of-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition ``` diff --git a/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md index 0d79431a42..79dca887c2 100644 --- a/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md @@ -1,20 +1,25 @@ # Families of types local at a map ```agda -module orthogonal-factorization-systems.families-of-types-local-at-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.families-of-types-local-at-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.precomposition-functions -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext open import foundation.universe-levels -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.orthogonal-maps funext +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md index 544627106f..bf6a19c7ad 100644 --- a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md @@ -1,27 +1,32 @@ # Fiberwise orthogonal maps ```agda -module orthogonal-factorization-systems.fiberwise-orthogonal-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.fiberwise-orthogonal-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopies -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.pullbacks +open import foundation.cartesian-morphisms-arrows funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.pullbacks funext open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.null-maps -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.null-maps funext +open import orthogonal-factorization-systems.orthogonal-maps funext +open import orthogonal-factorization-systems.pullback-hom funext ```
diff --git a/src/orthogonal-factorization-systems/function-classes.lagda.md b/src/orthogonal-factorization-systems/function-classes.lagda.md index 821f6aa51e..4f5fc23b8c 100644 --- a/src/orthogonal-factorization-systems/function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/function-classes.lagda.md @@ -1,28 +1,33 @@ # Function classes ```agda -module orthogonal-factorization-systems.function-classes where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.function-classes + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalence-induction -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.pullbacks -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalence-induction funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.pullbacks funext +open import foundation.subtypes funext open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md b/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md index 5bf2870bfe..c9f0f08cda 100644 --- a/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md @@ -1,7 +1,12 @@ # Functoriality of higher modalities ```agda -module orthogonal-factorization-systems.functoriality-higher-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.functoriality-higher-modalities + (funext : function-extensionality) + where ```
Imports @@ -9,21 +14,22 @@ module orthogonal-factorization-systems.functoriality-higher-modalities where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra -open import foundation.small-types +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext +open import foundation.small-types funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import orthogonal-factorization-systems.higher-modalities -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction +open import orthogonal-factorization-systems.higher-modalities funext +open import orthogonal-factorization-systems.modal-induction funext +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.modal-subuniverse-induction funext ```
diff --git a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md index 2ba05b568a..7e561032db 100644 --- a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md @@ -1,30 +1,34 @@ # Functoriality of localizations at global subuniverses ```agda -module orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.extensions-types-global-subuniverses -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types +open import foundation.equivalences funext +open import foundation.extensions-types-global-subuniverses funext +open import foundation.function-types funext +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext +open import foundation.retracts-of-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-global-subuniverses -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses +open import orthogonal-factorization-systems.localizations-at-global-subuniverses funext +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext ```
diff --git a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md index ba3af5d73b..223a39f814 100644 --- a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md @@ -1,19 +1,24 @@ # Functoriality of the pullback-hom ```agda -module orthogonal-factorization-systems.functoriality-pullback-hom where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.functoriality-pullback-hom + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.functoriality-morphisms-arrows -open import foundation.functoriality-pullbacks -open import foundation.morphisms-arrows +open import foundation.functoriality-morphisms-arrows funext +open import foundation.functoriality-pullbacks funext +open import foundation.morphisms-arrows funext open import foundation.morphisms-cospan-diagrams open import foundation.universe-levels -open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.pullback-hom funext ```
diff --git a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md index e3b1f8e7b4..9a319abc75 100644 --- a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md @@ -1,22 +1,27 @@ # Functoriality of reflective global subuniverses ```agda -module orthogonal-factorization-systems.functoriality-reflective-global-subuniverses where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.functoriality-reflective-global-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.retracts-of-types +open import foundation.commuting-squares-of-maps funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses -open import orthogonal-factorization-systems.reflective-global-subuniverses +open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses funext +open import orthogonal-factorization-systems.reflective-global-subuniverses funext ```
diff --git a/src/orthogonal-factorization-systems/global-function-classes.lagda.md b/src/orthogonal-factorization-systems/global-function-classes.lagda.md index b11fa84d13..b0601aeb2e 100644 --- a/src/orthogonal-factorization-systems/global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/global-function-classes.lagda.md @@ -1,23 +1,28 @@ # Global function classes ```agda -module orthogonal-factorization-systems.global-function-classes where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.global-function-classes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositions -open import foundation.pullbacks -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositions funext +open import foundation.pullbacks funext +open import foundation.subtypes funext open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.function-classes funext ```
diff --git a/src/orthogonal-factorization-systems/higher-modalities.lagda.md b/src/orthogonal-factorization-systems/higher-modalities.lagda.md index 54408c3970..6258fb3788 100644 --- a/src/orthogonal-factorization-systems/higher-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/higher-modalities.lagda.md @@ -1,33 +1,38 @@ # Higher modalities ```agda -module orthogonal-factorization-systems.higher-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.higher-modalities + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-dependent-functions -open import foundation.retractions -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-dependent-functions funext +open import foundation.retractions funext +open import foundation.small-types funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import orthogonal-factorization-systems.locally-small-modal-operators -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.locally-small-modal-operators funext +open import orthogonal-factorization-systems.modal-induction funext +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.modal-subuniverse-induction funext +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext ```
diff --git a/src/orthogonal-factorization-systems/identity-modality.lagda.md b/src/orthogonal-factorization-systems/identity-modality.lagda.md index 34bcadc7b1..583b0dd4f9 100644 --- a/src/orthogonal-factorization-systems/identity-modality.lagda.md +++ b/src/orthogonal-factorization-systems/identity-modality.lagda.md @@ -1,19 +1,24 @@ # The identity modality ```agda -module orthogonal-factorization-systems.identity-modality where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.identity-modality + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext ```
diff --git a/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md b/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md index b6fd6cabc1..78fe9cfcf8 100644 --- a/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md +++ b/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md @@ -1,22 +1,27 @@ # Large Lawvere–Tierney topologies ```agda -module orthogonal-factorization-systems.large-lawvere-tierney-topologies where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.large-lawvere-tierney-topologies + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.lawvere-tierney-topologies +open import orthogonal-factorization-systems.lawvere-tierney-topologies funext ```
diff --git a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md index 8976f0993e..79dd8d9771 100644 --- a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md +++ b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md @@ -1,22 +1,27 @@ # Lawvere–Tierney topologies ```agda -module orthogonal-factorization-systems.lawvere-tierney-topologies where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.lawvere-tierney-topologies + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.logical-equivalences -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.sets -open import foundation.subtypes +open import foundation.function-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-extensionality funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/lifting-operations.lagda.md b/src/orthogonal-factorization-systems/lifting-operations.lagda.md index 35f437fa9b..9d26c783ed 100644 --- a/src/orthogonal-factorization-systems/lifting-operations.lagda.md +++ b/src/orthogonal-factorization-systems/lifting-operations.lagda.md @@ -1,20 +1,25 @@ # Lifting operations ```agda -module orthogonal-factorization-systems.lifting-operations where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.lifting-operations + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.morphisms-arrows -open import foundation.sections +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext +open import foundation.sections funext open import foundation.universe-levels -open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.pullback-hom funext ```
diff --git a/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md b/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md index cd33ef10d2..05b22e3cc3 100644 --- a/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md +++ b/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md @@ -1,41 +1,46 @@ # Lifting structures on commuting squares of maps ```agda -module orthogonal-factorization-systems.lifting-structures-on-squares where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.lifting-structures-on-squares + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps -open import foundation.commuting-tetrahedra-of-homotopies -open import foundation.commuting-triangles-of-homotopies -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-tetrahedra-of-homotopies funext +open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.higher-homotopies-morphisms-arrows -open import foundation.homotopies -open import foundation.homotopies-morphisms-arrows -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.morphisms-arrows -open import foundation.path-algebra +open import foundation.higher-homotopies-morphisms-arrows funext +open import foundation.homotopies funext +open import foundation.homotopies funext-morphisms-arrows +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import orthogonal-factorization-systems.extensions-maps -open import orthogonal-factorization-systems.lifts-maps -open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.extensions-maps funext +open import orthogonal-factorization-systems.lifts-maps funext +open import orthogonal-factorization-systems.pullback-hom funext ```
diff --git a/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md index 2121b91eb6..7d1eb95bd0 100644 --- a/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md @@ -1,7 +1,12 @@ # Lifts of families of elements ```agda -module orthogonal-factorization-systems.lifts-families-of-elements where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.lifts-families-of-elements + (funext : function-extensionality) + where ```
Imports @@ -9,12 +14,12 @@ module orthogonal-factorization-systems.lifts-families-of-elements where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.precomposition-type-families -open import foundation.transport-along-homotopies +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.precomposition-type-families funext +open import foundation.transport-along-homotopies funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/lifts-maps.lagda.md b/src/orthogonal-factorization-systems/lifts-maps.lagda.md index 60cb9ba46c..e940821bde 100644 --- a/src/orthogonal-factorization-systems/lifts-maps.lagda.md +++ b/src/orthogonal-factorization-systems/lifts-maps.lagda.md @@ -1,28 +1,33 @@ # Lifts of maps ```agda -module orthogonal-factorization-systems.lifts-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.lifts-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.dependent-products-truncated-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.small-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.small-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.truncated-types +open import foundation.torsorial-type-families funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md index f4ba57ae36..b42708e378 100644 --- a/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md @@ -1,50 +1,56 @@ # Localizations at global subuniverses ```agda -module orthogonal-factorization-systems.localizations-at-global-subuniverses where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.localizations-at-global-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.cones-over-cospan-diagrams funext +open import foundation.constant-maps funext +open import foundation.contractible-types funext open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.extensions-types -open import foundation.extensions-types-global-subuniverses -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.pullback-cones -open import foundation.pullbacks -open import foundation.sequential-limits +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.extensions-types funext +open import foundation.extensions-types funext-global-subuniverses +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.pullback-cones funext +open import foundation.pullbacks funext +open import foundation.sequential-limits funext open import foundation.singleton-induction -open import foundation.subuniverses -open import foundation.type-theoretic-principle-of-choice +open import foundation.subuniverses funext +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.pullback-hom -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses +open import orthogonal-factorization-systems.orthogonal-maps funext +open import orthogonal-factorization-systems.pullback-hom funext +open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext ```
diff --git a/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md b/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md index 1144d685d4..027977c69f 100644 --- a/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md @@ -1,18 +1,23 @@ # Localizations at maps ```agda -module orthogonal-factorization-systems.localizations-at-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.localizations-at-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-subuniverses -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.localizations-at-subuniverses funext +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md b/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md index c12ced2306..69ca59a5d0 100644 --- a/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md @@ -1,18 +1,23 @@ # Localizations at subuniverses ```agda -module orthogonal-factorization-systems.localizations-at-subuniverses where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.localizations-at-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.subuniverses +open import foundation.subuniverses funext open import foundation.universe-levels -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md b/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md index 88185472d4..d331d0bcd3 100644 --- a/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md +++ b/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md @@ -1,17 +1,22 @@ # Locally small modal-operators ```agda -module orthogonal-factorization-systems.locally-small-modal-operators where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.locally-small-modal-operators + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.locally-small-types +open import foundation.locally-small-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-operators funext ```
diff --git a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md index dd2128327c..f6d0011b14 100644 --- a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md @@ -1,22 +1,27 @@ # Maps local at maps ```agda -module orthogonal-factorization-systems.maps-local-at-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.maps-local-at-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows -open import foundation.fibers-of-maps -open import foundation.propositions -open import foundation.retracts-of-maps +open import foundation.cartesian-morphisms-arrows funext +open import foundation.fibers-of-maps funext +open import foundation.propositions funext +open import foundation.retracts-of-maps funext open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.families-of-types-local-at-maps -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.families-of-types-local-at-maps funext +open import orthogonal-factorization-systems.orthogonal-maps funext +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md b/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md index ffc220075a..4f2a97b6b2 100644 --- a/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md +++ b/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md @@ -1,17 +1,22 @@ # Mere lifting properties ```agda -module orthogonal-factorization-systems.mere-lifting-properties where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.mere-lifting-properties + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.propositions funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.pullback-hom funext ```
diff --git a/src/orthogonal-factorization-systems/modal-induction.lagda.md b/src/orthogonal-factorization-systems/modal-induction.lagda.md index 9329a93810..9bb62f58cf 100644 --- a/src/orthogonal-factorization-systems/modal-induction.lagda.md +++ b/src/orthogonal-factorization-systems/modal-induction.lagda.md @@ -1,7 +1,12 @@ # Modal induction ```agda -module orthogonal-factorization-systems.modal-induction where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.modal-induction + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,25 @@ module orthogonal-factorization-systems.modal-induction where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.multivariable-sections -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.multivariable-sections funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.telescopes -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-operators funext ```
diff --git a/src/orthogonal-factorization-systems/modal-operators.lagda.md b/src/orthogonal-factorization-systems/modal-operators.lagda.md index 457aeddced..da8313d5a4 100644 --- a/src/orthogonal-factorization-systems/modal-operators.lagda.md +++ b/src/orthogonal-factorization-systems/modal-operators.lagda.md @@ -1,18 +1,23 @@ # Modal operators ```agda -module orthogonal-factorization-systems.modal-operators where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.modal-operators + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositions -open import foundation.small-types -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositions funext +open import foundation.small-types funext +open import foundation.subuniverses funext open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md b/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md index 32cc226bd3..9da9f4787c 100644 --- a/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md +++ b/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md @@ -1,7 +1,12 @@ # Modal subuniverse induction ```agda -module orthogonal-factorization-systems.modal-subuniverse-induction where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.modal-subuniverse-induction + (funext : function-extensionality) + where ```
Imports @@ -9,21 +14,21 @@ module orthogonal-factorization-systems.modal-subuniverse-induction where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.multivariable-sections -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.retractions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.multivariable-sections funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.retractions funext open import foundation.telescopes -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-induction funext +open import orthogonal-factorization-systems.modal-operators funext ```
diff --git a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md index 1ea050536a..f635119a73 100644 --- a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md @@ -1,21 +1,26 @@ # Null families of types ```agda -module orthogonal-factorization-systems.null-families-of-types where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.null-families-of-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retracts-of-types +open import foundation.equivalences funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext +open import foundation.retracts-of-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.null-types -open import orthogonal-factorization-systems.orthogonal-maps +open import orthogonal-factorization-systems.null-types funext +open import orthogonal-factorization-systems.orthogonal-maps funext ```
diff --git a/src/orthogonal-factorization-systems/null-maps.lagda.md b/src/orthogonal-factorization-systems/null-maps.lagda.md index abce4f90c5..adfa89291d 100644 --- a/src/orthogonal-factorization-systems/null-maps.lagda.md +++ b/src/orthogonal-factorization-systems/null-maps.lagda.md @@ -1,41 +1,46 @@ # Null maps ```agda -module orthogonal-factorization-systems.null-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.null-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.families-of-equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.pullbacks +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.families-of-equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext +open import foundation.pullbacks funext open import foundation.type-arithmetic-unit-type -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.universal-property-family-of-fibers-of-maps +open import foundation.universal-property-family-of-fibers-of-maps funext open import foundation.universe-levels open import foundation-core.diagonal-maps-of-types -open import orthogonal-factorization-systems.maps-local-at-maps -open import orthogonal-factorization-systems.null-families-of-types -open import orthogonal-factorization-systems.null-types -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.maps-local-at-maps funext +open import orthogonal-factorization-systems.null-families-of-types funext +open import orthogonal-factorization-systems.null-types funext +open import orthogonal-factorization-systems.orthogonal-maps funext +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/null-types.lagda.md b/src/orthogonal-factorization-systems/null-types.lagda.md index f6b07a4409..a8a932b24a 100644 --- a/src/orthogonal-factorization-systems/null-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-types.lagda.md @@ -1,44 +1,50 @@ # Null types ```agda -module orthogonal-factorization-systems.null-types where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.null-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.diagonal-maps-of-types funext +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext +open import foundation.retracts-of-types funext +open import foundation.sections funext open import foundation.type-arithmetic-unit-type -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.universal-property-equivalences -open import foundation.universal-property-family-of-fibers-of-maps -open import foundation.universal-property-unit-type +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-family-of-fibers-of-maps funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import orthogonal-factorization-systems.maps-local-at-maps -open import orthogonal-factorization-systems.orthogonal-maps -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.maps-local-at-maps funext +open import orthogonal-factorization-systems.orthogonal-maps funext +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/open-modalities.lagda.md b/src/orthogonal-factorization-systems/open-modalities.lagda.md index 3de73e9582..e6f6bdb891 100644 --- a/src/orthogonal-factorization-systems/open-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/open-modalities.lagda.md @@ -1,7 +1,12 @@ # The open modalities ```agda -module orthogonal-factorization-systems.open-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.open-modalities + (funext : function-extensionality) + where ```
Imports @@ -9,20 +14,20 @@ module orthogonal-factorization-systems.open-modalities where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.locally-small-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.locally-small-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import orthogonal-factorization-systems.higher-modalities -open import orthogonal-factorization-systems.locally-small-modal-operators -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.higher-modalities funext +open import orthogonal-factorization-systems.locally-small-modal-operators funext +open import orthogonal-factorization-systems.modal-induction funext +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext ```
diff --git a/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md index ccdba0c7e2..4befe136b2 100644 --- a/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md @@ -1,31 +1,36 @@ # Orthogonal factorization systems ```agda -module orthogonal-factorization-systems.orthogonal-factorization-systems where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.orthogonal-factorization-systems + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterated-dependent-product-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterated-dependent-product-types funext +open import foundation.propositions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorization-operations-function-classes -open import orthogonal-factorization-systems.factorizations-of-maps -open import orthogonal-factorization-systems.factorizations-of-maps-function-classes -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.lifting-structures-on-squares -open import orthogonal-factorization-systems.wide-function-classes +open import orthogonal-factorization-systems.factorization-operations-function-classes funext +open import orthogonal-factorization-systems.factorizations-of-maps funext +open import orthogonal-factorization-systems.factorizations-of-maps funext-function-classes +open import orthogonal-factorization-systems.function-classes funext +open import orthogonal-factorization-systems.lifting-structures-on-squares funext +open import orthogonal-factorization-systems.wide-function-classes funext ```
diff --git a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md index 0d98e6c2ea..c59b8efa88 100644 --- a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md @@ -1,56 +1,62 @@ # Orthogonal maps ```agda -module orthogonal-factorization-systems.orthogonal-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.orthogonal-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows -open import foundation.cartesian-product-types -open import foundation.composition-algebra -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.coproducts-pullbacks +open import foundation.cartesian-morphisms-arrows funext +open import foundation.cartesian-product-types funext +open import foundation.composition-algebra funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.coproducts-pullbacks funext open import foundation.dependent-pair-types -open import foundation.dependent-products-pullbacks -open import foundation.dependent-sums-pullbacks -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.fibered-maps -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.postcomposition-pullbacks -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.products-pullbacks -open import foundation.propositions -open import foundation.pullbacks -open import foundation.type-arithmetic-dependent-function-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.dependent-products-pullbacks funext +open import foundation.dependent-sums-pullbacks funext +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.fibered-maps funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.postcomposition-pullbacks funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.products-pullbacks funext +open import foundation.propositions funext +open import foundation.pullbacks funext +open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-equivalences -open import foundation.universal-property-pullbacks +open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.lifting-structures-on-squares -open import orthogonal-factorization-systems.pullback-hom -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.lifting-structures-on-squares funext +open import orthogonal-factorization-systems.pullback-hom funext +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md index 2292277230..7fc3bd2570 100644 --- a/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md @@ -1,33 +1,38 @@ # Precomposition of lifts of families of elements by maps ```agda -module orthogonal-factorization-systems.precomposition-lifts-families-of-elements where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.precomposition-lifts-families-of-elements + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-dependent-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.precomposition-functions +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements funext ```
diff --git a/src/orthogonal-factorization-systems/pullback-hom.lagda.md b/src/orthogonal-factorization-systems/pullback-hom.lagda.md index 6cd1e6d736..74e232d104 100644 --- a/src/orthogonal-factorization-systems/pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/pullback-hom.lagda.md @@ -1,40 +1,45 @@ # The pullback-hom ```agda -module orthogonal-factorization-systems.pullback-hom where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.pullback-hom + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-fibers-of-maps -open import foundation.functoriality-morphisms-arrows -open import foundation.higher-homotopies-morphisms-arrows -open import foundation.homotopies -open import foundation.homotopies-morphisms-arrows -open import foundation.identity-types -open import foundation.morphisms-arrows -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.pullback-cones -open import foundation.pullbacks -open import foundation.retractions -open import foundation.sections -open import foundation.standard-pullbacks -open import foundation.type-theoretic-principle-of-choice -open import foundation.universal-property-pullbacks +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.functoriality-morphisms-arrows funext +open import foundation.higher-homotopies-morphisms-arrows funext +open import foundation.homotopies funext +open import foundation.homotopies funext-morphisms-arrows +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.pullback-cones funext +open import foundation.pullbacks funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.standard-pullbacks funext +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.universal-property-pullbacks funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition ``` diff --git a/src/orthogonal-factorization-systems/raise-modalities.lagda.md b/src/orthogonal-factorization-systems/raise-modalities.lagda.md index 1f7569b41d..59844a3d8e 100644 --- a/src/orthogonal-factorization-systems/raise-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/raise-modalities.lagda.md @@ -1,19 +1,24 @@ # The raise modalities ```agda -module orthogonal-factorization-systems.raise-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.raise-modalities + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.function-types -open import foundation.raising-universe-levels +open import foundation.function-types funext +open import foundation.raising-universe-levels funext open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext ```
diff --git a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md index 440719b15d..e9d8035ec0 100644 --- a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md @@ -1,28 +1,33 @@ # Reflective global subuniverses ```agda -module orthogonal-factorization-systems.reflective-global-subuniverses where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.reflective-global-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.cospan-diagrams -open import foundation.equivalences -open import foundation.extensions-types-global-subuniverses -open import foundation.global-subuniverses -open import foundation.identity-types -open import foundation.propositions -open import foundation.pullback-cones -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.extensions-types-global-subuniverses funext +open import foundation.global-subuniverses funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.pullback-cones funext +open import foundation.subuniverses funext open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-global-subuniverses -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses +open import orthogonal-factorization-systems.localizations-at-global-subuniverses funext +open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext ```
diff --git a/src/orthogonal-factorization-systems/reflective-modalities.lagda.md b/src/orthogonal-factorization-systems/reflective-modalities.lagda.md index 46c235675f..88214ad1b2 100644 --- a/src/orthogonal-factorization-systems/reflective-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-modalities.lagda.md @@ -1,7 +1,12 @@ # Reflective modalities ```agda -module orthogonal-factorization-systems.reflective-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.reflective-modalities + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module orthogonal-factorization-systems.reflective-modalities where open import foundation.dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.reflective-subuniverses +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.reflective-subuniverses funext ```
diff --git a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md index 5c545e554c..648aa7cc88 100644 --- a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md @@ -1,23 +1,28 @@ # Reflective subuniverses ```agda -module orthogonal-factorization-systems.reflective-subuniverses where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.reflective-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.subuniverses funext open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-subuniverses -open import orthogonal-factorization-systems.modal-induction -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.modal-subuniverse-induction -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.localizations-at-subuniverses funext +open import orthogonal-factorization-systems.modal-induction funext +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.modal-subuniverse-induction funext +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md b/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md index 20370cd516..8bb8d36526 100644 --- a/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md @@ -1,18 +1,23 @@ # Σ-closed modalities ```agda -module orthogonal-factorization-systems.sigma-closed-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.sigma-closed-modalities + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.sigma-closed-subuniverses +open import foundation.function-types funext +open import foundation.sigma-closed-subuniverses funext open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-operators funext ```
diff --git a/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md b/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md index 4abbb4bf5d..82e198037c 100644 --- a/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md @@ -1,19 +1,24 @@ # Σ-closed reflective modalities ```agda -module orthogonal-factorization-systems.sigma-closed-reflective-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.sigma-closed-reflective-modalities + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.reflective-modalities -open import orthogonal-factorization-systems.sigma-closed-modalities +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.reflective-modalities funext +open import orthogonal-factorization-systems.sigma-closed-modalities funext ```
diff --git a/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md b/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md index 08cd6c74fc..04ccf4ba15 100644 --- a/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md @@ -1,17 +1,22 @@ # Σ-closed reflective subuniverses ```agda -module orthogonal-factorization-systems.sigma-closed-reflective-subuniverses where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.sigma-closed-reflective-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.sigma-closed-subuniverses +open import foundation.sigma-closed-subuniverses funext open import foundation.universe-levels -open import orthogonal-factorization-systems.reflective-subuniverses +open import orthogonal-factorization-systems.reflective-subuniverses funext ```
diff --git a/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md index 2d9c5958c2..f2252f1b84 100644 --- a/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md @@ -1,7 +1,12 @@ # Stable orthogonal factorization systems ```agda -module orthogonal-factorization-systems.stable-orthogonal-factorization-systems where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.stable-orthogonal-factorization-systems + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module orthogonal-factorization-systems.stable-orthogonal-factorization-systems ```agda open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.orthogonal-factorization-systems +open import orthogonal-factorization-systems.function-classes funext +open import orthogonal-factorization-systems.orthogonal-factorization-systems funext ```
diff --git a/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md index 7292a82aa0..542779c15c 100644 --- a/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md @@ -1,32 +1,38 @@ # Types colocal at maps ```agda -module orthogonal-factorization-systems.types-colocal-at-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.types-colocal-at-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-dependent-functions -open import foundation.postcomposition-functions -open import foundation.propositions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-dependent-functions funext +open import foundation.postcomposition-functions funext +open import foundation.propositions funext +open import foundation.retracts-of-maps funext +open import foundation.retracts-of-types funext open import foundation.unit-type -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md index 0e261e3ed9..868cceea8c 100644 --- a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md @@ -1,47 +1,52 @@ # Types local at maps ```agda -module orthogonal-factorization-systems.types-local-at-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.types-local-at-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.empty-types -open import foundation.equivalences -open import foundation.families-of-equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retractions -open import foundation.retracts-of-maps -open import foundation.retracts-of-types -open import foundation.sections -open import foundation.type-arithmetic-dependent-function-types +open import foundation.dependent-universal-property-equivalences funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.families-of-equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.retracts-of-maps funext +open import foundation.retracts-of-types funext +open import foundation.sections funext +open import foundation.type-arithmetic-dependent-function-types funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext open import foundation.universe-levels -open import orthogonal-factorization-systems.extensions-maps +open import orthogonal-factorization-systems.extensions-maps funext ```
diff --git a/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md index a909c66dac..2c7d92e0c2 100644 --- a/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md @@ -1,16 +1,21 @@ # Types separated at maps ```agda -module orthogonal-factorization-systems.types-separated-at-maps where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.types-separated-at-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md index d0a891d833..babb757ddc 100644 --- a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md @@ -1,28 +1,33 @@ # Uniquely eliminating modalities ```agda -module orthogonal-factorization-systems.uniquely-eliminating-modalities where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.uniquely-eliminating-modalities + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.univalence +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.univalence funext open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md index 59815d7643..56b0e454de 100644 --- a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md @@ -1,31 +1,35 @@ # The universal property of localizations at global subuniverses ```agda -module orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.extensions-types -open import foundation.extensions-types-global-subuniverses -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.global-subuniverses -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.univalence +open import foundation.equivalences funext +open import foundation.extensions-types funext +open import foundation.extensions-types funext-global-subuniverses +open import foundation.function-types funext +open import foundation.global-subuniverses funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.univalence funext open import foundation.universe-levels -open import orthogonal-factorization-systems.extensions-maps -open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.extensions-maps funext +open import orthogonal-factorization-systems.types-local-at-maps funext ```
diff --git a/src/orthogonal-factorization-systems/wide-function-classes.lagda.md b/src/orthogonal-factorization-systems/wide-function-classes.lagda.md index 7798c4379d..bc26079cd0 100644 --- a/src/orthogonal-factorization-systems/wide-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/wide-function-classes.lagda.md @@ -1,19 +1,24 @@ # Wide function classes ```agda -module orthogonal-factorization-systems.wide-function-classes where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.wide-function-classes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.function-classes funext ```
diff --git a/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md index e8ed36b96f..2272c231ac 100644 --- a/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md @@ -1,21 +1,26 @@ # Wide global function classes ```agda -module orthogonal-factorization-systems.wide-global-function-classes where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.wide-global-function-classes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.function-types -open import foundation.propositions +open import foundation.embeddings funext +open import foundation.function-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes -open import orthogonal-factorization-systems.global-function-classes +open import orthogonal-factorization-systems.function-classes funext +open import orthogonal-factorization-systems.global-function-classes funext ```
diff --git a/src/orthogonal-factorization-systems/zero-modality.lagda.md b/src/orthogonal-factorization-systems/zero-modality.lagda.md index 7725c93fb4..a5861514ad 100644 --- a/src/orthogonal-factorization-systems/zero-modality.lagda.md +++ b/src/orthogonal-factorization-systems/zero-modality.lagda.md @@ -1,19 +1,24 @@ # The zero modality ```agda -module orthogonal-factorization-systems.zero-modality where +open import foundation.function-extensionality-axiom + +module + orthogonal-factorization-systems.zero-modality + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.raising-universe-levels-unit-type +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators -open import orthogonal-factorization-systems.types-local-at-maps -open import orthogonal-factorization-systems.uniquely-eliminating-modalities +open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext ```
diff --git a/src/polytopes.lagda.md b/src/polytopes.lagda.md index 93741a955f..b90a8223bd 100644 --- a/src/polytopes.lagda.md +++ b/src/polytopes.lagda.md @@ -3,7 +3,12 @@ ## Modules in the polytopes namespace ```agda -module polytopes where +open import foundation.function-extensionality-axiom -open import polytopes.abstract-polytopes public +module + polytopes + (funext : function-extensionality) + where + +open import polytopes.abstract-polytopes funext public ``` diff --git a/src/polytopes/abstract-polytopes.lagda.md b/src/polytopes/abstract-polytopes.lagda.md index b2a62140af..d611fd93cb 100644 --- a/src/polytopes/abstract-polytopes.lagda.md +++ b/src/polytopes/abstract-polytopes.lagda.md @@ -1,34 +1,39 @@ # Abstract polytopes ```agda -module polytopes.abstract-polytopes where +open import foundation.function-extensionality-axiom + +module + polytopes.abstract-polytopes + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.sets +open import foundation.disjunction funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import order-theory.finitely-graded-posets -open import order-theory.posets +open import order-theory.finitely-graded-posets funext +open import order-theory.posets funext -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/real-numbers.lagda.md b/src/real-numbers.lagda.md index ef82f3855b..237e02efee 100644 --- a/src/real-numbers.lagda.md +++ b/src/real-numbers.lagda.md @@ -3,23 +3,28 @@ ## Modules in the real numbers namespace ```agda -module real-numbers where +open import foundation.function-extensionality-axiom -open import real-numbers.apartness-real-numbers public -open import real-numbers.arithmetically-located-dedekind-cuts public -open import real-numbers.dedekind-real-numbers public -open import real-numbers.inequality-lower-dedekind-real-numbers public -open import real-numbers.inequality-real-numbers public -open import real-numbers.inequality-upper-dedekind-real-numbers public -open import real-numbers.lower-dedekind-real-numbers public -open import real-numbers.metric-space-of-real-numbers public -open import real-numbers.negation-lower-upper-dedekind-real-numbers public -open import real-numbers.negation-real-numbers public -open import real-numbers.raising-universe-levels-real-numbers public -open import real-numbers.rational-lower-dedekind-real-numbers public -open import real-numbers.rational-real-numbers public -open import real-numbers.rational-upper-dedekind-real-numbers public -open import real-numbers.similarity-real-numbers public -open import real-numbers.strict-inequality-real-numbers public -open import real-numbers.upper-dedekind-real-numbers public +module + real-numbers + (funext : function-extensionality) + where + +open import real-numbers.apartness-real-numbers funext public +open import real-numbers.arithmetically-located-dedekind-cuts funext public +open import real-numbers.dedekind-real-numbers funext public +open import real-numbers.inequality-lower-dedekind-real-numbers funext public +open import real-numbers.inequality-real-numbers funext public +open import real-numbers.inequality-upper-dedekind-real-numbers funext public +open import real-numbers.lower-dedekind-real-numbers funext public +open import real-numbers.metric-space-of-real-numbers funext public +open import real-numbers.negation-lower-upper-dedekind-real-numbers funext public +open import real-numbers.negation-real-numbers funext public +open import real-numbers.raising-universe-levels-real-numbers funext public +open import real-numbers.rational-lower-dedekind-real-numbers funext public +open import real-numbers.rational-real-numbers funext public +open import real-numbers.rational-upper-dedekind-real-numbers funext public +open import real-numbers.similarity-real-numbers funext public +open import real-numbers.strict-inequality-real-numbers funext public +open import real-numbers.upper-dedekind-real-numbers funext public ``` diff --git a/src/real-numbers/apartness-real-numbers.lagda.md b/src/real-numbers/apartness-real-numbers.lagda.md index 610c8bcdbb..2106f4e595 100644 --- a/src/real-numbers/apartness-real-numbers.lagda.md +++ b/src/real-numbers/apartness-real-numbers.lagda.md @@ -1,24 +1,29 @@ # Apartness of real numbers ```agda -module real-numbers.apartness-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.apartness-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.disjunction -open import foundation.empty-types -open import foundation.function-types -open import foundation.large-apartness-relations -open import foundation.large-binary-relations -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions +open import foundation.disjunction funext +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.large-apartness-relations funext +open import foundation.large-binary-relations funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.universe-levels -open import real-numbers.dedekind-real-numbers -open import real-numbers.strict-inequality-real-numbers +open import real-numbers.dedekind-real-numbers funext +open import real-numbers.strict-inequality-real-numbers funext ```
diff --git a/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md b/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md index a378d58d72..bd7f2b0263 100644 --- a/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md +++ b/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md @@ -3,34 +3,39 @@ ```agda {-# OPTIONS --lossy-unification #-} -module real-numbers.arithmetically-located-dedekind-cuts where +open import foundation.function-extensionality-axiom + +module + real-numbers.arithmetically-located-dedekind-cuts + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.additive-group-of-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers - -open import foundation.cartesian-product-types -open import foundation.conjunction -open import foundation.coproduct-types +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.additive-group-of-rational-numbers funext +open import elementary-number-theory.difference-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext + +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification +open import foundation.disjunction funext +open import foundation.existential-quantification funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.abelian-groups +open import group-theory.abelian-groups funext -open import real-numbers.dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext +open import real-numbers.lower-dedekind-real-numbers funext +open import real-numbers.upper-dedekind-real-numbers funext ```
diff --git a/src/real-numbers/dedekind-real-numbers.lagda.md b/src/real-numbers/dedekind-real-numbers.lagda.md index 36f5e8e621..63bc7c7cfe 100644 --- a/src/real-numbers/dedekind-real-numbers.lagda.md +++ b/src/real-numbers/dedekind-real-numbers.lagda.md @@ -1,44 +1,49 @@ # Dedekind real numbers ```agda -module real-numbers.dedekind-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.dedekind-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.conjunction -open import foundation.coproduct-types +open import foundation.conjunction funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.disjoint-subtypes -open import foundation.disjunction -open import foundation.embeddings -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.powersets -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.disjoint-subtypes funext +open import foundation.disjunction funext +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.powersets funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.universal-quantification +open import foundation.universal-quantification funext open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers funext +open import real-numbers.upper-dedekind-real-numbers funext ```
diff --git a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md index 87a1154a7f..e38906cd17 100644 --- a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md @@ -1,30 +1,35 @@ # Inequality on the lower Dedekind real numbers ```agda -module real-numbers.inequality-lower-dedekind-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.inequality-lower-dedekind-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders +open import order-theory.large-posets funext +open import order-theory.large-preorders funext -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.rational-lower-dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers funext +open import real-numbers.rational-lower-dedekind-real-numbers funext ```
diff --git a/src/real-numbers/inequality-real-numbers.lagda.md b/src/real-numbers/inequality-real-numbers.lagda.md index 06313f63bb..dfdd39e19c 100644 --- a/src/real-numbers/inequality-real-numbers.lagda.md +++ b/src/real-numbers/inequality-real-numbers.lagda.md @@ -1,33 +1,38 @@ # Inequality on the real numbers ```agda -module real-numbers.inequality-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.inequality-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers funext -open import foundation.complements-subtypes +open import foundation.complements-subtypes funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.posets -open import order-theory.preorders +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.posets funext +open import order-theory.preorders funext -open import real-numbers.dedekind-real-numbers -open import real-numbers.inequality-lower-dedekind-real-numbers -open import real-numbers.inequality-upper-dedekind-real-numbers -open import real-numbers.rational-real-numbers +open import real-numbers.dedekind-real-numbers funext +open import real-numbers.inequality-lower-dedekind-real-numbers funext +open import real-numbers.inequality-upper-dedekind-real-numbers funext +open import real-numbers.rational-real-numbers funext ```
diff --git a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md index 1c124e2f50..e6341b15b6 100644 --- a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md @@ -1,30 +1,35 @@ # Inequality on the upper Dedekind real numbers ```agda -module real-numbers.inequality-upper-dedekind-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.inequality-upper-dedekind-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders +open import order-theory.large-posets funext +open import order-theory.large-preorders funext -open import real-numbers.rational-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.rational-upper-dedekind-real-numbers funext +open import real-numbers.upper-dedekind-real-numbers funext ```
diff --git a/src/real-numbers/lower-dedekind-real-numbers.lagda.md b/src/real-numbers/lower-dedekind-real-numbers.lagda.md index 2d9c8b829b..5f3529bd6b 100644 --- a/src/real-numbers/lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/lower-dedekind-real-numbers.lagda.md @@ -1,31 +1,36 @@ # Lower Dedekind real numbers ```agda -module real-numbers.lower-dedekind-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.lower-dedekind-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext -open import foundation.conjunction -open import foundation.coproduct-types +open import foundation.conjunction funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels -open import foundation.universal-quantification +open import foundation.universal-quantification funext open import foundation.universe-levels ``` diff --git a/src/real-numbers/metric-space-of-real-numbers.lagda.md b/src/real-numbers/metric-space-of-real-numbers.lagda.md index 7a4d12c506..74042bf1c2 100644 --- a/src/real-numbers/metric-space-of-real-numbers.lagda.md +++ b/src/real-numbers/metric-space-of-real-numbers.lagda.md @@ -3,45 +3,50 @@ ```agda {-# OPTIONS --lossy-unification #-} -module real-numbers.metric-space-of-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.metric-space-of-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers -open import elementary-number-theory.difference-rational-numbers -open import elementary-number-theory.positive-rational-numbers -open import elementary-number-theory.rational-numbers +open import elementary-number-theory.addition-rational-numbers funext +open import elementary-number-theory.difference-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.rational-numbers funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.diagonal-maps-cartesian-products-of-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.subtypes +open import foundation.diagonal-maps-cartesian-products-of-types funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures -open import metric-spaces.isometries-metric-spaces -open import metric-spaces.metric-space-of-rational-numbers -open import metric-spaces.metric-spaces -open import metric-spaces.metric-structures -open import metric-spaces.premetric-spaces -open import metric-spaces.premetric-structures -open import metric-spaces.pseudometric-structures -open import metric-spaces.reflexive-premetric-structures -open import metric-spaces.saturated-metric-spaces -open import metric-spaces.symmetric-premetric-structures -open import metric-spaces.triangular-premetric-structures - -open import real-numbers.dedekind-real-numbers -open import real-numbers.rational-real-numbers +open import metric-spaces.extensional-premetric-structures funext +open import metric-spaces.isometries-metric-spaces funext +open import metric-spaces.metric-space-of-rational-numbers funext +open import metric-spaces.metric-spaces funext +open import metric-spaces.metric-structures funext +open import metric-spaces.premetric-spaces funext +open import metric-spaces.premetric-structures funext +open import metric-spaces.pseudometric-structures funext +open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.saturated-metric-spaces funext +open import metric-spaces.symmetric-premetric-structures funext +open import metric-spaces.triangular-premetric-structures funext + +open import real-numbers.dedekind-real-numbers funext +open import real-numbers.rational-real-numbers funext ```
diff --git a/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md index 0fe42bfd07..d791c05774 100644 --- a/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md @@ -3,35 +3,40 @@ ```agda {-# OPTIONS --lossy-unification #-} -module real-numbers.negation-lower-upper-dedekind-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.negation-lower-upper-dedekind-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.retractions -open import foundation.sections -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.rational-lower-dedekind-real-numbers -open import real-numbers.rational-upper-dedekind-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers funext +open import real-numbers.rational-lower-dedekind-real-numbers funext +open import real-numbers.rational-upper-dedekind-real-numbers funext +open import real-numbers.upper-dedekind-real-numbers funext ```
diff --git a/src/real-numbers/negation-real-numbers.lagda.md b/src/real-numbers/negation-real-numbers.lagda.md index 54744b5d9d..60c8f216b5 100644 --- a/src/real-numbers/negation-real-numbers.lagda.md +++ b/src/real-numbers/negation-real-numbers.lagda.md @@ -3,29 +3,34 @@ ```agda {-# OPTIONS --lossy-unification #-} -module real-numbers.negation-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.negation-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.dependent-pair-types -open import foundation.disjoint-subtypes -open import foundation.disjunction -open import foundation.function-types -open import foundation.identity-types -open import foundation.subtypes +open import foundation.disjoint-subtypes funext +open import foundation.disjunction funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import real-numbers.dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.negation-lower-upper-dedekind-real-numbers -open import real-numbers.rational-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext +open import real-numbers.lower-dedekind-real-numbers funext +open import real-numbers.negation-lower-upper-dedekind-real-numbers funext +open import real-numbers.rational-real-numbers funext +open import real-numbers.upper-dedekind-real-numbers funext ```
diff --git a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md index 422760c592..6cb792b364 100644 --- a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md +++ b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md @@ -1,36 +1,41 @@ # Raising the universe levels of real numbers ```agda -module real-numbers.raising-universe-levels-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.raising-universe-levels-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext -open import foundation.cartesian-product-types -open import foundation.conjunction +open import foundation.cartesian-product-types funext +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.inhabited-subtypes -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.raising-universe-levels -open import foundation.subtypes +open import foundation.disjunction funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.inhabited-subtypes funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.raising-universe-levels funext +open import foundation.subtypes funext open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext -open import real-numbers.dedekind-real-numbers -open import real-numbers.lower-dedekind-real-numbers -open import real-numbers.similarity-real-numbers -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext +open import real-numbers.lower-dedekind-real-numbers funext +open import real-numbers.similarity-real-numbers funext +open import real-numbers.upper-dedekind-real-numbers funext ```
diff --git a/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md index 5176279b29..9eab421308 100644 --- a/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md @@ -1,23 +1,28 @@ # Rational lower Dedekind real numbers ```agda -module real-numbers.rational-lower-dedekind-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.rational-lower-dedekind-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.logical-equivalences funext +open import foundation.subtypes funext open import foundation.universe-levels -open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers funext ```
diff --git a/src/real-numbers/rational-real-numbers.lagda.md b/src/real-numbers/rational-real-numbers.lagda.md index c5dfe24fcc..cfa3ebd3a2 100644 --- a/src/real-numbers/rational-real-numbers.lagda.md +++ b/src/real-numbers/rational-real-numbers.lagda.md @@ -3,35 +3,40 @@ ```agda {-# OPTIONS --lossy-unification #-} -module real-numbers.rational-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.rational-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext open import foundation.action-on-identifications-functions -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.subtypes +open import foundation.disjunction funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import real-numbers.dedekind-real-numbers -open import real-numbers.rational-lower-dedekind-real-numbers -open import real-numbers.rational-upper-dedekind-real-numbers -open import real-numbers.similarity-real-numbers +open import real-numbers.dedekind-real-numbers funext +open import real-numbers.rational-lower-dedekind-real-numbers funext +open import real-numbers.rational-upper-dedekind-real-numbers funext +open import real-numbers.similarity-real-numbers funext ```
diff --git a/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md index f88c510a18..9c3b511383 100644 --- a/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md @@ -1,23 +1,28 @@ # Rational upper Dedekind real numbers ```agda -module real-numbers.rational-upper-dedekind-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.rational-upper-dedekind-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext -open import foundation.conjunction +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.logical-equivalences -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.logical-equivalences funext +open import foundation.subtypes funext open import foundation.universe-levels -open import real-numbers.upper-dedekind-real-numbers +open import real-numbers.upper-dedekind-real-numbers funext ```
diff --git a/src/real-numbers/similarity-real-numbers.lagda.md b/src/real-numbers/similarity-real-numbers.lagda.md index d7b13097d2..2589a0fe87 100644 --- a/src/real-numbers/similarity-real-numbers.lagda.md +++ b/src/real-numbers/similarity-real-numbers.lagda.md @@ -1,21 +1,26 @@ # Similarity of real numbers ```agda -module real-numbers.similarity-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.similarity-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import real-numbers.dedekind-real-numbers +open import real-numbers.dedekind-real-numbers funext ```
diff --git a/src/real-numbers/strict-inequality-real-numbers.lagda.md b/src/real-numbers/strict-inequality-real-numbers.lagda.md index 2b2ccc6a6b..71b39f01ff 100644 --- a/src/real-numbers/strict-inequality-real-numbers.lagda.md +++ b/src/real-numbers/strict-inequality-real-numbers.lagda.md @@ -3,38 +3,43 @@ ```agda {-# OPTIONS --lossy-unification #-} -module real-numbers.strict-inequality-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.strict-inequality-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext -open import foundation.conjunction -open import foundation.coproduct-types +open import foundation.conjunction funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.disjunction funext +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification +open import logic.functoriality-existential-quantification funext -open import real-numbers.dedekind-real-numbers -open import real-numbers.inequality-real-numbers -open import real-numbers.negation-real-numbers -open import real-numbers.rational-real-numbers +open import real-numbers.dedekind-real-numbers funext +open import real-numbers.inequality-real-numbers funext +open import real-numbers.negation-real-numbers funext +open import real-numbers.rational-real-numbers funext ```
diff --git a/src/real-numbers/upper-dedekind-real-numbers.lagda.md b/src/real-numbers/upper-dedekind-real-numbers.lagda.md index fa82905722..156894f09c 100644 --- a/src/real-numbers/upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/upper-dedekind-real-numbers.lagda.md @@ -1,31 +1,36 @@ # Upper Dedekind real numbers ```agda -module real-numbers.upper-dedekind-real-numbers where +open import foundation.function-extensionality-axiom + +module + real-numbers.upper-dedekind-real-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers -open import elementary-number-theory.rational-numbers -open import elementary-number-theory.strict-inequality-rational-numbers +open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.strict-inequality-rational-numbers funext -open import foundation.conjunction -open import foundation.coproduct-types +open import foundation.conjunction funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels -open import foundation.universal-quantification +open import foundation.universal-quantification funext open import foundation.universe-levels ``` diff --git a/src/reflection.lagda.md b/src/reflection.lagda.md index 0e4c56b9dc..5a4df12448 100644 --- a/src/reflection.lagda.md +++ b/src/reflection.lagda.md @@ -7,19 +7,24 @@ ## Modules in the reflection namespace ```agda -module reflection where +open import foundation.function-extensionality-axiom + +module + reflection + (funext : function-extensionality) + where open import reflection.abstractions public open import reflection.arguments public -open import reflection.boolean-reflection public +open import reflection.boolean-reflection funext public open import reflection.definitions public open import reflection.erasing-equality public -open import reflection.fixity public -open import reflection.group-solver public +open import reflection.fixity funext public +open import reflection.group-solver funext public open import reflection.literals public open import reflection.metavariables public open import reflection.names public -open import reflection.precategory-solver public +open import reflection.precategory-solver funext public open import reflection.rewriting public open import reflection.terms public open import reflection.type-checking-monad public diff --git a/src/reflection/boolean-reflection.lagda.md b/src/reflection/boolean-reflection.lagda.md index e4602783c7..909f3e3e08 100644 --- a/src/reflection/boolean-reflection.lagda.md +++ b/src/reflection/boolean-reflection.lagda.md @@ -1,13 +1,18 @@ # Boolean reflection ```agda -module reflection.boolean-reflection where +open import foundation.function-extensionality-axiom + +module + reflection.boolean-reflection + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.universe-levels open import foundation-core.booleans diff --git a/src/reflection/fixity.lagda.md b/src/reflection/fixity.lagda.md index 6f7961f5ce..83069c171d 100644 --- a/src/reflection/fixity.lagda.md +++ b/src/reflection/fixity.lagda.md @@ -1,13 +1,18 @@ # Fixity ```agda -module reflection.fixity where +open import foundation.function-extensionality-axiom + +module + reflection.fixity + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import foundation.universe-levels diff --git a/src/reflection/group-solver.lagda.md b/src/reflection/group-solver.lagda.md index 6fb762b69b..32d5a7edad 100644 --- a/src/reflection/group-solver.lagda.md +++ b/src/reflection/group-solver.lagda.md @@ -1,7 +1,12 @@ # Group solver ```agda -module reflection.group-solver where +open import foundation.function-extensionality-axiom + +module + reflection.group-solver + (funext : function-extensionality) + where ```
Imports @@ -10,21 +15,21 @@ module reflection.group-solver where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.identity-types -open import group-theory.groups +open import group-theory.groups funext -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext +open import lists.functoriality-lists funext open import lists.lists -open import lists.reversing-lists +open import lists.reversing-lists funext ```
diff --git a/src/reflection/precategory-solver.lagda.md b/src/reflection/precategory-solver.lagda.md index dd11d6389c..62d14b4e1c 100644 --- a/src/reflection/precategory-solver.lagda.md +++ b/src/reflection/precategory-solver.lagda.md @@ -3,23 +3,28 @@ ```agda {-# OPTIONS --no-exact-split #-} -module reflection.precategory-solver where +open import foundation.function-extensionality-axiom + +module + reflection.precategory-solver + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels open import foundation-core.identity-types -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists open import reflection.arguments diff --git a/src/ring-theory.lagda.md b/src/ring-theory.lagda.md index 9ea7cb8d0b..cbc30af145 100644 --- a/src/ring-theory.lagda.md +++ b/src/ring-theory.lagda.md @@ -3,83 +3,88 @@ ## Modules in the ring theory namespace ```agda -module ring-theory where +open import foundation.function-extensionality-axiom -open import ring-theory.additive-orders-of-elements-rings public -open import ring-theory.algebras-rings public -open import ring-theory.binomial-theorem-rings public -open import ring-theory.binomial-theorem-semirings public -open import ring-theory.category-of-cyclic-rings public -open import ring-theory.category-of-rings public -open import ring-theory.central-elements-rings public -open import ring-theory.central-elements-semirings public -open import ring-theory.characteristics-rings public -open import ring-theory.commuting-elements-rings public -open import ring-theory.congruence-relations-rings public -open import ring-theory.congruence-relations-semirings public -open import ring-theory.cyclic-rings public -open import ring-theory.dependent-products-rings public -open import ring-theory.dependent-products-semirings public -open import ring-theory.division-rings public -open import ring-theory.free-rings-with-one-generator public -open import ring-theory.full-ideals-rings public -open import ring-theory.function-rings public -open import ring-theory.function-semirings public -open import ring-theory.generating-elements-rings public -open import ring-theory.groups-of-units-rings public -open import ring-theory.homomorphisms-cyclic-rings public -open import ring-theory.homomorphisms-rings public -open import ring-theory.homomorphisms-semirings public -open import ring-theory.ideals-generated-by-subsets-rings public -open import ring-theory.ideals-rings public -open import ring-theory.ideals-semirings public -open import ring-theory.idempotent-elements-rings public -open import ring-theory.initial-rings public -open import ring-theory.integer-multiples-of-elements-rings public -open import ring-theory.intersections-ideals-rings public -open import ring-theory.intersections-ideals-semirings public -open import ring-theory.invariant-basis-property-rings public -open import ring-theory.invertible-elements-rings public -open import ring-theory.isomorphisms-rings public -open import ring-theory.joins-ideals-rings public -open import ring-theory.joins-left-ideals-rings public -open import ring-theory.joins-right-ideals-rings public -open import ring-theory.kernels-of-ring-homomorphisms public -open import ring-theory.left-ideals-generated-by-subsets-rings public -open import ring-theory.left-ideals-rings public -open import ring-theory.local-rings public -open import ring-theory.localizations-rings public +module + ring-theory + (funext : function-extensionality) + where + +open import ring-theory.additive-orders-of-elements-rings funext public +open import ring-theory.algebras-rings funext public +open import ring-theory.binomial-theorem-rings funext public +open import ring-theory.binomial-theorem-semirings funext public +open import ring-theory.category-of-cyclic-rings funext public +open import ring-theory.category-of-rings funext public +open import ring-theory.central-elements-rings funext public +open import ring-theory.central-elements-semirings funext public +open import ring-theory.characteristics-rings funext public +open import ring-theory.commuting-elements-rings funext public +open import ring-theory.congruence-relations-rings funext public +open import ring-theory.congruence-relations-semirings funext public +open import ring-theory.cyclic-rings funext public +open import ring-theory.dependent-products-rings funext public +open import ring-theory.dependent-products-semirings funext public +open import ring-theory.division-rings funext public +open import ring-theory.free-rings-with-one-generator funext public +open import ring-theory.full-ideals-rings funext public +open import ring-theory.function-rings funext public +open import ring-theory.function-semirings funext public +open import ring-theory.generating-elements-rings funext public +open import ring-theory.groups-of-units-rings funext public +open import ring-theory.homomorphisms-cyclic-rings funext public +open import ring-theory.homomorphisms-rings funext public +open import ring-theory.homomorphisms-semirings funext public +open import ring-theory.ideals-generated-by-subsets-rings funext public +open import ring-theory.ideals-rings funext public +open import ring-theory.ideals-semirings funext public +open import ring-theory.idempotent-elements-rings funext public +open import ring-theory.initial-rings funext public +open import ring-theory.integer-multiples-of-elements-rings funext public +open import ring-theory.intersections-ideals-rings funext public +open import ring-theory.intersections-ideals-semirings funext public +open import ring-theory.invariant-basis-property-rings funext public +open import ring-theory.invertible-elements-rings funext public +open import ring-theory.isomorphisms-rings funext public +open import ring-theory.joins-ideals-rings funext public +open import ring-theory.joins-left-ideals-rings funext public +open import ring-theory.joins-right-ideals-rings funext public +open import ring-theory.kernels-of-ring-homomorphisms funext public +open import ring-theory.left-ideals-generated-by-subsets-rings funext public +open import ring-theory.left-ideals-rings funext public +open import ring-theory.local-rings funext public +open import ring-theory.localizations-rings funext public open import ring-theory.maximal-ideals-rings public -open import ring-theory.modules-rings public -open import ring-theory.multiples-of-elements-rings public +open import ring-theory.modules-rings funext public +open import ring-theory.multiples-of-elements-rings funext public open import ring-theory.multiplicative-orders-of-units-rings public -open import ring-theory.nil-ideals-rings public -open import ring-theory.nilpotent-elements-rings public -open import ring-theory.nilpotent-elements-semirings public -open import ring-theory.opposite-rings public -open import ring-theory.poset-of-cyclic-rings public -open import ring-theory.poset-of-ideals-rings public -open import ring-theory.poset-of-left-ideals-rings public -open import ring-theory.poset-of-right-ideals-rings public -open import ring-theory.powers-of-elements-rings public -open import ring-theory.powers-of-elements-semirings public -open import ring-theory.precategory-of-rings public -open import ring-theory.precategory-of-semirings public -open import ring-theory.products-ideals-rings public -open import ring-theory.products-left-ideals-rings public -open import ring-theory.products-right-ideals-rings public -open import ring-theory.products-rings public -open import ring-theory.products-subsets-rings public -open import ring-theory.quotient-rings public -open import ring-theory.radical-ideals-rings public -open import ring-theory.right-ideals-generated-by-subsets-rings public -open import ring-theory.right-ideals-rings public -open import ring-theory.rings public -open import ring-theory.semirings public -open import ring-theory.subsets-rings public -open import ring-theory.subsets-semirings public -open import ring-theory.sums-rings public -open import ring-theory.sums-semirings public -open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups public -open import ring-theory.trivial-rings public +open import ring-theory.nil-ideals-rings funext public +open import ring-theory.nilpotent-elements-rings funext public +open import ring-theory.nilpotent-elements-semirings funext public +open import ring-theory.opposite-rings funext public +open import ring-theory.poset-of-cyclic-rings funext public +open import ring-theory.poset-of-ideals-rings funext public +open import ring-theory.poset-of-left-ideals-rings funext public +open import ring-theory.poset-of-right-ideals-rings funext public +open import ring-theory.powers-of-elements-rings funext public +open import ring-theory.powers-of-elements-semirings funext public +open import ring-theory.precategory-of-rings funext public +open import ring-theory.precategory-of-semirings funext public +open import ring-theory.products-ideals-rings funext public +open import ring-theory.products-left-ideals-rings funext public +open import ring-theory.products-right-ideals-rings funext public +open import ring-theory.products-rings funext public +open import ring-theory.products-subsets-rings funext public +open import ring-theory.quotient-rings funext public +open import ring-theory.radical-ideals-rings funext public +open import ring-theory.right-ideals-generated-by-subsets-rings funext public +open import ring-theory.right-ideals-rings funext public +open import ring-theory.rings funext public +open import ring-theory.semirings funext public +open import ring-theory.subsets-rings funext public +open import ring-theory.subsets-semirings funext public +open import ring-theory.sums-rings funext public +open import ring-theory.sums-semirings funext public +open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups funext public +open import ring-theory.trivial-rings funext public ``` diff --git a/src/ring-theory/additive-orders-of-elements-rings.lagda.md b/src/ring-theory/additive-orders-of-elements-rings.lagda.md index 8a8cf9374c..e6550b308c 100644 --- a/src/ring-theory/additive-orders-of-elements-rings.lagda.md +++ b/src/ring-theory/additive-orders-of-elements-rings.lagda.md @@ -1,28 +1,33 @@ # Additive orders of elements of rings ```agda -module ring-theory.additive-orders-of-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.additive-orders-of-elements-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.group-of-integers funext open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import group-theory.normal-subgroups -open import group-theory.orders-of-elements-groups -open import group-theory.subgroups -open import group-theory.subsets-groups +open import group-theory.normal-subgroups funext +open import group-theory.orders-of-elements-groups funext +open import group-theory.subgroups funext +open import group-theory.subsets-groups funext -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings +open import ring-theory.integer-multiples-of-elements-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/algebras-rings.lagda.md b/src/ring-theory/algebras-rings.lagda.md index ff618c84d6..e59d256076 100644 --- a/src/ring-theory/algebras-rings.lagda.md +++ b/src/ring-theory/algebras-rings.lagda.md @@ -1,19 +1,24 @@ # Algebras over rings ```agda -module ring-theory.algebras-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.algebras-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.modules-rings -open import ring-theory.rings +open import ring-theory.modules-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/binomial-theorem-rings.lagda.md b/src/ring-theory/binomial-theorem-rings.lagda.md index d951452476..a901e2f90e 100644 --- a/src/ring-theory/binomial-theorem-rings.lagda.md +++ b/src/ring-theory/binomial-theorem-rings.lagda.md @@ -1,29 +1,34 @@ # The binomial theorem for rings ```agda -module ring-theory.binomial-theorem-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.binomial-theorem-rings + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.binomial-coefficients funext +open import elementary-number-theory.distance-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors-on-rings +open import linear-algebra.vectors-on-rings funext -open import ring-theory.binomial-theorem-semirings -open import ring-theory.powers-of-elements-rings -open import ring-theory.rings -open import ring-theory.sums-rings +open import ring-theory.binomial-theorem-semirings funext +open import ring-theory.powers-of-elements-rings funext +open import ring-theory.rings funext +open import ring-theory.sums-rings funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/ring-theory/binomial-theorem-semirings.lagda.md b/src/ring-theory/binomial-theorem-semirings.lagda.md index 66679c0071..4286f0a12b 100644 --- a/src/ring-theory/binomial-theorem-semirings.lagda.md +++ b/src/ring-theory/binomial-theorem-semirings.lagda.md @@ -1,32 +1,37 @@ # The binomial theorem for semirings ```agda -module ring-theory.binomial-theorem-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.binomial-theorem-semirings + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.binomial-coefficients funext +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors-on-semirings +open import linear-algebra.vectors-on-semirings funext -open import ring-theory.powers-of-elements-semirings -open import ring-theory.semirings -open import ring-theory.sums-semirings +open import ring-theory.powers-of-elements-semirings funext +open import ring-theory.semirings funext +open import ring-theory.sums-semirings funext -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/ring-theory/category-of-cyclic-rings.lagda.md b/src/ring-theory/category-of-cyclic-rings.lagda.md index 27c4f61a07..628159d38c 100644 --- a/src/ring-theory/category-of-cyclic-rings.lagda.md +++ b/src/ring-theory/category-of-cyclic-rings.lagda.md @@ -1,25 +1,30 @@ # The category of cyclic rings ```agda -module ring-theory.category-of-cyclic-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.category-of-cyclic-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.full-large-subprecategories -open import category-theory.large-categories -open import category-theory.large-precategories +open import category-theory.categories funext +open import category-theory.full-large-subprecategories funext +open import category-theory.large-categories funext +open import category-theory.large-precategories funext open import foundation.universe-levels -open import order-theory.large-posets +open import order-theory.large-posets funext -open import ring-theory.category-of-rings -open import ring-theory.cyclic-rings -open import ring-theory.homomorphisms-cyclic-rings -open import ring-theory.precategory-of-rings +open import ring-theory.category-of-rings funext +open import ring-theory.cyclic-rings funext +open import ring-theory.homomorphisms-cyclic-rings funext +open import ring-theory.precategory-of-rings funext ```
diff --git a/src/ring-theory/category-of-rings.lagda.md b/src/ring-theory/category-of-rings.lagda.md index 8c06755027..7e870297cf 100644 --- a/src/ring-theory/category-of-rings.lagda.md +++ b/src/ring-theory/category-of-rings.lagda.md @@ -1,19 +1,24 @@ # The category of rings ```agda -module ring-theory.category-of-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.category-of-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.categories -open import category-theory.large-categories +open import category-theory.categories funext +open import category-theory.large-categories funext open import foundation.universe-levels -open import ring-theory.isomorphisms-rings -open import ring-theory.precategory-of-rings +open import ring-theory.isomorphisms-rings funext +open import ring-theory.precategory-of-rings funext ```
diff --git a/src/ring-theory/central-elements-rings.lagda.md b/src/ring-theory/central-elements-rings.lagda.md index 7ecc9dc806..1cb7eb7808 100644 --- a/src/ring-theory/central-elements-rings.lagda.md +++ b/src/ring-theory/central-elements-rings.lagda.md @@ -1,19 +1,24 @@ # Central elements of rings ```agda -module ring-theory.central-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.central-elements-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import ring-theory.central-elements-semirings -open import ring-theory.rings +open import ring-theory.central-elements-semirings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/central-elements-semirings.lagda.md b/src/ring-theory/central-elements-semirings.lagda.md index 41cb19f6ef..c37711c151 100644 --- a/src/ring-theory/central-elements-semirings.lagda.md +++ b/src/ring-theory/central-elements-semirings.lagda.md @@ -1,19 +1,24 @@ # Central elements of semirings ```agda -module ring-theory.central-elements-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.central-elements-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.central-elements-monoids +open import group-theory.central-elements-monoids funext -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/characteristics-rings.lagda.md b/src/ring-theory/characteristics-rings.lagda.md index 45bdfb7e8e..9f4298e796 100644 --- a/src/ring-theory/characteristics-rings.lagda.md +++ b/src/ring-theory/characteristics-rings.lagda.md @@ -1,19 +1,24 @@ # Characteristics of rings ```agda -module ring-theory.characteristics-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.characteristics-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.ring-of-integers +open import elementary-number-theory.ring-of-integers funext open import foundation.universe-levels -open import ring-theory.ideals-rings -open import ring-theory.kernels-of-ring-homomorphisms -open import ring-theory.rings +open import ring-theory.ideals-rings funext +open import ring-theory.kernels-of-ring-homomorphisms funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/commuting-elements-rings.lagda.md b/src/ring-theory/commuting-elements-rings.lagda.md index 3d35949217..be128ab07e 100644 --- a/src/ring-theory/commuting-elements-rings.lagda.md +++ b/src/ring-theory/commuting-elements-rings.lagda.md @@ -1,20 +1,25 @@ # Commuting elements of rings ```agda -module ring-theory.commuting-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.commuting-elements-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.commuting-elements-monoids +open import group-theory.commuting-elements-monoids funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/congruence-relations-rings.lagda.md b/src/ring-theory/congruence-relations-rings.lagda.md index 7b12139706..0ca8dea892 100644 --- a/src/ring-theory/congruence-relations-rings.lagda.md +++ b/src/ring-theory/congruence-relations-rings.lagda.md @@ -1,26 +1,31 @@ # Congruence relations on rings ```agda -module ring-theory.congruence-relations-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.congruence-relations-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.congruence-relations-abelian-groups -open import group-theory.congruence-relations-monoids +open import group-theory.congruence-relations-abelian-groups funext +open import group-theory.congruence-relations-monoids funext -open import ring-theory.congruence-relations-semirings -open import ring-theory.rings +open import ring-theory.congruence-relations-semirings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/congruence-relations-semirings.lagda.md b/src/ring-theory/congruence-relations-semirings.lagda.md index 2a0089a148..306af82fd4 100644 --- a/src/ring-theory/congruence-relations-semirings.lagda.md +++ b/src/ring-theory/congruence-relations-semirings.lagda.md @@ -1,27 +1,32 @@ # Congruence relations on semirings ```agda -module ring-theory.congruence-relations-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.congruence-relations-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences +open import foundation.equivalence-relations funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.congruence-relations-monoids +open import group-theory.congruence-relations-monoids funext -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/cyclic-rings.lagda.md b/src/ring-theory/cyclic-rings.lagda.md index e3b3ac6fca..8f6197d570 100644 --- a/src/ring-theory/cyclic-rings.lagda.md +++ b/src/ring-theory/cyclic-rings.lagda.md @@ -1,39 +1,44 @@ # Cyclic rings ```agda -module ring-theory.cyclic-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.cyclic-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-rings funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers -open import elementary-number-theory.ring-of-integers +open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.ring-of-integers funext open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.cyclic-groups -open import group-theory.free-groups-with-one-generator -open import group-theory.generating-elements-groups -open import group-theory.groups +open import group-theory.abelian-groups funext +open import group-theory.cyclic-groups funext +open import group-theory.free-groups-with-one-generator funext +open import group-theory.generating-elements-groups funext +open import group-theory.groups funext -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.integer-multiples-of-elements-rings funext +open import ring-theory.invertible-elements-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/dependent-products-rings.lagda.md b/src/ring-theory/dependent-products-rings.lagda.md index 409f515003..eebbea2b52 100644 --- a/src/ring-theory/dependent-products-rings.lagda.md +++ b/src/ring-theory/dependent-products-rings.lagda.md @@ -1,26 +1,31 @@ # Dependent products of rings ```agda -module ring-theory.dependent-products-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.dependent-products-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.dependent-products-abelian-groups -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.dependent-products-abelian-groups funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import ring-theory.dependent-products-semirings -open import ring-theory.rings -open import ring-theory.semirings +open import ring-theory.dependent-products-semirings funext +open import ring-theory.rings funext +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/dependent-products-semirings.lagda.md b/src/ring-theory/dependent-products-semirings.lagda.md index 5c59c14b05..d9d4e3cfd6 100644 --- a/src/ring-theory/dependent-products-semirings.lagda.md +++ b/src/ring-theory/dependent-products-semirings.lagda.md @@ -1,25 +1,31 @@ # Dependent products of semirings ```agda -module ring-theory.dependent-products-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.dependent-products-semirings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.sets +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.dependent-products-commutative-monoids -open import group-theory.dependent-products-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext +open import group-theory.dependent-products-commutative-monoids funext +open import group-theory.dependent-products-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/division-rings.lagda.md b/src/ring-theory/division-rings.lagda.md index fcdce2df44..10dd48fd8e 100644 --- a/src/ring-theory/division-rings.lagda.md +++ b/src/ring-theory/division-rings.lagda.md @@ -1,19 +1,24 @@ # Division rings ```agda -module ring-theory.division-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.division-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.negated-equality +open import foundation.cartesian-product-types funext +open import foundation.negated-equality funext open import foundation.universe-levels -open import ring-theory.invertible-elements-rings -open import ring-theory.rings -open import ring-theory.trivial-rings +open import ring-theory.invertible-elements-rings funext +open import ring-theory.rings funext +open import ring-theory.trivial-rings funext ```
diff --git a/src/ring-theory/free-rings-with-one-generator.lagda.md b/src/ring-theory/free-rings-with-one-generator.lagda.md index 4131005dfa..43e87dff73 100644 --- a/src/ring-theory/free-rings-with-one-generator.lagda.md +++ b/src/ring-theory/free-rings-with-one-generator.lagda.md @@ -1,17 +1,22 @@ # The free ring with one generator ```agda -module ring-theory.free-rings-with-one-generator where +open import foundation.function-extensionality-axiom + +module + ring-theory.free-rings-with-one-generator + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import ring-theory.homomorphisms-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/full-ideals-rings.lagda.md b/src/ring-theory/full-ideals-rings.lagda.md index 145fc154fa..b6444d987d 100644 --- a/src/ring-theory/full-ideals-rings.lagda.md +++ b/src/ring-theory/full-ideals-rings.lagda.md @@ -1,28 +1,33 @@ # Full ideals of rings ```agda -module ring-theory.full-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.full-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.full-subtypes -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.subtypes +open import foundation.full-subtypes funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.subtypes funext open import foundation.unit-type open import foundation.universe-levels -open import order-theory.top-elements-large-posets +open import order-theory.top-elements-large-posets funext -open import ring-theory.ideals-rings -open import ring-theory.left-ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-rings funext +open import ring-theory.left-ideals-rings funext +open import ring-theory.poset-of-ideals-rings funext +open import ring-theory.right-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/function-rings.lagda.md b/src/ring-theory/function-rings.lagda.md index 4a3837e0ec..7005d8a569 100644 --- a/src/ring-theory/function-rings.lagda.md +++ b/src/ring-theory/function-rings.lagda.md @@ -1,21 +1,26 @@ # Function rings ```agda -module ring-theory.function-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.function-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.monoids +open import group-theory.abelian-groups funext +open import group-theory.monoids funext -open import ring-theory.dependent-products-rings -open import ring-theory.rings +open import ring-theory.dependent-products-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/function-semirings.lagda.md b/src/ring-theory/function-semirings.lagda.md index 2aa4003612..dbb79aa450 100644 --- a/src/ring-theory/function-semirings.lagda.md +++ b/src/ring-theory/function-semirings.lagda.md @@ -1,22 +1,27 @@ # Function semirings ```agda -module ring-theory.function-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.function-semirings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext -open import ring-theory.dependent-products-semirings -open import ring-theory.semirings +open import ring-theory.dependent-products-semirings funext +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/generating-elements-rings.lagda.md b/src/ring-theory/generating-elements-rings.lagda.md index f143405f0f..a62fb21021 100644 --- a/src/ring-theory/generating-elements-rings.lagda.md +++ b/src/ring-theory/generating-elements-rings.lagda.md @@ -1,18 +1,23 @@ # Generating elements of rings ```agda -module ring-theory.generating-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.generating-elements-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.generating-elements-groups +open import group-theory.generating-elements-groups funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/groups-of-units-rings.lagda.md b/src/ring-theory/groups-of-units-rings.lagda.md index 16e293804e..6cad0e0d05 100644 --- a/src/ring-theory/groups-of-units-rings.lagda.md +++ b/src/ring-theory/groups-of-units-rings.lagda.md @@ -1,31 +1,36 @@ # The group of multiplicative units of a ring ```agda -module ring-theory.groups-of-units-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.groups-of-units-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-large-precategories +open import category-theory.functors-large-precategories funext -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.cores-monoids -open import group-theory.groups -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-monoids -open import group-theory.monoids -open import group-theory.precategory-of-groups -open import group-theory.semigroups -open import group-theory.submonoids - -open import ring-theory.homomorphisms-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.precategory-of-rings -open import ring-theory.rings +open import group-theory.cores-monoids funext +open import group-theory.groups funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-monoids funext +open import group-theory.monoids funext +open import group-theory.precategory-of-groups funext +open import group-theory.semigroups funext +open import group-theory.submonoids funext + +open import ring-theory.homomorphisms-rings funext +open import ring-theory.invertible-elements-rings funext +open import ring-theory.precategory-of-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/homomorphisms-cyclic-rings.lagda.md b/src/ring-theory/homomorphisms-cyclic-rings.lagda.md index 8bdb6d76cf..c485279eeb 100644 --- a/src/ring-theory/homomorphisms-cyclic-rings.lagda.md +++ b/src/ring-theory/homomorphisms-cyclic-rings.lagda.md @@ -1,7 +1,12 @@ # Homomorphisms of cyclic rings ```agda -module ring-theory.homomorphisms-cyclic-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.homomorphisms-cyclic-rings + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module ring-theory.homomorphisms-cyclic-rings where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import ring-theory.cyclic-rings -open import ring-theory.homomorphisms-rings -open import ring-theory.integer-multiples-of-elements-rings -open import ring-theory.rings +open import ring-theory.cyclic-rings funext +open import ring-theory.homomorphisms-rings funext +open import ring-theory.integer-multiples-of-elements-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/homomorphisms-rings.lagda.md b/src/ring-theory/homomorphisms-rings.lagda.md index 95f466ea7c..d9b221fdbe 100644 --- a/src/ring-theory/homomorphisms-rings.lagda.md +++ b/src/ring-theory/homomorphisms-rings.lagda.md @@ -1,32 +1,37 @@ # Homomorphisms of rings ```agda -module ring-theory.homomorphisms-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.homomorphisms-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.homomorphisms-groups -open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.homomorphisms-commutative-monoids funext +open import group-theory.homomorphisms-groups funext +open import group-theory.homomorphisms-monoids funext -open import ring-theory.homomorphisms-semirings -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-semirings funext +open import ring-theory.invertible-elements-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/homomorphisms-semirings.lagda.md b/src/ring-theory/homomorphisms-semirings.lagda.md index 9bd4acad47..cddc4bd631 100644 --- a/src/ring-theory/homomorphisms-semirings.lagda.md +++ b/src/ring-theory/homomorphisms-semirings.lagda.md @@ -1,29 +1,34 @@ # Homomorphisms of semirings ```agda -module ring-theory.homomorphisms-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.homomorphisms-semirings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.homomorphisms-commutative-monoids -open import group-theory.homomorphisms-monoids -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-commutative-monoids funext +open import group-theory.homomorphisms-monoids funext +open import group-theory.homomorphisms-semigroups funext -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md index 641996be99..77997c7ef5 100644 --- a/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md @@ -1,39 +1,44 @@ # Ideals generated by subsets of rings ```agda -module ring-theory.ideals-generated-by-subsets-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.ideals-generated-by-subsets-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.fibers-of-maps funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.unions-subtypes +open import foundation.unions-subtypes funext open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext +open import lists.functoriality-lists funext open import lists.lists -open import order-theory.galois-connections-large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.reflective-galois-connections-large-posets +open import order-theory.galois-connections-large-posets funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.reflective-galois-connections-large-posets funext -open import ring-theory.ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-rings funext +open import ring-theory.poset-of-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/ideals-rings.lagda.md b/src/ring-theory/ideals-rings.lagda.md index 74b99261c9..da879e3efe 100644 --- a/src/ring-theory/ideals-rings.lagda.md +++ b/src/ring-theory/ideals-rings.lagda.md @@ -1,37 +1,42 @@ # Ideals of rings ```agda -module ring-theory.ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.binary-transport -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import group-theory.congruence-relations-abelian-groups -open import group-theory.congruence-relations-monoids -open import group-theory.subgroups-abelian-groups +open import group-theory.congruence-relations-abelian-groups funext +open import group-theory.congruence-relations-monoids funext +open import group-theory.subgroups-abelian-groups funext -open import ring-theory.congruence-relations-rings -open import ring-theory.left-ideals-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.congruence-relations-rings funext +open import ring-theory.left-ideals-rings funext +open import ring-theory.right-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/ideals-semirings.lagda.md b/src/ring-theory/ideals-semirings.lagda.md index 801c43f0b9..b88f0f16a4 100644 --- a/src/ring-theory/ideals-semirings.lagda.md +++ b/src/ring-theory/ideals-semirings.lagda.md @@ -1,22 +1,27 @@ # Ideals of semirings ```agda -module ring-theory.ideals-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.ideals-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.submonoids +open import group-theory.submonoids funext -open import ring-theory.semirings -open import ring-theory.subsets-semirings +open import ring-theory.semirings funext +open import ring-theory.subsets-semirings funext ```
diff --git a/src/ring-theory/idempotent-elements-rings.lagda.md b/src/ring-theory/idempotent-elements-rings.lagda.md index 3d3369a849..a3f09dee43 100644 --- a/src/ring-theory/idempotent-elements-rings.lagda.md +++ b/src/ring-theory/idempotent-elements-rings.lagda.md @@ -1,18 +1,23 @@ # Idempotent elements in rings ```agda -module ring-theory.idempotent-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.idempotent-elements-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/initial-rings.lagda.md b/src/ring-theory/initial-rings.lagda.md index b3287aeae7..6673cd467e 100644 --- a/src/ring-theory/initial-rings.lagda.md +++ b/src/ring-theory/initial-rings.lagda.md @@ -1,18 +1,23 @@ # Initial rings ```agda -module ring-theory.initial-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.initial-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.initial-objects-large-categories +open import category-theory.initial-objects-large-categories funext open import foundation.universe-levels -open import ring-theory.category-of-rings -open import ring-theory.rings +open import ring-theory.category-of-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/integer-multiples-of-elements-rings.lagda.md b/src/ring-theory/integer-multiples-of-elements-rings.lagda.md index 9f66654609..3eabb4b3b0 100644 --- a/src/ring-theory/integer-multiples-of-elements-rings.lagda.md +++ b/src/ring-theory/integer-multiples-of-elements-rings.lagda.md @@ -1,31 +1,36 @@ # Integer multiples of elements of rings ```agda -module ring-theory.integer-multiples-of-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.integer-multiples-of-elements-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-integers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.coproduct-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.integer-multiples-of-elements-abelian-groups +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.integer-multiples-of-elements-abelian-groups funext -open import ring-theory.commuting-elements-rings -open import ring-theory.homomorphisms-rings -open import ring-theory.multiples-of-elements-rings -open import ring-theory.rings +open import ring-theory.commuting-elements-rings funext +open import ring-theory.homomorphisms-rings funext +open import ring-theory.multiples-of-elements-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/intersections-ideals-rings.lagda.md b/src/ring-theory/intersections-ideals-rings.lagda.md index 4444ab8716..f5b1623514 100644 --- a/src/ring-theory/intersections-ideals-rings.lagda.md +++ b/src/ring-theory/intersections-ideals-rings.lagda.md @@ -1,22 +1,27 @@ # Intersections of ideals of rings ```agda -module ring-theory.intersections-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.intersections-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.intersections-subtypes +open import foundation.intersections-subtypes funext open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.greatest-lower-bounds-large-posets funext -open import ring-theory.ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-rings funext +open import ring-theory.poset-of-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/intersections-ideals-semirings.lagda.md b/src/ring-theory/intersections-ideals-semirings.lagda.md index e263dc496c..7d114a7e64 100644 --- a/src/ring-theory/intersections-ideals-semirings.lagda.md +++ b/src/ring-theory/intersections-ideals-semirings.lagda.md @@ -1,19 +1,24 @@ # Intersections of ideals of semirings ```agda -module ring-theory.intersections-ideals-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.intersections-ideals-semirings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.intersections-subtypes +open import foundation.intersections-subtypes funext open import foundation.universe-levels -open import ring-theory.ideals-semirings -open import ring-theory.semirings -open import ring-theory.subsets-semirings +open import ring-theory.ideals-semirings funext +open import ring-theory.semirings funext +open import ring-theory.subsets-semirings funext ```
diff --git a/src/ring-theory/invariant-basis-property-rings.lagda.md b/src/ring-theory/invariant-basis-property-rings.lagda.md index ae9972819c..e9e1ad24a7 100644 --- a/src/ring-theory/invariant-basis-property-rings.lagda.md +++ b/src/ring-theory/invariant-basis-property-rings.lagda.md @@ -1,7 +1,12 @@ # The invariant basis property of rings ```agda -module ring-theory.invariant-basis-property-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.invariant-basis-property-rings + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module ring-theory.invariant-basis-property-rings where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.dependent-products-rings -open import ring-theory.isomorphisms-rings -open import ring-theory.rings +open import ring-theory.dependent-products-rings funext +open import ring-theory.isomorphisms-rings funext +open import ring-theory.rings funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/ring-theory/invertible-elements-rings.lagda.md b/src/ring-theory/invertible-elements-rings.lagda.md index 5066846791..79b6a7de9b 100644 --- a/src/ring-theory/invertible-elements-rings.lagda.md +++ b/src/ring-theory/invertible-elements-rings.lagda.md @@ -1,27 +1,32 @@ # Invertible elements in rings ```agda -module ring-theory.invertible-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.invertible-elements-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.contractible-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.invertible-elements-monoids +open import group-theory.invertible-elements-monoids funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/isomorphisms-rings.lagda.md b/src/ring-theory/isomorphisms-rings.lagda.md index 9ca0051cd9..1ee1eff325 100644 --- a/src/ring-theory/isomorphisms-rings.lagda.md +++ b/src/ring-theory/isomorphisms-rings.lagda.md @@ -1,48 +1,53 @@ # Isomorphisms of rings ```agda -module ring-theory.isomorphisms-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.isomorphisms-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-large-precategories funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.implicit-function-types -open import foundation.iterated-dependent-product-types -open import foundation.multivariable-homotopies -open import foundation.propositions +open import foundation.iterated-dependent-product-types funext +open import foundation.multivariable-homotopies funext +open import foundation.propositions funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.subtypes +open import foundation.subtypes funext open import foundation.telescopes -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups -open import group-theory.homomorphisms-monoids -open import group-theory.isomorphisms-abelian-groups -open import group-theory.isomorphisms-monoids +open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.homomorphisms-monoids funext +open import group-theory.isomorphisms-abelian-groups funext +open import group-theory.isomorphisms-monoids funext -open import ring-theory.homomorphisms-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.precategory-of-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.invertible-elements-rings funext +open import ring-theory.precategory-of-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/joins-ideals-rings.lagda.md b/src/ring-theory/joins-ideals-rings.lagda.md index cefa31e7f4..a0d2643a44 100644 --- a/src/ring-theory/joins-ideals-rings.lagda.md +++ b/src/ring-theory/joins-ideals-rings.lagda.md @@ -1,26 +1,31 @@ # Joins of ideals of rings ```agda -module ring-theory.joins-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.joins-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.unions-subtypes funext open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.similarity-of-elements-large-posets funext -open import ring-theory.ideals-generated-by-subsets-rings -open import ring-theory.ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-generated-by-subsets-rings funext +open import ring-theory.ideals-rings funext +open import ring-theory.poset-of-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/joins-left-ideals-rings.lagda.md b/src/ring-theory/joins-left-ideals-rings.lagda.md index 9b93c7d3c5..9cfb2c802b 100644 --- a/src/ring-theory/joins-left-ideals-rings.lagda.md +++ b/src/ring-theory/joins-left-ideals-rings.lagda.md @@ -1,26 +1,31 @@ # Joins of left ideals of rings ```agda -module ring-theory.joins-left-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.joins-left-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.unions-subtypes funext open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.similarity-of-elements-large-posets funext -open import ring-theory.left-ideals-generated-by-subsets-rings -open import ring-theory.left-ideals-rings -open import ring-theory.poset-of-left-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.left-ideals-generated-by-subsets-rings funext +open import ring-theory.left-ideals-rings funext +open import ring-theory.poset-of-left-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/joins-right-ideals-rings.lagda.md b/src/ring-theory/joins-right-ideals-rings.lagda.md index f1ce158230..1c02382c76 100644 --- a/src/ring-theory/joins-right-ideals-rings.lagda.md +++ b/src/ring-theory/joins-right-ideals-rings.lagda.md @@ -1,26 +1,31 @@ # Joins of right ideals of rings ```agda -module ring-theory.joins-right-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.joins-right-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.unions-subtypes funext open import foundation.universe-levels -open import order-theory.large-suplattices -open import order-theory.least-upper-bounds-large-posets -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-suplattices funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.similarity-of-elements-large-posets funext -open import ring-theory.poset-of-right-ideals-rings -open import ring-theory.right-ideals-generated-by-subsets-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.poset-of-right-ideals-rings funext +open import ring-theory.right-ideals-generated-by-subsets-rings funext +open import ring-theory.right-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md b/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md index 905d2411ee..7802312942 100644 --- a/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md +++ b/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md @@ -1,7 +1,12 @@ # Kernels of ring homomorphisms ```agda -module ring-theory.kernels-of-ring-homomorphisms where +open import foundation.function-extensionality-axiom + +module + ring-theory.kernels-of-ring-homomorphisms + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module ring-theory.kernels-of-ring-homomorphisms where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.kernels-homomorphisms-groups -open import group-theory.subgroups-abelian-groups +open import group-theory.kernels-homomorphisms-groups funext +open import group-theory.subgroups-abelian-groups funext -open import ring-theory.homomorphisms-rings -open import ring-theory.ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md index 45001b74cb..ea7458694a 100644 --- a/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md @@ -1,41 +1,46 @@ # Left ideals generated by subsets of rings ```agda -module ring-theory.left-ideals-generated-by-subsets-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.left-ideals-generated-by-subsets-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.unions-subtypes +open import foundation.unions-subtypes funext open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext +open import lists.functoriality-lists funext open import lists.lists -open import order-theory.galois-connections-large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.reflective-galois-connections-large-posets +open import order-theory.galois-connections-large-posets funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.reflective-galois-connections-large-posets funext -open import ring-theory.left-ideals-rings -open import ring-theory.poset-of-left-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.left-ideals-rings funext +open import ring-theory.poset-of-left-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/left-ideals-rings.lagda.md b/src/ring-theory/left-ideals-rings.lagda.md index c0d2710a89..dd924a061a 100644 --- a/src/ring-theory/left-ideals-rings.lagda.md +++ b/src/ring-theory/left-ideals-rings.lagda.md @@ -1,25 +1,30 @@ # Left ideals of rings ```agda -module ring-theory.left-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.left-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/local-rings.lagda.md b/src/ring-theory/local-rings.lagda.md index 6ec65472c7..dbf1bb60da 100644 --- a/src/ring-theory/local-rings.lagda.md +++ b/src/ring-theory/local-rings.lagda.md @@ -1,20 +1,25 @@ # Local rings ```agda -module ring-theory.local-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.local-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.propositions -open import foundation.sets +open import foundation.disjunction funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.invertible-elements-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/localizations-rings.lagda.md b/src/ring-theory/localizations-rings.lagda.md index 0c3aeb511a..2a82dcf8f3 100644 --- a/src/ring-theory/localizations-rings.lagda.md +++ b/src/ring-theory/localizations-rings.lagda.md @@ -1,28 +1,33 @@ # Localizations of rings ```agda -module ring-theory.localizations-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.localizations-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import ring-theory.homomorphisms-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.invertible-elements-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/modules-rings.lagda.md b/src/ring-theory/modules-rings.lagda.md index dd09b187e4..430896e153 100644 --- a/src/ring-theory/modules-rings.lagda.md +++ b/src/ring-theory/modules-rings.lagda.md @@ -1,25 +1,30 @@ # Modules over rings ```agda -module ring-theory.modules-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.modules-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.addition-homomorphisms-abelian-groups -open import group-theory.endomorphism-rings-abelian-groups -open import group-theory.homomorphisms-abelian-groups +open import group-theory.abelian-groups funext +open import group-theory.addition-homomorphisms-abelian-groups funext +open import group-theory.endomorphism-rings-abelian-groups funext +open import group-theory.homomorphisms-abelian-groups funext -open import ring-theory.homomorphisms-rings -open import ring-theory.opposite-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.opposite-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/multiples-of-elements-rings.lagda.md b/src/ring-theory/multiples-of-elements-rings.lagda.md index f0bf36215a..20a8f02d82 100644 --- a/src/ring-theory/multiples-of-elements-rings.lagda.md +++ b/src/ring-theory/multiples-of-elements-rings.lagda.md @@ -1,7 +1,12 @@ # Multiples of elements in rings ```agda -module ring-theory.multiples-of-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.multiples-of-elements-rings + (funext : function-extensionality) + where ```
Imports @@ -11,13 +16,13 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.multiples-of-elements-abelian-groups +open import group-theory.multiples-of-elements-abelian-groups funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/nil-ideals-rings.lagda.md b/src/ring-theory/nil-ideals-rings.lagda.md index 22688c8e4c..06662923ea 100644 --- a/src/ring-theory/nil-ideals-rings.lagda.md +++ b/src/ring-theory/nil-ideals-rings.lagda.md @@ -1,20 +1,25 @@ # Nil ideals of rings ```agda -module ring-theory.nil-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.nil-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import ring-theory.ideals-rings -open import ring-theory.left-ideals-rings -open import ring-theory.nilpotent-elements-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings +open import ring-theory.ideals-rings funext +open import ring-theory.left-ideals-rings funext +open import ring-theory.nilpotent-elements-rings funext +open import ring-theory.right-ideals-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/nilpotent-elements-rings.lagda.md b/src/ring-theory/nilpotent-elements-rings.lagda.md index 96f8512935..39b2ac18c8 100644 --- a/src/ring-theory/nilpotent-elements-rings.lagda.md +++ b/src/ring-theory/nilpotent-elements-rings.lagda.md @@ -1,7 +1,12 @@ # Nilpotent elements in rings ```agda -module ring-theory.nilpotent-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.nilpotent-elements-rings + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module ring-theory.nilpotent-elements-rings where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.universe-levels -open import ring-theory.nilpotent-elements-semirings -open import ring-theory.powers-of-elements-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.nilpotent-elements-semirings funext +open import ring-theory.powers-of-elements-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/nilpotent-elements-semirings.lagda.md b/src/ring-theory/nilpotent-elements-semirings.lagda.md index 434bdf7fb8..e3895705f5 100644 --- a/src/ring-theory/nilpotent-elements-semirings.lagda.md +++ b/src/ring-theory/nilpotent-elements-semirings.lagda.md @@ -1,7 +1,12 @@ # Nilpotent elements in semirings ```agda -module ring-theory.nilpotent-elements-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.nilpotent-elements-semirings + (funext : function-extensionality) + where ```
Imports @@ -12,16 +17,16 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import ring-theory.binomial-theorem-semirings -open import ring-theory.powers-of-elements-semirings -open import ring-theory.semirings +open import ring-theory.binomial-theorem-semirings funext +open import ring-theory.powers-of-elements-semirings funext +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/opposite-rings.lagda.md b/src/ring-theory/opposite-rings.lagda.md index 824b49515c..7d6540b83b 100644 --- a/src/ring-theory/opposite-rings.lagda.md +++ b/src/ring-theory/opposite-rings.lagda.md @@ -1,17 +1,22 @@ # Opposite rings ```agda -module ring-theory.opposite-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.opposite-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/poset-of-cyclic-rings.lagda.md b/src/ring-theory/poset-of-cyclic-rings.lagda.md index ef3023bcd0..4bda70c7f1 100644 --- a/src/ring-theory/poset-of-cyclic-rings.lagda.md +++ b/src/ring-theory/poset-of-cyclic-rings.lagda.md @@ -1,7 +1,12 @@ # The poset of cyclic rings ```agda -module ring-theory.poset-of-cyclic-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.poset-of-cyclic-rings + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module ring-theory.poset-of-cyclic-rings where ```agda open import foundation.universe-levels -open import order-theory.large-posets +open import order-theory.large-posets funext -open import ring-theory.category-of-cyclic-rings +open import ring-theory.category-of-cyclic-rings funext ```
diff --git a/src/ring-theory/poset-of-ideals-rings.lagda.md b/src/ring-theory/poset-of-ideals-rings.lagda.md index 7ac68be10d..b5fc9b2f77 100644 --- a/src/ring-theory/poset-of-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-ideals-rings.lagda.md @@ -1,28 +1,33 @@ # The poset of ideals of a ring ```agda -module ring-theory.poset-of-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.poset-of-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.powersets funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.similarity-of-elements-large-posets funext -open import ring-theory.ideals-rings -open import ring-theory.rings +open import ring-theory.ideals-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/poset-of-left-ideals-rings.lagda.md b/src/ring-theory/poset-of-left-ideals-rings.lagda.md index a34d3bad4a..885b1c7e7a 100644 --- a/src/ring-theory/poset-of-left-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-left-ideals-rings.lagda.md @@ -1,28 +1,33 @@ # The poset of left ideals of a ring ```agda -module ring-theory.poset-of-left-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.poset-of-left-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.powersets funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.similarity-of-elements-large-posets funext -open import ring-theory.left-ideals-rings -open import ring-theory.rings +open import ring-theory.left-ideals-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/poset-of-right-ideals-rings.lagda.md b/src/ring-theory/poset-of-right-ideals-rings.lagda.md index 9ddb7754b7..04854226db 100644 --- a/src/ring-theory/poset-of-right-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-right-ideals-rings.lagda.md @@ -1,28 +1,33 @@ # The poset of right ideals of a ring ```agda -module ring-theory.poset-of-right-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.poset-of-right-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.powersets -open import foundation.propositions -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.powersets funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.universe-levels -open import order-theory.large-posets -open import order-theory.large-preorders -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.similarity-of-elements-large-posets +open import order-theory.large-posets funext +open import order-theory.large-preorders funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.similarity-of-elements-large-posets funext -open import ring-theory.right-ideals-rings -open import ring-theory.rings +open import ring-theory.right-ideals-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/powers-of-elements-rings.lagda.md b/src/ring-theory/powers-of-elements-rings.lagda.md index e7a4956cc4..452f666b71 100644 --- a/src/ring-theory/powers-of-elements-rings.lagda.md +++ b/src/ring-theory/powers-of-elements-rings.lagda.md @@ -1,7 +1,12 @@ # Powers of elements in rings ```agda -module ring-theory.powers-of-elements-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.powers-of-elements-rings + (funext : function-extensionality) + where ```
Imports @@ -10,17 +15,17 @@ module ring-theory.powers-of-elements-rings where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers +open import elementary-number-theory.parity-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.empty-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.central-elements-rings -open import ring-theory.powers-of-elements-semirings -open import ring-theory.rings +open import ring-theory.central-elements-rings funext +open import ring-theory.powers-of-elements-semirings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/powers-of-elements-semirings.lagda.md b/src/ring-theory/powers-of-elements-semirings.lagda.md index ca2f29b47c..40ff6b2692 100644 --- a/src/ring-theory/powers-of-elements-semirings.lagda.md +++ b/src/ring-theory/powers-of-elements-semirings.lagda.md @@ -1,7 +1,12 @@ # Powers of elements in semirings ```agda -module ring-theory.powers-of-elements-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.powers-of-elements-semirings + (funext : function-extensionality) + where ```
Imports @@ -11,12 +16,12 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.powers-of-elements-monoids +open import group-theory.powers-of-elements-monoids funext -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/precategory-of-rings.lagda.md b/src/ring-theory/precategory-of-rings.lagda.md index e22cb72547..e7e15052ef 100644 --- a/src/ring-theory/precategory-of-rings.lagda.md +++ b/src/ring-theory/precategory-of-rings.lagda.md @@ -1,19 +1,24 @@ # The precategory of rings ```agda -module ring-theory.precategory-of-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.precategory-of-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import ring-theory.homomorphisms-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/precategory-of-semirings.lagda.md b/src/ring-theory/precategory-of-semirings.lagda.md index 8b84a0d3e0..b23ef29f64 100644 --- a/src/ring-theory/precategory-of-semirings.lagda.md +++ b/src/ring-theory/precategory-of-semirings.lagda.md @@ -1,19 +1,24 @@ # The precategory of semirings ```agda -module ring-theory.precategory-of-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.precategory-of-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories -open import category-theory.precategories +open import category-theory.large-precategories funext +open import category-theory.precategories funext open import foundation.universe-levels -open import ring-theory.homomorphisms-semirings -open import ring-theory.semirings +open import ring-theory.homomorphisms-semirings funext +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/products-ideals-rings.lagda.md b/src/ring-theory/products-ideals-rings.lagda.md index 73cb6e9253..6ea7eea658 100644 --- a/src/ring-theory/products-ideals-rings.lagda.md +++ b/src/ring-theory/products-ideals-rings.lagda.md @@ -1,23 +1,28 @@ # Products of ideals of rings ```agda -module ring-theory.products-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.products-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import ring-theory.ideals-generated-by-subsets-rings -open import ring-theory.ideals-rings -open import ring-theory.poset-of-ideals-rings -open import ring-theory.products-subsets-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.ideals-generated-by-subsets-rings funext +open import ring-theory.ideals-rings funext +open import ring-theory.poset-of-ideals-rings funext +open import ring-theory.products-subsets-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/products-left-ideals-rings.lagda.md b/src/ring-theory/products-left-ideals-rings.lagda.md index 553c0eacf9..e9f4ece37a 100644 --- a/src/ring-theory/products-left-ideals-rings.lagda.md +++ b/src/ring-theory/products-left-ideals-rings.lagda.md @@ -1,23 +1,28 @@ # Products of left ideals of rings ```agda -module ring-theory.products-left-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.products-left-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import ring-theory.left-ideals-generated-by-subsets-rings -open import ring-theory.left-ideals-rings -open import ring-theory.poset-of-left-ideals-rings -open import ring-theory.products-subsets-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.left-ideals-generated-by-subsets-rings funext +open import ring-theory.left-ideals-rings funext +open import ring-theory.poset-of-left-ideals-rings funext +open import ring-theory.products-subsets-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/products-right-ideals-rings.lagda.md b/src/ring-theory/products-right-ideals-rings.lagda.md index 22cf1b4cfe..4cbb7bca31 100644 --- a/src/ring-theory/products-right-ideals-rings.lagda.md +++ b/src/ring-theory/products-right-ideals-rings.lagda.md @@ -1,23 +1,28 @@ # Products of right ideals of rings ```agda -module ring-theory.products-right-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.products-right-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import ring-theory.poset-of-right-ideals-rings -open import ring-theory.products-subsets-rings -open import ring-theory.right-ideals-generated-by-subsets-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.poset-of-right-ideals-rings funext +open import ring-theory.products-subsets-rings funext +open import ring-theory.right-ideals-generated-by-subsets-rings funext +open import ring-theory.right-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/products-rings.lagda.md b/src/ring-theory/products-rings.lagda.md index fcebad162a..29e2312b8b 100644 --- a/src/ring-theory/products-rings.lagda.md +++ b/src/ring-theory/products-rings.lagda.md @@ -1,7 +1,12 @@ # Products of rings ```agda -module ring-theory.products-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.products-rings + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module ring-theory.products-rings where ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.groups funext +open import group-theory.semigroups funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/products-subsets-rings.lagda.md b/src/ring-theory/products-subsets-rings.lagda.md index 157d8910ef..dfeb1ae9a1 100644 --- a/src/ring-theory/products-subsets-rings.lagda.md +++ b/src/ring-theory/products-subsets-rings.lagda.md @@ -1,21 +1,26 @@ # Products of subsets of rings ```agda -module ring-theory.products-subsets-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.products-subsets-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.unions-subtypes +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext +open import foundation.unions-subtypes funext open import foundation.universe-levels -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/quotient-rings.lagda.md b/src/ring-theory/quotient-rings.lagda.md index cf3fdbe28f..4554e40a56 100644 --- a/src/ring-theory/quotient-rings.lagda.md +++ b/src/ring-theory/quotient-rings.lagda.md @@ -1,7 +1,12 @@ # Quotient rings ```agda -module ring-theory.quotient-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.quotient-rings + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module ring-theory.quotient-rings where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import ring-theory.homomorphisms-rings -open import ring-theory.ideals-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.ideals-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/radical-ideals-rings.lagda.md b/src/ring-theory/radical-ideals-rings.lagda.md index 964017ee37..894236432b 100644 --- a/src/ring-theory/radical-ideals-rings.lagda.md +++ b/src/ring-theory/radical-ideals-rings.lagda.md @@ -1,18 +1,23 @@ # Radical ideals of rings ```agda -module ring-theory.radical-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.radical-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import ring-theory.ideals-rings -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.ideals-rings funext +open import ring-theory.invertible-elements-rings funext +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md index ec913d21e3..03e141f826 100644 --- a/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md @@ -1,41 +1,46 @@ # Right ideals generated by subsets of rings ```agda -module ring-theory.right-ideals-generated-by-subsets-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.right-ideals-generated-by-subsets-rings + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.powersets -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.powersets funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.unions-subtypes +open import foundation.unions-subtypes funext open import foundation.universe-levels -open import lists.concatenation-lists -open import lists.functoriality-lists +open import lists.concatenation-lists funext +open import lists.functoriality-lists funext open import lists.lists -open import order-theory.galois-connections-large-posets -open import order-theory.least-upper-bounds-large-posets -open import order-theory.order-preserving-maps-large-posets -open import order-theory.order-preserving-maps-large-preorders -open import order-theory.reflective-galois-connections-large-posets +open import order-theory.galois-connections-large-posets funext +open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.reflective-galois-connections-large-posets funext -open import ring-theory.poset-of-right-ideals-rings -open import ring-theory.right-ideals-rings -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.poset-of-right-ideals-rings funext +open import ring-theory.right-ideals-rings funext +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/right-ideals-rings.lagda.md b/src/ring-theory/right-ideals-rings.lagda.md index 1da87674fc..d564389a3c 100644 --- a/src/ring-theory/right-ideals-rings.lagda.md +++ b/src/ring-theory/right-ideals-rings.lagda.md @@ -1,25 +1,30 @@ # Right ideals of rings ```agda -module ring-theory.right-ideals-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.right-ideals-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import ring-theory.rings -open import ring-theory.subsets-rings +open import ring-theory.rings funext +open import ring-theory.subsets-rings funext ```
diff --git a/src/ring-theory/rings.lagda.md b/src/ring-theory/rings.lagda.md index 757f7994ee..29ba5a4d4d 100644 --- a/src/ring-theory/rings.lagda.md +++ b/src/ring-theory/rings.lagda.md @@ -1,7 +1,12 @@ # Rings ```agda -module ring-theory.rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.rings + (funext : function-extensionality) + where ```
Imports @@ -12,33 +17,33 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings +open import foundation.binary-embeddings funext open import foundation.binary-equivalences -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.commutative-monoids -open import group-theory.groups -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.commutative-monoids funext +open import group-theory.groups funext +open import group-theory.monoids funext +open import group-theory.semigroups funext -open import lists.concatenation-lists +open import lists.concatenation-lists funext open import lists.lists -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/semirings.lagda.md b/src/ring-theory/semirings.lagda.md index 982869d8d3..ba4782e20c 100644 --- a/src/ring-theory/semirings.lagda.md +++ b/src/ring-theory/semirings.lagda.md @@ -1,7 +1,12 @@ # Semirings ```agda -module ring-theory.semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.semirings + (funext : function-extensionality) + where ```
Imports @@ -12,18 +17,18 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids -open import group-theory.monoids -open import group-theory.semigroups +open import group-theory.commutative-monoids funext +open import group-theory.monoids funext +open import group-theory.semigroups funext ```
diff --git a/src/ring-theory/subsets-rings.lagda.md b/src/ring-theory/subsets-rings.lagda.md index df9a3f2c84..0a31ce5a5b 100644 --- a/src/ring-theory/subsets-rings.lagda.md +++ b/src/ring-theory/subsets-rings.lagda.md @@ -1,22 +1,27 @@ # Subsets of rings ```agda -module ring-theory.subsets-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.subsets-rings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositional-extensionality funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import group-theory.subgroups-abelian-groups +open import group-theory.subgroups-abelian-groups funext -open import ring-theory.rings +open import ring-theory.rings funext ```
diff --git a/src/ring-theory/subsets-semirings.lagda.md b/src/ring-theory/subsets-semirings.lagda.md index 0236a79809..ea24d6e52f 100644 --- a/src/ring-theory/subsets-semirings.lagda.md +++ b/src/ring-theory/subsets-semirings.lagda.md @@ -1,20 +1,25 @@ # Subsets of semirings ```agda -module ring-theory.subsets-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.subsets-semirings + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositional-extensionality funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels -open import ring-theory.semirings +open import ring-theory.semirings funext ```
diff --git a/src/ring-theory/sums-rings.lagda.md b/src/ring-theory/sums-rings.lagda.md index f2f5859aa9..eeb6852f08 100644 --- a/src/ring-theory/sums-rings.lagda.md +++ b/src/ring-theory/sums-rings.lagda.md @@ -1,7 +1,12 @@ # Sums of elements in rings ```agda -module ring-theory.sums-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.sums-rings + (funext : function-extensionality) + where ```
Imports @@ -10,19 +15,19 @@ module ring-theory.sums-rings where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.vectors -open import linear-algebra.vectors-on-rings +open import linear-algebra.vectors funext +open import linear-algebra.vectors funext-on-rings -open import ring-theory.rings -open import ring-theory.sums-semirings +open import ring-theory.rings funext +open import ring-theory.sums-semirings funext -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/ring-theory/sums-semirings.lagda.md b/src/ring-theory/sums-semirings.lagda.md index 3f42f0a446..dc618859b3 100644 --- a/src/ring-theory/sums-semirings.lagda.md +++ b/src/ring-theory/sums-semirings.lagda.md @@ -1,7 +1,12 @@ # Sums of elements in semirings ```agda -module ring-theory.sums-semirings where +open import foundation.function-extensionality-axiom + +module + ring-theory.sums-semirings + (funext : function-extensionality) + where ```
Imports @@ -11,21 +16,21 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.coproduct-types funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import linear-algebra.vectors -open import linear-algebra.vectors-on-semirings +open import linear-algebra.vectors funext +open import linear-algebra.vectors funext-on-semirings -open import ring-theory.semirings +open import ring-theory.semirings funext -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md b/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md index d69f003772..db394a93e7 100644 --- a/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md +++ b/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md @@ -11,17 +11,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups -open import group-theory.isomorphisms-abelian-groups -open import group-theory.semigroups +open import group-theory.abelian-groups funext +open import group-theory.isomorphisms-abelian-groups funext +open import group-theory.semigroups funext -open import ring-theory.homomorphisms-rings -open import ring-theory.isomorphisms-rings -open import ring-theory.rings +open import ring-theory.homomorphisms-rings funext +open import ring-theory.isomorphisms-rings funext +open import ring-theory.rings funext ```
@@ -44,7 +44,12 @@ transported ring structure. ### Transporting the multiplicative structure of a ring along an isomorphism of abelian groups ```agda -module _ +open import foundation.function-extensionality-axiom + +module + _ + (funext : function-extensionality) + where {l1 l2 : Level} (R : Ring l1) (A : Ab l2) (f : iso-Ab (ab-Ring R) A) where diff --git a/src/ring-theory/trivial-rings.lagda.md b/src/ring-theory/trivial-rings.lagda.md index 4173514622..c0b8c06b3d 100644 --- a/src/ring-theory/trivial-rings.lagda.md +++ b/src/ring-theory/trivial-rings.lagda.md @@ -1,7 +1,12 @@ # Trivial rings ```agda -module ring-theory.trivial-rings where +open import foundation.function-extensionality-axiom + +module + ring-theory.trivial-rings + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,17 @@ module ring-theory.trivial-rings where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import ring-theory.invertible-elements-rings -open import ring-theory.rings +open import ring-theory.invertible-elements-rings funext +open import ring-theory.rings funext ```
diff --git a/src/set-theory.lagda.md b/src/set-theory.lagda.md index 054f1135dc..17685338a6 100644 --- a/src/set-theory.lagda.md +++ b/src/set-theory.lagda.md @@ -42,17 +42,22 @@ theory, and [Russell's paradox](set-theory.russells-paradox.md). ## Modules in the set theory namespace ```agda -module set-theory where - -open import set-theory.baire-space public -open import set-theory.cantor-space public -open import set-theory.cantors-diagonal-argument public -open import set-theory.cardinalities public -open import set-theory.countable-sets public -open import set-theory.cumulative-hierarchy public -open import set-theory.infinite-sets public -open import set-theory.russells-paradox public -open import set-theory.uncountable-sets public +open import foundation.function-extensionality-axiom + +module + set-theory + (funext : function-extensionality) + where + +open import set-theory.baire-space funext public +open import set-theory.cantor-space funext public +open import set-theory.cantors-diagonal-argument funext public +open import set-theory.cardinalities funext public +open import set-theory.countable-sets funext public +open import set-theory.cumulative-hierarchy funext public +open import set-theory.infinite-sets funext public +open import set-theory.russells-paradox funext public +open import set-theory.uncountable-sets funext public ``` ## References diff --git a/src/set-theory/baire-space.lagda.md b/src/set-theory/baire-space.lagda.md index 884e7587bd..c261f2ca38 100644 --- a/src/set-theory/baire-space.lagda.md +++ b/src/set-theory/baire-space.lagda.md @@ -1,29 +1,34 @@ # Baire space ```agda -module set-theory.baire-space where +open import foundation.function-extensionality-axiom + +module + set-theory.baire-space + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.lawveres-fixed-point-theorem -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.function-types funext +open import foundation.lawveres-fixed-point-theorem funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.identity-types -open import set-theory.cantors-diagonal-argument -open import set-theory.countable-sets -open import set-theory.uncountable-sets +open import set-theory.cantors-diagonal-argument funext +open import set-theory.countable-sets funext +open import set-theory.uncountable-sets funext ```
diff --git a/src/set-theory/cantor-space.lagda.md b/src/set-theory/cantor-space.lagda.md index 41ea6e9e47..26a7b5356d 100644 --- a/src/set-theory/cantor-space.lagda.md +++ b/src/set-theory/cantor-space.lagda.md @@ -1,7 +1,12 @@ # Cantor space ```agda -module set-theory.cantor-space where +open import foundation.function-extensionality-axiom + +module + set-theory.cantor-space + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,24 @@ module set-theory.cantor-space where ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.coproduct-types +open import foundation.booleans funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.lawveres-fixed-point-theorem -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.tight-apartness-relations +open import foundation.empty-types funext +open import foundation.lawveres-fixed-point-theorem funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.sets funext +open import foundation.tight-apartness-relations funext open import foundation.unit-type open import foundation.universe-levels -open import set-theory.cantors-diagonal-argument -open import set-theory.countable-sets -open import set-theory.uncountable-sets +open import set-theory.cantors-diagonal-argument funext +open import set-theory.countable-sets funext +open import set-theory.uncountable-sets funext -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/set-theory/cantors-diagonal-argument.lagda.md b/src/set-theory/cantors-diagonal-argument.lagda.md index 1ff1284a90..4907c2ed28 100644 --- a/src/set-theory/cantors-diagonal-argument.lagda.md +++ b/src/set-theory/cantors-diagonal-argument.lagda.md @@ -1,7 +1,12 @@ # Cantor's diagonal argument ```agda -module set-theory.cantors-diagonal-argument where +open import foundation.function-extensionality-axiom + +module + set-theory.cantors-diagonal-argument + (funext : function-extensionality) + where ```
Imports @@ -10,25 +15,24 @@ module set-theory.cantors-diagonal-argument where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.surjective-maps +open import foundation.discrete-types funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.sets funext +open import foundation.surjective-maps funext open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.fibers-of-maps open import foundation-core.propositions -open import set-theory.countable-sets -open import set-theory.uncountable-sets +open import set-theory.countable-sets funext +open import set-theory.uncountable-sets funext ```
diff --git a/src/set-theory/cardinalities.lagda.md b/src/set-theory/cardinalities.lagda.md index 27c781d4cc..8a21df98be 100644 --- a/src/set-theory/cardinalities.lagda.md +++ b/src/set-theory/cardinalities.lagda.md @@ -1,25 +1,29 @@ # Cardinalities of sets ```agda -module set-theory.cardinalities where +open import foundation.function-extensionality-axiom + +module + set-theory.cardinalities + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.large-binary-relations -open import foundation.law-of-excluded-middle -open import foundation.mere-embeddings -open import foundation.mere-equivalences -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets +open import foundation.equivalences funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.identity-types funext +open import foundation.large-binary-relations funext +open import foundation.law-of-excluded-middle funext +open import foundation.mere-embeddings funext +open import foundation.mere-equivalences funext +open import foundation.propositional-extensionality funext +open import foundation.propositions funext +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/set-theory/countable-sets.lagda.md b/src/set-theory/countable-sets.lagda.md index ab92a803d5..f6bc29f075 100644 --- a/src/set-theory/countable-sets.lagda.md +++ b/src/set-theory/countable-sets.lagda.md @@ -1,41 +1,46 @@ # Countable sets ```agda -module set-theory.countable-sets where +open import foundation.function-extensionality-axiom + +module + set-theory.countable-sets + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.type-arithmetic-natural-numbers +open import elementary-number-theory.type-arithmetic-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-subtypes -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-subtypes funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.maybe -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.retracts-of-types -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equality-coproduct-types funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.maybe funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.retracts-of-types funext +open import foundation.sets funext open import foundation.shifting-sequences -open import foundation.surjective-maps +open import foundation.surjective-maps funext open import foundation.unit-type open import foundation.universe-levels @@ -43,7 +48,7 @@ open import foundation-core.cartesian-product-types open import foundation-core.fibers-of-maps open import foundation-core.identity-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/set-theory/cumulative-hierarchy.lagda.md b/src/set-theory/cumulative-hierarchy.lagda.md index baa1ddad21..bb385bf185 100644 --- a/src/set-theory/cumulative-hierarchy.lagda.md +++ b/src/set-theory/cumulative-hierarchy.lagda.md @@ -1,7 +1,12 @@ # Cumulative hierarchy ```agda -module set-theory.cumulative-hierarchy where +open import foundation.function-extensionality-axiom + +module + set-theory.cumulative-hierarchy + (funext : function-extensionality) + where ```
Imports @@ -10,27 +15,27 @@ module set-theory.cumulative-hierarchy where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.booleans -open import foundation.cartesian-product-types -open import foundation.constant-type-families -open import foundation.coproduct-types +open import foundation.booleans funext +open import foundation.cartesian-product-types funext +open import foundation.constant-type-families funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-booleans -open import foundation.raising-universe-levels-unit-type -open import foundation.sets +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-booleans +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sets funext open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/set-theory/infinite-sets.lagda.md b/src/set-theory/infinite-sets.lagda.md index d94e6be82f..481cb50381 100644 --- a/src/set-theory/infinite-sets.lagda.md +++ b/src/set-theory/infinite-sets.lagda.md @@ -1,7 +1,12 @@ # Infinite sets ```agda -module set-theory.infinite-sets where +open import foundation.function-extensionality-axiom + +module + set-theory.infinite-sets + (funext : function-extensionality) + where ```
Imports @@ -10,12 +15,12 @@ module set-theory.infinite-sets where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.mere-embeddings -open import foundation.propositions -open import foundation.sets +open import foundation.mere-embeddings funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/set-theory/russells-paradox.lagda.md b/src/set-theory/russells-paradox.lagda.md index 9ca07432a8..94750c0c21 100644 --- a/src/set-theory/russells-paradox.lagda.md +++ b/src/set-theory/russells-paradox.lagda.md @@ -3,24 +3,29 @@ ```agda {-# OPTIONS --lossy-unification #-} -module set-theory.russells-paradox where +open import foundation.function-extensionality-axiom + +module + set-theory.russells-paradox + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types -open import foundation.identity-types -open import foundation.locally-small-types -open import foundation.negation -open import foundation.small-types -open import foundation.small-universes -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.functoriality-cartesian-product-types funext +open import foundation.identity-types funext +open import foundation.locally-small-types funext +open import foundation.negation funext +open import foundation.small-types funext +open import foundation.small-universes funext +open import foundation.surjective-maps funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation-core.contractible-types @@ -28,9 +33,9 @@ open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types -open import trees.multisets -open import trees.small-multisets -open import trees.universal-multiset +open import trees.multisets funext +open import trees.small-multisets funext +open import trees.universal-multiset funext ```
diff --git a/src/set-theory/uncountable-sets.lagda.md b/src/set-theory/uncountable-sets.lagda.md index f1cb306d08..b5f767514c 100644 --- a/src/set-theory/uncountable-sets.lagda.md +++ b/src/set-theory/uncountable-sets.lagda.md @@ -1,18 +1,23 @@ # Uncountable sets ```agda -module set-theory.uncountable-sets where +open import foundation.function-extensionality-axiom + +module + set-theory.uncountable-sets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.negation -open import foundation.propositions -open import foundation.sets +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import set-theory.countable-sets +open import set-theory.countable-sets funext ```
diff --git a/src/species.lagda.md b/src/species.lagda.md index c36d98ea52..35e8d68e99 100644 --- a/src/species.lagda.md +++ b/src/species.lagda.md @@ -3,53 +3,58 @@ ## Modules in the species namespace ```agda -module species where +open import foundation.function-extensionality-axiom -open import species.cartesian-exponents-species-of-types public -open import species.cartesian-products-species-of-types public -open import species.cauchy-composition-species-of-types public -open import species.cauchy-composition-species-of-types-in-subuniverses public -open import species.cauchy-exponentials-species-of-types public -open import species.cauchy-exponentials-species-of-types-in-subuniverses public -open import species.cauchy-products-species-of-types public -open import species.cauchy-products-species-of-types-in-subuniverses public -open import species.cauchy-series-species-of-types public -open import species.cauchy-series-species-of-types-in-subuniverses public -open import species.composition-cauchy-series-species-of-types public -open import species.composition-cauchy-series-species-of-types-in-subuniverses public -open import species.coproducts-species-of-types public -open import species.coproducts-species-of-types-in-subuniverses public -open import species.cycle-index-series-species-of-types public -open import species.derivatives-species-of-types public -open import species.dirichlet-exponentials-species-of-types public -open import species.dirichlet-exponentials-species-of-types-in-subuniverses public -open import species.dirichlet-products-species-of-types public -open import species.dirichlet-products-species-of-types-in-subuniverses public -open import species.dirichlet-series-species-of-finite-inhabited-types public -open import species.dirichlet-series-species-of-types public -open import species.dirichlet-series-species-of-types-in-subuniverses public -open import species.equivalences-species-of-types public -open import species.equivalences-species-of-types-in-subuniverses public -open import species.exponentials-cauchy-series-of-types public -open import species.exponentials-cauchy-series-of-types-in-subuniverses public -open import species.hasse-weil-species public -open import species.morphisms-finite-species public -open import species.morphisms-species-of-types public -open import species.pointing-species-of-types public -open import species.precategory-of-finite-species public -open import species.products-cauchy-series-species-of-types public -open import species.products-cauchy-series-species-of-types-in-subuniverses public -open import species.products-dirichlet-series-species-of-finite-inhabited-types public -open import species.products-dirichlet-series-species-of-types public -open import species.products-dirichlet-series-species-of-types-in-subuniverses public -open import species.small-cauchy-composition-species-of-finite-inhabited-types public -open import species.small-cauchy-composition-species-of-types-in-subuniverses public -open import species.species-of-finite-inhabited-types public -open import species.species-of-finite-types public -open import species.species-of-inhabited-types public -open import species.species-of-types public -open import species.species-of-types-in-subuniverses public -open import species.unit-cauchy-composition-species-of-types public -open import species.unit-cauchy-composition-species-of-types-in-subuniverses public -open import species.unlabeled-structures-species public +module + species + (funext : function-extensionality) + where + +open import species.cartesian-exponents-species-of-types funext public +open import species.cartesian-products-species-of-types funext public +open import species.cauchy-composition-species-of-types funext public +open import species.cauchy-composition-species-of-types-in-subuniverses funext public +open import species.cauchy-exponentials-species-of-types funext public +open import species.cauchy-exponentials-species-of-types-in-subuniverses funext public +open import species.cauchy-products-species-of-types funext public +open import species.cauchy-products-species-of-types-in-subuniverses funext public +open import species.cauchy-series-species-of-types funext public +open import species.cauchy-series-species-of-types-in-subuniverses funext public +open import species.composition-cauchy-series-species-of-types funext public +open import species.composition-cauchy-series-species-of-types-in-subuniverses funext public +open import species.coproducts-species-of-types funext public +open import species.coproducts-species-of-types-in-subuniverses funext public +open import species.cycle-index-series-species-of-types funext public +open import species.derivatives-species-of-types funext public +open import species.dirichlet-exponentials-species-of-types funext public +open import species.dirichlet-exponentials-species-of-types-in-subuniverses funext public +open import species.dirichlet-products-species-of-types funext public +open import species.dirichlet-products-species-of-types-in-subuniverses funext public +open import species.dirichlet-series-species-of-finite-inhabited-types funext public +open import species.dirichlet-series-species-of-types funext public +open import species.dirichlet-series-species-of-types-in-subuniverses funext public +open import species.equivalences-species-of-types funext public +open import species.equivalences-species-of-types-in-subuniverses funext public +open import species.exponentials-cauchy-series-of-types funext public +open import species.exponentials-cauchy-series-of-types-in-subuniverses funext public +open import species.hasse-weil-species funext public +open import species.morphisms-finite-species funext public +open import species.morphisms-species-of-types funext public +open import species.pointing-species-of-types funext public +open import species.precategory-of-finite-species funext public +open import species.products-cauchy-series-species-of-types funext public +open import species.products-cauchy-series-species-of-types-in-subuniverses funext public +open import species.products-dirichlet-series-species-of-finite-inhabited-types funext public +open import species.products-dirichlet-series-species-of-types funext public +open import species.products-dirichlet-series-species-of-types-in-subuniverses funext public +open import species.small-cauchy-composition-species-of-finite-inhabited-types funext public +open import species.small-cauchy-composition-species-of-types-in-subuniverses funext public +open import species.species-of-finite-inhabited-types funext public +open import species.species-of-finite-types funext public +open import species.species-of-inhabited-types funext public +open import species.species-of-types funext public +open import species.species-of-types-in-subuniverses funext public +open import species.unit-cauchy-composition-species-of-types funext public +open import species.unit-cauchy-composition-species-of-types-in-subuniverses funext public +open import species.unlabeled-structures-species funext public ``` diff --git a/src/species/cartesian-exponents-species-of-types.lagda.md b/src/species/cartesian-exponents-species-of-types.lagda.md index 8f07241384..cd335ba1b7 100644 --- a/src/species/cartesian-exponents-species-of-types.lagda.md +++ b/src/species/cartesian-exponents-species-of-types.lagda.md @@ -1,7 +1,12 @@ # Cartesian exponents of species ```agda -module species.cartesian-exponents-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.cartesian-exponents-species-of-types + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module species.cartesian-exponents-species-of-types where ```agda open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/cartesian-products-species-of-types.lagda.md b/src/species/cartesian-products-species-of-types.lagda.md index 60e524d6b4..02d73fcc99 100644 --- a/src/species/cartesian-products-species-of-types.lagda.md +++ b/src/species/cartesian-products-species-of-types.lagda.md @@ -1,21 +1,26 @@ # Cartesian products of species of types ```agda -module species.cartesian-products-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.cartesian-products-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.universal-property-dependent-pair-types +open import foundation.cartesian-product-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import species.cartesian-exponents-species-of-types -open import species.morphisms-species-of-types -open import species.species-of-types +open import species.cartesian-exponents-species-of-types funext +open import species.morphisms-species-of-types funext +open import species.species-of-types funext ```
diff --git a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md index d3642b399f..8686388d7e 100644 --- a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -1,41 +1,46 @@ # Cauchy composition of species of types in a subuniverse ```agda -module species.cauchy-composition-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.cauchy-composition-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.relaxed-sigma-decompositions -open import foundation.sigma-closed-subuniverses -open import foundation.sigma-decomposition-subuniverse -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.relaxed-sigma-decompositions funext +open import foundation.sigma-closed-subuniverses funext +open import foundation.sigma-decomposition-subuniverse funext +open import foundation.subuniverses funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.species-of-types-in-subuniverses -open import species.unit-cauchy-composition-species-of-types -open import species.unit-cauchy-composition-species-of-types-in-subuniverses +open import species.cauchy-composition-species-of-types funext +open import species.species-of-types-in-subuniverses funext +open import species.unit-cauchy-composition-species-of-types funext +open import species.unit-cauchy-composition-species-of-types funext-in-subuniverses ```
diff --git a/src/species/cauchy-composition-species-of-types.lagda.md b/src/species/cauchy-composition-species-of-types.lagda.md index 05943435c9..6539d0e6ac 100644 --- a/src/species/cauchy-composition-species-of-types.lagda.md +++ b/src/species/cauchy-composition-species-of-types.lagda.md @@ -1,35 +1,41 @@ # Cauchy composition of species of types ```agda -module species.cauchy-composition-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.cauchy-composition-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.discrete-relaxed-sigma-decompositions -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.relaxed-sigma-decompositions -open import foundation.trivial-relaxed-sigma-decompositions +open import foundation.dependent-universal-property-equivalences funext +open import foundation.discrete-relaxed-sigma-decompositions funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.relaxed-sigma-decompositions funext +open import foundation.trivial-relaxed-sigma-decompositions funext open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-arithmetic-dependent-function-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.univalence -open import foundation.universal-property-dependent-pair-types +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.univalence funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import species.species-of-types -open import species.unit-cauchy-composition-species-of-types +open import species.species-of-types funext +open import species.unit-cauchy-composition-species-of-types funext ```
diff --git a/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md index a5d3b8b486..388b504def 100644 --- a/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md @@ -1,40 +1,45 @@ # Cauchy exponentials of species of types in a subuniverse ```agda -module species.cauchy-exponentials-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.cauchy-exponentials-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-decompositions funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.propositions -open import foundation.relaxed-sigma-decompositions -open import foundation.sigma-closed-subuniverses -open import foundation.sigma-decomposition-subuniverse -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.propositions funext +open import foundation.relaxed-sigma-decompositions funext +open import foundation.sigma-closed-subuniverses funext +open import foundation.sigma-decomposition-subuniverse funext +open import foundation.subuniverses funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import species.cauchy-composition-species-of-types-in-subuniverses -open import species.cauchy-exponentials-species-of-types -open import species.cauchy-products-species-of-types-in-subuniverses -open import species.coproducts-species-of-types -open import species.coproducts-species-of-types-in-subuniverses -open import species.species-of-types-in-subuniverses +open import species.cauchy-composition-species-of-types-in-subuniverses funext +open import species.cauchy-exponentials-species-of-types funext +open import species.cauchy-products-species-of-types-in-subuniverses funext +open import species.coproducts-species-of-types funext +open import species.coproducts-species-of-types funext-in-subuniverses +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/cauchy-exponentials-species-of-types.lagda.md b/src/species/cauchy-exponentials-species-of-types.lagda.md index 0a4e3d7d9c..b2dd239580 100644 --- a/src/species/cauchy-exponentials-species-of-types.lagda.md +++ b/src/species/cauchy-exponentials-species-of-types.lagda.md @@ -1,36 +1,41 @@ # Cauchy exponentials of species of types ```agda -module species.cauchy-exponentials-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.cauchy-exponentials-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.arithmetic-law-coproduct-and-sigma-decompositions -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions -open import foundation.dependent-binomial-theorem +open import foundation.arithmetic-law-coproduct-and-sigma-decompositions funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-decompositions funext +open import foundation.dependent-binomial-theorem funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.relaxed-sigma-decompositions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.relaxed-sigma-decompositions funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.cauchy-products-species-of-types -open import species.coproducts-species-of-types -open import species.equivalences-species-of-types -open import species.species-of-types +open import species.cauchy-composition-species-of-types funext +open import species.cauchy-products-species-of-types funext +open import species.coproducts-species-of-types funext +open import species.equivalences-species-of-types funext +open import species.species-of-types funext ```
diff --git a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md index dc5f62299c..e3e23f69d6 100644 --- a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md @@ -1,34 +1,39 @@ # Cauchy products of species of types in a subuniverse ```agda -module species.cauchy-products-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.cauchy-products-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions -open import foundation.coproduct-decompositions-subuniverse -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-decompositions funext +open import foundation.coproduct-decompositions funext-subuniverse +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.subuniverses +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subuniverses funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import species.cauchy-products-species-of-types -open import species.species-of-types-in-subuniverses +open import species.cauchy-products-species-of-types funext +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/cauchy-products-species-of-types.lagda.md b/src/species/cauchy-products-species-of-types.lagda.md index 1d4560f78f..3c778bb522 100644 --- a/src/species/cauchy-products-species-of-types.lagda.md +++ b/src/species/cauchy-products-species-of-types.lagda.md @@ -1,18 +1,23 @@ # Cauchy products of species of types ```agda -module species.cauchy-products-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.cauchy-products-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions +open import foundation.cartesian-product-types funext +open import foundation.coproduct-decompositions funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md index 4e9a36c29a..9c73385dc2 100644 --- a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -1,26 +1,31 @@ # Cauchy series of species of types in a subuniverse ```agda -module species.cauchy-series-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.cauchy-series-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.postcomposition-functions -open import foundation.propositions -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext +open import foundation.postcomposition-functions funext +open import foundation.propositions funext +open import foundation.subuniverses funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import species.cauchy-series-species-of-types -open import species.species-of-types-in-subuniverses +open import species.cauchy-series-species-of-types funext +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/cauchy-series-species-of-types.lagda.md b/src/species/cauchy-series-species-of-types.lagda.md index a7a7a35a51..aa420f1ccc 100644 --- a/src/species/cauchy-series-species-of-types.lagda.md +++ b/src/species/cauchy-series-species-of-types.lagda.md @@ -1,21 +1,26 @@ # Cauchy series of species of types ```agda -module species.cauchy-series-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.cauchy-series-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.postcomposition-functions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.postcomposition-functions funext open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md index e0eb8cc904..b4845f33c2 100644 --- a/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -1,24 +1,29 @@ # Composition of Cauchy series of species of types in subuniverses ```agda -module species.composition-cauchy-series-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.composition-cauchy-series-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.global-subuniverses -open import foundation.sigma-closed-subuniverses -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.global-subuniverses funext +open import foundation.sigma-closed-subuniverses funext +open import foundation.subuniverses funext open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.cauchy-composition-species-of-types-in-subuniverses -open import species.cauchy-series-species-of-types -open import species.cauchy-series-species-of-types-in-subuniverses -open import species.composition-cauchy-series-species-of-types -open import species.species-of-types-in-subuniverses +open import species.cauchy-composition-species-of-types funext +open import species.cauchy-composition-species-of-types funext-in-subuniverses +open import species.cauchy-series-species-of-types funext +open import species.cauchy-series-species-of-types funext-in-subuniverses +open import species.composition-cauchy-series-species-of-types funext +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/composition-cauchy-series-species-of-types.lagda.md b/src/species/composition-cauchy-series-species-of-types.lagda.md index 729af0a56f..f74867851e 100644 --- a/src/species/composition-cauchy-series-species-of-types.lagda.md +++ b/src/species/composition-cauchy-series-species-of-types.lagda.md @@ -1,28 +1,33 @@ # Composition of Cauchy series of species of types ```agda -module species.composition-cauchy-series-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.composition-cauchy-series-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.univalence -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-dependent-pair-types +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.univalence funext +open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.cauchy-series-species-of-types -open import species.species-of-types +open import species.cauchy-composition-species-of-types funext +open import species.cauchy-series-species-of-types funext +open import species.species-of-types funext ```
diff --git a/src/species/coproducts-species-of-types-in-subuniverses.lagda.md b/src/species/coproducts-species-of-types-in-subuniverses.lagda.md index 2900441e71..a2cc54e8a5 100644 --- a/src/species/coproducts-species-of-types-in-subuniverses.lagda.md +++ b/src/species/coproducts-species-of-types-in-subuniverses.lagda.md @@ -1,24 +1,29 @@ # Coproducts of species of types in subuniverses ```agda -module species.coproducts-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.coproducts-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.subuniverses funext open import foundation.universe-levels -open import species.coproducts-species-of-types -open import species.species-of-types-in-subuniverses +open import species.coproducts-species-of-types funext +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/coproducts-species-of-types.lagda.md b/src/species/coproducts-species-of-types.lagda.md index b38a5e44ee..b37ad6b34e 100644 --- a/src/species/coproducts-species-of-types.lagda.md +++ b/src/species/coproducts-species-of-types.lagda.md @@ -1,22 +1,27 @@ # Coproducts of species of types ```agda -module species.coproducts-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.coproducts-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.type-theoretic-principle-of-choice -open import foundation.universal-property-coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.type-theoretic-principle-of-choice funext +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels -open import species.morphisms-species-of-types -open import species.species-of-types +open import species.morphisms-species-of-types funext +open import species.species-of-types funext ```
diff --git a/src/species/cycle-index-series-species-of-types.lagda.md b/src/species/cycle-index-series-species-of-types.lagda.md index 36fe229ae9..874f031816 100644 --- a/src/species/cycle-index-series-species-of-types.lagda.md +++ b/src/species/cycle-index-series-species-of-types.lagda.md @@ -1,7 +1,12 @@ # Cycle index series of species ```agda -module species.cycle-index-series-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.cycle-index-series-species-of-types + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.cyclic-finite-types +open import univalent-combinatorics.cyclic-finite-types funext ```
diff --git a/src/species/derivatives-species-of-types.lagda.md b/src/species/derivatives-species-of-types.lagda.md index 089dca1f20..4d714901e7 100644 --- a/src/species/derivatives-species-of-types.lagda.md +++ b/src/species/derivatives-species-of-types.lagda.md @@ -1,17 +1,22 @@ # Derivatives of species ```agda -module species.derivatives-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.derivatives-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.unit-type open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md index caf7c99d4d..ab945e06e9 100644 --- a/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md @@ -1,36 +1,41 @@ # Dirichlet exponentials of species of types in a subuniverse ```agda -module species.dirichlet-exponentials-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.dirichlet-exponentials-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.pi-decompositions -open import foundation.pi-decompositions-subuniverse +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.pi-decompositions funext +open import foundation.pi-decompositions funext-subuniverse open import foundation.product-decompositions -open import foundation.propositions -open import foundation.subuniverses +open import foundation.propositions funext +open import foundation.subuniverses funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import species.coproducts-species-of-types -open import species.coproducts-species-of-types-in-subuniverses -open import species.dirichlet-exponentials-species-of-types -open import species.dirichlet-products-species-of-types-in-subuniverses -open import species.species-of-types-in-subuniverses +open import species.coproducts-species-of-types funext +open import species.coproducts-species-of-types funext-in-subuniverses +open import species.dirichlet-exponentials-species-of-types funext +open import species.dirichlet-products-species-of-types-in-subuniverses funext +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/dirichlet-exponentials-species-of-types.lagda.md b/src/species/dirichlet-exponentials-species-of-types.lagda.md index 4a1ac22104..ab3b1a07a5 100644 --- a/src/species/dirichlet-exponentials-species-of-types.lagda.md +++ b/src/species/dirichlet-exponentials-species-of-types.lagda.md @@ -1,34 +1,39 @@ # Dirichlet exponentials of a species of types ```agda -module species.dirichlet-exponentials-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.dirichlet-exponentials-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.arithmetic-law-product-and-pi-decompositions -open import foundation.cartesian-product-types -open import foundation.coproduct-decompositions -open import foundation.dependent-binomial-theorem +open import foundation.arithmetic-law-product-and-pi-decompositions funext +open import foundation.cartesian-product-types funext +open import foundation.coproduct-decompositions funext +open import foundation.dependent-binomial-theorem funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.pi-decompositions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.pi-decompositions funext open import foundation.product-decompositions open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import species.coproducts-species-of-types -open import species.dirichlet-products-species-of-types -open import species.equivalences-species-of-types -open import species.species-of-types +open import species.coproducts-species-of-types funext +open import species.dirichlet-products-species-of-types funext +open import species.equivalences-species-of-types funext +open import species.species-of-types funext ```
diff --git a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md index b2e6b43e7c..c05eaabfc0 100644 --- a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md @@ -1,34 +1,39 @@ # Dirichlet products of species of types in subuniverses ```agda -module species.dirichlet-products-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.dirichlet-products-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.product-decompositions -open import foundation.product-decompositions-subuniverse -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.subuniverses +open import foundation.product-decompositions-subuniverse funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.subuniverses funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import species.dirichlet-products-species-of-types -open import species.species-of-types-in-subuniverses +open import species.dirichlet-products-species-of-types funext +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/dirichlet-products-species-of-types.lagda.md b/src/species/dirichlet-products-species-of-types.lagda.md index ba7ab3e640..16108a12e8 100644 --- a/src/species/dirichlet-products-species-of-types.lagda.md +++ b/src/species/dirichlet-products-species-of-types.lagda.md @@ -1,18 +1,23 @@ # Dirichlet products of species of types ```agda -module species.dirichlet-products-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.dirichlet-products-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.product-decompositions open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md b/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md index d5d0a07c20..22f7e833c2 100644 --- a/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md +++ b/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md @@ -1,7 +1,12 @@ # Dirichlet series of species of finite inhabited types ```agda -module species.dirichlet-series-species-of-finite-inhabited-types where +open import foundation.function-extensionality-axiom + +module + species.dirichlet-series-species-of-finite-inhabited-types + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module species.dirichlet-series-species-of-finite-inhabited-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-finite-inhabited-types +open import species.species-of-finite-inhabited-types funext -open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types +open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.inhabited-finite-types funext ```
diff --git a/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md index 22ff7d6265..8cb57f62c4 100644 --- a/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md @@ -1,18 +1,23 @@ # Dirichlet series of species of types in subuniverses ```agda -module species.dirichlet-series-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.dirichlet-series-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.subuniverses +open import foundation.subuniverses funext open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/dirichlet-series-species-of-types.lagda.md b/src/species/dirichlet-series-species-of-types.lagda.md index a3e2595e36..64a77cd91c 100644 --- a/src/species/dirichlet-series-species-of-types.lagda.md +++ b/src/species/dirichlet-series-species-of-types.lagda.md @@ -1,17 +1,22 @@ # Dirichlet series of species of types ```agda -module species.dirichlet-series-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.dirichlet-series-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/equivalences-species-of-types-in-subuniverses.lagda.md b/src/species/equivalences-species-of-types-in-subuniverses.lagda.md index e2a0f54a3f..471813f816 100644 --- a/src/species/equivalences-species-of-types-in-subuniverses.lagda.md +++ b/src/species/equivalences-species-of-types-in-subuniverses.lagda.md @@ -1,18 +1,23 @@ # Equivalences of species of types in subuniverses ```agda -module species.equivalences-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.equivalences-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.subuniverses funext open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/equivalences-species-of-types.lagda.md b/src/species/equivalences-species-of-types.lagda.md index a0e35581a6..8e24168356 100644 --- a/src/species/equivalences-species-of-types.lagda.md +++ b/src/species/equivalences-species-of-types.lagda.md @@ -1,18 +1,23 @@ # Equivalences of species of types ```agda -module species.equivalences-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.equivalences-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types -open import foundation.univalence +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.univalence funext open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md b/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md index 4f1628ab45..356d4f4345 100644 --- a/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md +++ b/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md @@ -1,28 +1,33 @@ # Exponential of Cauchy series of species of types in subuniverses ```agda -module species.exponentials-cauchy-series-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.exponentials-cauchy-series-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.sigma-closed-subuniverses -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext +open import foundation.sigma-closed-subuniverses funext +open import foundation.subuniverses funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type open import foundation.universe-levels -open import species.cauchy-composition-species-of-types-in-subuniverses -open import species.cauchy-exponentials-species-of-types-in-subuniverses -open import species.cauchy-series-species-of-types-in-subuniverses -open import species.composition-cauchy-series-species-of-types-in-subuniverses -open import species.species-of-types-in-subuniverses +open import species.cauchy-composition-species-of-types-in-subuniverses funext +open import species.cauchy-exponentials-species-of-types-in-subuniverses funext +open import species.cauchy-series-species-of-types-in-subuniverses funext +open import species.composition-cauchy-series-species-of-types-in-subuniverses funext +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/exponentials-cauchy-series-of-types.lagda.md b/src/species/exponentials-cauchy-series-of-types.lagda.md index 39cbfbf9be..fd94d9755b 100644 --- a/src/species/exponentials-cauchy-series-of-types.lagda.md +++ b/src/species/exponentials-cauchy-series-of-types.lagda.md @@ -1,25 +1,30 @@ # Exponential of Cauchy series of species of types ```agda -module species.exponentials-cauchy-series-of-types where +open import foundation.function-extensionality-axiom + +module + species.exponentials-cauchy-series-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.cauchy-exponentials-species-of-types -open import species.cauchy-series-species-of-types -open import species.composition-cauchy-series-species-of-types -open import species.species-of-types +open import species.cauchy-composition-species-of-types funext +open import species.cauchy-exponentials-species-of-types funext +open import species.cauchy-series-species-of-types funext +open import species.composition-cauchy-series-species-of-types funext +open import species.species-of-types funext ```
diff --git a/src/species/hasse-weil-species.lagda.md b/src/species/hasse-weil-species.lagda.md index 4538f31367..a1d8cee721 100644 --- a/src/species/hasse-weil-species.lagda.md +++ b/src/species/hasse-weil-species.lagda.md @@ -1,20 +1,25 @@ # Hasse-Weil species ```agda -module species.hasse-weil-species where +open import foundation.function-extensionality-axiom + +module + species.hasse-weil-species + (funext : function-extensionality) + where ```
Imports ```agda -open import finite-algebra.commutative-finite-rings -open import finite-algebra.products-commutative-finite-rings +open import finite-algebra.commutative-finite-rings funext +open import finite-algebra.products-commutative-finite-rings funext -open import foundation.cartesian-product-types -open import foundation.equivalences +open import foundation.cartesian-product-types funext +open import foundation.equivalences funext open import foundation.universe-levels -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/species/morphisms-finite-species.lagda.md b/src/species/morphisms-finite-species.lagda.md index 52f2991b25..92b58f06ad 100644 --- a/src/species/morphisms-finite-species.lagda.md +++ b/src/species/morphisms-finite-species.lagda.md @@ -1,28 +1,33 @@ # Morphisms of finite species ```agda -module species.morphisms-finite-species where +open import foundation.function-extensionality-axiom + +module + species.morphisms-finite-species + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import species.species-of-finite-types +open import species.species-of-finite-types funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/species/morphisms-species-of-types.lagda.md b/src/species/morphisms-species-of-types.lagda.md index 713b51777c..e21ab35cbe 100644 --- a/src/species/morphisms-species-of-types.lagda.md +++ b/src/species/morphisms-species-of-types.lagda.md @@ -1,23 +1,28 @@ # Morphisms of species of types ```agda -module species.morphisms-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.morphisms-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/pointing-species-of-types.lagda.md b/src/species/pointing-species-of-types.lagda.md index 6761bb997f..ea7ff88b07 100644 --- a/src/species/pointing-species-of-types.lagda.md +++ b/src/species/pointing-species-of-types.lagda.md @@ -1,16 +1,21 @@ # Pointing of species of types ```agda -module species.pointing-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.pointing-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/precategory-of-finite-species.lagda.md b/src/species/precategory-of-finite-species.lagda.md index d2de76dfc8..c51432d6a4 100644 --- a/src/species/precategory-of-finite-species.lagda.md +++ b/src/species/precategory-of-finite-species.lagda.md @@ -1,18 +1,23 @@ # The precategory of finite species ```agda -module species.precategory-of-finite-species where +open import foundation.function-extensionality-axiom + +module + species.precategory-of-finite-species + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.large-precategories +open import category-theory.large-precategories funext open import foundation.universe-levels -open import species.morphisms-finite-species -open import species.species-of-finite-types +open import species.morphisms-finite-species funext +open import species.species-of-finite-types funext ```
diff --git a/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md index 946d2dd088..4633f412b4 100644 --- a/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -1,26 +1,31 @@ # Products of Cauchy series of species of types in subuniverses ```agda -module species.products-cauchy-series-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.products-cauchy-series-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.global-subuniverses -open import foundation.subuniverses +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.global-subuniverses funext +open import foundation.subuniverses funext open import foundation.universe-levels -open import species.cauchy-products-species-of-types -open import species.cauchy-products-species-of-types-in-subuniverses -open import species.cauchy-series-species-of-types -open import species.cauchy-series-species-of-types-in-subuniverses -open import species.products-cauchy-series-species-of-types -open import species.species-of-types-in-subuniverses +open import species.cauchy-products-species-of-types funext +open import species.cauchy-products-species-of-types funext-in-subuniverses +open import species.cauchy-series-species-of-types funext +open import species.cauchy-series-species-of-types funext-in-subuniverses +open import species.products-cauchy-series-species-of-types funext +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/products-cauchy-series-species-of-types.lagda.md b/src/species/products-cauchy-series-species-of-types.lagda.md index 347682538c..f466a8705c 100644 --- a/src/species/products-cauchy-series-species-of-types.lagda.md +++ b/src/species/products-cauchy-series-species-of-types.lagda.md @@ -1,27 +1,32 @@ # Products of Cauchy series of species of types ```agda -module species.products-cauchy-series-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.products-cauchy-series-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence -open import foundation.universal-property-coproduct-types +open import foundation.univalence funext +open import foundation.universal-property-coproduct-types funext open import foundation.universe-levels -open import species.cauchy-products-species-of-types -open import species.cauchy-series-species-of-types -open import species.species-of-types +open import species.cauchy-products-species-of-types funext +open import species.cauchy-series-species-of-types funext +open import species.species-of-types funext ```
diff --git a/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md b/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md index 26fac97788..188a806322 100644 --- a/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md +++ b/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md @@ -1,17 +1,22 @@ # Products of Dirichlet series of species of finite inhabited types ```agda -module species.products-dirichlet-series-species-of-finite-inhabited-types where +open import foundation.function-extensionality-axiom + +module + species.products-dirichlet-series-species-of-finite-inhabited-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.universe-levels -open import species.dirichlet-series-species-of-finite-inhabited-types -open import species.species-of-finite-inhabited-types +open import species.dirichlet-series-species-of-finite-inhabited-types funext +open import species.species-of-finite-inhabited-types funext ```
diff --git a/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md b/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md index 0618179c6c..67e447d388 100644 --- a/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md @@ -1,29 +1,34 @@ # Products of Dirichlet series of species of types in subuniverses ```agda -module species.products-dirichlet-series-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.products-dirichlet-series-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.global-subuniverses -open import foundation.homotopies -open import foundation.postcomposition-functions -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.global-subuniverses funext +open import foundation.homotopies funext +open import foundation.postcomposition-functions funext +open import foundation.subuniverses funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels -open import species.dirichlet-products-species-of-types-in-subuniverses -open import species.dirichlet-series-species-of-types-in-subuniverses -open import species.species-of-types-in-subuniverses +open import species.dirichlet-products-species-of-types-in-subuniverses funext +open import species.dirichlet-series-species-of-types-in-subuniverses funext +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/products-dirichlet-series-species-of-types.lagda.md b/src/species/products-dirichlet-series-species-of-types.lagda.md index 1b015bd412..cd625482e8 100644 --- a/src/species/products-dirichlet-series-species-of-types.lagda.md +++ b/src/species/products-dirichlet-series-species-of-types.lagda.md @@ -1,27 +1,32 @@ # Products of Dirichlet series of species of types ```agda -module species.products-dirichlet-series-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.products-dirichlet-series-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.postcomposition-functions +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.postcomposition-functions funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence -open import foundation.universal-property-cartesian-product-types +open import foundation.univalence funext +open import foundation.universal-property-cartesian-product-types funext open import foundation.universe-levels -open import species.dirichlet-products-species-of-types -open import species.dirichlet-series-species-of-types -open import species.species-of-types +open import species.dirichlet-products-species-of-types funext +open import species.dirichlet-series-species-of-types funext +open import species.species-of-types funext ```
diff --git a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md index 2b7b0202fd..c2cee7d1ae 100644 --- a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md +++ b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md @@ -3,41 +3,46 @@ ```agda {-# OPTIONS --lossy-unification #-} -module species.small-cauchy-composition-species-of-finite-inhabited-types where +open import foundation.function-extensionality-axiom + +module + species.small-cauchy-composition-species-of-finite-inhabited-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.decidable-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.relaxed-sigma-decompositions -open import foundation.sigma-closed-subuniverses -open import foundation.sigma-decomposition-subuniverse -open import foundation.subuniverses +open import foundation.contractible-types funext +open import foundation.decidable-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.relaxed-sigma-decompositions funext +open import foundation.sigma-closed-subuniverses funext +open import foundation.sigma-decomposition-subuniverse funext +open import foundation.subuniverses funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type open import foundation.universe-levels -open import species.small-cauchy-composition-species-of-types-in-subuniverses -open import species.species-of-finite-inhabited-types +open import species.small-cauchy-composition-species-of-types-in-subuniverses funext +open import species.species-of-finite-inhabited-types funext -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types -open import univalent-combinatorics.sigma-decompositions -open import univalent-combinatorics.small-types +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.inhabited-finite-types funext +open import univalent-combinatorics.sigma-decompositions funext +open import univalent-combinatorics.small-types funext ```
diff --git a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md index 22cb26f896..8b8d8645df 100644 --- a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -1,39 +1,44 @@ # Small Cauchy composition of species types in subuniverses ```agda -module species.small-cauchy-composition-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.small-cauchy-composition-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.relaxed-sigma-decompositions -open import foundation.sigma-closed-subuniverses -open import foundation.sigma-decomposition-subuniverse -open import foundation.small-types -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.relaxed-sigma-decompositions funext +open import foundation.sigma-closed-subuniverses funext +open import foundation.sigma-decomposition-subuniverse funext +open import foundation.small-types funext +open import foundation.subuniverses funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import species.cauchy-composition-species-of-types -open import species.species-of-types-in-subuniverses -open import species.unit-cauchy-composition-species-of-types +open import species.cauchy-composition-species-of-types funext +open import species.species-of-types-in-subuniverses funext +open import species.unit-cauchy-composition-species-of-types funext ```
diff --git a/src/species/species-of-finite-inhabited-types.lagda.md b/src/species/species-of-finite-inhabited-types.lagda.md index fa9ba4bc14..01a25fa4ee 100644 --- a/src/species/species-of-finite-inhabited-types.lagda.md +++ b/src/species/species-of-finite-inhabited-types.lagda.md @@ -1,7 +1,12 @@ # Species of finite inhabited types ```agda -module species.species-of-finite-inhabited-types where +open import foundation.function-extensionality-axiom + +module + species.species-of-finite-inhabited-types + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module species.species-of-finite-inhabited-types where ```agda open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.inhabited-finite-types funext ```
diff --git a/src/species/species-of-finite-types.lagda.md b/src/species/species-of-finite-types.lagda.md index 24eb4eb3b3..fb9d783a82 100644 --- a/src/species/species-of-finite-types.lagda.md +++ b/src/species/species-of-finite-types.lagda.md @@ -1,7 +1,12 @@ # Species of finite types ```agda -module species.species-of-finite-types where +open import foundation.function-extensionality-axiom + +module + species.species-of-finite-types + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module species.species-of-finite-types where ```agda open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/species/species-of-inhabited-types.lagda.md b/src/species/species-of-inhabited-types.lagda.md index 92c51b4adf..0c4f53809b 100644 --- a/src/species/species-of-inhabited-types.lagda.md +++ b/src/species/species-of-inhabited-types.lagda.md @@ -1,17 +1,22 @@ # Species of inhabited types ```agda -module species.species-of-inhabited-types where +open import foundation.function-extensionality-axiom + +module + species.species-of-inhabited-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.inhabited-types +open import foundation.inhabited-types funext open import foundation.unit-type open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/species-of-types-in-subuniverses.lagda.md b/src/species/species-of-types-in-subuniverses.lagda.md index 1ef1c85fec..4421d6d350 100644 --- a/src/species/species-of-types-in-subuniverses.lagda.md +++ b/src/species/species-of-types-in-subuniverses.lagda.md @@ -1,23 +1,28 @@ # Species of types in subuniverses ```agda -module species.species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositions -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositions funext +open import foundation.subuniverses funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/species-of-types.lagda.md b/src/species/species-of-types.lagda.md index e300981b9b..5e36e13616 100644 --- a/src/species/species-of-types.lagda.md +++ b/src/species/species-of-types.lagda.md @@ -1,16 +1,21 @@ # Species of types ```agda -module species.species-of-types where +open import foundation.function-extensionality-axiom + +module + species.species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.equivalences +open import foundation.cartesian-product-types funext +open import foundation.equivalences funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels ``` diff --git a/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md index 030f8440d0..b068d199c2 100644 --- a/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -1,19 +1,24 @@ # The unit of Cauchy composition of species of types in subuniverses ```agda -module species.unit-cauchy-composition-species-of-types-in-subuniverses where +open import foundation.function-extensionality-axiom + +module + species.unit-cauchy-composition-species-of-types-in-subuniverses + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.global-subuniverses -open import foundation.subuniverses +open import foundation.global-subuniverses funext +open import foundation.subuniverses funext open import foundation.universe-levels -open import species.species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses funext ```
diff --git a/src/species/unit-cauchy-composition-species-of-types.lagda.md b/src/species/unit-cauchy-composition-species-of-types.lagda.md index 15884d5b45..8667d9812c 100644 --- a/src/species/unit-cauchy-composition-species-of-types.lagda.md +++ b/src/species/unit-cauchy-composition-species-of-types.lagda.md @@ -1,16 +1,21 @@ # The unit of Cauchy composition of types ```agda -module species.unit-cauchy-composition-species-of-types where +open import foundation.function-extensionality-axiom + +module + species.unit-cauchy-composition-species-of-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext ```
diff --git a/src/species/unlabeled-structures-species.lagda.md b/src/species/unlabeled-structures-species.lagda.md index 2ed30b8522..cf4e2d290a 100644 --- a/src/species/unlabeled-structures-species.lagda.md +++ b/src/species/unlabeled-structures-species.lagda.md @@ -1,7 +1,12 @@ # Unlabeled structures of finite species ```agda -module species.unlabeled-structures-species where +open import foundation.function-extensionality-axiom + +module + species.unlabeled-structures-species + (funext : function-extensionality) + where ```
Imports @@ -12,9 +17,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-types +open import species.species-of-types funext -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/structured-types.lagda.md b/src/structured-types.lagda.md index 081ebda794..d2f064bebf 100644 --- a/src/structured-types.lagda.md +++ b/src/structured-types.lagda.md @@ -7,83 +7,88 @@ ## Modules in the structured types namespace ```agda -module structured-types where +open import foundation.function-extensionality-axiom -open import structured-types.cartesian-products-types-equipped-with-endomorphisms public -open import structured-types.central-h-spaces public -open import structured-types.commuting-squares-of-pointed-homotopies public -open import structured-types.commuting-squares-of-pointed-maps public -open import structured-types.commuting-triangles-of-pointed-maps public -open import structured-types.conjugation-pointed-types public -open import structured-types.constant-pointed-maps public -open import structured-types.contractible-pointed-types public -open import structured-types.cyclic-types public -open import structured-types.dependent-products-h-spaces public +module + structured-types + (funext : function-extensionality) + where + +open import structured-types.cartesian-products-types-equipped-with-endomorphisms funext public +open import structured-types.central-h-spaces funext public +open import structured-types.commuting-squares-of-pointed-homotopies funext public +open import structured-types.commuting-squares-of-pointed-maps funext public +open import structured-types.commuting-triangles-of-pointed-maps funext public +open import structured-types.conjugation-pointed-types funext public +open import structured-types.constant-pointed-maps funext public +open import structured-types.contractible-pointed-types funext public +open import structured-types.cyclic-types funext public +open import structured-types.dependent-products-h-spaces funext public open import structured-types.dependent-products-pointed-types public -open import structured-types.dependent-products-wild-monoids public -open import structured-types.dependent-types-equipped-with-automorphisms public -open import structured-types.equivalences-h-spaces public -open import structured-types.equivalences-pointed-arrows public -open import structured-types.equivalences-types-equipped-with-automorphisms public -open import structured-types.equivalences-types-equipped-with-endomorphisms public -open import structured-types.faithful-pointed-maps public -open import structured-types.fibers-of-pointed-maps public -open import structured-types.finite-multiplication-magmas public -open import structured-types.function-h-spaces public -open import structured-types.function-magmas public -open import structured-types.function-wild-monoids public -open import structured-types.h-spaces public -open import structured-types.initial-pointed-type-equipped-with-automorphism public -open import structured-types.involutive-type-of-h-space-structures public -open import structured-types.involutive-types public -open import structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms public -open import structured-types.iterated-pointed-cartesian-product-types public -open import structured-types.magmas public -open import structured-types.mere-equivalences-types-equipped-with-endomorphisms public -open import structured-types.morphisms-h-spaces public -open import structured-types.morphisms-magmas public -open import structured-types.morphisms-pointed-arrows public -open import structured-types.morphisms-twisted-pointed-arrows public -open import structured-types.morphisms-types-equipped-with-automorphisms public -open import structured-types.morphisms-types-equipped-with-endomorphisms public -open import structured-types.morphisms-wild-monoids public -open import structured-types.noncoherent-h-spaces public -open import structured-types.opposite-pointed-spans public -open import structured-types.pointed-2-homotopies public -open import structured-types.pointed-cartesian-product-types public -open import structured-types.pointed-dependent-functions public +open import structured-types.dependent-products-wild-monoids funext public +open import structured-types.dependent-types-equipped-with-automorphisms funext public +open import structured-types.equivalences-h-spaces funext public +open import structured-types.equivalences-pointed-arrows funext public +open import structured-types.equivalences-types-equipped-with-automorphisms funext public +open import structured-types.equivalences-types-equipped-with-endomorphisms funext public +open import structured-types.faithful-pointed-maps funext public +open import structured-types.fibers-of-pointed-maps funext public +open import structured-types.finite-multiplication-magmas funext public +open import structured-types.function-h-spaces funext public +open import structured-types.function-magmas funext public +open import structured-types.function-wild-monoids funext public +open import structured-types.h-spaces funext public +open import structured-types.initial-pointed-type-equipped-with-automorphism funext public +open import structured-types.involutive-type-of-h-space-structures funext public +open import structured-types.involutive-types funext public +open import structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms funext public +open import structured-types.iterated-pointed-cartesian-product-types funext public +open import structured-types.magmas funext public +open import structured-types.mere-equivalences-types-equipped-with-endomorphisms funext public +open import structured-types.morphisms-h-spaces funext public +open import structured-types.morphisms-magmas funext public +open import structured-types.morphisms-pointed-arrows funext public +open import structured-types.morphisms-twisted-pointed-arrows funext public +open import structured-types.morphisms-types-equipped-with-automorphisms funext public +open import structured-types.morphisms-types-equipped-with-endomorphisms funext public +open import structured-types.morphisms-wild-monoids funext public +open import structured-types.noncoherent-h-spaces funext public +open import structured-types.opposite-pointed-spans funext public +open import structured-types.pointed-2-homotopies funext public +open import structured-types.pointed-cartesian-product-types funext public +open import structured-types.pointed-dependent-functions funext public open import structured-types.pointed-dependent-pair-types public -open import structured-types.pointed-equivalences public +open import structured-types.pointed-equivalences funext public open import structured-types.pointed-families-of-types public -open import structured-types.pointed-homotopies public -open import structured-types.pointed-isomorphisms public -open import structured-types.pointed-maps public -open import structured-types.pointed-retractions public -open import structured-types.pointed-sections public -open import structured-types.pointed-span-diagrams public -open import structured-types.pointed-spans public +open import structured-types.pointed-homotopies funext public +open import structured-types.pointed-isomorphisms funext public +open import structured-types.pointed-maps funext public +open import structured-types.pointed-retractions funext public +open import structured-types.pointed-sections funext public +open import structured-types.pointed-span-diagrams funext public +open import structured-types.pointed-spans funext public open import structured-types.pointed-types public -open import structured-types.pointed-types-equipped-with-automorphisms public -open import structured-types.pointed-unit-type public -open import structured-types.pointed-universal-property-contractible-types public -open import structured-types.postcomposition-pointed-maps public -open import structured-types.precomposition-pointed-maps public -open import structured-types.sets-equipped-with-automorphisms public -open import structured-types.small-pointed-types public -open import structured-types.symmetric-elements-involutive-types public -open import structured-types.symmetric-h-spaces public -open import structured-types.transposition-pointed-span-diagrams public -open import structured-types.types-equipped-with-automorphisms public -open import structured-types.types-equipped-with-endomorphisms public -open import structured-types.uniform-pointed-homotopies public -open import structured-types.universal-property-pointed-equivalences public +open import structured-types.pointed-types-equipped-with-automorphisms funext public +open import structured-types.pointed-unit-type funext public +open import structured-types.pointed-universal-property-contractible-types funext public +open import structured-types.postcomposition-pointed-maps funext public +open import structured-types.precomposition-pointed-maps funext public +open import structured-types.sets-equipped-with-automorphisms funext public +open import structured-types.small-pointed-types funext public +open import structured-types.symmetric-elements-involutive-types funext public +open import structured-types.symmetric-h-spaces funext public +open import structured-types.transposition-pointed-span-diagrams funext public +open import structured-types.types-equipped-with-automorphisms funext public +open import structured-types.types-equipped-with-endomorphisms funext public +open import structured-types.uniform-pointed-homotopies funext public +open import structured-types.universal-property-pointed-equivalences funext public open import structured-types.unpointed-maps public -open import structured-types.whiskering-pointed-2-homotopies-concatenation public -open import structured-types.whiskering-pointed-homotopies-composition public -open import structured-types.wild-category-of-pointed-types public -open import structured-types.wild-groups public -open import structured-types.wild-loops public -open import structured-types.wild-monoids public -open import structured-types.wild-quasigroups public -open import structured-types.wild-semigroups public +open import structured-types.whiskering-pointed-2-homotopies-concatenation funext public +open import structured-types.whiskering-pointed-homotopies-composition funext public +open import structured-types.wild-category-of-pointed-types funext public +open import structured-types.wild-groups funext public +open import structured-types.wild-loops funext public +open import structured-types.wild-monoids funext public +open import structured-types.wild-quasigroups funext public +open import structured-types.wild-semigroups funext public ``` diff --git a/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md index e8593cf7cf..7c06bfbf56 100644 --- a/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md @@ -1,18 +1,23 @@ # Cartesian products of types equipped with endomorphisms ```agda -module structured-types.cartesian-products-types-equipped-with-endomorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.cartesian-products-types-equipped-with-endomorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-cartesian-product-types funext open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext ```
diff --git a/src/structured-types/central-h-spaces.lagda.md b/src/structured-types/central-h-spaces.lagda.md index c0ea967513..0039b94c9f 100644 --- a/src/structured-types/central-h-spaces.lagda.md +++ b/src/structured-types/central-h-spaces.lagda.md @@ -1,13 +1,18 @@ # Central H-spaces ```agda -module structured-types.central-h-spaces where +open import foundation.function-extensionality-axiom + +module + structured-types.central-h-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels open import structured-types.pointed-types diff --git a/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md b/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md index 0bd38407d8..377f09fc97 100644 --- a/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md +++ b/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md @@ -1,7 +1,12 @@ # Commuting squares of pointed homotopies ```agda -module structured-types.commuting-squares-of-pointed-homotopies where +open import foundation.function-extensionality-axiom + +module + structured-types.commuting-squares-of-pointed-homotopies + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module structured-types.commuting-squares-of-pointed-homotopies where ```agda open import foundation.universe-levels -open import structured-types.pointed-2-homotopies -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-2-homotopies funext +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies +open import structured-types.pointed-homotopies funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/commuting-squares-of-pointed-maps.lagda.md b/src/structured-types/commuting-squares-of-pointed-maps.lagda.md index ed8779ac44..6346fde801 100644 --- a/src/structured-types/commuting-squares-of-pointed-maps.lagda.md +++ b/src/structured-types/commuting-squares-of-pointed-maps.lagda.md @@ -1,25 +1,30 @@ # Commuting squares of pointed maps ```agda -module structured-types.commuting-squares-of-pointed-maps where +open import foundation.function-extensionality-axiom + +module + structured-types.commuting-squares-of-pointed-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.whiskering-pointed-homotopies-composition +open import structured-types.whiskering-pointed-homotopies-composition funext ```
diff --git a/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md b/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md index 34a14fabd0..fe4041fece 100644 --- a/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md +++ b/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md @@ -1,7 +1,12 @@ # Commuting triangles of pointed maps ```agda -module structured-types.commuting-triangles-of-pointed-maps where +open import foundation.function-extensionality-axiom + +module + structured-types.commuting-triangles-of-pointed-maps + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module structured-types.commuting-triangles-of-pointed-maps where ```agda open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.whiskering-pointed-homotopies-composition +open import structured-types.whiskering-pointed-homotopies-composition funext ```
diff --git a/src/structured-types/conjugation-pointed-types.lagda.md b/src/structured-types/conjugation-pointed-types.lagda.md index fb95e9ed66..a60f1c08d9 100644 --- a/src/structured-types/conjugation-pointed-types.lagda.md +++ b/src/structured-types/conjugation-pointed-types.lagda.md @@ -1,7 +1,12 @@ # Conjugation of pointed types ```agda -module structured-types.conjugation-pointed-types where +open import foundation.function-extensionality-axiom + +module + structured-types.conjugation-pointed-types + (funext : function-extensionality) + where ```
Imports @@ -9,18 +14,18 @@ module structured-types.conjugation-pointed-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.conjugation-loops -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.conjugation-loops funext +open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/structured-types/constant-pointed-maps.lagda.md b/src/structured-types/constant-pointed-maps.lagda.md index 327fb4e80a..0fce81e7ff 100644 --- a/src/structured-types/constant-pointed-maps.lagda.md +++ b/src/structured-types/constant-pointed-maps.lagda.md @@ -1,18 +1,23 @@ # Constant pointed maps ```agda -module structured-types.constant-pointed-maps where +open import foundation.function-extensionality-axiom + +module + structured-types.constant-pointed-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.constant-maps +open import foundation.constant-maps funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/contractible-pointed-types.lagda.md b/src/structured-types/contractible-pointed-types.lagda.md index 67d5b144e8..255e3d3930 100644 --- a/src/structured-types/contractible-pointed-types.lagda.md +++ b/src/structured-types/contractible-pointed-types.lagda.md @@ -1,14 +1,19 @@ # Contractible pointed types ```agda -module structured-types.contractible-pointed-types where +open import foundation.function-extensionality-axiom + +module + structured-types.contractible-pointed-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.propositions +open import foundation.contractible-types funext +open import foundation.propositions funext open import foundation.universe-levels open import structured-types.pointed-types diff --git a/src/structured-types/cyclic-types.lagda.md b/src/structured-types/cyclic-types.lagda.md index dcd59c7116..906df221eb 100644 --- a/src/structured-types/cyclic-types.lagda.md +++ b/src/structured-types/cyclic-types.lagda.md @@ -1,22 +1,27 @@ # Cyclic types ```agda -module structured-types.cyclic-types where +open import foundation.function-extensionality-axiom + +module + structured-types.cyclic-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext open import foundation.dependent-pair-types -open import foundation.iterating-automorphisms -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.surjective-maps +open import foundation.iterating-automorphisms funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import structured-types.sets-equipped-with-automorphisms +open import structured-types.sets-equipped-with-automorphisms funext ```
diff --git a/src/structured-types/dependent-products-h-spaces.lagda.md b/src/structured-types/dependent-products-h-spaces.lagda.md index 535481be7f..84afbe86e8 100644 --- a/src/structured-types/dependent-products-h-spaces.lagda.md +++ b/src/structured-types/dependent-products-h-spaces.lagda.md @@ -1,7 +1,12 @@ # Dependent products of H-spaces ```agda -module structured-types.dependent-products-h-spaces where +open import foundation.function-extensionality-axiom + +module + structured-types.dependent-products-h-spaces + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,14 @@ module structured-types.dependent-products-h-spaces where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.identity-types +open import foundation.function-extensionality funext + +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels open import structured-types.dependent-products-pointed-types -open import structured-types.h-spaces +open import structured-types.h-spaces funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/dependent-products-wild-monoids.lagda.md b/src/structured-types/dependent-products-wild-monoids.lagda.md index 183ccb58a5..f84c7fcf7d 100644 --- a/src/structured-types/dependent-products-wild-monoids.lagda.md +++ b/src/structured-types/dependent-products-wild-monoids.lagda.md @@ -1,7 +1,12 @@ # Dependent products of wild monoids ```agda -module structured-types.dependent-products-wild-monoids where +open import foundation.function-extensionality-axiom + +module + structured-types.dependent-products-wild-monoids + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,17 @@ module structured-types.dependent-products-wild-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-extensionality funext + +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.dependent-products-h-spaces -open import structured-types.h-spaces +open import structured-types.dependent-products-h-spaces funext +open import structured-types.h-spaces funext open import structured-types.pointed-types -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext ```
diff --git a/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md b/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md index 5cc34bb515..155f82ba02 100644 --- a/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md @@ -1,27 +1,32 @@ # Dependent types equipped with automorphisms ```agda -module structured-types.dependent-types-equipped-with-automorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.dependent-types-equipped-with-automorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels -open import structured-types.types-equipped-with-automorphisms +open import structured-types.types-equipped-with-automorphisms funext ```
diff --git a/src/structured-types/equivalences-h-spaces.lagda.md b/src/structured-types/equivalences-h-spaces.lagda.md index 3a8285ea5c..27d83b75f0 100644 --- a/src/structured-types/equivalences-h-spaces.lagda.md +++ b/src/structured-types/equivalences-h-spaces.lagda.md @@ -1,31 +1,36 @@ # Equivalences of H-spaces ```agda -module structured-types.equivalences-h-spaces where +open import foundation.function-extensionality-axiom + +module + structured-types.equivalences-h-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext -open import structured-types.h-spaces -open import structured-types.morphisms-h-spaces -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.h-spaces funext +open import structured-types.morphisms-h-spaces funext +open import structured-types.pointed-equivalences funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/equivalences-pointed-arrows.lagda.md b/src/structured-types/equivalences-pointed-arrows.lagda.md index 0d1aacbfd7..97b3a7d133 100644 --- a/src/structured-types/equivalences-pointed-arrows.lagda.md +++ b/src/structured-types/equivalences-pointed-arrows.lagda.md @@ -1,23 +1,28 @@ # Equivalences of pointed arrows ```agda -module structured-types.equivalences-pointed-arrows where +open import foundation.function-extensionality-axiom + +module + structured-types.equivalences-pointed-arrows + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.function-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.pointed-equivalences -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.commuting-squares-of-pointed-maps funext +open import structured-types.pointed-equivalences funext +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md b/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md index a9d7268372..55101f97bd 100644 --- a/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md @@ -1,26 +1,31 @@ # Equivalences of types equipped with automorphisms ```agda -module structured-types.equivalences-types-equipped-with-automorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.equivalences-types-equipped-with-automorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-endomorphisms -open import structured-types.morphisms-types-equipped-with-automorphisms -open import structured-types.types-equipped-with-automorphisms +open import structured-types.equivalences-types-equipped-with-endomorphisms funext +open import structured-types.morphisms-types-equipped-with-automorphisms funext +open import structured-types.types-equipped-with-automorphisms funext ```
diff --git a/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md index 3b8b45fb50..fe4ae4cfb3 100644 --- a/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md @@ -1,32 +1,37 @@ # Equivalences of types equipped with endomorphisms ```agda -module structured-types.equivalences-types-equipped-with-endomorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.equivalences-types-equipped-with-endomorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import structured-types.morphisms-types-equipped-with-endomorphisms -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.morphisms-types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms funext ```
diff --git a/src/structured-types/faithful-pointed-maps.lagda.md b/src/structured-types/faithful-pointed-maps.lagda.md index eeb654cf27..a88ec96450 100644 --- a/src/structured-types/faithful-pointed-maps.lagda.md +++ b/src/structured-types/faithful-pointed-maps.lagda.md @@ -1,18 +1,23 @@ # Faithful pointed maps ```agda -module structured-types.faithful-pointed-maps where +open import foundation.function-extensionality-axiom + +module + structured-types.faithful-pointed-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.faithful-maps -open import foundation.identity-types +open import foundation.faithful-maps funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/fibers-of-pointed-maps.lagda.md b/src/structured-types/fibers-of-pointed-maps.lagda.md index 3564027bd2..cdcaf5a39e 100644 --- a/src/structured-types/fibers-of-pointed-maps.lagda.md +++ b/src/structured-types/fibers-of-pointed-maps.lagda.md @@ -1,17 +1,22 @@ # Fibers of pointed maps ```agda -module structured-types.fibers-of-pointed-maps where +open import foundation.function-extensionality-axiom + +module + structured-types.fibers-of-pointed-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps +open import foundation.fibers-of-maps funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/finite-multiplication-magmas.lagda.md b/src/structured-types/finite-multiplication-magmas.lagda.md index 6c31a6bd9a..b7a529952e 100644 --- a/src/structured-types/finite-multiplication-magmas.lagda.md +++ b/src/structured-types/finite-multiplication-magmas.lagda.md @@ -1,7 +1,12 @@ # Finite multiplication in magmas ```agda -module structured-types.finite-multiplication-magmas where +open import foundation.function-extensionality-axiom + +module + structured-types.finite-multiplication-magmas + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module structured-types.finite-multiplication-magmas where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.coproduct-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/structured-types/function-h-spaces.lagda.md b/src/structured-types/function-h-spaces.lagda.md index 05b8a63e3c..67488bbb24 100644 --- a/src/structured-types/function-h-spaces.lagda.md +++ b/src/structured-types/function-h-spaces.lagda.md @@ -1,18 +1,23 @@ # Function H-spaces ```agda -module structured-types.function-h-spaces where +open import foundation.function-extensionality-axiom + +module + structured-types.function-h-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels -open import structured-types.dependent-products-h-spaces -open import structured-types.h-spaces +open import structured-types.dependent-products-h-spaces funext +open import structured-types.h-spaces funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/function-magmas.lagda.md b/src/structured-types/function-magmas.lagda.md index e5eef3f42a..d1d767239a 100644 --- a/src/structured-types/function-magmas.lagda.md +++ b/src/structured-types/function-magmas.lagda.md @@ -1,7 +1,12 @@ # Function magmas ```agda -module structured-types.function-magmas where +open import foundation.function-extensionality-axiom + +module + structured-types.function-magmas + (funext : function-extensionality) + where ```
Imports @@ -10,7 +15,7 @@ module structured-types.function-magmas where open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext ```
diff --git a/src/structured-types/function-wild-monoids.lagda.md b/src/structured-types/function-wild-monoids.lagda.md index 154a0e8116..079a8ec6a6 100644 --- a/src/structured-types/function-wild-monoids.lagda.md +++ b/src/structured-types/function-wild-monoids.lagda.md @@ -1,19 +1,24 @@ # Function wild monoids ```agda -module structured-types.function-wild-monoids where +open import foundation.function-extensionality-axiom + +module + structured-types.function-wild-monoids + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.dependent-products-wild-monoids -open import structured-types.h-spaces +open import structured-types.dependent-products-wild-monoids funext +open import structured-types.h-spaces funext open import structured-types.pointed-types -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext ```
diff --git a/src/structured-types/h-spaces.lagda.md b/src/structured-types/h-spaces.lagda.md index be217b8539..8cec45ccce 100644 --- a/src/structured-types/h-spaces.lagda.md +++ b/src/structured-types/h-spaces.lagda.md @@ -1,7 +1,12 @@ # H-spaces ```agda -module structured-types.h-spaces where +open import foundation.function-extensionality-axiom + +module + structured-types.h-spaces + (funext : function-extensionality) + where ```
Imports @@ -10,24 +15,25 @@ module structured-types.h-spaces where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.evaluation-functions -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import foundation-core.endomorphisms +open import foundation-core.endomorphisms funext -open import structured-types.magmas -open import structured-types.noncoherent-h-spaces -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.pointed-sections +open import structured-types.magmas funext +open import structured-types.noncoherent-h-spaces funext +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext +open import structured-types.pointed-sections funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md b/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md index cab4124961..2eceaeb464 100644 --- a/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md +++ b/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md @@ -1,7 +1,12 @@ # The initial pointed type equipped with an automorphism ```agda -module structured-types.initial-pointed-type-equipped-with-automorphism where +open import foundation.function-extensionality-axiom + +module + structured-types.initial-pointed-type-equipped-with-automorphism + (funext : function-extensionality) + where ```
Imports @@ -11,18 +16,18 @@ open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types -open import foundation.iterating-automorphisms -open import foundation.transposition-identifications-along-equivalences +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.iterating-automorphisms funext +open import foundation.transposition-identifications-along-equivalences funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-types-equipped-with-automorphisms +open import structured-types.pointed-types-equipped-with-automorphisms funext ```
diff --git a/src/structured-types/involutive-type-of-h-space-structures.lagda.md b/src/structured-types/involutive-type-of-h-space-structures.lagda.md index a9109305c2..efe2dc3aa8 100644 --- a/src/structured-types/involutive-type-of-h-space-structures.lagda.md +++ b/src/structured-types/involutive-type-of-h-space-structures.lagda.md @@ -1,7 +1,12 @@ # The involutive type of H-space structures on a pointed type ```agda -module structured-types.involutive-type-of-h-space-structures where +open import foundation.function-extensionality-axiom + +module + structured-types.involutive-type-of-h-space-structures + (funext : function-extensionality) + where ```
Imports @@ -9,25 +14,25 @@ module structured-types.involutive-type-of-h-space-structures where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.constant-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.symmetric-identity-types -open import foundation.torsorial-type-families +open import foundation.symmetric-identity-types funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import structured-types.constant-pointed-maps +open import structured-types.constant-pointed-maps funext open import structured-types.pointed-types -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext ```
diff --git a/src/structured-types/involutive-types.lagda.md b/src/structured-types/involutive-types.lagda.md index 14c1459d5d..af59a2318f 100644 --- a/src/structured-types/involutive-types.lagda.md +++ b/src/structured-types/involutive-types.lagda.md @@ -1,17 +1,22 @@ # Involutive types ```agda -module structured-types.involutive-types where +open import foundation.function-extensionality-axiom + +module + structured-types.involutive-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext ```
diff --git a/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md index 58ed426a9e..1f15dde562 100644 --- a/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md @@ -13,8 +13,8 @@ open import foundation.universe-levels open import lists.lists -open import structured-types.cartesian-products-types-equipped-with-endomorphisms -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.cartesian-products-types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms funext ```
diff --git a/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md b/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md index 305993ecf4..b2f70f218f 100644 --- a/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md +++ b/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md @@ -1,20 +1,25 @@ # Iterated cartesian products of pointed types ```agda -module structured-types.iterated-pointed-cartesian-product-types where +open import foundation.function-extensionality-axiom + +module + structured-types.iterated-pointed-cartesian-product-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.raising-universe-levels-unit-type +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels open import lists.lists -open import structured-types.pointed-cartesian-product-types +open import structured-types.pointed-cartesian-product-types funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/magmas.lagda.md b/src/structured-types/magmas.lagda.md index 13372059eb..da402fe17b 100644 --- a/src/structured-types/magmas.lagda.md +++ b/src/structured-types/magmas.lagda.md @@ -1,15 +1,20 @@ # Magmas ```agda -module structured-types.magmas where +open import foundation.function-extensionality-axiom + +module + structured-types.magmas + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels ``` diff --git a/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md index 0d43b47932..ab90827857 100644 --- a/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md @@ -1,25 +1,30 @@ # Mere equivalences of types equipped with endomorphisms ```agda -module structured-types.mere-equivalences-types-equipped-with-endomorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.mere-equivalences-types-equipped-with-endomorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-endomorphisms -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.equivalences-types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms funext ```
diff --git a/src/structured-types/morphisms-h-spaces.lagda.md b/src/structured-types/morphisms-h-spaces.lagda.md index 15fe75ebf3..f0b746e082 100644 --- a/src/structured-types/morphisms-h-spaces.lagda.md +++ b/src/structured-types/morphisms-h-spaces.lagda.md @@ -1,29 +1,34 @@ # Morphisms of H-spaces ```agda -module structured-types.morphisms-h-spaces where +open import foundation.function-extensionality-axiom + +module + structured-types.morphisms-h-spaces + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext -open import structured-types.h-spaces -open import structured-types.pointed-maps +open import structured-types.h-spaces funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/morphisms-magmas.lagda.md b/src/structured-types/morphisms-magmas.lagda.md index e5d3920e3b..fab320fe37 100644 --- a/src/structured-types/morphisms-magmas.lagda.md +++ b/src/structured-types/morphisms-magmas.lagda.md @@ -1,17 +1,22 @@ # Morphisms of magmas ```agda -module structured-types.morphisms-magmas where +open import foundation.function-extensionality-axiom + +module + structured-types.morphisms-magmas + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext ```
diff --git a/src/structured-types/morphisms-pointed-arrows.lagda.md b/src/structured-types/morphisms-pointed-arrows.lagda.md index a7f8e2d3fe..7e730463c2 100644 --- a/src/structured-types/morphisms-pointed-arrows.lagda.md +++ b/src/structured-types/morphisms-pointed-arrows.lagda.md @@ -1,42 +1,47 @@ # Morphisms of pointed arrows ```agda -module structured-types.morphisms-pointed-arrows where +open import foundation.function-extensionality-axiom + +module + structured-types.morphisms-pointed-arrows + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications -open import foundation.contractible-types +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.path-algebra +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.torsorial-type-families -open import structured-types.commuting-squares-of-pointed-homotopies -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.pointed-2-homotopies -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.commuting-squares-of-pointed-homotopies funext +open import structured-types.commuting-squares-of-pointed-maps funext +open import structured-types.pointed-2-homotopies funext +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.whiskering-pointed-2-homotopies-concatenation -open import structured-types.whiskering-pointed-homotopies-composition +open import structured-types.whiskering-pointed-2-homotopies-concatenation funext +open import structured-types.whiskering-pointed-homotopies-composition funext ```
diff --git a/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md b/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md index 42373c4872..2c770f6a7e 100644 --- a/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md +++ b/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md @@ -1,20 +1,25 @@ # Morphisms of twisted pointed arrows ```agda -module structured-types.morphisms-twisted-pointed-arrows where +open import foundation.function-extensionality-axiom + +module + structured-types.morphisms-twisted-pointed-arrows + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.morphisms-twisted-arrows open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md b/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md index 2f74c32b78..ea6be7b259 100644 --- a/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md @@ -1,20 +1,25 @@ # Morphisms of types equipped with automorphisms ```agda -module structured-types.morphisms-types-equipped-with-automorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.morphisms-types-equipped-with-automorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.equivalences -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.commuting-squares-of-maps funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import structured-types.morphisms-types-equipped-with-endomorphisms -open import structured-types.types-equipped-with-automorphisms +open import structured-types.morphisms-types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-automorphisms funext ```
diff --git a/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md index 3215246b06..e16a617d4d 100644 --- a/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md @@ -1,27 +1,32 @@ # Morphisms of types equipped with endomorphisms ```agda -module structured-types.morphisms-types-equipped-with-endomorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.morphisms-types-equipped-with-endomorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext ```
diff --git a/src/structured-types/morphisms-wild-monoids.lagda.md b/src/structured-types/morphisms-wild-monoids.lagda.md index 93df4f6dd1..16f5633889 100644 --- a/src/structured-types/morphisms-wild-monoids.lagda.md +++ b/src/structured-types/morphisms-wild-monoids.lagda.md @@ -1,21 +1,26 @@ # Morphisms of wild monoids ```agda -module structured-types.morphisms-wild-monoids where +open import foundation.function-extensionality-axiom + +module + structured-types.morphisms-wild-monoids + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups +open import group-theory.homomorphisms-semigroups funext -open import structured-types.morphisms-h-spaces -open import structured-types.pointed-maps -open import structured-types.wild-monoids +open import structured-types.morphisms-h-spaces funext +open import structured-types.pointed-maps funext +open import structured-types.wild-monoids funext ```
diff --git a/src/structured-types/noncoherent-h-spaces.lagda.md b/src/structured-types/noncoherent-h-spaces.lagda.md index bf3ba3b5d1..0fec4a09e3 100644 --- a/src/structured-types/noncoherent-h-spaces.lagda.md +++ b/src/structured-types/noncoherent-h-spaces.lagda.md @@ -1,14 +1,19 @@ # Noncoherent H-spaces ```agda -module structured-types.noncoherent-h-spaces where +open import foundation.function-extensionality-axiom + +module + structured-types.noncoherent-h-spaces + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unital-binary-operations open import foundation.universe-levels diff --git a/src/structured-types/opposite-pointed-spans.lagda.md b/src/structured-types/opposite-pointed-spans.lagda.md index 2c29bc256f..3b902c2967 100644 --- a/src/structured-types/opposite-pointed-spans.lagda.md +++ b/src/structured-types/opposite-pointed-spans.lagda.md @@ -1,7 +1,12 @@ # Opposite pointed spans ```agda -module structured-types.opposite-pointed-spans where +open import foundation.function-extensionality-axiom + +module + structured-types.opposite-pointed-spans + (funext : function-extensionality) + where ```
Imports @@ -10,7 +15,7 @@ module structured-types.opposite-pointed-spans where open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-spans +open import structured-types.pointed-spans funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-2-homotopies.lagda.md b/src/structured-types/pointed-2-homotopies.lagda.md index 7b40b04004..dbe1306d42 100644 --- a/src/structured-types/pointed-2-homotopies.lagda.md +++ b/src/structured-types/pointed-2-homotopies.lagda.md @@ -1,7 +1,12 @@ # Pointed `2`-homotopies ```agda -module structured-types.pointed-2-homotopies where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-2-homotopies + (funext : function-extensionality) + where ```
Imports @@ -9,27 +14,27 @@ module structured-types.pointed-2-homotopies where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-equivalences -open import foundation.commuting-triangles-of-identifications -open import foundation.contractible-types +open import foundation.commuting-triangles-of-identifications funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.uniform-pointed-homotopies +open import structured-types.uniform-pointed-homotopies funext ```
diff --git a/src/structured-types/pointed-cartesian-product-types.lagda.md b/src/structured-types/pointed-cartesian-product-types.lagda.md index 6e40cdb641..0429868475 100644 --- a/src/structured-types/pointed-cartesian-product-types.lagda.md +++ b/src/structured-types/pointed-cartesian-product-types.lagda.md @@ -1,21 +1,26 @@ # Pointed cartesian product types ```agda -module structured-types.pointed-cartesian-product-types where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-cartesian-product-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-dependent-functions.lagda.md b/src/structured-types/pointed-dependent-functions.lagda.md index 7df9e3085d..fcf95c937e 100644 --- a/src/structured-types/pointed-dependent-functions.lagda.md +++ b/src/structured-types/pointed-dependent-functions.lagda.md @@ -1,16 +1,21 @@ # Pointed dependent functions ```agda -module structured-types.pointed-dependent-functions where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-dependent-functions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.identity-types +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels open import structured-types.pointed-families-of-types diff --git a/src/structured-types/pointed-equivalences.lagda.md b/src/structured-types/pointed-equivalences.lagda.md index 0305b2134d..fb9819cb19 100644 --- a/src/structured-types/pointed-equivalences.lagda.md +++ b/src/structured-types/pointed-equivalences.lagda.md @@ -1,7 +1,12 @@ # Pointed equivalences ```agda -module structured-types.pointed-equivalences where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-equivalences + (funext : function-extensionality) + where ```
Imports @@ -10,32 +15,32 @@ module structured-types.pointed-equivalences where open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.path-algebra -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.path-algebra funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.pointed-retractions -open import structured-types.pointed-sections +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext +open import structured-types.pointed-retractions funext +open import structured-types.pointed-sections funext open import structured-types.pointed-types -open import structured-types.postcomposition-pointed-maps -open import structured-types.precomposition-pointed-maps -open import structured-types.universal-property-pointed-equivalences -open import structured-types.whiskering-pointed-homotopies-composition +open import structured-types.postcomposition-pointed-maps funext +open import structured-types.precomposition-pointed-maps funext +open import structured-types.universal-property-pointed-equivalences funext +open import structured-types.whiskering-pointed-homotopies-composition funext ```
diff --git a/src/structured-types/pointed-homotopies.lagda.md b/src/structured-types/pointed-homotopies.lagda.md index dabdeef3c9..6d1ca2e57c 100644 --- a/src/structured-types/pointed-homotopies.lagda.md +++ b/src/structured-types/pointed-homotopies.lagda.md @@ -1,7 +1,12 @@ # Pointed homotopies ```agda -module structured-types.pointed-homotopies where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-homotopies + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,24 @@ module structured-types.pointed-homotopies where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-equivalences -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext open import foundation-core.torsorial-type-families -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-isomorphisms.lagda.md b/src/structured-types/pointed-isomorphisms.lagda.md index f38534a262..cc30482f74 100644 --- a/src/structured-types/pointed-isomorphisms.lagda.md +++ b/src/structured-types/pointed-isomorphisms.lagda.md @@ -1,30 +1,35 @@ # Pointed isomorphisms ```agda -module structured-types.pointed-isomorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-isomorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.pointed-retractions -open import structured-types.pointed-sections +open import structured-types.pointed-equivalences funext +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext +open import structured-types.pointed-retractions funext +open import structured-types.pointed-sections funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-maps.lagda.md b/src/structured-types/pointed-maps.lagda.md index 1a8de69535..674bd77994 100644 --- a/src/structured-types/pointed-maps.lagda.md +++ b/src/structured-types/pointed-maps.lagda.md @@ -1,7 +1,12 @@ # Pointed maps ```agda -module structured-types.pointed-maps where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-maps + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module structured-types.pointed-maps where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.constant-maps +open import foundation.constant-maps funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-retractions.lagda.md b/src/structured-types/pointed-retractions.lagda.md index d4b837ac66..5571cf61d5 100644 --- a/src/structured-types/pointed-retractions.lagda.md +++ b/src/structured-types/pointed-retractions.lagda.md @@ -1,24 +1,29 @@ # Pointed retractions of pointed maps ```agda -module structured-types.pointed-retractions where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-retractions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.retractions -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-sections.lagda.md b/src/structured-types/pointed-sections.lagda.md index a3dfdb69f3..8fd23278e9 100644 --- a/src/structured-types/pointed-sections.lagda.md +++ b/src/structured-types/pointed-sections.lagda.md @@ -1,19 +1,24 @@ # Pointed sections of pointed maps ```agda -module structured-types.pointed-sections where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-sections + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sections +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-span-diagrams.lagda.md b/src/structured-types/pointed-span-diagrams.lagda.md index 95f98ce716..d5db510a0a 100644 --- a/src/structured-types/pointed-span-diagrams.lagda.md +++ b/src/structured-types/pointed-span-diagrams.lagda.md @@ -1,20 +1,25 @@ # Pointed span diagrams ```agda -module structured-types.pointed-span-diagrams where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.morphisms-arrows +open import foundation.identity-types funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels -open import structured-types.morphisms-pointed-arrows -open import structured-types.pointed-maps -open import structured-types.pointed-spans +open import structured-types.morphisms-pointed-arrows funext +open import structured-types.pointed-maps funext +open import structured-types.pointed-spans funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-spans.lagda.md b/src/structured-types/pointed-spans.lagda.md index 125e01bee5..5e96e5bf17 100644 --- a/src/structured-types/pointed-spans.lagda.md +++ b/src/structured-types/pointed-spans.lagda.md @@ -1,19 +1,24 @@ # Pointed spans ```agda -module structured-types.pointed-spans where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-spans + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.spans open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md b/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md index b97e8e7ae3..b82f5b5f20 100644 --- a/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md @@ -1,26 +1,31 @@ # Pointed types equipped with automorphisms ```agda -module structured-types.pointed-types-equipped-with-automorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-types-equipped-with-automorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.automorphisms funext +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import structured-types.pointed-types diff --git a/src/structured-types/pointed-unit-type.lagda.md b/src/structured-types/pointed-unit-type.lagda.md index af2130cf0b..927a96670b 100644 --- a/src/structured-types/pointed-unit-type.lagda.md +++ b/src/structured-types/pointed-unit-type.lagda.md @@ -1,19 +1,24 @@ # The pointed unit type ```agda -module structured-types.pointed-unit-type where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-unit-type + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-universal-property-contractible-types.lagda.md b/src/structured-types/pointed-universal-property-contractible-types.lagda.md index 296b91ee4b..64e79fd00d 100644 --- a/src/structured-types/pointed-universal-property-contractible-types.lagda.md +++ b/src/structured-types/pointed-universal-property-contractible-types.lagda.md @@ -1,24 +1,29 @@ # Universal property of contractible types with respect to pointed types and maps ```agda -module structured-types.pointed-universal-property-contractible-types where +open import foundation.function-extensionality-axiom + +module + structured-types.pointed-universal-property-contractible-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-contractible-types +open import foundation.universal-property-contractible-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/postcomposition-pointed-maps.lagda.md b/src/structured-types/postcomposition-pointed-maps.lagda.md index 03629c2259..21c5ec0f02 100644 --- a/src/structured-types/postcomposition-pointed-maps.lagda.md +++ b/src/structured-types/postcomposition-pointed-maps.lagda.md @@ -1,7 +1,12 @@ # Postcomposition of pointed maps ```agda -module structured-types.postcomposition-pointed-maps where +open import foundation.function-extensionality-axiom + +module + structured-types.postcomposition-pointed-maps + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module structured-types.postcomposition-pointed-maps where ```agda open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/precomposition-pointed-maps.lagda.md b/src/structured-types/precomposition-pointed-maps.lagda.md index da91cbc088..ba3e2ada46 100644 --- a/src/structured-types/precomposition-pointed-maps.lagda.md +++ b/src/structured-types/precomposition-pointed-maps.lagda.md @@ -1,7 +1,12 @@ # Precomposition of pointed maps ```agda -module structured-types.precomposition-pointed-maps where +open import foundation.function-extensionality-axiom + +module + structured-types.precomposition-pointed-maps + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module structured-types.precomposition-pointed-maps where ```agda open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/sets-equipped-with-automorphisms.lagda.md b/src/structured-types/sets-equipped-with-automorphisms.lagda.md index 2d0431fa3f..ca24903b47 100644 --- a/src/structured-types/sets-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/sets-equipped-with-automorphisms.lagda.md @@ -1,17 +1,22 @@ # Sets equipped with automorphisms ```agda -module structured-types.sets-equipped-with-automorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.sets-equipped-with-automorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.sets +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/structured-types/small-pointed-types.lagda.md b/src/structured-types/small-pointed-types.lagda.md index c1ee5d36fa..30ebe6bcb9 100644 --- a/src/structured-types/small-pointed-types.lagda.md +++ b/src/structured-types/small-pointed-types.lagda.md @@ -1,22 +1,27 @@ # Small pointed types ```agda -module structured-types.small-pointed-types where +open import foundation.function-extensionality-axiom + +module + structured-types.small-pointed-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.small-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.small-types funext open import foundation.universe-levels -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/symmetric-elements-involutive-types.lagda.md b/src/structured-types/symmetric-elements-involutive-types.lagda.md index d9f5ee8705..4c2621cab5 100644 --- a/src/structured-types/symmetric-elements-involutive-types.lagda.md +++ b/src/structured-types/symmetric-elements-involutive-types.lagda.md @@ -1,7 +1,12 @@ # Symmetric elements of involutive types ```agda -module structured-types.symmetric-elements-involutive-types where +open import foundation.function-extensionality-axiom + +module + structured-types.symmetric-elements-involutive-types + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module structured-types.symmetric-elements-involutive-types where ```agda open import foundation.universe-levels -open import structured-types.involutive-types +open import structured-types.involutive-types funext -open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.2-element-types funext ```
diff --git a/src/structured-types/symmetric-h-spaces.lagda.md b/src/structured-types/symmetric-h-spaces.lagda.md index 95d5e73667..1de28b6122 100644 --- a/src/structured-types/symmetric-h-spaces.lagda.md +++ b/src/structured-types/symmetric-h-spaces.lagda.md @@ -1,19 +1,24 @@ # Symmetric H-spaces ```agda -module structured-types.symmetric-h-spaces where +open import foundation.function-extensionality-axiom + +module + structured-types.symmetric-h-spaces + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.symmetric-operations +open import foundation.symmetric-operations funext open import foundation.universe-levels -open import structured-types.involutive-type-of-h-space-structures +open import structured-types.involutive-type-of-h-space-structures funext open import structured-types.pointed-types -open import structured-types.symmetric-elements-involutive-types +open import structured-types.symmetric-elements-involutive-types funext ```
diff --git a/src/structured-types/transposition-pointed-span-diagrams.lagda.md b/src/structured-types/transposition-pointed-span-diagrams.lagda.md index 3b21a8cd57..460b11fa1c 100644 --- a/src/structured-types/transposition-pointed-span-diagrams.lagda.md +++ b/src/structured-types/transposition-pointed-span-diagrams.lagda.md @@ -1,7 +1,12 @@ # Transposition of pointed span diagrams ```agda -module structured-types.transposition-pointed-span-diagrams where +open import foundation.function-extensionality-axiom + +module + structured-types.transposition-pointed-span-diagrams + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module structured-types.transposition-pointed-span-diagrams where open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.opposite-pointed-spans -open import structured-types.pointed-span-diagrams +open import structured-types.opposite-pointed-spans funext +open import structured-types.pointed-span-diagrams funext ```
diff --git a/src/structured-types/types-equipped-with-automorphisms.lagda.md b/src/structured-types/types-equipped-with-automorphisms.lagda.md index 56e43e8efd..551a3e2493 100644 --- a/src/structured-types/types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/types-equipped-with-automorphisms.lagda.md @@ -1,18 +1,23 @@ # Types equipped with automorphisms ```agda -module structured-types.types-equipped-with-automorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.types-equipped-with-automorphisms + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext ```
diff --git a/src/structured-types/types-equipped-with-endomorphisms.lagda.md b/src/structured-types/types-equipped-with-endomorphisms.lagda.md index beffcc9d59..499c2977f8 100644 --- a/src/structured-types/types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/types-equipped-with-endomorphisms.lagda.md @@ -1,18 +1,23 @@ # Types equipped with endomorphisms ```agda -module structured-types.types-equipped-with-endomorphisms where +open import foundation.function-extensionality-axiom + +module + structured-types.types-equipped-with-endomorphisms + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.raising-universe-levels-unit-type +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.endomorphisms +open import foundation-core.endomorphisms funext open import foundation-core.function-types ``` diff --git a/src/structured-types/uniform-pointed-homotopies.lagda.md b/src/structured-types/uniform-pointed-homotopies.lagda.md index eb98f22918..f2fa6b4349 100644 --- a/src/structured-types/uniform-pointed-homotopies.lagda.md +++ b/src/structured-types/uniform-pointed-homotopies.lagda.md @@ -1,27 +1,33 @@ # Uniform pointed homotopies ```agda -module structured-types.uniform-pointed-homotopies where +open import foundation.function-extensionality-axiom + +module + structured-types.uniform-pointed-homotopies + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/universal-property-pointed-equivalences.lagda.md b/src/structured-types/universal-property-pointed-equivalences.lagda.md index 1ed069812f..e6acc824ac 100644 --- a/src/structured-types/universal-property-pointed-equivalences.lagda.md +++ b/src/structured-types/universal-property-pointed-equivalences.lagda.md @@ -1,18 +1,23 @@ # The universal property of pointed equivalences ```agda -module structured-types.universal-property-pointed-equivalences where +open import foundation.function-extensionality-axiom + +module + structured-types.universal-property-pointed-equivalences + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.precomposition-pointed-maps +open import structured-types.precomposition-pointed-maps funext ```
diff --git a/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md b/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md index 7e99884c46..c211e5bcde 100644 --- a/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md +++ b/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md @@ -1,24 +1,29 @@ # Whiskering pointed homotopies with respect to concatenation ```agda -module structured-types.whiskering-pointed-2-homotopies-concatenation where +open import foundation.function-extensionality-axiom + +module + structured-types.whiskering-pointed-2-homotopies-concatenation + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels -open import foundation.whiskering-homotopies-concatenation -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-homotopies-concatenation funext +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-2-homotopies -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-2-homotopies funext +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md b/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md index ce71678ce6..0819340370 100644 --- a/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md +++ b/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md @@ -1,7 +1,12 @@ # Whiskering of pointed homotopies with respect to composition of pointed maps ```agda -module structured-types.whiskering-pointed-homotopies-composition where +open import foundation.function-extensionality-axiom + +module + structured-types.whiskering-pointed-homotopies-composition + (funext : function-extensionality) + where ```
Imports @@ -9,19 +14,19 @@ module structured-types.whiskering-pointed-homotopies-composition where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-identifications funext open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-2-homotopies +open import structured-types.pointed-2-homotopies funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/wild-category-of-pointed-types.lagda.md b/src/structured-types/wild-category-of-pointed-types.lagda.md index 3ff1429d27..e421500afe 100644 --- a/src/structured-types/wild-category-of-pointed-types.lagda.md +++ b/src/structured-types/wild-category-of-pointed-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module structured-types.wild-category-of-pointed-types where +open import foundation.function-extensionality-axiom + +module + structured-types.wild-category-of-pointed-types + (funext : function-extensionality) + where ```
Imports @@ -11,29 +16,29 @@ module structured-types.wild-category-of-pointed-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import globular-types.discrete-reflexive-globular-types +open import globular-types.discrete-reflexive-globular-types funext open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.large-reflexive-globular-types -open import globular-types.large-transitive-globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.large-reflexive-globular-types funext +open import globular-types.large-transitive-globular-types funext +open import globular-types.reflexive-globular-types funext +open import globular-types.transitive-globular-types funext -open import structured-types.pointed-2-homotopies -open import structured-types.pointed-dependent-functions +open import structured-types.pointed-2-homotopies funext +open import structured-types.pointed-dependent-functions funext open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.uniform-pointed-homotopies +open import structured-types.uniform-pointed-homotopies funext -open import wild-category-theory.noncoherent-large-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-large-omega-precategories funext +open import wild-category-theory.noncoherent-omega-precategories funext ```
diff --git a/src/structured-types/wild-groups.lagda.md b/src/structured-types/wild-groups.lagda.md index a743c1d556..2620052ec1 100644 --- a/src/structured-types/wild-groups.lagda.md +++ b/src/structured-types/wild-groups.lagda.md @@ -1,7 +1,12 @@ # Wild groups ```agda -module structured-types.wild-groups where +open import foundation.function-extensionality-axiom + +module + structured-types.wild-groups + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ open import foundation.binary-equivalences open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.wild-monoids +open import structured-types.wild-monoids funext ```
diff --git a/src/structured-types/wild-loops.lagda.md b/src/structured-types/wild-loops.lagda.md index 0abc01f7c2..9aad4b47a9 100644 --- a/src/structured-types/wild-loops.lagda.md +++ b/src/structured-types/wild-loops.lagda.md @@ -1,23 +1,28 @@ # Wild loops ```agda -module structured-types.wild-loops where +open import foundation.function-extensionality-axiom + +module + structured-types.wild-loops + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.h-spaces -open import structured-types.magmas +open import structured-types.h-spaces funext +open import structured-types.magmas funext open import structured-types.pointed-types -open import structured-types.wild-quasigroups +open import structured-types.wild-quasigroups funext ```
diff --git a/src/structured-types/wild-monoids.lagda.md b/src/structured-types/wild-monoids.lagda.md index 250cabb823..289302fb1e 100644 --- a/src/structured-types/wild-monoids.lagda.md +++ b/src/structured-types/wild-monoids.lagda.md @@ -1,7 +1,12 @@ # Wild monoids ```agda -module structured-types.wild-monoids where +open import foundation.function-extensionality-axiom + +module + structured-types.wild-monoids + (funext : function-extensionality) + where ```
Imports @@ -9,11 +14,11 @@ module structured-types.wild-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.h-spaces +open import structured-types.h-spaces funext open import structured-types.pointed-types ``` diff --git a/src/structured-types/wild-quasigroups.lagda.md b/src/structured-types/wild-quasigroups.lagda.md index a9e84acf35..e878fbd92d 100644 --- a/src/structured-types/wild-quasigroups.lagda.md +++ b/src/structured-types/wild-quasigroups.lagda.md @@ -1,19 +1,24 @@ # Wild quasigroups ```agda -module structured-types.wild-quasigroups where +open import foundation.function-extensionality-axiom + +module + structured-types.wild-quasigroups + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.automorphisms +open import foundation.automorphisms funext open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext ```
diff --git a/src/structured-types/wild-semigroups.lagda.md b/src/structured-types/wild-semigroups.lagda.md index f1a0642256..fdd37df39b 100644 --- a/src/structured-types/wild-semigroups.lagda.md +++ b/src/structured-types/wild-semigroups.lagda.md @@ -1,17 +1,22 @@ # Wild semigroups ```agda -module structured-types.wild-semigroups where +open import foundation.function-extensionality-axiom + +module + structured-types.wild-semigroups + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.magmas +open import structured-types.magmas funext ```
diff --git a/src/synthetic-category-theory.lagda.md b/src/synthetic-category-theory.lagda.md index 5ff89a2169..666571a2ad 100644 --- a/src/synthetic-category-theory.lagda.md +++ b/src/synthetic-category-theory.lagda.md @@ -23,13 +23,18 @@ Some core principles of higher category theory include: ## Modules in the synthetic category theory namespace ```agda -module synthetic-category-theory where - -open import synthetic-category-theory.cone-diagrams-synthetic-categories public -open import synthetic-category-theory.cospans-synthetic-categories public -open import synthetic-category-theory.equivalences-synthetic-categories public -open import synthetic-category-theory.invertible-functors-synthetic-categories public -open import synthetic-category-theory.pullbacks-synthetic-categories public +open import foundation.function-extensionality-axiom + +module + synthetic-category-theory + (funext : function-extensionality) + where + +open import synthetic-category-theory.cone-diagrams-synthetic-categories funext public +open import synthetic-category-theory.cospans-synthetic-categories funext public +open import synthetic-category-theory.equivalences-synthetic-categories funext public +open import synthetic-category-theory.invertible-functors-synthetic-categories funext public +open import synthetic-category-theory.pullbacks-synthetic-categories funext public open import synthetic-category-theory.retractions-synthetic-categories public open import synthetic-category-theory.sections-synthetic-categories public open import synthetic-category-theory.synthetic-categories public diff --git a/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md b/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md index 793041a163..796eb45698 100644 --- a/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module synthetic-category-theory.cone-diagrams-synthetic-categories where +open import foundation.function-extensionality-axiom + +module + synthetic-category-theory.cone-diagrams-synthetic-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.cospans-synthetic-categories +open import synthetic-category-theory.cospans-synthetic-categories funext open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md b/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md index d4385ae17e..ec90b69f08 100644 --- a/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module synthetic-category-theory.cospans-synthetic-categories where +open import foundation.function-extensionality-axiom + +module + synthetic-category-theory.cospans-synthetic-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.equivalences-synthetic-categories +open import synthetic-category-theory.equivalences-synthetic-categories funext open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md b/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md index e616153e9f..d4f6753834 100644 --- a/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md @@ -3,13 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -module synthetic-category-theory.equivalences-synthetic-categories where +open import foundation.function-extensionality-axiom + +module + synthetic-category-theory.equivalences-synthetic-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md b/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md index 79a237ffc1..237d8a69db 100644 --- a/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md @@ -3,19 +3,24 @@ ```agda {-# OPTIONS --guardedness #-} -module synthetic-category-theory.invertible-functors-synthetic-categories where +open import foundation.function-extensionality-axiom + +module + synthetic-category-theory.invertible-functors-synthetic-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.equivalences-synthetic-categories +open import synthetic-category-theory.equivalences-synthetic-categories funext open import synthetic-category-theory.retractions-synthetic-categories open import synthetic-category-theory.sections-synthetic-categories open import synthetic-category-theory.synthetic-categories diff --git a/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md b/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md index c57580a72d..05bba2ff48 100644 --- a/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md @@ -3,21 +3,26 @@ ```agda {-# OPTIONS --guardedness #-} -module synthetic-category-theory.pullbacks-synthetic-categories where +open import foundation.function-extensionality-axiom + +module + synthetic-category-theory.pullbacks-synthetic-categories + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.cone-diagrams-synthetic-categories -open import synthetic-category-theory.cospans-synthetic-categories -open import synthetic-category-theory.equivalences-synthetic-categories +open import synthetic-category-theory.cone-diagrams-synthetic-categories funext +open import synthetic-category-theory.cospans-synthetic-categories funext +open import synthetic-category-theory.equivalences-synthetic-categories funext open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-homotopy-theory.lagda.md b/src/synthetic-homotopy-theory.lagda.md index f05ba2976d..f7c74a60b0 100644 --- a/src/synthetic-homotopy-theory.lagda.md +++ b/src/synthetic-homotopy-theory.lagda.md @@ -7,137 +7,142 @@ ## Modules in the synthetic homotopy theory namespace ```agda -module synthetic-homotopy-theory where +open import foundation.function-extensionality-axiom -open import synthetic-homotopy-theory.0-acyclic-maps public -open import synthetic-homotopy-theory.0-acyclic-types public -open import synthetic-homotopy-theory.1-acyclic-types public -open import synthetic-homotopy-theory.acyclic-maps public -open import synthetic-homotopy-theory.acyclic-types public -open import synthetic-homotopy-theory.category-of-connected-set-bundles-circle public -open import synthetic-homotopy-theory.cavallos-trick public -open import synthetic-homotopy-theory.circle public -open import synthetic-homotopy-theory.cocartesian-morphisms-arrows public -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams public -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams public -open import synthetic-homotopy-theory.cocones-under-spans public -open import synthetic-homotopy-theory.codiagonals-of-maps public -open import synthetic-homotopy-theory.coequalizers public -open import synthetic-homotopy-theory.cofibers-of-maps public -open import synthetic-homotopy-theory.cofibers-of-pointed-maps public -open import synthetic-homotopy-theory.coforks public -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams public -open import synthetic-homotopy-theory.conjugation-loops public -open import synthetic-homotopy-theory.connected-set-bundles-circle public -open import synthetic-homotopy-theory.connective-prespectra public -open import synthetic-homotopy-theory.connective-spectra public -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams public -open import synthetic-homotopy-theory.dependent-cocones-under-spans public -open import synthetic-homotopy-theory.dependent-coforks public -open import synthetic-homotopy-theory.dependent-descent-circle public -open import synthetic-homotopy-theory.dependent-pullback-property-pushouts public -open import synthetic-homotopy-theory.dependent-pushout-products public -open import synthetic-homotopy-theory.dependent-sequential-diagrams public -open import synthetic-homotopy-theory.dependent-suspension-structures public -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers public -open import synthetic-homotopy-theory.dependent-universal-property-pushouts public -open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits public -open import synthetic-homotopy-theory.dependent-universal-property-suspensions public -open import synthetic-homotopy-theory.descent-circle public -open import synthetic-homotopy-theory.descent-circle-constant-families public -open import synthetic-homotopy-theory.descent-circle-dependent-pair-types public -open import synthetic-homotopy-theory.descent-circle-equivalence-types public -open import synthetic-homotopy-theory.descent-circle-function-types public -open import synthetic-homotopy-theory.descent-circle-subtypes public -open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts public -open import synthetic-homotopy-theory.descent-data-function-types-over-pushouts public -open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts public -open import synthetic-homotopy-theory.descent-data-pushouts public -open import synthetic-homotopy-theory.descent-data-sequential-colimits public -open import synthetic-homotopy-theory.descent-property-pushouts public -open import synthetic-homotopy-theory.descent-property-sequential-colimits public -open import synthetic-homotopy-theory.double-loop-spaces public -open import synthetic-homotopy-theory.eckmann-hilton-argument public -open import synthetic-homotopy-theory.equifibered-sequential-diagrams public -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams public -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows public -open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams public -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts public -open import synthetic-homotopy-theory.equivalences-sequential-diagrams public -open import synthetic-homotopy-theory.families-descent-data-pushouts public -open import synthetic-homotopy-theory.families-descent-data-sequential-colimits public -open import synthetic-homotopy-theory.flattening-lemma-coequalizers public -open import synthetic-homotopy-theory.flattening-lemma-pushouts public -open import synthetic-homotopy-theory.flattening-lemma-sequential-colimits public -open import synthetic-homotopy-theory.free-loops public -open import synthetic-homotopy-theory.functoriality-loop-spaces public -open import synthetic-homotopy-theory.functoriality-sequential-colimits public -open import synthetic-homotopy-theory.functoriality-suspensions public -open import synthetic-homotopy-theory.groups-of-loops-in-1-types public -open import synthetic-homotopy-theory.hatchers-acyclic-type public -open import synthetic-homotopy-theory.homotopy-groups public -open import synthetic-homotopy-theory.identity-systems-descent-data-pushouts public -open import synthetic-homotopy-theory.induction-principle-pushouts public -open import synthetic-homotopy-theory.infinite-complex-projective-space public -open import synthetic-homotopy-theory.infinite-cyclic-types public -open import synthetic-homotopy-theory.interval-type public -open import synthetic-homotopy-theory.iterated-loop-spaces public -open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types public -open import synthetic-homotopy-theory.join-powers-of-types public -open import synthetic-homotopy-theory.joins-of-maps public -open import synthetic-homotopy-theory.joins-of-types public -open import synthetic-homotopy-theory.left-half-smash-products public -open import synthetic-homotopy-theory.loop-homotopy-circle public -open import synthetic-homotopy-theory.loop-spaces public -open import synthetic-homotopy-theory.maps-of-prespectra public -open import synthetic-homotopy-theory.mere-spheres public -open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams public -open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows public -open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams public -open import synthetic-homotopy-theory.morphisms-descent-data-circle public -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts public -open import synthetic-homotopy-theory.morphisms-sequential-diagrams public -open import synthetic-homotopy-theory.multiplication-circle public -open import synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams public -open import synthetic-homotopy-theory.plus-principle public -open import synthetic-homotopy-theory.powers-of-loops public -open import synthetic-homotopy-theory.premanifolds public -open import synthetic-homotopy-theory.prespectra public -open import synthetic-homotopy-theory.pullback-property-pushouts public -open import synthetic-homotopy-theory.pushout-products public -open import synthetic-homotopy-theory.pushouts public -open import synthetic-homotopy-theory.pushouts-of-pointed-types public -open import synthetic-homotopy-theory.recursion-principle-pushouts public -open import synthetic-homotopy-theory.retracts-of-sequential-diagrams public -open import synthetic-homotopy-theory.rewriting-pushouts public -open import synthetic-homotopy-theory.sections-descent-circle public -open import synthetic-homotopy-theory.sections-descent-data-pushouts public -open import synthetic-homotopy-theory.sequential-colimits public -open import synthetic-homotopy-theory.sequential-diagrams public -open import synthetic-homotopy-theory.sequentially-compact-types public -open import synthetic-homotopy-theory.shifts-sequential-diagrams public -open import synthetic-homotopy-theory.smash-products-of-pointed-types public -open import synthetic-homotopy-theory.spectra public -open import synthetic-homotopy-theory.sphere-prespectrum public -open import synthetic-homotopy-theory.spheres public -open import synthetic-homotopy-theory.suspension-prespectra public -open import synthetic-homotopy-theory.suspension-structures public -open import synthetic-homotopy-theory.suspensions-of-pointed-types public -open import synthetic-homotopy-theory.suspensions-of-propositions public -open import synthetic-homotopy-theory.suspensions-of-types public -open import synthetic-homotopy-theory.tangent-spheres public -open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams public -open import synthetic-homotopy-theory.total-sequential-diagrams public -open import synthetic-homotopy-theory.triple-loop-spaces public -open import synthetic-homotopy-theory.truncated-acyclic-maps public -open import synthetic-homotopy-theory.truncated-acyclic-types public -open import synthetic-homotopy-theory.universal-cover-circle public -open import synthetic-homotopy-theory.universal-property-circle public -open import synthetic-homotopy-theory.universal-property-coequalizers public -open import synthetic-homotopy-theory.universal-property-pushouts public -open import synthetic-homotopy-theory.universal-property-sequential-colimits public -open import synthetic-homotopy-theory.universal-property-suspensions public -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types public -open import synthetic-homotopy-theory.wedges-of-pointed-types public -open import synthetic-homotopy-theory.zigzags-sequential-diagrams public +module + synthetic-homotopy-theory + (funext : function-extensionality) + where + +open import synthetic-homotopy-theory.0-acyclic-maps funext public +open import synthetic-homotopy-theory.0-acyclic-types funext public +open import synthetic-homotopy-theory.1-acyclic-types funext public +open import synthetic-homotopy-theory.acyclic-maps funext public +open import synthetic-homotopy-theory.acyclic-types funext public +open import synthetic-homotopy-theory.category-of-connected-set-bundles-circle funext public +open import synthetic-homotopy-theory.cavallos-trick funext public +open import synthetic-homotopy-theory.circle funext public +open import synthetic-homotopy-theory.cocartesian-morphisms-arrows funext public +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext public +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext public +open import synthetic-homotopy-theory.cocones-under-spans funext public +open import synthetic-homotopy-theory.codiagonals-of-maps funext public +open import synthetic-homotopy-theory.coequalizers funext public +open import synthetic-homotopy-theory.cofibers-of-maps funext public +open import synthetic-homotopy-theory.cofibers-of-pointed-maps funext public +open import synthetic-homotopy-theory.coforks funext public +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams funext public +open import synthetic-homotopy-theory.conjugation-loops funext public +open import synthetic-homotopy-theory.connected-set-bundles-circle funext public +open import synthetic-homotopy-theory.connective-prespectra funext public +open import synthetic-homotopy-theory.connective-spectra funext public +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext public +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext public +open import synthetic-homotopy-theory.dependent-coforks funext public +open import synthetic-homotopy-theory.dependent-descent-circle funext public +open import synthetic-homotopy-theory.dependent-pullback-property-pushouts funext public +open import synthetic-homotopy-theory.dependent-pushout-products funext public +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext public +open import synthetic-homotopy-theory.dependent-suspension-structures funext public +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext public +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext public +open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits funext public +open import synthetic-homotopy-theory.dependent-universal-property-suspensions funext public +open import synthetic-homotopy-theory.descent-circle funext public +open import synthetic-homotopy-theory.descent-circle-constant-families funext public +open import synthetic-homotopy-theory.descent-circle-dependent-pair-types funext public +open import synthetic-homotopy-theory.descent-circle-equivalence-types funext public +open import synthetic-homotopy-theory.descent-circle-function-types funext public +open import synthetic-homotopy-theory.descent-circle-subtypes funext public +open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts funext public +open import synthetic-homotopy-theory.descent-data-function-types-over-pushouts funext public +open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts funext public +open import synthetic-homotopy-theory.descent-data-pushouts funext public +open import synthetic-homotopy-theory.descent-data-sequential-colimits funext public +open import synthetic-homotopy-theory.descent-property-pushouts funext public +open import synthetic-homotopy-theory.descent-property-sequential-colimits funext public +open import synthetic-homotopy-theory.double-loop-spaces funext public +open import synthetic-homotopy-theory.eckmann-hilton-argument funext public +open import synthetic-homotopy-theory.equifibered-sequential-diagrams funext public +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext public +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext public +open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams funext public +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext public +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext public +open import synthetic-homotopy-theory.families-descent-data-pushouts funext public +open import synthetic-homotopy-theory.families-descent-data-sequential-colimits funext public +open import synthetic-homotopy-theory.flattening-lemma-coequalizers funext public +open import synthetic-homotopy-theory.flattening-lemma-pushouts funext public +open import synthetic-homotopy-theory.flattening-lemma-sequential-colimits funext public +open import synthetic-homotopy-theory.free-loops funext public +open import synthetic-homotopy-theory.functoriality-loop-spaces funext public +open import synthetic-homotopy-theory.functoriality-sequential-colimits funext public +open import synthetic-homotopy-theory.functoriality-suspensions funext public +open import synthetic-homotopy-theory.groups-of-loops-in-1-types funext public +open import synthetic-homotopy-theory.hatchers-acyclic-type funext public +open import synthetic-homotopy-theory.homotopy-groups funext public +open import synthetic-homotopy-theory.identity-systems-descent-data-pushouts funext public +open import synthetic-homotopy-theory.induction-principle-pushouts funext public +open import synthetic-homotopy-theory.infinite-complex-projective-space funext public +open import synthetic-homotopy-theory.infinite-cyclic-types funext public +open import synthetic-homotopy-theory.interval-type funext public +open import synthetic-homotopy-theory.iterated-loop-spaces funext public +open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types funext public +open import synthetic-homotopy-theory.join-powers-of-types funext public +open import synthetic-homotopy-theory.joins-of-maps funext public +open import synthetic-homotopy-theory.joins-of-types funext public +open import synthetic-homotopy-theory.left-half-smash-products funext public +open import synthetic-homotopy-theory.loop-homotopy-circle funext public +open import synthetic-homotopy-theory.loop-spaces funext public +open import synthetic-homotopy-theory.maps-of-prespectra funext public +open import synthetic-homotopy-theory.mere-spheres funext public +open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams funext public +open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows funext public +open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams funext public +open import synthetic-homotopy-theory.morphisms-descent-data-circle funext public +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext public +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext public +open import synthetic-homotopy-theory.multiplication-circle funext public +open import synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams funext public +open import synthetic-homotopy-theory.plus-principle funext public +open import synthetic-homotopy-theory.powers-of-loops funext public +open import synthetic-homotopy-theory.premanifolds funext public +open import synthetic-homotopy-theory.prespectra funext public +open import synthetic-homotopy-theory.pullback-property-pushouts funext public +open import synthetic-homotopy-theory.pushout-products funext public +open import synthetic-homotopy-theory.pushouts funext public +open import synthetic-homotopy-theory.pushouts-of-pointed-types funext public +open import synthetic-homotopy-theory.recursion-principle-pushouts funext public +open import synthetic-homotopy-theory.retracts-of-sequential-diagrams funext public +open import synthetic-homotopy-theory.rewriting-pushouts funext public +open import synthetic-homotopy-theory.sections-descent-circle funext public +open import synthetic-homotopy-theory.sections-descent-data-pushouts funext public +open import synthetic-homotopy-theory.sequential-colimits funext public +open import synthetic-homotopy-theory.sequential-diagrams funext public +open import synthetic-homotopy-theory.sequentially-compact-types funext public +open import synthetic-homotopy-theory.shifts-sequential-diagrams funext public +open import synthetic-homotopy-theory.smash-products-of-pointed-types funext public +open import synthetic-homotopy-theory.spectra funext public +open import synthetic-homotopy-theory.sphere-prespectrum funext public +open import synthetic-homotopy-theory.spheres funext public +open import synthetic-homotopy-theory.suspension-prespectra funext public +open import synthetic-homotopy-theory.suspension-structures funext public +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext public +open import synthetic-homotopy-theory.suspensions-of-propositions funext public +open import synthetic-homotopy-theory.suspensions-of-types funext public +open import synthetic-homotopy-theory.tangent-spheres funext public +open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams funext public +open import synthetic-homotopy-theory.total-sequential-diagrams funext public +open import synthetic-homotopy-theory.triple-loop-spaces funext public +open import synthetic-homotopy-theory.truncated-acyclic-maps funext public +open import synthetic-homotopy-theory.truncated-acyclic-types funext public +open import synthetic-homotopy-theory.universal-cover-circle funext public +open import synthetic-homotopy-theory.universal-property-circle funext public +open import synthetic-homotopy-theory.universal-property-coequalizers funext public +open import synthetic-homotopy-theory.universal-property-pushouts funext public +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext public +open import synthetic-homotopy-theory.universal-property-suspensions funext public +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext public +open import synthetic-homotopy-theory.wedges-of-pointed-types funext public +open import synthetic-homotopy-theory.zigzags-sequential-diagrams funext public ``` diff --git a/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md index aaa7ec0e76..421e64fe72 100644 --- a/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md @@ -1,19 +1,24 @@ # `0`-acyclic maps ```agda -module synthetic-homotopy-theory.0-acyclic-maps where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.0-acyclic-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.epimorphisms-with-respect-to-sets -open import foundation.propositions -open import foundation.surjective-maps +open import foundation.epimorphisms-with-respect-to-sets funext +open import foundation.propositions funext +open import foundation.surjective-maps funext open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.truncated-acyclic-maps +open import synthetic-homotopy-theory.truncated-acyclic-maps funext ```
diff --git a/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md index cdfaabba69..e3bb2c9e31 100644 --- a/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md @@ -1,25 +1,30 @@ # `0`-acyclic types ```agda -module synthetic-homotopy-theory.0-acyclic-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.0-acyclic-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.inhabited-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.functoriality-propositional-truncation funext +open import foundation.inhabited-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.0-acyclic-maps -open import synthetic-homotopy-theory.truncated-acyclic-maps -open import synthetic-homotopy-theory.truncated-acyclic-types +open import synthetic-homotopy-theory.0-acyclic-maps funext +open import synthetic-homotopy-theory.truncated-acyclic-maps funext +open import synthetic-homotopy-theory.truncated-acyclic-types funext ```
diff --git a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md index c7e47d89d0..170977c1ec 100644 --- a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md @@ -1,33 +1,37 @@ # `1`-acyclic types ```agda -module synthetic-homotopy-theory.1-acyclic-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.1-acyclic-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.injective-maps -open import foundation.propositions -open import foundation.set-truncations -open import foundation.sets -open import foundation.truncated-types +open import foundation.diagonal-maps-of-types funext +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.injective-maps funext +open import foundation.propositions funext +open import foundation.set-truncations funext +open import foundation.sets funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.0-acyclic-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.truncated-acyclic-maps -open import synthetic-homotopy-theory.truncated-acyclic-types +open import synthetic-homotopy-theory.0-acyclic-types funext +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.truncated-acyclic-maps funext +open import synthetic-homotopy-theory.truncated-acyclic-types funext ```
diff --git a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md index 3bf63f4ed1..a14c63cb25 100644 --- a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md @@ -1,55 +1,60 @@ # Acyclic maps ```agda -module synthetic-homotopy-theory.acyclic-maps where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.acyclic-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams -open import foundation.constant-maps -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.dependent-epimorphisms +open import foundation.cartesian-product-types funext +open import foundation.cones-over-cospan-diagrams funext +open import foundation.constant-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext +open import foundation.dependent-epimorphisms funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.diagonal-maps-of-types -open import foundation.embeddings -open import foundation.epimorphisms -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.pullbacks -open import foundation.retracts-of-maps -open import foundation.torsorial-type-families +open import foundation.dependent-universal-property-equivalences funext +open import foundation.diagonal-maps-of-types funext +open import foundation.embeddings funext +open import foundation.epimorphisms funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.pullbacks funext +open import foundation.retracts-of-maps funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.acyclic-types -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.codiagonals-of-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.suspensions-of-types -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.acyclic-types funext +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.codiagonals-of-maps funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/acyclic-types.lagda.md b/src/synthetic-homotopy-theory/acyclic-types.lagda.md index 35473b70bf..5072fb7fcd 100644 --- a/src/synthetic-homotopy-theory/acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/acyclic-types.lagda.md @@ -1,21 +1,26 @@ # Acyclic types ```agda -module synthetic-homotopy-theory.acyclic-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.acyclic-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.equivalences -open import foundation.propositions -open import foundation.retracts-of-types +open import foundation.contractible-types funext +open import foundation.equivalences funext +open import foundation.propositions funext +open import foundation.retracts-of-types funext open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.functoriality-suspensions -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.functoriality-suspensions funext +open import synthetic-homotopy-theory.suspensions-of-types funext ```
diff --git a/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md b/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md index c03b92fe6a..3b590c8193 100644 --- a/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md +++ b/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md @@ -1,20 +1,25 @@ # The category of connected set bundles over the circle ```agda -module synthetic-homotopy-theory.category-of-connected-set-bundles-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.category-of-connected-set-bundles-circle + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.full-large-subcategories -open import category-theory.large-categories +open import category-theory.full-large-subcategories funext +open import category-theory.large-categories funext -open import foundation.category-of-families-of-sets +open import foundation.category-of-families-of-sets funext open import foundation.universe-levels -open import synthetic-homotopy-theory.circle -open import synthetic-homotopy-theory.connected-set-bundles-circle +open import synthetic-homotopy-theory.circle funext +open import synthetic-homotopy-theory.connected-set-bundles-circle funext ```
diff --git a/src/synthetic-homotopy-theory/cavallos-trick.lagda.md b/src/synthetic-homotopy-theory/cavallos-trick.lagda.md index 54d3a7e599..e3475c89d8 100644 --- a/src/synthetic-homotopy-theory/cavallos-trick.lagda.md +++ b/src/synthetic-homotopy-theory/cavallos-trick.lagda.md @@ -1,7 +1,12 @@ # Cavallo's trick ```agda -module synthetic-homotopy-theory.cavallos-trick where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.cavallos-trick + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module synthetic-homotopy-theory.cavallos-trick where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sections +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types ``` diff --git a/src/synthetic-homotopy-theory/circle.lagda.md b/src/synthetic-homotopy-theory/circle.lagda.md index 0340db0b69..457a1c3e27 100644 --- a/src/synthetic-homotopy-theory/circle.lagda.md +++ b/src/synthetic-homotopy-theory/circle.lagda.md @@ -1,48 +1,53 @@ # The circle ```agda -module synthetic-homotopy-theory.circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.circle + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.dependent-suspension-structures -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.spheres -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types -open import synthetic-homotopy-theory.universal-cover-circle -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.dependent-suspension-structures funext +open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.spheres funext +open import synthetic-homotopy-theory.suspension-structures funext +open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.universal-cover-circle funext +open import synthetic-homotopy-theory.universal-property-circle funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md b/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md index 9e34713e9c..75632d5143 100644 --- a/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md @@ -1,21 +1,26 @@ # Cocartesian morphisms of arrows ```agda -module synthetic-homotopy-theory.cocartesian-morphisms-arrows where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.cocartesian-morphisms-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.morphisms-arrows -open import foundation.propositions +open import foundation.morphisms-arrows funext +open import foundation.propositions funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md b/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md index cec36cef2d..18cf55cc98 100644 --- a/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md @@ -1,7 +1,12 @@ # Cocones under pointed span diagrams ```agda -module synthetic-homotopy-theory.cocones-under-pointed-span-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.cocones-under-pointed-span-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module synthetic-homotopy-theory.cocones-under-pointed-span-diagrams where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.pointed-maps +open import structured-types.commuting-squares-of-pointed-maps funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md index ca4adb47b0..bb328e7bd9 100644 --- a/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Cocones under sequential diagrams ```agda -module synthetic-homotopy-theory.cocones-under-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.cocones-under-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,25 +14,25 @@ module synthetic-homotopy-theory.cocones-under-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-triangles-of-maps +open import foundation.binary-homotopies funext +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.equifibered-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.equifibered-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md b/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md index b3ac5c1716..384f3ad2c6 100644 --- a/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md +++ b/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md @@ -1,7 +1,12 @@ # Cocones under spans ```agda -module synthetic-homotopy-theory.cocones-under-spans where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.cocones-under-spans + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,18 @@ module synthetic-homotopy-theory.cocones-under-spans where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality +open import foundation.function-extensionality funext + open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.morphisms-arrows -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.morphisms-arrows funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps +open import foundation-core.commuting-squares-of-maps funext open import foundation-core.contractible-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences diff --git a/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md b/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md index b483d3e9a8..10693a275b 100644 --- a/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md @@ -1,27 +1,32 @@ # Codiagonals of maps ```agda -module synthetic-homotopy-theory.codiagonals-of-maps where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.codiagonals-of-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.homotopies -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.torsorial-type-families funext open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.suspension-structures funext +open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/coequalizers.lagda.md b/src/synthetic-homotopy-theory/coequalizers.lagda.md index a89b394839..afcd7476f2 100644 --- a/src/synthetic-homotopy-theory/coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/coequalizers.lagda.md @@ -1,23 +1,28 @@ # Coequalizers ```agda -module synthetic-homotopy-theory.coequalizers where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.coequalizers + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.double-arrows -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-coequalizers +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.universal-property-coequalizers funext ```
diff --git a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md index e14dce732d..41d78c8b42 100644 --- a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md @@ -1,27 +1,32 @@ # Cofibers of maps ```agda -module synthetic-homotopy-theory.cofibers-of-maps where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.cofibers-of-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.pointed-unit-type +open import structured-types.pointed-unit-type funext -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md b/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md index 0da2de0601..837ac0ff8b 100644 --- a/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md +++ b/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md @@ -1,7 +1,12 @@ # Cofibers of pointed maps ```agda -module synthetic-homotopy-theory.cofibers-of-pointed-maps where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.cofibers-of-pointed-maps + (funext : function-extensionality) + where ```
Imports @@ -9,12 +14,12 @@ module synthetic-homotopy-theory.cofibers-of-pointed-maps where ```agda open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.pointed-unit-type +open import structured-types.pointed-unit-type funext -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.pushouts-of-pointed-types +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext +open import synthetic-homotopy-theory.pushouts-of-pointed-types funext ```
diff --git a/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md index 0efd91005f..e746026b2a 100644 --- a/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Correspondence between cocones under sequential diagrams and certain coforks ```agda -module synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,33 +14,33 @@ module synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-prisms-of-maps funext +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-double-arrows -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.morphisms-double-arrows -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.equivalences funext-double-arrows +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.morphisms-double-arrows funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation - -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-coforks -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import foundation.whiskering-homotopies-concatenation funext + +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-coforks funext +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext +open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows funext +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/coforks.lagda.md b/src/synthetic-homotopy-theory/coforks.lagda.md index fa5ea65e19..12aaa42f23 100644 --- a/src/synthetic-homotopy-theory/coforks.lagda.md +++ b/src/synthetic-homotopy-theory/coforks.lagda.md @@ -1,38 +1,43 @@ # Coforks ```agda -module synthetic-homotopy-theory.coforks where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.coforks + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.codiagonal-maps-of-types -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-double-arrows -open import foundation.equivalences-span-diagrams -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.equivalences funext-double-arrows +open import foundation.equivalences-span-diagrams funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.morphisms-double-arrows -open import foundation.morphisms-span-diagrams -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.morphisms-double-arrows funext +open import foundation.morphisms-span-diagrams funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/conjugation-loops.lagda.md b/src/synthetic-homotopy-theory/conjugation-loops.lagda.md index 589c5d457d..82521cbf9b 100644 --- a/src/synthetic-homotopy-theory/conjugation-loops.lagda.md +++ b/src/synthetic-homotopy-theory/conjugation-loops.lagda.md @@ -1,21 +1,26 @@ # Conjugation of loops ```agda -module synthetic-homotopy-theory.conjugation-loops where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.conjugation-loops + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md b/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md index 46a02e248f..a7dcac5657 100644 --- a/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md +++ b/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md @@ -1,32 +1,37 @@ # Connected set bundles over the circle ```agda -module synthetic-homotopy-theory.connected-set-bundles-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.connected-set-bundles-circle + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.0-connected-types -open import foundation.automorphisms +open import foundation.0-connected-types funext +open import foundation.automorphisms funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.mere-equality -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.mere-equality funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.transitive-higher-group-actions +open import higher-group-theory.transitive-higher-group-actions funext -open import structured-types.sets-equipped-with-automorphisms +open import structured-types.sets-equipped-with-automorphisms funext -open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.circle funext ```
diff --git a/src/synthetic-homotopy-theory/connective-prespectra.lagda.md b/src/synthetic-homotopy-theory/connective-prespectra.lagda.md index db0ebe5577..55e1d7c8e0 100644 --- a/src/synthetic-homotopy-theory/connective-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/connective-prespectra.lagda.md @@ -1,7 +1,12 @@ # Connective prespectra ```agda -module synthetic-homotopy-theory.connective-prespectra where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.connective-prespectra + (funext : function-extensionality) + where ```
Imports @@ -9,23 +14,23 @@ module synthetic-homotopy-theory.connective-prespectra where ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-types +open import foundation.connected-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.truncation-levels open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.pointed-equivalences funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.prespectra funext +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.suspensions-of-types funext ```
diff --git a/src/synthetic-homotopy-theory/connective-spectra.lagda.md b/src/synthetic-homotopy-theory/connective-spectra.lagda.md index 939ec9243c..99c4bd7a0f 100644 --- a/src/synthetic-homotopy-theory/connective-spectra.lagda.md +++ b/src/synthetic-homotopy-theory/connective-spectra.lagda.md @@ -1,7 +1,12 @@ # Connective spectra ```agda -module synthetic-homotopy-theory.connective-spectra where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.connective-spectra + (funext : function-extensionality) + where ```
Imports @@ -9,25 +14,25 @@ module synthetic-homotopy-theory.connective-spectra where ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-types +open import foundation.connected-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.truncation-levels open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.pointed-equivalences funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.connective-prespectra -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.spectra -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.connective-prespectra funext +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.prespectra funext +open import synthetic-homotopy-theory.spectra funext +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.suspensions-of-types funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md index debb9262d7..81829edd7c 100644 --- a/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Dependent cocones under sequential diagrams ```agda -module synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -11,27 +16,27 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.binary-homotopies -open import foundation.commuting-triangles-of-maps -open import foundation.constant-type-families +open import foundation.binary-homotopies funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.constant-type-families funext open import foundation.dependent-homotopies -open import foundation.dependent-identifications +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-coforks -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-coforks funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md b/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md index cfba684dd3..df585aa620 100644 --- a/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md @@ -1,7 +1,12 @@ # Dependent cocones under spans ```agda -module synthetic-homotopy-theory.dependent-cocones-under-spans where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-cocones-under-spans + (funext : function-extensionality) + where ```
Imports @@ -9,35 +14,36 @@ module synthetic-homotopy-theory.dependent-cocones-under-spans where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-squares-of-maps -open import foundation.constant-type-families -open import foundation.contractible-types +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-maps funext +open import foundation.constant-type-families funext +open import foundation.contractible-types funext open import foundation.dependent-homotopies -open import foundation.dependent-identifications +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.transport-along-higher-identifications +open import foundation.torsorial-type-families funext +open import foundation.transport-along-higher-identifications funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.injective-maps -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-coforks.lagda.md b/src/synthetic-homotopy-theory/dependent-coforks.lagda.md index 39b40000f5..5e039920db 100644 --- a/src/synthetic-homotopy-theory/dependent-coforks.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-coforks.lagda.md @@ -1,7 +1,12 @@ # Dependent coforks ```agda -module synthetic-homotopy-theory.dependent-coforks where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-coforks + (funext : function-extensionality) + where ```
Imports @@ -9,29 +14,29 @@ module synthetic-homotopy-theory.dependent-coforks where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.constant-type-families -open import foundation.coproduct-types -open import foundation.dependent-identifications +open import foundation.commuting-triangles-of-maps funext +open import foundation.constant-type-families funext +open import foundation.coproduct-types funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md b/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md index a847a0abfa..78add2c3cf 100644 --- a/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md @@ -1,28 +1,33 @@ # Dependent descent for the circle ```agda -module synthetic-homotopy-theory.dependent-descent-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-descent-circle + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import structured-types.dependent-types-equipped-with-automorphisms +open import structured-types.dependent-types-equipped-with-automorphisms funext -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.descent-circle funext +open import synthetic-homotopy-theory.free-loops funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md index 977930ff08..e7dbf83999 100644 --- a/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md @@ -1,7 +1,12 @@ # The dependent pullback property of pushouts ```agda -module synthetic-homotopy-theory.dependent-pullback-property-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-pullback-property-pushouts + (funext : function-extensionality) + where ```
Imports @@ -9,26 +14,27 @@ module synthetic-homotopy-theory.dependent-pullback-property-pushouts where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams -open import foundation.constant-type-families +open import foundation.cones-over-cospan-diagrams funext +open import foundation.constant-type-families funext open import foundation.dependent-pair-types -open import foundation.dependent-sums-pullbacks -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.pullbacks +open import foundation.dependent-sums-pullbacks funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.pullbacks funext open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.lifts-families-of-elements -open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements funext +open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements funext -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pullback-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pullback-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md b/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md index 265ce6a2c9..cee4079b6e 100644 --- a/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md @@ -1,22 +1,27 @@ # Dependent pushout-products ```agda -module synthetic-homotopy-theory.dependent-pushout-products where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-pushout-products + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md index 04bd1a9b0a..364b0efc04 100644 --- a/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Dependent sequential diagrams ```agda -module synthetic-homotopy-theory.dependent-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module synthetic-homotopy-theory.dependent-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md b/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md index 8000b52d60..58edce6886 100644 --- a/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md @@ -1,32 +1,38 @@ # Dependent suspension structures ```agda -module synthetic-homotopy-theory.dependent-suspension-structures where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-suspension-structures + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.constant-maps -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.constant-maps funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.structure-identity-principle open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.suspension-structures funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md index ba60811fcb..0a6329a395 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md @@ -1,26 +1,31 @@ # The dependent universal property of coequalizers ```agda -module synthetic-homotopy-theory.dependent-universal-property-coequalizers where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-universal-property-coequalizers + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-coforks -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.universal-property-coequalizers +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-coforks funext +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext +open import synthetic-homotopy-theory.universal-property-coequalizers funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md index c0b9760150..797539c2c8 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md @@ -1,35 +1,40 @@ # The dependent universal property of pushouts ```agda -module synthetic-homotopy-theory.dependent-universal-property-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-universal-property-pushouts + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-dependent-functions -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.standard-pullbacks +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.standard-pullbacks funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-pullback-property-pushouts -open import synthetic-homotopy-theory.induction-principle-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-pullback-property-pushouts funext +open import synthetic-homotopy-theory.induction-principle-pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md index 449c744b8e..8b8c92ef2b 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md @@ -1,38 +1,43 @@ # The dependent universal property of sequential colimits ```agda -module synthetic-homotopy-theory.dependent-universal-property-sequential-colimits where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-universal-property-sequential-colimits + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext open import foundation.subtype-identity-principle -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-coforks -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-coequalizers -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.coforks funext-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-coforks funext +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-coequalizers funext +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md index 0b545c7c69..80adcdfb9c 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md @@ -1,24 +1,29 @@ # Dependent universal property of suspensions ```agda -module synthetic-homotopy-theory.dependent-universal-property-suspensions where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.dependent-universal-property-suspensions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-dependent-functions -open import foundation.constant-maps +open import foundation.constant-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-suspension-structures -open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-suspension-structures funext +open import synthetic-homotopy-theory.suspension-structures funext ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md b/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md index 8ae23e0e55..0faaa8a8c5 100644 --- a/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md @@ -1,20 +1,25 @@ # Descent data for constant type families over the circle ```agda -module synthetic-homotopy-theory.descent-circle-constant-families where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-circle-constant-families + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.constant-type-families +open import foundation.constant-type-families funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.descent-circle funext +open import synthetic-homotopy-theory.free-loops funext ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md index b9abaf71f4..d8a7c20093 100644 --- a/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md @@ -1,21 +1,26 @@ # Descent data for families of dependent pair types over the circle ```agda -module synthetic-homotopy-theory.descent-circle-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-circle-dependent-pair-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-descent-circle -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.dependent-descent-circle funext +open import synthetic-homotopy-theory.descent-circle funext +open import synthetic-homotopy-theory.free-loops funext ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md index cec4371a5e..a9d8e53450 100644 --- a/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md @@ -1,27 +1,32 @@ # Descent data for families of equivalence types over the circle ```agda -module synthetic-homotopy-theory.descent-circle-equivalence-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-circle-equivalence-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-descent-circle -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.descent-circle-dependent-pair-types -open import synthetic-homotopy-theory.descent-circle-function-types -open import synthetic-homotopy-theory.descent-circle-subtypes -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.morphisms-descent-data-circle -open import synthetic-homotopy-theory.sections-descent-circle -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.dependent-descent-circle funext +open import synthetic-homotopy-theory.descent-circle funext +open import synthetic-homotopy-theory.descent-circle funext-dependent-pair-types +open import synthetic-homotopy-theory.descent-circle-function-types funext +open import synthetic-homotopy-theory.descent-circle-subtypes funext +open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.morphisms-descent-data-circle funext +open import synthetic-homotopy-theory.sections-descent-circle funext +open import synthetic-homotopy-theory.universal-property-circle funext ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md index 447911b467..8bd7885ece 100644 --- a/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md @@ -1,34 +1,40 @@ # Descent data for families of function types over the circle ```agda -module synthetic-homotopy-theory.descent-circle-function-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-circle-function-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-function-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-function-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.identity-types -open import foundation.postcomposition-functions +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.morphisms-descent-data-circle -open import synthetic-homotopy-theory.sections-descent-circle -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.descent-circle funext +open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.morphisms-descent-data-circle funext +open import synthetic-homotopy-theory.sections-descent-circle funext +open import synthetic-homotopy-theory.universal-property-circle funext ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md index 8b2ed00fc2..2623c2b279 100644 --- a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md @@ -1,29 +1,34 @@ # Subtypes of descent data for the circle ```agda -module synthetic-homotopy-theory.descent-circle-subtypes where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-circle-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-descent-circle -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.descent-circle-dependent-pair-types -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.sections-descent-circle -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.dependent-descent-circle funext +open import synthetic-homotopy-theory.descent-circle funext +open import synthetic-homotopy-theory.descent-circle funext-dependent-pair-types +open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.sections-descent-circle funext +open import synthetic-homotopy-theory.universal-property-circle funext ```
diff --git a/src/synthetic-homotopy-theory/descent-circle.lagda.md b/src/synthetic-homotopy-theory/descent-circle.lagda.md index 26cb9592d3..bbaf503df4 100644 --- a/src/synthetic-homotopy-theory/descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle.lagda.md @@ -1,34 +1,38 @@ # The descent property of the circle ```agda -module synthetic-homotopy-theory.descent-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-circle + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.automorphisms -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.automorphisms funext +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-automorphisms -open import structured-types.types-equipped-with-automorphisms +open import structured-types.equivalences-types-equipped-with-automorphisms funext +open import structured-types.types-equipped-with-automorphisms funext -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.universal-property-circle funext ```
diff --git a/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md index 7095433e23..c1665cbf15 100644 --- a/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md @@ -3,39 +3,44 @@ ```agda {-# OPTIONS --lossy-unification #-} -module synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.postcomposition-functions -open import foundation.span-diagrams +open import foundation.postcomposition-functions funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts -open import synthetic-homotopy-theory.sections-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext +open import synthetic-homotopy-theory.families-descent-data-pushouts funext +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext +open import synthetic-homotopy-theory.sections-descent-data-pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md index 35a5f3e58d..1b2df64c8a 100644 --- a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md @@ -3,40 +3,45 @@ ```agda {-# OPTIONS --lossy-unification #-} -module synthetic-homotopy-theory.descent-data-function-types-over-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-data-function-types-over-pushouts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.postcomposition-functions -open import foundation.span-diagrams +open import foundation.postcomposition-functions funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts -open import synthetic-homotopy-theory.sections-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext +open import synthetic-homotopy-theory.families-descent-data-pushouts funext +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext +open import synthetic-homotopy-theory.sections-descent-data-pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md index 6244d587ce..dd8fc5ce36 100644 --- a/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md @@ -3,23 +3,28 @@ ```agda {-# OPTIONS --lossy-unification #-} -module synthetic-homotopy-theory.descent-data-identity-types-over-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-data-identity-types-over-pushouts + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext +open import synthetic-homotopy-theory.families-descent-data-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md index 020d2dcefb..50e8d40c6f 100644 --- a/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md @@ -1,20 +1,25 @@ # Descent data for pushouts ```agda -module synthetic-homotopy-theory.descent-data-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-data-pushouts + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.span-diagrams +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md index d498ebe3db..650fb7ea21 100644 --- a/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md @@ -1,7 +1,12 @@ # Descent data for sequential colimits ```agda -module synthetic-homotopy-theory.descent-data-sequential-colimits where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-data-sequential-colimits + (funext : function-extensionality) + where ```
Imports @@ -10,15 +15,15 @@ module synthetic-homotopy-theory.descent-data-sequential-colimits where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.equifibered-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.equifibered-sequential-diagrams funext +open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md index 6d1f56638f..65369c9ba4 100644 --- a/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md @@ -1,32 +1,38 @@ # Descent property of pushouts ```agda -module synthetic-homotopy-theory.descent-property-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-property-pushouts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.span-diagrams -open import foundation.univalence +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext +open import foundation.univalence funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext +open import synthetic-homotopy-theory.families-descent-data-pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md index 20b9c33dc7..a49fc3bf86 100644 --- a/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md @@ -1,7 +1,12 @@ # Descent property of sequential colimits ```agda -module synthetic-homotopy-theory.descent-property-sequential-colimits where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.descent-property-sequential-colimits + (funext : function-extensionality) + where ```
Imports @@ -9,21 +14,21 @@ module synthetic-homotopy-theory.descent-property-sequential-colimits where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies -open import foundation.commuting-triangles-of-maps +open import foundation.binary-homotopies funext +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.univalence +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.univalence funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.descent-data-sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.descent-data-sequential-colimits funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext ```
diff --git a/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md index 03c7e352fa..9d29be2407 100644 --- a/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md @@ -1,26 +1,31 @@ # Double loop spaces ```agda -module synthetic-homotopy-theory.double-loop-spaces where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.double-loop-spaces + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.iterated-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.iterated-loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md b/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md index bef7699d56..5bdd946f71 100644 --- a/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md +++ b/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md @@ -1,33 +1,38 @@ # The Eckmann-Hilton argument ```agda -module synthetic-homotopy-theory.eckmann-hilton-argument where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.eckmann-hilton-argument + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-homotopies funext open import foundation.dependent-pair-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.interchange-law -open import foundation.path-algebra -open import foundation.transport-along-higher-identifications +open import foundation.path-algebra funext +open import foundation.transport-along-higher-identifications funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-homotopies-concatenation funext +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-equivalences +open import structured-types.pointed-equivalences funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.double-loop-spaces -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.triple-loop-spaces +open import synthetic-homotopy-theory.double-loop-spaces funext +open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.triple-loop-spaces funext ```
diff --git a/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md index 07cb2a030f..b758442881 100644 --- a/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Equifibered sequential diagrams ```agda -module synthetic-homotopy-theory.equifibered-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.equifibered-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module synthetic-homotopy-theory.equifibered-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md index c8954be17c..edf12de7c8 100644 --- a/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Equivalences of cocones under sequential diagrams ```agda -module synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequent ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-squares-of-maps +open import foundation.commuting-prisms-of-maps funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext +open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md b/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md index a5fa74bee9..88675b25e2 100644 --- a/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md @@ -1,25 +1,30 @@ # Equivalences of coforks ```agda -module synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-arrows -open import foundation.equivalences-double-arrows -open import foundation.homotopies -open import foundation.morphisms-arrows +open import foundation.equivalences funext +open import foundation.equivalences funext-arrows +open import foundation.equivalences-double-arrows funext +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows funext ```
diff --git a/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md index 54b42eb7ca..11fbe8e7a8 100644 --- a/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Equivalances of dependent sequential diagrams ```agda -module synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,22 +14,22 @@ module synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams wher ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md index a95a4a12a1..5990d72846 100644 --- a/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md @@ -1,29 +1,34 @@ # Equivalences of descent data for pushouts ```agda -module synthetic-homotopy-theory.equivalences-descent-data-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.equivalences-descent-data-pushouts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md index b82afe8957..85781c6581 100644 --- a/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Equivalences of sequential diagrams ```agda -module synthetic-homotopy-theory.equivalences-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.equivalences-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,23 +14,23 @@ module synthetic-homotopy-theory.equivalences-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.retracts-of-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.retracts-of-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md index 0a68a9200c..f22adb8742 100644 --- a/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md @@ -1,22 +1,27 @@ # Families with descent data for pushouts ```agda -module synthetic-homotopy-theory.families-descent-data-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.families-descent-data-pushouts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.span-diagrams +open import foundation.equivalences funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md index 4343695a69..c8aff2bd82 100644 --- a/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md @@ -1,7 +1,12 @@ # Families with descent data for sequential colimits ```agda -module synthetic-homotopy-theory.families-descent-data-sequential-colimits where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.families-descent-data-sequential-colimits + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module synthetic-homotopy-theory.families-descent-data-sequential-colimits where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.descent-data-sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.descent-data-sequential-colimits funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md index 552c91b146..bc01c56688 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md @@ -1,30 +1,35 @@ # The flattening lemma for coequalizers ```agda -module synthetic-homotopy-theory.flattening-lemma-coequalizers where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.flattening-lemma-coequalizers + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers -open import synthetic-homotopy-theory.flattening-lemma-pushouts -open import synthetic-homotopy-theory.universal-property-coequalizers -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext +open import synthetic-homotopy-theory.flattening-lemma-pushouts funext +open import synthetic-homotopy-theory.universal-property-coequalizers funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md index a5842aaa89..b36252fc9b 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md @@ -1,36 +1,42 @@ # The flattening lemma for pushouts ```agda -module synthetic-homotopy-theory.flattening-lemma-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.flattening-lemma-pushouts + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-cubes-of-maps -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-cubes-of-maps funext +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.transport-along-identifications -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md index 1e014f974d..90f2b602a3 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md @@ -1,7 +1,12 @@ # The flattening lemma for sequential colimits ```agda -module synthetic-homotopy-theory.flattening-lemma-sequential-colimits where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.flattening-lemma-sequential-colimits + (funext : function-extensionality) + where ```
Imports @@ -10,26 +15,26 @@ module synthetic-homotopy-theory.flattening-lemma-sequential-colimits where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-double-arrows -open import foundation.function-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.equivalences funext-double-arrows +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows -open import synthetic-homotopy-theory.families-descent-data-sequential-colimits -open import synthetic-homotopy-theory.flattening-lemma-coequalizers -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams -open import synthetic-homotopy-theory.total-sequential-diagrams -open import synthetic-homotopy-theory.universal-property-coequalizers -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.coforks funext-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext +open import synthetic-homotopy-theory.families-descent-data-sequential-colimits funext +open import synthetic-homotopy-theory.flattening-lemma-coequalizers funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams funext +open import synthetic-homotopy-theory.total-sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-coequalizers funext +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext ```
diff --git a/src/synthetic-homotopy-theory/free-loops.lagda.md b/src/synthetic-homotopy-theory/free-loops.lagda.md index 2ca408cc36..7af38afed2 100644 --- a/src/synthetic-homotopy-theory/free-loops.lagda.md +++ b/src/synthetic-homotopy-theory/free-loops.lagda.md @@ -1,22 +1,27 @@ # Free loops ```agda -module synthetic-homotopy-theory.free-loops where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.free-loops + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.constant-type-families -open import foundation.contractible-types +open import foundation.constant-type-families funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md index 32cc8a5ffa..86a7ec2a31 100644 --- a/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md @@ -1,7 +1,12 @@ # Functoriality of the loop space operation ```agda -module synthetic-homotopy-theory.functoriality-loop-spaces where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.functoriality-loop-spaces + (funext : function-extensionality) + where ```
Imports @@ -9,21 +14,21 @@ module synthetic-homotopy-theory.functoriality-loop-spaces where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.faithful-maps -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.faithful-maps funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.faithful-pointed-maps -open import structured-types.pointed-equivalences -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.faithful-pointed-maps funext +open import structured-types.pointed-equivalences funext +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md index 52944f00cd..34eb9ddcfb 100644 --- a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md @@ -1,7 +1,12 @@ # Functoriality of sequential colimits ```agda -module synthetic-homotopy-theory.functoriality-sequential-colimits where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.functoriality-sequential-colimits + (funext : function-extensionality) + where ```
Imports @@ -10,27 +15,26 @@ module synthetic-homotopy-theory.functoriality-sequential-colimits where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps +open import foundation.commuting-prisms-of-maps funext +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.homotopies -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext +open import foundation.sections funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.retracts-of-sequential-diagrams -open import synthetic-homotopy-theory.sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.retracts-of-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-colimits funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext ```
diff --git a/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md b/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md index 477236e983..a86b0a0faf 100644 --- a/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md @@ -1,28 +1,33 @@ # Functoriality of suspensions ```agda -module synthetic-homotopy-theory.functoriality-suspensions where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.functoriality-suspensions + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.retractions -open import foundation.retracts-of-types -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext +open import foundation.sections funext open import foundation.universe-levels -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.suspension-structures funext +open import synthetic-homotopy-theory.suspensions-of-types funext ```
diff --git a/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md b/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md index cfa1ef495a..c7ff512efa 100644 --- a/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md +++ b/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md @@ -1,24 +1,29 @@ # Groups of loops in `1`-types ```agda -module synthetic-homotopy-theory.groups-of-loops-in-1-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.groups-of-loops-in-1-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.1-types +open import foundation.1-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.groups -open import group-theory.semigroups +open import group-theory.groups funext +open import group-theory.semigroups funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md index 10609483e0..c4d417fc81 100644 --- a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md +++ b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md @@ -1,7 +1,12 @@ # Hatcher's acyclic type ```agda -module synthetic-homotopy-theory.hatchers-acyclic-type where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.hatchers-acyclic-type + (funext : function-extensionality) + where ```
Imports @@ -9,33 +14,33 @@ module synthetic-homotopy-theory.hatchers-acyclic-type where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.commuting-squares-of-identifications funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.pointed-universal-property-contractible-types - -open import synthetic-homotopy-theory.acyclic-types -open import synthetic-homotopy-theory.eckmann-hilton-argument -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.powers-of-loops -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types +open import structured-types.pointed-universal-property-contractible-types funext + +open import synthetic-homotopy-theory.acyclic-types funext +open import synthetic-homotopy-theory.eckmann-hilton-argument funext +open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.powers-of-loops funext +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext ```
diff --git a/src/synthetic-homotopy-theory/homotopy-groups.lagda.md b/src/synthetic-homotopy-theory/homotopy-groups.lagda.md index 2576e23f3b..27341b92b0 100644 --- a/src/synthetic-homotopy-theory/homotopy-groups.lagda.md +++ b/src/synthetic-homotopy-theory/homotopy-groups.lagda.md @@ -1,7 +1,12 @@ # Homotopy groups ```agda -module synthetic-homotopy-theory.homotopy-groups where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.homotopy-groups + (funext : function-extensionality) + where ```
Imports @@ -10,16 +15,16 @@ module synthetic-homotopy-theory.homotopy-groups where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.set-truncations -open import foundation.sets +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.homotopy-automorphism-groups +open import group-theory.concrete-groups funext +open import group-theory.homotopy-automorphism-groups funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-loop-spaces +open import synthetic-homotopy-theory.iterated-loop-spaces funext ```
diff --git a/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md index ed4ca2232d..1bb8968baf 100644 --- a/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md @@ -3,43 +3,48 @@ ```agda {-# OPTIONS --lossy-unification #-} -module synthetic-homotopy-theory.identity-systems-descent-data-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.identity-systems-descent-data-pushouts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.identity-systems -open import foundation.identity-types -open import foundation.sections +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.singleton-induction -open import foundation.span-diagrams -open import foundation.torsorial-type-families -open import foundation.transposition-identifications-along-equivalences -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-identity-types +open import foundation.span-diagrams funext +open import foundation.torsorial-type-families funext +open import foundation.transposition-identifications-along-equivalences funext +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-identity-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts -open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.descent-property-pushouts -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.flattening-lemma-pushouts -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts -open import synthetic-homotopy-theory.sections-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext +open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts funext +open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.descent-property-pushouts funext +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext +open import synthetic-homotopy-theory.families-descent-data-pushouts funext +open import synthetic-homotopy-theory.flattening-lemma-pushouts funext +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext +open import synthetic-homotopy-theory.sections-descent-data-pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md b/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md index f18ec14ff3..d9df3600e1 100644 --- a/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md @@ -1,19 +1,24 @@ # The induction principle of pushouts ```agda -module synthetic-homotopy-theory.induction-principle-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.induction-principle-pushouts + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sections +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md b/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md index 3492b6e4ea..9c14ed1e0b 100644 --- a/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md @@ -1,18 +1,23 @@ # The infinite complex projective space ```agda -module synthetic-homotopy-theory.infinite-complex-projective-space where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.infinite-complex-projective-space + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.set-truncations +open import foundation.equivalences funext +open import foundation.set-truncations funext open import foundation.universe-levels -open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.circle funext ```
diff --git a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md index c651ce59fa..104da02fe0 100644 --- a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md @@ -1,45 +1,49 @@ # Infinite cyclic types ```agda -module synthetic-homotopy-theory.infinite-cyclic-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.infinite-cyclic-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers -open import elementary-number-theory.group-of-integers +open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.group-of-integers funext open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-endomorphisms -open import structured-types.initial-pointed-type-equipped-with-automorphism -open import structured-types.mere-equivalences-types-equipped-with-endomorphisms +open import structured-types.equivalences-types-equipped-with-endomorphisms funext +open import structured-types.initial-pointed-type-equipped-with-automorphism funext +open import structured-types.mere-equivalences-types-equipped-with-endomorphisms funext open import structured-types.pointed-types -open import structured-types.pointed-types-equipped-with-automorphisms -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.pointed-types-equipped-with-automorphisms funext +open import structured-types.types-equipped-with-endomorphisms funext -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext -open import univalent-combinatorics.cyclic-finite-types +open import univalent-combinatorics.cyclic-finite-types funext ```
diff --git a/src/synthetic-homotopy-theory/interval-type.lagda.md b/src/synthetic-homotopy-theory/interval-type.lagda.md index eb421618ba..1279234515 100644 --- a/src/synthetic-homotopy-theory/interval-type.lagda.md +++ b/src/synthetic-homotopy-theory/interval-type.lagda.md @@ -1,7 +1,12 @@ # The interval ```agda -module synthetic-homotopy-theory.interval-type where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.interval-type + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,15 @@ module synthetic-homotopy-theory.interval-type where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-identifications funext +open import foundation.contractible-types funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md index 22f8b3630e..4f642d0a7a 100644 --- a/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md @@ -1,7 +1,12 @@ # Iterated loop spaces ```agda -module synthetic-homotopy-theory.iterated-loop-spaces where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.iterated-loop-spaces + (funext : function-extensionality) + where ```
Imports @@ -9,13 +14,13 @@ module synthetic-homotopy-theory.iterated-loop-spaces where ```agda open import elementary-number-theory.natural-numbers -open import foundation.iterating-functions +open import foundation.iterating-functions funext open import foundation.universe-levels -open import structured-types.h-spaces +open import structured-types.h-spaces funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md index 831ae41a13..4d97b08cd3 100644 --- a/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md @@ -1,7 +1,12 @@ # Iterated suspensions of pointed types ```agda -module synthetic-homotopy-theory.iterated-suspensions-of-pointed-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.iterated-suspensions-of-pointed-types + (funext : function-extensionality) + where ```
Imports @@ -9,12 +14,12 @@ module synthetic-homotopy-theory.iterated-suspensions-of-pointed-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.iterating-functions +open import foundation.iterating-functions funext open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.suspensions-of-pointed-types +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext ```
diff --git a/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md b/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md index 3229530426..e493c45aaa 100644 --- a/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md @@ -1,7 +1,12 @@ # Join powers of types ```agda -module synthetic-homotopy-theory.join-powers-of-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.join-powers-of-types + (funext : function-extensionality) + where ```
Imports @@ -9,11 +14,11 @@ module synthetic-homotopy-theory.join-powers-of-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.empty-types -open import foundation.iterating-functions +open import foundation.empty-types funext +open import foundation.iterating-functions funext open import foundation.universe-levels -open import synthetic-homotopy-theory.joins-of-types +open import synthetic-homotopy-theory.joins-of-types funext ```
diff --git a/src/synthetic-homotopy-theory/joins-of-maps.lagda.md b/src/synthetic-homotopy-theory/joins-of-maps.lagda.md index d31b23c331..4afa049b9f 100644 --- a/src/synthetic-homotopy-theory/joins-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/joins-of-maps.lagda.md @@ -1,22 +1,27 @@ # Joins of maps ```agda -module synthetic-homotopy-theory.joins-of-maps where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.joins-of-maps + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.standard-pullbacks +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.standard-pullbacks funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/joins-of-types.lagda.md b/src/synthetic-homotopy-theory/joins-of-types.lagda.md index 8b6ea38172..564a43a008 100644 --- a/src/synthetic-homotopy-theory/joins-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/joins-of-types.lagda.md @@ -1,36 +1,41 @@ # Joins of types ```agda -module synthetic-homotopy-theory.joins-of-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.joins-of-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.disjunction -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositions +open import foundation.disjunction funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md b/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md index 73c0d3f6e8..c6a9f2fbe7 100644 --- a/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md +++ b/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md @@ -1,19 +1,24 @@ # Left half-smash products ```agda -module synthetic-homotopy-theory.left-half-smash-products where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.left-half-smash-products + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.cofibers-of-maps +open import synthetic-homotopy-theory.cofibers-of-maps funext ```
diff --git a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md index 350415b83a..d4b3bf0018 100644 --- a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md +++ b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md @@ -1,19 +1,24 @@ # The loop homotopy on the circle ```agda -module synthetic-homotopy-theory.loop-homotopy-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.loop-homotopy-circle + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.negated-equality -open import foundation.negation +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.negated-equality funext +open import foundation.negation funext -open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.circle funext ```
diff --git a/src/synthetic-homotopy-theory/loop-spaces.lagda.md b/src/synthetic-homotopy-theory/loop-spaces.lagda.md index d150a83996..561ea93724 100644 --- a/src/synthetic-homotopy-theory/loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/loop-spaces.lagda.md @@ -1,22 +1,27 @@ # Loop spaces ```agda -module synthetic-homotopy-theory.loop-spaces where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.loop-spaces + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.h-spaces -open import structured-types.magmas -open import structured-types.pointed-equivalences +open import structured-types.h-spaces funext +open import structured-types.magmas funext +open import structured-types.pointed-equivalences funext open import structured-types.pointed-types -open import structured-types.wild-quasigroups +open import structured-types.wild-quasigroups funext ```
diff --git a/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md b/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md index 4f3e139b27..70071200f9 100644 --- a/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module synthetic-homotopy-theory.maps-of-prespectra where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.maps-of-prespectra + (funext : function-extensionality) + where ```
Imports @@ -13,17 +18,17 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.universe-levels -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.whiskering-pointed-homotopies-composition -open import structured-types.wild-category-of-pointed-types +open import structured-types.commuting-squares-of-pointed-maps funext +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext +open import structured-types.whiskering-pointed-homotopies-composition funext +open import structured-types.wild-category-of-pointed-types funext -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.prespectra +open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.prespectra funext ```
diff --git a/src/synthetic-homotopy-theory/mere-spheres.lagda.md b/src/synthetic-homotopy-theory/mere-spheres.lagda.md index 70a895594b..fa698acf51 100644 --- a/src/synthetic-homotopy-theory/mere-spheres.lagda.md +++ b/src/synthetic-homotopy-theory/mere-spheres.lagda.md @@ -1,7 +1,12 @@ # Mere spheres ```agda -module synthetic-homotopy-theory.mere-spheres where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.mere-spheres + (funext : function-extensionality) + where ```
Imports
 @@ -10,11 +15,11 @@ module synthetic-homotopy-theory.mere-spheres where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.mere-equivalences -open import foundation.propositions +open import foundation.mere-equivalences funext +open import foundation.propositions funext open import foundation.universe-levels -open import synthetic-homotopy-theory.spheres +open import synthetic-homotopy-theory.spheres funext ```
diff --git a/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md index ab2a8b89e3..44d7ec9623 100644 --- a/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Morphisms of cocones under morphisms of sequential diagrams ```agda -module synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-di ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-prisms-of-maps -open import foundation.commuting-squares-of-maps +open import foundation.commuting-prisms-of-maps funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md b/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md index 05c6762c56..45e10d9cdb 100644 --- a/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md @@ -1,22 +1,27 @@ # Morphisms of coforks ```agda -module synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.homotopies -open import foundation.morphisms-arrows -open import foundation.morphisms-double-arrows +open import foundation.homotopies funext +open import foundation.morphisms-arrows funext +open import foundation.morphisms-double-arrows funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.coforks funext ```
diff --git a/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md index 129a0c0eca..43ef1ed44e 100644 --- a/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Morphisms of dependent sequential diagrams ```agda -module synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,12 +14,12 @@ module synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md b/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md index d579804e93..30b97f9572 100644 --- a/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md @@ -1,18 +1,23 @@ # Morphisms of descent data of the circle ```agda -module synthetic-homotopy-theory.morphisms-descent-data-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.morphisms-descent-data-circle + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.universe-levels -open import structured-types.morphisms-types-equipped-with-automorphisms +open import structured-types.morphisms-types-equipped-with-automorphisms funext -open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.descent-circle funext ```
diff --git a/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md index 27f747d90f..6f13b42ecb 100644 --- a/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md @@ -1,29 +1,34 @@ # Morphisms of descent data for pushouts ```agda -module synthetic-homotopy-theory.morphisms-descent-data-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.morphisms-descent-data-pushouts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.descent-data-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md index a094834153..3fc192fa7b 100644 --- a/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Morphisms of sequential diagrams ```agda -module synthetic-homotopy-theory.morphisms-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.morphisms-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,24 @@ module synthetic-homotopy-theory.morphisms-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps +open import foundation.binary-homotopies funext +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md index 7e6b3a6784..f95542e0be 100644 --- a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md +++ b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md @@ -1,7 +1,12 @@ # The multiplication operation on the circle ```agda -module synthetic-homotopy-theory.multiplication-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.multiplication-circle + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,16 @@ module synthetic-homotopy-theory.multiplication-circle where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality-axiom -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext -open import synthetic-homotopy-theory.circle -open import synthetic-homotopy-theory.loop-homotopy-circle +open import synthetic-homotopy-theory.circle funext +open import synthetic-homotopy-theory.loop-homotopy-circle funext ```
diff --git a/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md b/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md index 277a8788fb..9c3a69fe06 100644 --- a/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md @@ -1,28 +1,33 @@ # Null cocones under pointed span diagrams ```agda -module synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.commuting-squares-of-pointed-maps -open import structured-types.constant-pointed-maps -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps -open import structured-types.pointed-span-diagrams +open import structured-types.commuting-squares-of-pointed-maps funext +open import structured-types.constant-pointed-maps funext +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext +open import structured-types.pointed-span-diagrams funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/plus-principle.lagda.md b/src/synthetic-homotopy-theory/plus-principle.lagda.md index 30af8ac24a..40eeda9f18 100644 --- a/src/synthetic-homotopy-theory/plus-principle.lagda.md +++ b/src/synthetic-homotopy-theory/plus-principle.lagda.md @@ -1,18 +1,23 @@ # The plus-principle ```agda -module synthetic-homotopy-theory.plus-principle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.plus-principle + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.connected-types -open import foundation.contractible-types +open import foundation.connected-types funext +open import foundation.contractible-types funext open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.acyclic-types +open import synthetic-homotopy-theory.acyclic-types funext ```
diff --git a/src/synthetic-homotopy-theory/powers-of-loops.lagda.md b/src/synthetic-homotopy-theory/powers-of-loops.lagda.md index 37c127d6f1..4b9e1ef197 100644 --- a/src/synthetic-homotopy-theory/powers-of-loops.lagda.md +++ b/src/synthetic-homotopy-theory/powers-of-loops.lagda.md @@ -1,7 +1,12 @@ # Powers of loops ```agda -module synthetic-homotopy-theory.powers-of-loops where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.powers-of-loops + (funext : function-extensionality) + where ```
Imports @@ -13,18 +18,18 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.equivalences -open import foundation.identity-types -open import foundation.iterating-automorphisms -open import foundation.iterating-functions +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.iterating-automorphisms funext +open import foundation.iterating-functions funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/synthetic-homotopy-theory/premanifolds.lagda.md b/src/synthetic-homotopy-theory/premanifolds.lagda.md index 9702bfc037..cf0e9d0e14 100644 --- a/src/synthetic-homotopy-theory/premanifolds.lagda.md +++ b/src/synthetic-homotopy-theory/premanifolds.lagda.md @@ -1,7 +1,12 @@ # Premanifolds ```agda -module synthetic-homotopy-theory.premanifolds where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.premanifolds + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,17 @@ module synthetic-homotopy-theory.premanifolds where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.mere-equivalences +open import foundation.mere-equivalences funext open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.mere-spheres -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.spheres -open import synthetic-homotopy-theory.tangent-spheres +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.mere-spheres funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.spheres funext +open import synthetic-homotopy-theory.tangent-spheres funext ```
diff --git a/src/synthetic-homotopy-theory/prespectra.lagda.md b/src/synthetic-homotopy-theory/prespectra.lagda.md index b4318725d3..742a13954c 100644 --- a/src/synthetic-homotopy-theory/prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/prespectra.lagda.md @@ -1,7 +1,12 @@ # Prespectra ```agda -module synthetic-homotopy-theory.prespectra where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.prespectra + (funext : function-extensionality) + where ```
Imports @@ -10,16 +15,16 @@ module synthetic-homotopy-theory.prespectra where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext ```
diff --git a/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md index 73103fae01..080d6ce7b5 100644 --- a/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md @@ -1,21 +1,26 @@ # The pullback property of pushouts ```agda -module synthetic-homotopy-theory.pullback-property-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.pullback-property-pushouts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.cones-over-cospan-diagrams +open import foundation.commuting-squares-of-maps funext +open import foundation.cones-over-cospan-diagrams funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.precomposition-functions -open import foundation.pullbacks +open import foundation.function-types funext +open import foundation.precomposition-functions funext +open import foundation.pullbacks funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/pushout-products.lagda.md b/src/synthetic-homotopy-theory/pushout-products.lagda.md index 5756497b68..579ea2e75c 100644 --- a/src/synthetic-homotopy-theory/pushout-products.lagda.md +++ b/src/synthetic-homotopy-theory/pushout-products.lagda.md @@ -1,23 +1,28 @@ # Pushout-products ```agda -module synthetic-homotopy-theory.pushout-products where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.pushout-products + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopies +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md index 53105ba5b8..0ee383c19b 100644 --- a/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md @@ -1,7 +1,12 @@ # Pushouts of pointed types ```agda -module synthetic-homotopy-theory.pushouts-of-pointed-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.pushouts-of-pointed-types + (funext : function-extensionality) + where ```
Imports @@ -9,14 +14,14 @@ module synthetic-homotopy-theory.pushouts-of-pointed-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext +open import synthetic-homotopy-theory.pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/pushouts.lagda.md b/src/synthetic-homotopy-theory/pushouts.lagda.md index 1b5112681f..308f91b3ad 100644 --- a/src/synthetic-homotopy-theory/pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/pushouts.lagda.md @@ -1,7 +1,12 @@ # Pushouts ```agda -module synthetic-homotopy-theory.pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.pushouts + (funext : function-extensionality) + where ```
Imports @@ -9,31 +14,31 @@ module synthetic-homotopy-theory.pushouts where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.constant-type-families +open import foundation.commuting-squares-of-maps funext +open import foundation.constant-type-families funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.transport-along-homotopies +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.transport-along-homotopies funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import reflection.erasing-equality -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.flattening-lemma-pushouts -open import synthetic-homotopy-theory.induction-principle-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext +open import synthetic-homotopy-theory.flattening-lemma-pushouts funext +open import synthetic-homotopy-theory.induction-principle-pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md b/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md index af0fa511a5..9c82dd1347 100644 --- a/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md @@ -1,19 +1,24 @@ # The recursion principle of pushouts ```agda -module synthetic-homotopy-theory.recursion-principle-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.recursion-principle-pushouts + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sections +open import foundation.identity-types funext +open import foundation.sections funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md index 13ad9399bb..abb60c401a 100644 --- a/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Retracts of sequential diagrams ```agda -module synthetic-homotopy-theory.retracts-of-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.retracts-of-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,20 +14,20 @@ module synthetic-homotopy-theory.retracts-of-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.retractions -open import foundation.retracts-of-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md b/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md index 5b471fe9ff..52f521c9fd 100644 --- a/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md @@ -3,21 +3,26 @@ ```agda {-# OPTIONS --rewriting #-} -module synthetic-homotopy-theory.rewriting-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.rewriting-pushouts + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels open import reflection.rewriting -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md b/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md index 77c8924b1c..585cd39b97 100644 --- a/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md @@ -1,7 +1,12 @@ # Sections of families over the circle ```agda -module synthetic-homotopy-theory.sections-descent-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.sections-descent-circle + (funext : function-extensionality) + where ```
Imports @@ -9,27 +14,27 @@ module synthetic-homotopy-theory.sections-descent-circle where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-identifications -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.descent-circle funext +open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.universal-property-circle funext ```
diff --git a/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md index 583235db13..067f3b3aab 100644 --- a/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md @@ -1,7 +1,12 @@ # Sections of descent data for pushouts ```agda -module synthetic-homotopy-theory.sections-descent-data-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.sections-descent-data-pushouts + (funext : function-extensionality) + where ```
Imports @@ -9,31 +14,31 @@ module synthetic-homotopy-theory.sections-descent-data-pushouts where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.span-diagrams +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.span-diagrams funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-universal-property-pushouts -open import synthetic-homotopy-theory.descent-data-pushouts -open import synthetic-homotopy-theory.families-descent-data-pushouts -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext +open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.families-descent-data-pushouts funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/sequential-colimits.lagda.md index e0767413bd..d5337cad00 100644 --- a/src/synthetic-homotopy-theory/sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/sequential-colimits.lagda.md @@ -1,7 +1,12 @@ # Sequential colimits ```agda -module synthetic-homotopy-theory.sequential-colimits where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.sequential-colimits + (funext : function-extensionality) + where ```
Imports @@ -9,23 +14,23 @@ module synthetic-homotopy-theory.sequential-colimits where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.propositions funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coequalizers -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.coequalizers funext +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext ```
diff --git a/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md index 44b7e094cb..6e44a4ffbc 100644 --- a/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Sequential diagrams ```agda -module synthetic-homotopy-theory.sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,9 +14,9 @@ module synthetic-homotopy-theory.sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels ``` diff --git a/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md b/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md index bd20d04559..b73928730b 100644 --- a/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md +++ b/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md @@ -1,18 +1,23 @@ # Sequentially compact types ```agda -module synthetic-homotopy-theory.sequentially-compact-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.sequentially-compact-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.propositions +open import foundation.propositions funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext ```
diff --git a/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md index c7c6e22f6f..5387d22e66 100644 --- a/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Shifts of sequential diagrams ```agda -module synthetic-homotopy-theory.shifts-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.shifts-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,26 +14,26 @@ module synthetic-homotopy-theory.shifts-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext open import foundation.homotopy-algebra -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation - -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.functoriality-sequential-colimits -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import foundation.whiskering-homotopies-concatenation funext + +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.functoriality-sequential-colimits funext +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-colimits funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext ```
diff --git a/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md index 92f38de1c4..c77a7759b1 100644 --- a/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md @@ -1,33 +1,38 @@ # Smash products of pointed types ```agda -module synthetic-homotopy-theory.smash-products-of-pointed-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.smash-products-of-pointed-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import structured-types.constant-pointed-maps -open import structured-types.pointed-cartesian-product-types -open import structured-types.pointed-homotopies -open import structured-types.pointed-maps +open import structured-types.constant-pointed-maps funext +open import structured-types.pointed-cartesian-product-types funext +open import structured-types.pointed-homotopies funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.pointed-unit-type +open import structured-types.pointed-unit-type funext -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.cofibers-of-pointed-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.wedges-of-pointed-types +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext +open import synthetic-homotopy-theory.cofibers-of-pointed-maps funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.wedges-of-pointed-types funext ```
diff --git a/src/synthetic-homotopy-theory/spectra.lagda.md b/src/synthetic-homotopy-theory/spectra.lagda.md index ba8278a8ec..ebec793c9c 100644 --- a/src/synthetic-homotopy-theory/spectra.lagda.md +++ b/src/synthetic-homotopy-theory/spectra.lagda.md @@ -1,7 +1,12 @@ # Spectra ```agda -module synthetic-homotopy-theory.spectra where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.spectra + (funext : function-extensionality) + where ```
Imports @@ -10,20 +15,20 @@ module synthetic-homotopy-theory.spectra where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.pointed-equivalences funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.prespectra funext +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.suspensions-of-types funext ```
diff --git a/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md b/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md index 2a8ad9eab1..75b682c38d 100644 --- a/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md +++ b/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md @@ -1,7 +1,12 @@ # The sphere prespectrum ```agda -module synthetic-homotopy-theory.sphere-prespectrum where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.sphere-prespectrum + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module synthetic-homotopy-theory.sphere-prespectrum where open import foundation.dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.suspension-prespectra +open import synthetic-homotopy-theory.prespectra funext +open import synthetic-homotopy-theory.suspension-prespectra funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/synthetic-homotopy-theory/spheres.lagda.md b/src/synthetic-homotopy-theory/spheres.lagda.md index 85490fc5db..228674efbb 100644 --- a/src/synthetic-homotopy-theory/spheres.lagda.md +++ b/src/synthetic-homotopy-theory/spheres.lagda.md @@ -1,7 +1,12 @@ # Spheres ```agda -module synthetic-homotopy-theory.spheres where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.spheres + (funext : function-extensionality) + where ```
Imports @@ -10,16 +15,16 @@ module synthetic-homotopy-theory.spheres where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.suspensions-of-types funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md b/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md index 54a0453fb9..9e38e39644 100644 --- a/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md @@ -1,7 +1,12 @@ # Suspension prespectra ```agda -module synthetic-homotopy-theory.suspension-prespectra where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.suspension-prespectra + (funext : function-extensionality) + where ```
Imports @@ -12,14 +17,14 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-maps +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.prespectra -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types +open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.prespectra funext +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext ```
diff --git a/src/synthetic-homotopy-theory/suspension-structures.lagda.md b/src/synthetic-homotopy-theory/suspension-structures.lagda.md index 7d579d350f..15166954da 100644 --- a/src/synthetic-homotopy-theory/suspension-structures.lagda.md +++ b/src/synthetic-homotopy-theory/suspension-structures.lagda.md @@ -1,33 +1,39 @@ # Suspension Structures ```agda -module synthetic-homotopy-theory.suspension-structures where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.suspension-structures + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications -open import foundation.constant-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-identifications funext +open import foundation.constant-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.identity-systems -open import foundation.identity-types -open import foundation.injective-maps +open import foundation.identity-types funext +open import foundation.injective-maps funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.unit-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext -open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.cocones-under-spans funext ```
diff --git a/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md index 3e57879259..2436f70d05 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md @@ -1,22 +1,27 @@ # Suspensions of pointed types ```agda -module synthetic-homotopy-theory.suspensions-of-pointed-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.suspensions-of-pointed-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.constant-maps +open import foundation.constant-maps funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.suspension-structures funext +open import synthetic-homotopy-theory.suspensions-of-types funext ```
diff --git a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md index 511ff1e9b6..c9d20286ff 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md @@ -1,39 +1,44 @@ # Suspensions of propositions ```agda -module synthetic-homotopy-theory.suspensions-of-propositions where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.suspensions-of-propositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.booleans -open import foundation.contractible-types +open import foundation.booleans funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sets funext open import foundation.subsingleton-induction -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.surjective-maps funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-suspension-structures -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.dependent-suspension-structures funext +open import synthetic-homotopy-theory.suspension-structures funext +open import synthetic-homotopy-theory.suspensions-of-types funext -open import univalent-combinatorics.kuratowski-finite-sets +open import univalent-combinatorics.kuratowski-finite-sets funext ```
diff --git a/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md index b0d6084cbc..d899fd67dd 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md @@ -1,7 +1,12 @@ # Suspensions of types ```agda -module synthetic-homotopy-theory.suspensions-of-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.suspensions-of-types + (funext : function-extensionality) + where ```
Imports @@ -9,46 +14,47 @@ module synthetic-homotopy-theory.suspensions-of-types where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.booleans -open import foundation.commuting-squares-of-identifications -open import foundation.connected-types -open import foundation.constant-maps -open import foundation.contractible-types -open import foundation.dependent-identifications +open import foundation.booleans funext +open import foundation.commuting-squares-of-identifications funext +open import foundation.connected-types funext +open import foundation.constant-maps funext +open import foundation.contractible-types funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retractions -open import foundation.sections -open import foundation.surjective-maps -open import foundation.torsorial-type-families +open import foundation.diagonal-maps-of-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.retractions funext +open import foundation.sections funext +open import foundation.surjective-maps funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.dependent-cocones-under-spans -open import synthetic-homotopy-theory.dependent-suspension-structures -open import synthetic-homotopy-theory.dependent-universal-property-suspensions -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.universal-property-pushouts -open import synthetic-homotopy-theory.universal-property-suspensions +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.dependent-suspension-structures funext +open import synthetic-homotopy-theory.dependent-universal-property-suspensions funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.suspension-structures funext +open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.universal-property-suspensions funext ```
diff --git a/src/synthetic-homotopy-theory/tangent-spheres.lagda.md b/src/synthetic-homotopy-theory/tangent-spheres.lagda.md index ec35fb7cab..e8436abc95 100644 --- a/src/synthetic-homotopy-theory/tangent-spheres.lagda.md +++ b/src/synthetic-homotopy-theory/tangent-spheres.lagda.md @@ -1,7 +1,12 @@ # Tangent spheres ```agda -module synthetic-homotopy-theory.tangent-spheres where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.tangent-spheres + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module synthetic-homotopy-theory.tangent-spheres where ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps +open import foundation.commuting-squares-of-maps funext open import foundation.dependent-pair-types -open import foundation.mere-equivalences +open import foundation.mere-equivalences funext open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.mere-spheres -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.spheres +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.mere-spheres funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.spheres funext ```
diff --git a/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md index 5c6d86df34..428f47fd7e 100644 --- a/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Total cocones of type families over cocones under sequential diagrams ```agda -module synthetic-homotopy-theory.total-cocones-families-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.total-cocones-families-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -11,20 +16,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation - -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.families-descent-data-sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.total-sequential-diagrams +open import foundation.whiskering-identifications-concatenation funext + +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext +open import synthetic-homotopy-theory.families-descent-data-sequential-colimits funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.total-sequential-diagrams funext ```
diff --git a/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md index 22e1060a68..48730d7cd2 100644 --- a/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Total sequential diagrams of dependent sequential diagrams ```agda -module synthetic-homotopy-theory.total-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.total-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -10,19 +15,19 @@ module synthetic-homotopy-theory.total-sequential-diagrams where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.functoriality-sequential-colimits -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-colimits -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams funext +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext +open import synthetic-homotopy-theory.functoriality-sequential-colimits funext +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-colimits funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext ```
diff --git a/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md index cdb70b73bf..2454018226 100644 --- a/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md @@ -1,7 +1,12 @@ # Triple loop spaces ```agda -module synthetic-homotopy-theory.triple-loop-spaces where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.triple-loop-spaces + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module synthetic-homotopy-theory.triple-loop-spaces where ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.homotopies -open import foundation.identity-types -open import foundation.path-algebra +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.path-algebra funext open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.double-loop-spaces -open import synthetic-homotopy-theory.iterated-loop-spaces +open import synthetic-homotopy-theory.double-loop-spaces funext +open import synthetic-homotopy-theory.iterated-loop-spaces funext ```
diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md index 95872ea9f7..5135298f66 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md @@ -1,58 +1,63 @@ # `k`-acyclic maps ```agda -module synthetic-homotopy-theory.truncated-acyclic-maps where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.truncated-acyclic-maps + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.cones-over-cospan-diagrams -open import foundation.connected-maps -open import foundation.connected-types -open import foundation.constant-maps -open import foundation.dependent-epimorphisms-with-respect-to-truncated-types +open import foundation.cartesian-product-types funext +open import foundation.cones-over-cospan-diagrams funext +open import foundation.connected-maps funext +open import foundation.connected-types funext +open import foundation.constant-maps funext +open import foundation.dependent-epimorphisms-with-respect-to-truncated-types funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.diagonal-maps-of-types -open import foundation.embeddings -open import foundation.epimorphisms-with-respect-to-truncated-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-fibers-of-maps -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.pullbacks -open import foundation.retracts-of-maps -open import foundation.torsorial-type-families -open import foundation.truncated-types -open import foundation.truncation-equivalences +open import foundation.dependent-universal-property-equivalences funext +open import foundation.diagonal-maps-of-types funext +open import foundation.embeddings funext +open import foundation.epimorphisms-with-respect-to-truncated-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-fibers-of-maps funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.pullbacks funext +open import foundation.retracts-of-maps funext +open import foundation.torsorial-type-families funext +open import foundation.truncated-types funext +open import foundation.truncation-equivalences funext open import foundation.truncation-levels -open import foundation.truncations +open import foundation.truncations funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types -open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-dependent-pair-types funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.codiagonals-of-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.truncated-acyclic-types -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.codiagonals-of-maps funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.truncated-acyclic-types funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md index 6324c36e58..aa46246c1f 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md @@ -1,23 +1,28 @@ # `k`-acyclic types ```agda -module synthetic-homotopy-theory.truncated-acyclic-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.truncated-acyclic-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.connected-types -open import foundation.contractible-types -open import foundation.equivalences -open import foundation.propositions -open import foundation.retracts-of-types +open import foundation.connected-types funext +open import foundation.contractible-types funext +open import foundation.equivalences funext +open import foundation.propositions funext +open import foundation.retracts-of-types funext open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.functoriality-suspensions -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.functoriality-suspensions funext +open import synthetic-homotopy-theory.suspensions-of-types funext ```
diff --git a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md index 55603d9eb5..957dfac0e1 100644 --- a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md @@ -3,48 +3,54 @@ ```agda {-# OPTIONS --lossy-unification #-} -module synthetic-homotopy-theory.universal-cover-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.universal-cover-circle + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-integers +open import elementary-number-theory.equality-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.nonzero-integers -open import elementary-number-theory.universal-property-integers +open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.universal-property-integers funext open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.dependent-identifications +open import foundation.commuting-squares-of-maps funext +open import foundation.dependent-identifications funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.dependent-universal-property-equivalences funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.precomposition-dependent-functions -open import foundation.raising-universe-levels -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.precomposition-dependent-functions funext +open import foundation.raising-universe-levels funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-circle -open import synthetic-homotopy-theory.free-loops -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.universal-property-circle +open import synthetic-homotopy-theory.descent-circle funext +open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.universal-property-circle funext ```
diff --git a/src/synthetic-homotopy-theory/universal-property-circle.lagda.md b/src/synthetic-homotopy-theory/universal-property-circle.lagda.md index 9698cb554f..01bec1af5c 100644 --- a/src/synthetic-homotopy-theory/universal-property-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-circle.lagda.md @@ -1,7 +1,12 @@ # The universal property of the circle ```agda -module synthetic-homotopy-theory.universal-property-circle where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.universal-property-circle + (funext : function-extensionality) + where ```
Imports @@ -9,23 +14,24 @@ module synthetic-homotopy-theory.universal-property-circle where ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.constant-type-families -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.constant-type-families funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sections funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.free-loops funext ```
diff --git a/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md b/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md index 14abaccfc2..2c545c540a 100644 --- a/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md @@ -1,31 +1,36 @@ # The universal property of coequalizers ```agda -module synthetic-homotopy-theory.universal-property-coequalizers where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.universal-property-coequalizers + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-cubes-of-maps -open import foundation.commuting-squares-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.commuting-cubes-of-maps funext +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences -open import foundation.equivalences-double-arrows -open import foundation.fibers-of-maps -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies +open import foundation.equivalences funext +open import foundation.equivalences funext-double-arrows +open import foundation.fibers-of-maps funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md index 171038972c..96dcee0752 100644 --- a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md @@ -3,39 +3,44 @@ ```agda {-# OPTIONS --lossy-unification #-} -module synthetic-homotopy-theory.universal-property-pushouts where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.universal-property-pushouts + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-cubes-of-maps -open import foundation.commuting-squares-of-maps -open import foundation.cones-over-cospan-diagrams -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-cubes-of-maps funext +open import foundation.commuting-squares-of-maps funext +open import foundation.cones-over-cospan-diagrams funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.pullbacks -open import foundation.standard-pullbacks +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.pullbacks funext +open import foundation.standard-pullbacks funext open import foundation.subtype-identity-principle open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.pullback-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.pullback-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md index 7969ee8012..1af2f81977 100644 --- a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md @@ -1,7 +1,12 @@ # The universal property of sequential colimits ```agda -module synthetic-homotopy-theory.universal-property-sequential-colimits where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.universal-property-sequential-colimits + (funext : function-extensionality) + where ```
Imports @@ -10,34 +15,33 @@ module synthetic-homotopy-theory.universal-property-sequential-colimits where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.precomposition-functions -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.precomposition-functions funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.subtype-identity-principle -open import foundation.universal-property-equivalences +open import foundation.universal-property-equivalences funext open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.coforks -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.universal-property-coequalizers +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.coforks funext-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext +open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-coequalizers funext ```
diff --git a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md index a8b0a7025c..64ed2338e3 100644 --- a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md @@ -1,30 +1,35 @@ # Universal Property of suspensions of pointed types ```agda -module synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-equivalences -open import structured-types.pointed-maps +open import structured-types.pointed-equivalences funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces -open import synthetic-homotopy-theory.loop-spaces -open import synthetic-homotopy-theory.suspensions-of-pointed-types -open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.suspensions-of-types funext ```
diff --git a/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md b/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md index b990b79bed..4dbb9eeb18 100644 --- a/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md @@ -1,25 +1,30 @@ # Universal property of suspensions ```agda -module synthetic-homotopy-theory.universal-property-suspensions where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.universal-property-suspensions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.constant-maps +open import foundation.constant-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans -open import synthetic-homotopy-theory.suspension-structures -open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.suspension-structures funext +open import synthetic-homotopy-theory.universal-property-pushouts funext ```
diff --git a/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md index 669ca31a56..2d0d184d5a 100644 --- a/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md @@ -1,26 +1,31 @@ # Wedges of pointed types ```agda -module synthetic-homotopy-theory.wedges-of-pointed-types where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.wedges-of-pointed-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import structured-types.pointed-cartesian-product-types -open import structured-types.pointed-maps +open import structured-types.pointed-cartesian-product-types funext +open import structured-types.pointed-maps funext open import structured-types.pointed-types -open import structured-types.pointed-unit-type +open import structured-types.pointed-unit-type funext -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams -open import synthetic-homotopy-theory.cofibers-of-maps -open import synthetic-homotopy-theory.pushouts -open import synthetic-homotopy-theory.pushouts-of-pointed-types +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext +open import synthetic-homotopy-theory.cofibers-of-maps funext +open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.pushouts funext-of-pointed-types ```
diff --git a/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md index 71068b80e1..0e7729232d 100644 --- a/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md @@ -1,7 +1,12 @@ # Zigzags between sequential diagrams ```agda -module synthetic-homotopy-theory.zigzags-sequential-diagrams where +open import foundation.function-extensionality-axiom + +module + synthetic-homotopy-theory.zigzags-sequential-diagrams + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,24 @@ module synthetic-homotopy-theory.zigzags-sequential-diagrams where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.commuting-squares-of-homotopies -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.cartesian-product-types funext +open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.retractions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.retractions funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.functoriality-sequential-colimits -open import synthetic-homotopy-theory.morphisms-sequential-diagrams -open import synthetic-homotopy-theory.sequential-diagrams -open import synthetic-homotopy-theory.shifts-sequential-diagrams -open import synthetic-homotopy-theory.universal-property-sequential-colimits +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext +open import synthetic-homotopy-theory.functoriality-sequential-colimits funext +open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.shifts-sequential-diagrams funext +open import synthetic-homotopy-theory.universal-property-sequential-colimits funext ```
diff --git a/src/trees.lagda.md b/src/trees.lagda.md index 4da5e8d445..c1258e38c7 100644 --- a/src/trees.lagda.md +++ b/src/trees.lagda.md @@ -7,61 +7,66 @@ ## Files in the `trees` module ```agda -module trees where +open import foundation.function-extensionality-axiom -open import trees.algebras-polynomial-endofunctors public -open import trees.bases-directed-trees public -open import trees.bases-enriched-directed-trees public +module + trees + (funext : function-extensionality) + where + +open import trees.algebras-polynomial-endofunctors funext public +open import trees.bases-directed-trees funext public +open import trees.bases-enriched-directed-trees funext public open import trees.binary-w-types public -open import trees.bounded-multisets public -open import trees.coalgebra-of-directed-trees public -open import trees.coalgebra-of-enriched-directed-trees public -open import trees.coalgebras-polynomial-endofunctors public -open import trees.combinator-directed-trees public -open import trees.combinator-enriched-directed-trees public -open import trees.directed-trees public -open import trees.elementhood-relation-coalgebras-polynomial-endofunctors public -open import trees.elementhood-relation-w-types public -open import trees.empty-multisets public -open import trees.enriched-directed-trees public -open import trees.equivalences-directed-trees public -open import trees.equivalences-enriched-directed-trees public -open import trees.extensional-w-types public -open import trees.fibers-directed-trees public -open import trees.fibers-enriched-directed-trees public -open import trees.full-binary-trees public -open import trees.functoriality-combinator-directed-trees public -open import trees.functoriality-fiber-directed-tree public -open import trees.functoriality-w-types public -open import trees.hereditary-w-types public +open import trees.bounded-multisets funext public +open import trees.coalgebra-of-directed-trees funext public +open import trees.coalgebra-of-enriched-directed-trees funext public +open import trees.coalgebras-polynomial-endofunctors funext public +open import trees.combinator-directed-trees funext public +open import trees.combinator-enriched-directed-trees funext public +open import trees.directed-trees funext public +open import trees.elementhood-relation-coalgebras-polynomial-endofunctors funext public +open import trees.elementhood-relation-w-types funext public +open import trees.empty-multisets funext public +open import trees.enriched-directed-trees funext public +open import trees.equivalences-directed-trees funext public +open import trees.equivalences-enriched-directed-trees funext public +open import trees.extensional-w-types funext public +open import trees.fibers-directed-trees funext public +open import trees.fibers-enriched-directed-trees funext public +open import trees.full-binary-trees funext public +open import trees.functoriality-combinator-directed-trees funext public +open import trees.functoriality-fiber-directed-tree funext public +open import trees.functoriality-w-types funext public +open import trees.hereditary-w-types funext public open import trees.indexed-w-types public -open import trees.induction-w-types public -open import trees.inequality-w-types public -open import trees.lower-types-w-types public -open import trees.morphisms-algebras-polynomial-endofunctors public -open import trees.morphisms-coalgebras-polynomial-endofunctors public -open import trees.morphisms-directed-trees public -open import trees.morphisms-enriched-directed-trees public -open import trees.multiset-indexed-dependent-products-of-types public -open import trees.multisets public -open import trees.planar-binary-trees public -open import trees.plane-trees public -open import trees.polynomial-endofunctors public -open import trees.raising-universe-levels-directed-trees public -open import trees.ranks-of-elements-w-types public -open import trees.rooted-morphisms-directed-trees public -open import trees.rooted-morphisms-enriched-directed-trees public -open import trees.rooted-quasitrees public -open import trees.rooted-undirected-trees public -open import trees.small-multisets public -open import trees.submultisets public -open import trees.transitive-multisets public -open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors public -open import trees.underlying-trees-of-elements-of-w-types public -open import trees.undirected-trees public -open import trees.universal-multiset public +open import trees.induction-w-types funext public +open import trees.inequality-w-types funext public +open import trees.lower-types-w-types funext public +open import trees.morphisms-algebras-polynomial-endofunctors funext public +open import trees.morphisms-coalgebras-polynomial-endofunctors funext public +open import trees.morphisms-directed-trees funext public +open import trees.morphisms-enriched-directed-trees funext public +open import trees.multiset-indexed-dependent-products-of-types funext public +open import trees.multisets funext public +open import trees.planar-binary-trees funext public +open import trees.plane-trees funext public +open import trees.polynomial-endofunctors funext public +open import trees.raising-universe-levels-directed-trees funext public +open import trees.ranks-of-elements-w-types funext public +open import trees.rooted-morphisms-directed-trees funext public +open import trees.rooted-morphisms-enriched-directed-trees funext public +open import trees.rooted-quasitrees funext public +open import trees.rooted-undirected-trees funext public +open import trees.small-multisets funext public +open import trees.submultisets funext public +open import trees.transitive-multisets funext public +open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors funext public +open import trees.underlying-trees-of-elements-of-w-types funext public +open import trees.undirected-trees funext public +open import trees.universal-multiset funext public open import trees.universal-tree public -open import trees.w-type-of-natural-numbers public -open import trees.w-type-of-propositions public -open import trees.w-types public +open import trees.w-type-of-natural-numbers funext public +open import trees.w-type-of-propositions funext public +open import trees.w-types funext public ``` diff --git a/src/trees/algebras-polynomial-endofunctors.lagda.md b/src/trees/algebras-polynomial-endofunctors.lagda.md index ca1ac4e432..8964993518 100644 --- a/src/trees/algebras-polynomial-endofunctors.lagda.md +++ b/src/trees/algebras-polynomial-endofunctors.lagda.md @@ -1,7 +1,12 @@ # Algebras for polynomial endofunctors ```agda -module trees.algebras-polynomial-endofunctors where +open import foundation.function-extensionality-axiom + +module + trees.algebras-polynomial-endofunctors + (funext : function-extensionality) + where ```
Imports @@ -10,7 +15,7 @@ module trees.algebras-polynomial-endofunctors where open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext ```
diff --git a/src/trees/bases-directed-trees.lagda.md b/src/trees/bases-directed-trees.lagda.md index 2e96641277..966f29407a 100644 --- a/src/trees/bases-directed-trees.lagda.md +++ b/src/trees/bases-directed-trees.lagda.md @@ -1,7 +1,12 @@ # Bases of directed trees ```agda -module trees.bases-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.bases-directed-trees + (funext : function-extensionality) + where ```
Imports @@ -10,26 +15,26 @@ module trees.bases-directed-trees where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negation -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.universe-levels -open import graph-theory.walks-directed-graphs +open import graph-theory.walks-directed-graphs funext -open import trees.directed-trees +open import trees.directed-trees funext ```
diff --git a/src/trees/bases-enriched-directed-trees.lagda.md b/src/trees/bases-enriched-directed-trees.lagda.md index 6d2feee2cc..8d55af2aa4 100644 --- a/src/trees/bases-enriched-directed-trees.lagda.md +++ b/src/trees/bases-enriched-directed-trees.lagda.md @@ -1,26 +1,31 @@ # Bases of enriched directed trees ```agda -module trees.bases-enriched-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.bases-enriched-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.negation -open import foundation.type-arithmetic-empty-type +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.type-arithmetic-empty-type funext open import foundation.universe-levels -open import trees.bases-directed-trees -open import trees.enriched-directed-trees +open import trees.bases-directed-trees funext +open import trees.enriched-directed-trees funext ```
diff --git a/src/trees/bounded-multisets.lagda.md b/src/trees/bounded-multisets.lagda.md index ceda35ae57..c9cd740194 100644 --- a/src/trees/bounded-multisets.lagda.md +++ b/src/trees/bounded-multisets.lagda.md @@ -1,7 +1,12 @@ # Bounded multisets ```agda -module trees.bounded-multisets where +open import foundation.function-extensionality-axiom + +module + trees.bounded-multisets + (funext : function-extensionality) + where ```
Imports @@ -10,14 +15,14 @@ module trees.bounded-multisets where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.propositions funext open import foundation.universe-levels -open import trees.empty-multisets -open import trees.multisets -open import trees.w-types +open import trees.empty-multisets funext +open import trees.multisets funext +open import trees.w-types funext ```
diff --git a/src/trees/coalgebra-of-directed-trees.lagda.md b/src/trees/coalgebra-of-directed-trees.lagda.md index e581169de0..a6deaa23a7 100644 --- a/src/trees/coalgebra-of-directed-trees.lagda.md +++ b/src/trees/coalgebra-of-directed-trees.lagda.md @@ -1,7 +1,12 @@ # The coalgebra of directed trees ```agda -module trees.coalgebra-of-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.coalgebra-of-directed-trees + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module trees.coalgebra-of-directed-trees where open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.bases-directed-trees -open import trees.coalgebras-polynomial-endofunctors -open import trees.directed-trees -open import trees.fibers-directed-trees +open import trees.bases-directed-trees funext +open import trees.coalgebras-polynomial-endofunctors funext +open import trees.directed-trees funext +open import trees.fibers-directed-trees funext ```
diff --git a/src/trees/coalgebra-of-enriched-directed-trees.lagda.md b/src/trees/coalgebra-of-enriched-directed-trees.lagda.md index 32cae5c137..688785211f 100644 --- a/src/trees/coalgebra-of-enriched-directed-trees.lagda.md +++ b/src/trees/coalgebra-of-enriched-directed-trees.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --lossy-unification #-} -module trees.coalgebra-of-enriched-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.coalgebra-of-enriched-directed-trees + (funext : function-extensionality) + where ```
Imports @@ -12,10 +17,10 @@ module trees.coalgebra-of-enriched-directed-trees where open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.coalgebras-polynomial-endofunctors -open import trees.enriched-directed-trees -open import trees.fibers-enriched-directed-trees -open import trees.polynomial-endofunctors +open import trees.coalgebras-polynomial-endofunctors funext +open import trees.enriched-directed-trees funext +open import trees.fibers-enriched-directed-trees funext +open import trees.polynomial-endofunctors funext ```
diff --git a/src/trees/coalgebras-polynomial-endofunctors.lagda.md b/src/trees/coalgebras-polynomial-endofunctors.lagda.md index 85f9f915c3..66f271ca4c 100644 --- a/src/trees/coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/coalgebras-polynomial-endofunctors.lagda.md @@ -1,7 +1,12 @@ # Coalgebras of polynomial endofunctors ```agda -module trees.coalgebras-polynomial-endofunctors where +open import foundation.function-extensionality-axiom + +module + trees.coalgebras-polynomial-endofunctors + (funext : function-extensionality) + where ```
Imports @@ -10,7 +15,7 @@ module trees.coalgebras-polynomial-endofunctors where open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.polynomial-endofunctors +open import trees.polynomial-endofunctors funext ```
diff --git a/src/trees/combinator-directed-trees.lagda.md b/src/trees/combinator-directed-trees.lagda.md index 4d2862298f..f09ad142bc 100644 --- a/src/trees/combinator-directed-trees.lagda.md +++ b/src/trees/combinator-directed-trees.lagda.md @@ -1,39 +1,44 @@ # The combinator of directed trees ```agda -module trees.combinator-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.combinator-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.maybe -open import foundation.negation -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext +open import foundation.maybe funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.walks-directed-graphs funext -open import trees.bases-directed-trees -open import trees.directed-trees -open import trees.equivalences-directed-trees -open import trees.fibers-directed-trees -open import trees.morphisms-directed-trees +open import trees.bases-directed-trees funext +open import trees.directed-trees funext +open import trees.equivalences-directed-trees funext +open import trees.fibers-directed-trees funext +open import trees.morphisms-directed-trees funext ```
diff --git a/src/trees/combinator-enriched-directed-trees.lagda.md b/src/trees/combinator-enriched-directed-trees.lagda.md index 87f07372ae..5fdd7fc5ea 100644 --- a/src/trees/combinator-enriched-directed-trees.lagda.md +++ b/src/trees/combinator-enriched-directed-trees.lagda.md @@ -1,29 +1,34 @@ # Combinators of enriched directed trees ```agda -module trees.combinator-enriched-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.combinator-enriched-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.maybe +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.maybe funext open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext -open import trees.combinator-directed-trees -open import trees.directed-trees -open import trees.enriched-directed-trees -open import trees.equivalences-directed-trees -open import trees.equivalences-enriched-directed-trees -open import trees.fibers-enriched-directed-trees -open import trees.morphisms-directed-trees +open import trees.combinator-directed-trees funext +open import trees.directed-trees funext +open import trees.enriched-directed-trees funext +open import trees.equivalences-directed-trees funext +open import trees.equivalences-enriched-directed-trees funext +open import trees.fibers-enriched-directed-trees funext +open import trees.morphisms-directed-trees funext ```
diff --git a/src/trees/directed-trees.lagda.md b/src/trees/directed-trees.lagda.md index 5c60f5b264..989a36041e 100644 --- a/src/trees/directed-trees.lagda.md +++ b/src/trees/directed-trees.lagda.md @@ -1,7 +1,12 @@ # Directed trees ```agda -module trees.directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.directed-trees + (funext : function-extensionality) + where ```
Imports @@ -10,31 +15,31 @@ module trees.directed-trees where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.walks-directed-graphs funext ```
diff --git a/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md index 283aa1f4a3..531dae4498 100644 --- a/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md @@ -1,20 +1,25 @@ # The elementhood relation on coalgebras of polynomial endofunctors ```agda -module trees.elementhood-relation-coalgebras-polynomial-endofunctors where +open import foundation.function-extensionality-axiom + +module + trees.elementhood-relation-coalgebras-polynomial-endofunctors + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps +open import foundation.fibers-of-maps funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.walks-directed-graphs funext -open import trees.coalgebras-polynomial-endofunctors +open import trees.coalgebras-polynomial-endofunctors funext ```
diff --git a/src/trees/elementhood-relation-w-types.lagda.md b/src/trees/elementhood-relation-w-types.lagda.md index df5c81a9b4..f8ced8f4fb 100644 --- a/src/trees/elementhood-relation-w-types.lagda.md +++ b/src/trees/elementhood-relation-w-types.lagda.md @@ -1,20 +1,25 @@ # The elementhood relation on W-types ```agda -module trees.elementhood-relation-w-types where +open import foundation.function-extensionality-axiom + +module + trees.elementhood-relation-w-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.elementhood-relation-coalgebras-polynomial-endofunctors -open import trees.w-types +open import trees.elementhood-relation-coalgebras-polynomial-endofunctors funext +open import trees.w-types funext ```
diff --git a/src/trees/empty-multisets.lagda.md b/src/trees/empty-multisets.lagda.md index d31b3e8a6b..58b29eed59 100644 --- a/src/trees/empty-multisets.lagda.md +++ b/src/trees/empty-multisets.lagda.md @@ -1,21 +1,26 @@ # Empty multisets ```agda -module trees.empty-multisets where +open import foundation.function-extensionality-axiom + +module + trees.empty-multisets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.multisets -open import trees.w-types +open import trees.elementhood-relation-w-types funext +open import trees.multisets funext +open import trees.w-types funext ```
diff --git a/src/trees/enriched-directed-trees.lagda.md b/src/trees/enriched-directed-trees.lagda.md index f17320ca15..6cc8a8817c 100644 --- a/src/trees/enriched-directed-trees.lagda.md +++ b/src/trees/enriched-directed-trees.lagda.md @@ -1,7 +1,12 @@ # Enriched directed trees ```agda -module trees.enriched-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.enriched-directed-trees + (funext : function-extensionality) + where ```
Imports @@ -10,22 +15,22 @@ module trees.enriched-directed-trees where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.negation -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext +open import foundation.negation funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.directed-graphs +open import graph-theory.directed-graphs funext -open import trees.directed-trees +open import trees.directed-trees funext ```
diff --git a/src/trees/equivalences-directed-trees.lagda.md b/src/trees/equivalences-directed-trees.lagda.md index 5b7a6ffa00..d54a63691a 100644 --- a/src/trees/equivalences-directed-trees.lagda.md +++ b/src/trees/equivalences-directed-trees.lagda.md @@ -1,7 +1,12 @@ # Equivalences of directed trees ```agda -module trees.equivalences-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.equivalences-directed-trees + (funext : function-extensionality) + where ```
Imports @@ -9,26 +14,26 @@ module trees.equivalences-directed-trees where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.equivalences-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.equivalences-directed-graphs funext +open import graph-theory.walks-directed-graphs funext -open import trees.directed-trees -open import trees.morphisms-directed-trees -open import trees.rooted-morphisms-directed-trees +open import trees.directed-trees funext +open import trees.morphisms-directed-trees funext +open import trees.rooted-morphisms-directed-trees funext ```
diff --git a/src/trees/equivalences-enriched-directed-trees.lagda.md b/src/trees/equivalences-enriched-directed-trees.lagda.md index 410b7c1709..4f30a8d34a 100644 --- a/src/trees/equivalences-enriched-directed-trees.lagda.md +++ b/src/trees/equivalences-enriched-directed-trees.lagda.md @@ -1,34 +1,40 @@ # Equivalences of enriched directed trees ```agda -module trees.equivalences-enriched-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.equivalences-enriched-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.enriched-directed-trees -open import trees.equivalences-directed-trees -open import trees.morphisms-directed-trees -open import trees.morphisms-enriched-directed-trees -open import trees.rooted-morphisms-enriched-directed-trees +open import trees.enriched-directed-trees funext +open import trees.equivalences-directed-trees funext +open import trees.morphisms-directed-trees funext +open import trees.morphisms-enriched-directed-trees funext +open import trees.rooted-morphisms-enriched-directed-trees funext ```
diff --git a/src/trees/extensional-w-types.lagda.md b/src/trees/extensional-w-types.lagda.md index 257d84375e..cb3d332cca 100644 --- a/src/trees/extensional-w-types.lagda.md +++ b/src/trees/extensional-w-types.lagda.md @@ -1,36 +1,41 @@ # Extensional W-types ```agda -module trees.extensional-w-types where +open import foundation.function-extensionality-axiom + +module + trees.extensional-w-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.slice -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.slice funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalent-type-families +open import foundation.univalent-type-families funext open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext +open import trees.w-types funext ```
diff --git a/src/trees/fibers-directed-trees.lagda.md b/src/trees/fibers-directed-trees.lagda.md index b1cff222b1..1646230d0a 100644 --- a/src/trees/fibers-directed-trees.lagda.md +++ b/src/trees/fibers-directed-trees.lagda.md @@ -1,25 +1,30 @@ # Fibers of directed trees ```agda -module trees.fibers-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.fibers-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.fibers-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.fibers-directed-graphs funext -open import trees.bases-directed-trees -open import trees.directed-trees -open import trees.morphisms-directed-trees +open import trees.bases-directed-trees funext +open import trees.directed-trees funext +open import trees.morphisms-directed-trees funext ```
diff --git a/src/trees/fibers-enriched-directed-trees.lagda.md b/src/trees/fibers-enriched-directed-trees.lagda.md index d6c2a7b325..11d459fafc 100644 --- a/src/trees/fibers-enriched-directed-trees.lagda.md +++ b/src/trees/fibers-enriched-directed-trees.lagda.md @@ -1,26 +1,31 @@ # Fibers of enriched directed trees ```agda -module trees.fibers-enriched-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.fibers-enriched-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import graph-theory.walks-directed-graphs +open import graph-theory.walks-directed-graphs funext -open import trees.bases-enriched-directed-trees -open import trees.directed-trees -open import trees.enriched-directed-trees -open import trees.fibers-directed-trees +open import trees.bases-enriched-directed-trees funext +open import trees.directed-trees funext +open import trees.enriched-directed-trees funext +open import trees.fibers-directed-trees funext ```
diff --git a/src/trees/full-binary-trees.lagda.md b/src/trees/full-binary-trees.lagda.md index 00ed1e42a8..70a7583c13 100644 --- a/src/trees/full-binary-trees.lagda.md +++ b/src/trees/full-binary-trees.lagda.md @@ -1,7 +1,12 @@ # Full binary trees ```agda -module trees.full-binary-trees where +open import foundation.function-extensionality-axiom + +module + trees.full-binary-trees + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module trees.full-binary-trees where ```agda open import elementary-number-theory.natural-numbers -open import foundation.empty-types +open import foundation.empty-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/trees/functoriality-combinator-directed-trees.lagda.md b/src/trees/functoriality-combinator-directed-trees.lagda.md index 62ecdf2b9c..e1b2c4d747 100644 --- a/src/trees/functoriality-combinator-directed-trees.lagda.md +++ b/src/trees/functoriality-combinator-directed-trees.lagda.md @@ -1,7 +1,12 @@ # Functoriality of the combinator of directed trees ```agda -module trees.functoriality-combinator-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.functoriality-combinator-directed-trees + (funext : function-extensionality) + where ```
Imports @@ -9,19 +14,19 @@ module trees.functoriality-combinator-directed-trees where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.combinator-directed-trees -open import trees.directed-trees -open import trees.equivalences-directed-trees -open import trees.morphisms-directed-trees -open import trees.rooted-morphisms-directed-trees +open import trees.combinator-directed-trees funext +open import trees.directed-trees funext +open import trees.equivalences-directed-trees funext +open import trees.morphisms-directed-trees funext +open import trees.rooted-morphisms-directed-trees funext ```
diff --git a/src/trees/functoriality-fiber-directed-tree.lagda.md b/src/trees/functoriality-fiber-directed-tree.lagda.md index 2338441e60..2613cbf555 100644 --- a/src/trees/functoriality-fiber-directed-tree.lagda.md +++ b/src/trees/functoriality-fiber-directed-tree.lagda.md @@ -1,7 +1,12 @@ # Functoriality of the fiber operation on directed trees ```agda -module trees.functoriality-fiber-directed-tree where +open import foundation.function-extensionality-axiom + +module + trees.functoriality-fiber-directed-tree + (funext : function-extensionality) + where ```
Imports @@ -9,17 +14,17 @@ module trees.functoriality-fiber-directed-tree where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import graph-theory.walks-directed-graphs +open import graph-theory.walks-directed-graphs funext -open import trees.directed-trees -open import trees.equivalences-directed-trees -open import trees.fibers-directed-trees -open import trees.morphisms-directed-trees +open import trees.directed-trees funext +open import trees.equivalences-directed-trees funext +open import trees.fibers-directed-trees funext +open import trees.morphisms-directed-trees funext ```
diff --git a/src/trees/functoriality-w-types.lagda.md b/src/trees/functoriality-w-types.lagda.md index b664531fd5..f8f0370cf0 100644 --- a/src/trees/functoriality-w-types.lagda.md +++ b/src/trees/functoriality-w-types.lagda.md @@ -1,34 +1,39 @@ # Functoriality of W-types ```agda -module trees.functoriality-w-types where +open import foundation.function-extensionality-axiom + +module + trees.functoriality-w-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-maps +open import foundation.cartesian-product-types funext +open import foundation.contractible-maps funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-maps +open import foundation.dependent-products-truncated-types funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext open import foundation.transport-along-identifications -open import foundation.truncated-maps -open import foundation.truncated-types +open import foundation.truncated-maps funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import trees.w-types +open import trees.w-types funext ```
diff --git a/src/trees/hereditary-w-types.lagda.md b/src/trees/hereditary-w-types.lagda.md index 3e0ff510c9..b27bf69b19 100644 --- a/src/trees/hereditary-w-types.lagda.md +++ b/src/trees/hereditary-w-types.lagda.md @@ -1,7 +1,12 @@ # Hereditary W-types ```agda -module trees.hereditary-w-types where +open import foundation.function-extensionality-axiom + +module + trees.hereditary-w-types + (funext : function-extensionality) + where ```
Imports @@ -10,12 +15,13 @@ module trees.hereditary-w-types where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import trees.binary-w-types diff --git a/src/trees/induction-w-types.lagda.md b/src/trees/induction-w-types.lagda.md index 1805b55311..91f71f5c9b 100644 --- a/src/trees/induction-w-types.lagda.md +++ b/src/trees/induction-w-types.lagda.md @@ -1,7 +1,12 @@ # Induction principles on W-types ```agda -module trees.induction-w-types where +open import foundation.function-extensionality-axiom + +module + trees.induction-w-types + (funext : function-extensionality) + where ```
Imports @@ -11,16 +16,17 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.identity-types -open import foundation.negation +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.inequality-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext +open import trees.inequality-w-types funext +open import trees.w-types funext ```
diff --git a/src/trees/inequality-w-types.lagda.md b/src/trees/inequality-w-types.lagda.md index e8ba671c13..3c1342ee17 100644 --- a/src/trees/inequality-w-types.lagda.md +++ b/src/trees/inequality-w-types.lagda.md @@ -1,7 +1,12 @@ # Inequality on W-types ```agda -module trees.inequality-w-types where +open import foundation.function-extensionality-axiom + +module + trees.inequality-w-types + (funext : function-extensionality) + where ```
Imports @@ -10,13 +15,13 @@ module trees.inequality-w-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.negation +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.negation funext open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext +open import trees.w-types funext ```
diff --git a/src/trees/lower-types-w-types.lagda.md b/src/trees/lower-types-w-types.lagda.md index 5e283be7bb..8d1d225009 100644 --- a/src/trees/lower-types-w-types.lagda.md +++ b/src/trees/lower-types-w-types.lagda.md @@ -1,17 +1,22 @@ # Lower types of elements in W-types ```agda -module trees.lower-types-w-types where +open import foundation.function-extensionality-axiom + +module + trees.lower-types-w-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.existential-quantification +open import foundation.existential-quantification funext open import foundation.universe-levels -open import trees.ranks-of-elements-w-types -open import trees.w-types +open import trees.ranks-of-elements-w-types funext +open import trees.w-types funext ```
diff --git a/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md b/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md index 12364a1b34..c73e9fc746 100644 --- a/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md +++ b/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md @@ -1,29 +1,34 @@ # Morphisms of algebras of polynomial endofunctors ```agda -module trees.morphisms-algebras-polynomial-endofunctors where +open import foundation.function-extensionality-axiom + +module + trees.morphisms-algebras-polynomial-endofunctors + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.algebras-polynomial-endofunctors -open import trees.polynomial-endofunctors +open import trees.algebras-polynomial-endofunctors funext +open import trees.polynomial-endofunctors funext ```
diff --git a/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md index f6771ba67b..fbb67bf1e8 100644 --- a/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md @@ -1,29 +1,34 @@ # Morphisms of coalgebras of polynomial endofunctors ```agda -module trees.morphisms-coalgebras-polynomial-endofunctors where +open import foundation.function-extensionality-axiom + +module + trees.morphisms-coalgebras-polynomial-endofunctors + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.coalgebras-polynomial-endofunctors -open import trees.polynomial-endofunctors +open import trees.coalgebras-polynomial-endofunctors funext +open import trees.polynomial-endofunctors funext ```
diff --git a/src/trees/morphisms-directed-trees.lagda.md b/src/trees/morphisms-directed-trees.lagda.md index 925111eb85..12c9df167c 100644 --- a/src/trees/morphisms-directed-trees.lagda.md +++ b/src/trees/morphisms-directed-trees.lagda.md @@ -1,31 +1,36 @@ # Morphisms of directed trees ```agda -module trees.morphisms-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.morphisms-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.negation -open import foundation.torsorial-type-families +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.universe-levels -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.walks-directed-graphs funext -open import trees.directed-trees +open import trees.directed-trees funext ```
diff --git a/src/trees/morphisms-enriched-directed-trees.lagda.md b/src/trees/morphisms-enriched-directed-trees.lagda.md index 968efd173c..f3c8aea77f 100644 --- a/src/trees/morphisms-enriched-directed-trees.lagda.md +++ b/src/trees/morphisms-enriched-directed-trees.lagda.md @@ -1,25 +1,30 @@ # Morphisms of enriched directed trees ```agda -module trees.morphisms-enriched-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.morphisms-enriched-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.commuting-triangles-of-maps +open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-triangles-of-maps funext open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.enriched-directed-trees -open import trees.morphisms-directed-trees +open import trees.enriched-directed-trees funext +open import trees.morphisms-directed-trees funext ```
diff --git a/src/trees/multiset-indexed-dependent-products-of-types.lagda.md b/src/trees/multiset-indexed-dependent-products-of-types.lagda.md index ed16d82c4d..f06a12883f 100644 --- a/src/trees/multiset-indexed-dependent-products-of-types.lagda.md +++ b/src/trees/multiset-indexed-dependent-products-of-types.lagda.md @@ -1,7 +1,12 @@ # Multiset-indexed dependent products of types ```agda -module trees.multiset-indexed-dependent-products-of-types where +open import foundation.function-extensionality-axiom + +module + trees.multiset-indexed-dependent-products-of-types + (funext : function-extensionality) + where ```
Imports @@ -11,8 +16,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import trees.multisets -open import trees.w-types +open import trees.multisets funext +open import trees.w-types funext ```
diff --git a/src/trees/multisets.lagda.md b/src/trees/multisets.lagda.md index ed24b4339c..4aa26286ad 100644 --- a/src/trees/multisets.lagda.md +++ b/src/trees/multisets.lagda.md @@ -1,19 +1,24 @@ # Multisets ```agda -module trees.multisets where +open import foundation.function-extensionality-axiom + +module + trees.multisets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.function-types +open import foundation.empty-types funext +open import foundation.function-types funext open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext +open import trees.w-types funext ```
diff --git a/src/trees/planar-binary-trees.lagda.md b/src/trees/planar-binary-trees.lagda.md index 3e60500e59..5495fe9e73 100644 --- a/src/trees/planar-binary-trees.lagda.md +++ b/src/trees/planar-binary-trees.lagda.md @@ -1,18 +1,23 @@ # Planar binary trees ```agda -module trees.planar-binary-trees where +open import foundation.function-extensionality-axiom + +module + trees.planar-binary-trees + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.booleans -open import foundation.empty-types -open import foundation.function-types +open import foundation.booleans funext +open import foundation.empty-types funext +open import foundation.function-types funext open import foundation.universe-levels -open import trees.w-types +open import trees.w-types funext ```
diff --git a/src/trees/plane-trees.lagda.md b/src/trees/plane-trees.lagda.md index 12c443c8e3..4b0f2c3477 100644 --- a/src/trees/plane-trees.lagda.md +++ b/src/trees/plane-trees.lagda.md @@ -1,7 +1,12 @@ # Plane trees ```agda -module trees.plane-trees where +open import foundation.function-extensionality-axiom + +module + trees.plane-trees + (funext : function-extensionality) + where ```
Imports @@ -12,20 +17,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.maybe -open import foundation.retractions -open import foundation.sections +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.maybe funext +open import foundation.retractions funext +open import foundation.sections funext open import foundation.universe-levels open import lists.lists -open import trees.full-binary-trees -open import trees.w-types +open import trees.full-binary-trees funext +open import trees.w-types funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/trees/polynomial-endofunctors.lagda.md b/src/trees/polynomial-endofunctors.lagda.md index 793fbf9b59..cca3de9d96 100644 --- a/src/trees/polynomial-endofunctors.lagda.md +++ b/src/trees/polynomial-endofunctors.lagda.md @@ -1,21 +1,26 @@ # Polynomial endofunctors ```agda -module trees.polynomial-endofunctors where +open import foundation.function-extensionality-axiom + +module + trees.polynomial-endofunctors + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/trees/raising-universe-levels-directed-trees.lagda.md b/src/trees/raising-universe-levels-directed-trees.lagda.md index 8f1e1ac294..8e60821837 100644 --- a/src/trees/raising-universe-levels-directed-trees.lagda.md +++ b/src/trees/raising-universe-levels-directed-trees.lagda.md @@ -1,24 +1,29 @@ # Raising universe levels of directed trees ```agda -module trees.raising-universe-levels-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.raising-universe-levels-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.raising-universe-levels +open import foundation.equivalences funext +open import foundation.raising-universe-levels funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.raising-universe-levels-directed-graphs -open import graph-theory.walks-directed-graphs +open import graph-theory.directed-graphs funext +open import graph-theory.raising-universe-levels-directed-graphs funext +open import graph-theory.walks-directed-graphs funext -open import trees.directed-trees -open import trees.equivalences-directed-trees +open import trees.directed-trees funext +open import trees.equivalences-directed-trees funext ```
diff --git a/src/trees/ranks-of-elements-w-types.lagda.md b/src/trees/ranks-of-elements-w-types.lagda.md index 26e9e63740..4026e6eb34 100644 --- a/src/trees/ranks-of-elements-w-types.lagda.md +++ b/src/trees/ranks-of-elements-w-types.lagda.md @@ -1,26 +1,31 @@ # Ranks of elements in W-types ```agda -module trees.ranks-of-elements-w-types where +open import foundation.function-extensionality-axiom + +module + trees.ranks-of-elements-w-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.existential-quantification -open import foundation.identity-types -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.empty-types funext +open import foundation.existential-quantification funext +open import foundation.identity-types funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.elementhood-relation-w-types -open import trees.inequality-w-types -open import trees.w-types +open import trees.elementhood-relation-w-types funext +open import trees.inequality-w-types funext +open import trees.w-types funext ```
diff --git a/src/trees/rooted-morphisms-directed-trees.lagda.md b/src/trees/rooted-morphisms-directed-trees.lagda.md index 81c9d5fc01..74f5ec2274 100644 --- a/src/trees/rooted-morphisms-directed-trees.lagda.md +++ b/src/trees/rooted-morphisms-directed-trees.lagda.md @@ -1,7 +1,12 @@ # Rooted morphisms of directed trees ```agda -module trees.rooted-morphisms-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.rooted-morphisms-directed-trees + (funext : function-extensionality) + where ```
Imports @@ -9,22 +14,22 @@ module trees.rooted-morphisms-directed-trees where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.bases-directed-trees -open import trees.directed-trees -open import trees.morphisms-directed-trees +open import trees.bases-directed-trees funext +open import trees.directed-trees funext +open import trees.morphisms-directed-trees funext ```
diff --git a/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md b/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md index f876ff518a..2cae2ec1d1 100644 --- a/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md +++ b/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md @@ -1,23 +1,28 @@ # Rooted morphisms of enriched directed trees ```agda -module trees.rooted-morphisms-enriched-directed-trees where +open import foundation.function-extensionality-axiom + +module + trees.rooted-morphisms-enriched-directed-trees + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.enriched-directed-trees -open import trees.morphisms-enriched-directed-trees -open import trees.rooted-morphisms-directed-trees +open import trees.enriched-directed-trees funext +open import trees.morphisms-enriched-directed-trees funext +open import trees.rooted-morphisms-directed-trees funext ```
diff --git a/src/trees/rooted-quasitrees.lagda.md b/src/trees/rooted-quasitrees.lagda.md index 596e9e1061..a89cb5c584 100644 --- a/src/trees/rooted-quasitrees.lagda.md +++ b/src/trees/rooted-quasitrees.lagda.md @@ -1,18 +1,23 @@ # Rooted quasitrees ```agda -module trees.rooted-quasitrees where +open import foundation.function-extensionality-axiom + +module + trees.rooted-quasitrees + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.trails-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.trails-undirected-graphs funext +open import graph-theory.undirected-graphs funext ```
diff --git a/src/trees/rooted-undirected-trees.lagda.md b/src/trees/rooted-undirected-trees.lagda.md index 52cf306b9b..bbe771ca31 100644 --- a/src/trees/rooted-undirected-trees.lagda.md +++ b/src/trees/rooted-undirected-trees.lagda.md @@ -1,7 +1,12 @@ # Rooted undirected trees ```agda -module trees.rooted-undirected-trees where +open import foundation.function-extensionality-axiom + +module + trees.rooted-undirected-trees + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module trees.rooted-undirected-trees where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs +open import foundation.unordered-pairs funext -open import graph-theory.trails-undirected-graphs -open import graph-theory.undirected-graphs +open import graph-theory.trails-undirected-graphs funext +open import graph-theory.undirected-graphs funext -open import trees.undirected-trees +open import trees.undirected-trees funext ```
diff --git a/src/trees/small-multisets.lagda.md b/src/trees/small-multisets.lagda.md index 6a8bc2b79f..a7af9b7537 100644 --- a/src/trees/small-multisets.lagda.md +++ b/src/trees/small-multisets.lagda.md @@ -1,7 +1,12 @@ # Small multisets ```agda -module trees.small-multisets where +open import foundation.function-extensionality-axiom + +module + trees.small-multisets + (funext : function-extensionality) + where ```
Imports @@ -9,22 +14,22 @@ module trees.small-multisets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.subtypes +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.small-types funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import trees.multisets -open import trees.w-types +open import trees.multisets funext +open import trees.w-types funext ```
diff --git a/src/trees/submultisets.lagda.md b/src/trees/submultisets.lagda.md index f04365fa46..c23122b0f7 100644 --- a/src/trees/submultisets.lagda.md +++ b/src/trees/submultisets.lagda.md @@ -1,17 +1,22 @@ # Submultisets ```agda -module trees.submultisets where +open import foundation.function-extensionality-axiom + +module + trees.submultisets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.embeddings -open import foundation.equivalences +open import foundation.embeddings funext +open import foundation.equivalences funext open import foundation.universe-levels -open import trees.multisets +open import trees.multisets funext ```
diff --git a/src/trees/transitive-multisets.lagda.md b/src/trees/transitive-multisets.lagda.md index e09627c816..6b1fda3d71 100644 --- a/src/trees/transitive-multisets.lagda.md +++ b/src/trees/transitive-multisets.lagda.md @@ -1,7 +1,12 @@ # Transitive multisets ```agda -module trees.transitive-multisets where +open import foundation.function-extensionality-axiom + +module + trees.transitive-multisets + (funext : function-extensionality) + where ```
Imports @@ -9,8 +14,8 @@ module trees.transitive-multisets where ```agda open import foundation.universe-levels -open import trees.multisets -open import trees.submultisets +open import trees.multisets funext +open import trees.submultisets funext ```
diff --git a/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md index 9184f6da42..1aec74f927 100644 --- a/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md @@ -1,7 +1,12 @@ # The underlying trees of elements of coalgebras of polynomial endofunctors ```agda -module trees.underlying-trees-elements-coalgebras-polynomial-endofunctors where +open import foundation.function-extensionality-axiom + +module + trees.underlying-trees-elements-coalgebras-polynomial-endofunctors + (funext : function-extensionality) + where ```
Imports @@ -9,37 +14,37 @@ module trees.underlying-trees-elements-coalgebras-polynomial-endofunctors where ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.empty-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.negated-equality -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext +open import foundation.negated-equality funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs - -open import trees.coalgebras-polynomial-endofunctors -open import trees.combinator-directed-trees -open import trees.combinator-enriched-directed-trees -open import trees.directed-trees -open import trees.elementhood-relation-coalgebras-polynomial-endofunctors -open import trees.enriched-directed-trees -open import trees.equivalences-directed-trees -open import trees.equivalences-enriched-directed-trees +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.walks-directed-graphs funext + +open import trees.coalgebras-polynomial-endofunctors funext +open import trees.combinator-directed-trees funext +open import trees.combinator-enriched-directed-trees funext +open import trees.directed-trees funext +open import trees.elementhood-relation-coalgebras-polynomial-endofunctors funext +open import trees.enriched-directed-trees funext +open import trees.equivalences-directed-trees funext +open import trees.equivalences-enriched-directed-trees funext ```
diff --git a/src/trees/underlying-trees-of-elements-of-w-types.lagda.md b/src/trees/underlying-trees-of-elements-of-w-types.lagda.md index bd9f754279..d05a62ec35 100644 --- a/src/trees/underlying-trees-of-elements-of-w-types.lagda.md +++ b/src/trees/underlying-trees-of-elements-of-w-types.lagda.md @@ -1,41 +1,46 @@ # The underlying trees of elements of W-types ```agda -module trees.underlying-trees-of-elements-of-w-types where +open import foundation.function-extensionality-axiom + +module + trees.underlying-trees-of-elements-of-w-types + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.negated-equality -open import foundation.propositions -open import foundation.torsorial-type-families +open import foundation.empty-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.isolated-elements funext +open import foundation.negated-equality funext +open import foundation.propositions funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.directed-graphs -open import graph-theory.morphisms-directed-graphs -open import graph-theory.walks-directed-graphs - -open import trees.combinator-directed-trees -open import trees.combinator-enriched-directed-trees -open import trees.directed-trees -open import trees.elementhood-relation-w-types -open import trees.enriched-directed-trees -open import trees.equivalences-directed-trees -open import trees.equivalences-enriched-directed-trees -open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors -open import trees.w-types +open import graph-theory.directed-graphs funext +open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.walks-directed-graphs funext + +open import trees.combinator-directed-trees funext +open import trees.combinator-enriched-directed-trees funext +open import trees.directed-trees funext +open import trees.elementhood-relation-w-types funext +open import trees.enriched-directed-trees funext +open import trees.equivalences-directed-trees funext +open import trees.equivalences-enriched-directed-trees funext +open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors funext +open import trees.w-types funext ```
diff --git a/src/trees/undirected-trees.lagda.md b/src/trees/undirected-trees.lagda.md index f60cce11cf..2ac64dbb5b 100644 --- a/src/trees/undirected-trees.lagda.md +++ b/src/trees/undirected-trees.lagda.md @@ -1,7 +1,12 @@ # Undirected trees ```agda -module trees.undirected-trees where +open import foundation.function-extensionality-axiom + +module + trees.undirected-trees + (funext : function-extensionality) + where ```
Imports @@ -10,23 +15,23 @@ module trees.undirected-trees where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.contractible-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.paths-undirected-graphs -open import graph-theory.trails-undirected-graphs -open import graph-theory.undirected-graphs -open import graph-theory.walks-undirected-graphs +open import graph-theory.paths-undirected-graphs funext +open import graph-theory.trails-undirected-graphs funext +open import graph-theory.undirected-graphs funext +open import graph-theory.walks-undirected-graphs funext ```
diff --git a/src/trees/universal-multiset.lagda.md b/src/trees/universal-multiset.lagda.md index 954321d15a..ec8b278cd7 100644 --- a/src/trees/universal-multiset.lagda.md +++ b/src/trees/universal-multiset.lagda.md @@ -1,25 +1,30 @@ # The universal multiset ```agda -module trees.universal-multiset where +open import foundation.function-extensionality-axiom + +module + trees.universal-multiset + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.raising-universe-levels -open import foundation.small-types -open import foundation.small-universes +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.raising-universe-levels funext +open import foundation.small-types funext +open import foundation.small-universes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.functoriality-w-types -open import trees.multisets -open import trees.small-multisets -open import trees.w-types +open import trees.functoriality-w-types funext +open import trees.multisets funext +open import trees.small-multisets funext +open import trees.w-types funext ```
diff --git a/src/trees/w-type-of-natural-numbers.lagda.md b/src/trees/w-type-of-natural-numbers.lagda.md index 0d61f98e88..f394e72e1e 100644 --- a/src/trees/w-type-of-natural-numbers.lagda.md +++ b/src/trees/w-type-of-natural-numbers.lagda.md @@ -1,7 +1,12 @@ # The W-type of natural numbers ```agda -module trees.w-type-of-natural-numbers where +open import foundation.function-extensionality-axiom + +module + trees.w-type-of-natural-numbers + (funext : function-extensionality) + where ```
Imports @@ -10,19 +15,20 @@ module trees.w-type-of-natural-numbers where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.booleans -open import foundation.contractible-types +open import foundation.booleans funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.unit-type -open import foundation.universal-property-empty-type +open import foundation.universal-property-empty-type funext open import foundation.universe-levels -open import trees.w-types +open import trees.w-types funext ```
diff --git a/src/trees/w-type-of-propositions.lagda.md b/src/trees/w-type-of-propositions.lagda.md index 8b460d8d29..81bf34c4c9 100644 --- a/src/trees/w-type-of-propositions.lagda.md +++ b/src/trees/w-type-of-propositions.lagda.md @@ -1,24 +1,29 @@ # The W-type of the type of propositions ```agda -module trees.w-type-of-propositions where +open import foundation.function-extensionality-axiom + +module + trees.w-type-of-propositions + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.propositional-extensionality -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.sets +open import foundation.empty-types funext +open import foundation.propositional-extensionality funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import trees.extensional-w-types -open import trees.w-types +open import trees.extensional-w-types funext +open import trees.w-types funext ```
diff --git a/src/trees/w-types.lagda.md b/src/trees/w-types.lagda.md index 9e3ae175b9..58ae562716 100644 --- a/src/trees/w-types.lagda.md +++ b/src/trees/w-types.lagda.md @@ -1,39 +1,45 @@ # W-types ```agda -module trees.w-types where +open import foundation.function-extensionality-axiom + +module + trees.w-types + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types +open import foundation.dependent-products-truncated-types funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.homotopy-induction -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.propositional-truncations -open import foundation.sets -open import foundation.torsorial-type-families +open import foundation.homotopies funext +open import foundation.homotopy-induction funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.propositional-truncations funext +open import foundation.sets funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.truncated-types +open import foundation.truncated-types funext open import foundation.truncation-levels -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.algebras-polynomial-endofunctors -open import trees.coalgebras-polynomial-endofunctors -open import trees.morphisms-algebras-polynomial-endofunctors -open import trees.polynomial-endofunctors +open import trees.algebras-polynomial-endofunctors funext +open import trees.coalgebras-polynomial-endofunctors funext +open import trees.morphisms-algebras-polynomial-endofunctors funext +open import trees.polynomial-endofunctors funext ```
diff --git a/src/type-theories.lagda.md b/src/type-theories.lagda.md index 1255733d03..ab4878964a 100644 --- a/src/type-theories.lagda.md +++ b/src/type-theories.lagda.md @@ -7,16 +7,21 @@ ## Modules in the type theories namespace ```agda -module type-theories where +open import foundation.function-extensionality-axiom + +module + type-theories + (funext : function-extensionality) + where open import type-theories.comprehension-type-theories public -open import type-theories.dependent-type-theories public -open import type-theories.fibered-dependent-type-theories public -open import type-theories.pi-types-precategories-with-attributes public -open import type-theories.pi-types-precategories-with-families public -open import type-theories.precategories-with-attributes public -open import type-theories.precategories-with-families public -open import type-theories.sections-dependent-type-theories public -open import type-theories.simple-type-theories public -open import type-theories.unityped-type-theories public +open import type-theories.dependent-type-theories funext public +open import type-theories.fibered-dependent-type-theories funext public +open import type-theories.pi-types-precategories-with-attributes funext public +open import type-theories.pi-types-precategories-with-families funext public +open import type-theories.precategories-with-attributes funext public +open import type-theories.precategories-with-families funext public +open import type-theories.sections-dependent-type-theories funext public +open import type-theories.simple-type-theories funext public +open import type-theories.unityped-type-theories funext public ``` diff --git a/src/type-theories/dependent-type-theories.lagda.md b/src/type-theories/dependent-type-theories.lagda.md index 6f40eba0bc..f7fd49336d 100644 --- a/src/type-theories/dependent-type-theories.lagda.md +++ b/src/type-theories/dependent-type-theories.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module type-theories.dependent-type-theories where +open import foundation.function-extensionality-axiom + +module + type-theories.dependent-type-theories + (funext : function-extensionality) + where ```
Imports @@ -12,14 +17,14 @@ module type-theories.dependent-type-theories where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation +open import foundation.whiskering-identifications-concatenation funext ```
diff --git a/src/type-theories/fibered-dependent-type-theories.lagda.md b/src/type-theories/fibered-dependent-type-theories.lagda.md index a5da36d53a..7d0e7242ff 100644 --- a/src/type-theories/fibered-dependent-type-theories.lagda.md +++ b/src/type-theories/fibered-dependent-type-theories.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module type-theories.fibered-dependent-type-theories where +open import foundation.function-extensionality-axiom + +module + type-theories.fibered-dependent-type-theories + (funext : function-extensionality) + where ```
Imports @@ -11,12 +16,12 @@ module type-theories.fibered-dependent-type-theories where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.dependent-type-theories +open import type-theories.dependent-type-theories funext ```
diff --git a/src/type-theories/pi-types-precategories-with-attributes.lagda.md b/src/type-theories/pi-types-precategories-with-attributes.lagda.md index bb36bc9fc8..4f8e70e49c 100644 --- a/src/type-theories/pi-types-precategories-with-attributes.lagda.md +++ b/src/type-theories/pi-types-precategories-with-attributes.lagda.md @@ -1,18 +1,23 @@ # `Π`-types in precategories with attributes ```agda -module type-theories.pi-types-precategories-with-attributes where +open import foundation.function-extensionality-axiom + +module + type-theories.pi-types-precategories-with-attributes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.precategories-with-attributes +open import type-theories.precategories-with-attributes funext ```
diff --git a/src/type-theories/pi-types-precategories-with-families.lagda.md b/src/type-theories/pi-types-precategories-with-families.lagda.md index 95f6a2b8e2..30b3122287 100644 --- a/src/type-theories/pi-types-precategories-with-families.lagda.md +++ b/src/type-theories/pi-types-precategories-with-families.lagda.md @@ -1,18 +1,23 @@ # Π-types in precategories with families ```agda -module type-theories.pi-types-precategories-with-families where +open import foundation.function-extensionality-axiom + +module + type-theories.pi-types-precategories-with-families + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.precategories-with-families +open import type-theories.precategories-with-families funext ```
diff --git a/src/type-theories/precategories-with-attributes.lagda.md b/src/type-theories/precategories-with-attributes.lagda.md index c092065934..c25248a51f 100644 --- a/src/type-theories/precategories-with-attributes.lagda.md +++ b/src/type-theories/precategories-with-attributes.lagda.md @@ -1,26 +1,31 @@ # Precategories with attributes ```agda -module type-theories.precategories-with-attributes where +open import foundation.function-extensionality-axiom + +module + type-theories.precategories-with-attributes + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories -open import category-theory.functors-precategories -open import category-theory.natural-transformations-functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-elements-of-a-presheaf -open import category-theory.presheaf-categories -open import category-theory.pullbacks-in-precategories +open import category-theory.commuting-squares-of-morphisms-in-precategories funext +open import category-theory.functors-precategories funext +open import category-theory.natural-transformations-functors-precategories funext +open import category-theory.precategories funext +open import category-theory.precategory-of-elements-of-a-presheaf funext +open import category-theory.presheaf-categories funext +open import category-theory.pullbacks-in-precategories funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.sets -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.universe-levels ``` diff --git a/src/type-theories/precategories-with-families.lagda.md b/src/type-theories/precategories-with-families.lagda.md index 5a8bc8f46e..a61e18f4bc 100644 --- a/src/type-theories/precategories-with-families.lagda.md +++ b/src/type-theories/precategories-with-families.lagda.md @@ -1,20 +1,25 @@ # Precategories with families ```agda -module type-theories.precategories-with-families where +open import foundation.function-extensionality-axiom + +module + type-theories.precategories-with-families + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.functors-precategories -open import category-theory.precategories -open import category-theory.precategory-of-elements-of-a-presheaf -open import category-theory.presheaf-categories +open import category-theory.functors-precategories funext +open import category-theory.precategories funext +open import category-theory.precategory-of-elements-of-a-presheaf funext +open import category-theory.presheaf-categories funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/type-theories/sections-dependent-type-theories.lagda.md b/src/type-theories/sections-dependent-type-theories.lagda.md index 339dc4c6e7..5fa8018c95 100644 --- a/src/type-theories/sections-dependent-type-theories.lagda.md +++ b/src/type-theories/sections-dependent-type-theories.lagda.md @@ -3,18 +3,23 @@ ```agda {-# OPTIONS --guardedness #-} -module type-theories.sections-dependent-type-theories where +open import foundation.function-extensionality-axiom + +module + type-theories.sections-dependent-type-theories + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.dependent-type-theories -open import type-theories.fibered-dependent-type-theories +open import type-theories.dependent-type-theories funext +open import type-theories.fibered-dependent-type-theories funext ```
diff --git a/src/type-theories/simple-type-theories.lagda.md b/src/type-theories/simple-type-theories.lagda.md index b8e45f3112..e975f9cf07 100644 --- a/src/type-theories/simple-type-theories.lagda.md +++ b/src/type-theories/simple-type-theories.lagda.md @@ -3,16 +3,21 @@ ```agda {-# OPTIONS --guardedness --allow-unsolved-metas #-} -module type-theories.simple-type-theories where +open import foundation.function-extensionality-axiom + +module + type-theories.simple-type-theories + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.transport-along-identifications open import foundation.universe-levels ``` @@ -539,8 +544,8 @@ We specialize the above definitions to nonhomogenous homotopies. module dependent-simple where - open import type-theories.dependent-type-theories - open import type-theories.fibered-dependent-type-theories + open import type-theories.dependent-type-theories funext + open import type-theories.fibered-dependent-type-theories funext system : {l1 l2 : Level} {T : UU l1} → simple.system l2 T → dependent.system l1 l2 diff --git a/src/type-theories/unityped-type-theories.lagda.md b/src/type-theories/unityped-type-theories.lagda.md index 99c7fb918f..19b64300a5 100644 --- a/src/type-theories/unityped-type-theories.lagda.md +++ b/src/type-theories/unityped-type-theories.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness --allow-unsolved-metas #-} -module type-theories.unityped-type-theories where +open import foundation.function-extensionality-axiom + +module + type-theories.unityped-type-theories + (funext : function-extensionality) + where ```
Imports @@ -12,10 +17,10 @@ module type-theories.unityped-type-theories where open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics.lagda.md b/src/univalent-combinatorics.lagda.md index 96025ac714..8a2804e99e 100644 --- a/src/univalent-combinatorics.lagda.md +++ b/src/univalent-combinatorics.lagda.md @@ -23,101 +23,106 @@ and closedness under Π under a mild condition {{#cite Anel24}}. ## Modules in the univalent combinatorics namespace ```agda -module univalent-combinatorics where +open import foundation.function-extensionality-axiom -open import univalent-combinatorics.2-element-decidable-subtypes public -open import univalent-combinatorics.2-element-subtypes public -open import univalent-combinatorics.2-element-types public -open import univalent-combinatorics.binomial-types public -open import univalent-combinatorics.bracelets public -open import univalent-combinatorics.cartesian-product-types public -open import univalent-combinatorics.classical-finite-types public -open import univalent-combinatorics.complements-isolated-elements public -open import univalent-combinatorics.coproduct-types public -open import univalent-combinatorics.counting public -open import univalent-combinatorics.counting-decidable-subtypes public -open import univalent-combinatorics.counting-dependent-pair-types public +module + univalent-combinatorics + (funext : function-extensionality) + where + +open import univalent-combinatorics.2-element-decidable-subtypes funext public +open import univalent-combinatorics.2-element-subtypes funext public +open import univalent-combinatorics.2-element-types funext public +open import univalent-combinatorics.binomial-types funext public +open import univalent-combinatorics.bracelets funext public +open import univalent-combinatorics.cartesian-product-types funext public +open import univalent-combinatorics.classical-finite-types funext public +open import univalent-combinatorics.complements-isolated-elements funext public +open import univalent-combinatorics.coproduct-types funext public +open import univalent-combinatorics.counting funext public +open import univalent-combinatorics.counting-decidable-subtypes funext public +open import univalent-combinatorics.counting-dependent-pair-types funext public open import univalent-combinatorics.counting-fibers-of-maps public -open import univalent-combinatorics.counting-maybe public -open import univalent-combinatorics.cubes public -open import univalent-combinatorics.cycle-partitions public -open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers public -open import univalent-combinatorics.cyclic-finite-types public -open import univalent-combinatorics.de-morgans-law public -open import univalent-combinatorics.decidable-dependent-function-types public -open import univalent-combinatorics.decidable-dependent-pair-types public -open import univalent-combinatorics.decidable-equivalence-relations public -open import univalent-combinatorics.decidable-propositions public -open import univalent-combinatorics.decidable-subtypes public -open import univalent-combinatorics.dedekind-finite-sets public -open import univalent-combinatorics.dependent-function-types public -open import univalent-combinatorics.dependent-pair-types public -open import univalent-combinatorics.discrete-sigma-decompositions public -open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products public -open import univalent-combinatorics.double-counting public -open import univalent-combinatorics.embeddings public -open import univalent-combinatorics.embeddings-standard-finite-types public -open import univalent-combinatorics.equality-finite-types public -open import univalent-combinatorics.equality-standard-finite-types public -open import univalent-combinatorics.equivalences public -open import univalent-combinatorics.equivalences-cubes public -open import univalent-combinatorics.equivalences-standard-finite-types public -open import univalent-combinatorics.ferrers-diagrams public -open import univalent-combinatorics.fibers-of-maps public -open import univalent-combinatorics.finite-choice public +open import univalent-combinatorics.counting-maybe funext public +open import univalent-combinatorics.cubes funext public +open import univalent-combinatorics.cycle-partitions funext public +open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers funext public +open import univalent-combinatorics.cyclic-finite-types funext public +open import univalent-combinatorics.de-morgans-law funext public +open import univalent-combinatorics.decidable-dependent-function-types funext public +open import univalent-combinatorics.decidable-dependent-pair-types funext public +open import univalent-combinatorics.decidable-equivalence-relations funext public +open import univalent-combinatorics.decidable-propositions funext public +open import univalent-combinatorics.decidable-subtypes funext public +open import univalent-combinatorics.dedekind-finite-sets funext public +open import univalent-combinatorics.dependent-function-types funext public +open import univalent-combinatorics.dependent-pair-types funext public +open import univalent-combinatorics.discrete-sigma-decompositions funext public +open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products funext public +open import univalent-combinatorics.double-counting funext public +open import univalent-combinatorics.embeddings funext public +open import univalent-combinatorics.embeddings-standard-finite-types funext public +open import univalent-combinatorics.equality-finite-types funext public +open import univalent-combinatorics.equality-standard-finite-types funext public +open import univalent-combinatorics.equivalences funext public +open import univalent-combinatorics.equivalences-cubes funext public +open import univalent-combinatorics.equivalences-standard-finite-types funext public +open import univalent-combinatorics.ferrers-diagrams funext public +open import univalent-combinatorics.fibers-of-maps funext public +open import univalent-combinatorics.finite-choice funext public open import univalent-combinatorics.finite-presentations public -open import univalent-combinatorics.finite-types public -open import univalent-combinatorics.finitely-many-connected-components public -open import univalent-combinatorics.finitely-presented-types public -open import univalent-combinatorics.function-types public -open import univalent-combinatorics.image-of-maps public -open import univalent-combinatorics.inequality-types-with-counting public -open import univalent-combinatorics.inhabited-finite-types public -open import univalent-combinatorics.injective-maps public -open import univalent-combinatorics.involution-standard-finite-types public -open import univalent-combinatorics.isotopies-latin-squares public -open import univalent-combinatorics.kuratowski-finite-sets public -open import univalent-combinatorics.latin-squares public -open import univalent-combinatorics.locally-finite-types public -open import univalent-combinatorics.main-classes-of-latin-hypercubes public -open import univalent-combinatorics.main-classes-of-latin-squares public -open import univalent-combinatorics.maybe public -open import univalent-combinatorics.necklaces public -open import univalent-combinatorics.orientations-complete-undirected-graph public -open import univalent-combinatorics.orientations-cubes public -open import univalent-combinatorics.partitions public -open import univalent-combinatorics.petri-nets public -open import univalent-combinatorics.pi-finite-types public -open import univalent-combinatorics.pigeonhole-principle public +open import univalent-combinatorics.finite-types funext public +open import univalent-combinatorics.finitely-many-connected-components funext public +open import univalent-combinatorics.finitely-presented-types funext public +open import univalent-combinatorics.function-types funext public +open import univalent-combinatorics.image-of-maps funext public +open import univalent-combinatorics.inequality-types-with-counting funext public +open import univalent-combinatorics.inhabited-finite-types funext public +open import univalent-combinatorics.injective-maps funext public +open import univalent-combinatorics.involution-standard-finite-types funext public +open import univalent-combinatorics.isotopies-latin-squares funext public +open import univalent-combinatorics.kuratowski-finite-sets funext public +open import univalent-combinatorics.latin-squares funext public +open import univalent-combinatorics.locally-finite-types funext public +open import univalent-combinatorics.main-classes-of-latin-hypercubes funext public +open import univalent-combinatorics.main-classes-of-latin-squares funext public +open import univalent-combinatorics.maybe funext public +open import univalent-combinatorics.necklaces funext public +open import univalent-combinatorics.orientations-complete-undirected-graph funext public +open import univalent-combinatorics.orientations-cubes funext public +open import univalent-combinatorics.partitions funext public +open import univalent-combinatorics.petri-nets funext public +open import univalent-combinatorics.pi-finite-types funext public +open import univalent-combinatorics.pigeonhole-principle funext public open import univalent-combinatorics.presented-pi-finite-types public -open import univalent-combinatorics.quotients-finite-types public -open import univalent-combinatorics.ramsey-theory public -open import univalent-combinatorics.repetitions-of-values public +open import univalent-combinatorics.quotients-finite-types funext public +open import univalent-combinatorics.ramsey-theory funext public +open import univalent-combinatorics.repetitions-of-values funext public open import univalent-combinatorics.repetitions-of-values-sequences public -open import univalent-combinatorics.retracts-of-finite-types public -open import univalent-combinatorics.riffle-shuffles public -open import univalent-combinatorics.sequences-finite-types public -open import univalent-combinatorics.set-quotients-of-index-two public -open import univalent-combinatorics.sigma-decompositions public -open import univalent-combinatorics.skipping-element-standard-finite-types public -open import univalent-combinatorics.small-types public -open import univalent-combinatorics.standard-finite-pruned-trees public -open import univalent-combinatorics.standard-finite-trees public -open import univalent-combinatorics.standard-finite-types public -open import univalent-combinatorics.steiner-systems public -open import univalent-combinatorics.steiner-triple-systems public -open import univalent-combinatorics.sums-of-natural-numbers public -open import univalent-combinatorics.surjective-maps public -open import univalent-combinatorics.symmetric-difference public -open import univalent-combinatorics.trivial-sigma-decompositions public -open import univalent-combinatorics.type-duality public -open import univalent-combinatorics.unbounded-pi-finite-types public -open import univalent-combinatorics.unions-subtypes public -open import univalent-combinatorics.universal-property-standard-finite-types public +open import univalent-combinatorics.retracts-of-finite-types funext public +open import univalent-combinatorics.riffle-shuffles funext public +open import univalent-combinatorics.sequences-finite-types funext public +open import univalent-combinatorics.set-quotients-of-index-two funext public +open import univalent-combinatorics.sigma-decompositions funext public +open import univalent-combinatorics.skipping-element-standard-finite-types funext public +open import univalent-combinatorics.small-types funext public +open import univalent-combinatorics.standard-finite-pruned-trees funext public +open import univalent-combinatorics.standard-finite-trees funext public +open import univalent-combinatorics.standard-finite-types funext public +open import univalent-combinatorics.steiner-systems funext public +open import univalent-combinatorics.steiner-triple-systems funext public +open import univalent-combinatorics.sums-of-natural-numbers funext public +open import univalent-combinatorics.surjective-maps funext public +open import univalent-combinatorics.symmetric-difference funext public +open import univalent-combinatorics.trivial-sigma-decompositions funext public +open import univalent-combinatorics.type-duality funext public +open import univalent-combinatorics.unbounded-pi-finite-types funext public +open import univalent-combinatorics.unions-subtypes funext public +open import univalent-combinatorics.universal-property-standard-finite-types funext public open import univalent-combinatorics.unlabeled-partitions public open import univalent-combinatorics.unlabeled-rooted-trees public open import univalent-combinatorics.unlabeled-trees public -open import univalent-combinatorics.untruncated-pi-finite-types public +open import univalent-combinatorics.untruncated-pi-finite-types funext public ``` ## References diff --git a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md index eec01ce47a..3d43f3d67e 100644 --- a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md @@ -1,50 +1,56 @@ # `2`-element decidable subtypes ```agda -module univalent-combinatorics.2-element-decidable-subtypes where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.2-element-decidable-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext -open import foundation.automorphisms -open import foundation.booleans -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.automorphisms funext +open import foundation.booleans funext +open import foundation.decidable-equality funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes +open import foundation.embeddings funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types -open import foundation.univalence +open import foundation.type-arithmetic-coproduct-types funext +open import foundation.univalence funext open import foundation.universe-levels -open import univalent-combinatorics.2-element-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-subtypes funext +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.decidable-subtypes funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/2-element-subtypes.lagda.md b/src/univalent-combinatorics/2-element-subtypes.lagda.md index 9c1bd2707d..1b72867410 100644 --- a/src/univalent-combinatorics/2-element-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-subtypes.lagda.md @@ -1,37 +1,42 @@ # `2`-element subtypes ```agda -module univalent-combinatorics.2-element-subtypes where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.2-element-subtypes + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.automorphisms -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.automorphisms funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext +open import foundation.negated-equality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/2-element-types.lagda.md b/src/univalent-combinatorics/2-element-types.lagda.md index b44650d1ca..caf8837393 100644 --- a/src/univalent-combinatorics/2-element-types.lagda.md +++ b/src/univalent-combinatorics/2-element-types.lagda.md @@ -1,58 +1,63 @@ # `2`-element types ```agda -module univalent-combinatorics.2-element-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.2-element-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import foundation.action-on-identifications-functions -open import foundation.automorphisms -open import foundation.connected-components-universes -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.automorphisms funext +open import foundation.connected-components-universes funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.double-negation -open import foundation.empty-types -open import foundation.equivalence-extensionality -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types +open import foundation.double-negation funext +open import foundation.empty-types funext +open import foundation.equivalence-extensionality funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies +open import foundation.homotopies funext open import foundation.identity-systems -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.involutions -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.sets -open import foundation.subuniverses -open import foundation.torsorial-type-families +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.involutions funext +open import foundation.mere-equivalences funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.sets funext +open import foundation.subuniverses funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-identity-systems +open import foundation.universal-property-identity-systems funext open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.equivalences -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.equivalences funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index 7effe481d3..2816b63702 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -1,57 +1,62 @@ # The binomial types ```agda -module univalent-combinatorics.binomial-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.binomial-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.binomial-coefficients +open import elementary-number-theory.binomial-coefficients funext open import elementary-number-theory.natural-numbers -open import foundation.booleans -open import foundation.connected-components-universes -open import foundation.contractible-maps -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-embeddings -open import foundation.decidable-propositions -open import foundation.decidable-subtypes +open import foundation.booleans funext +open import foundation.connected-components-universes funext +open import foundation.contractible-maps funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-embeddings funext +open import foundation.decidable-propositions funext +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.logical-equivalences -open import foundation.maybe -open import foundation.mere-equivalences -open import foundation.negation -open import foundation.postcomposition-functions -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.equivalences funext-maybe +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.logical-equivalences funext +open import foundation.maybe funext +open import foundation.mere-equivalences funext +open import foundation.negation funext +open import foundation.postcomposition-functions funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences -open import foundation.universal-property-maybe +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-maybe funext open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/bracelets.lagda.md b/src/univalent-combinatorics/bracelets.lagda.md index f2e65151d7..35a0f6098e 100644 --- a/src/univalent-combinatorics/bracelets.lagda.md +++ b/src/univalent-combinatorics/bracelets.lagda.md @@ -1,7 +1,12 @@ # Bracelets ```agda -module univalent-combinatorics.bracelets where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.bracelets + (funext : function-extensionality) + where ```
Imports @@ -12,9 +17,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.polygons +open import graph-theory.polygons funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/cartesian-product-types.lagda.md b/src/univalent-combinatorics/cartesian-product-types.lagda.md index 43dee54458..d2f8951a56 100644 --- a/src/univalent-combinatorics/cartesian-product-types.lagda.md +++ b/src/univalent-combinatorics/cartesian-product-types.lagda.md @@ -1,7 +1,12 @@ # Cartesian products of finite types ```agda -module univalent-combinatorics.cartesian-product-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.cartesian-product-types + (funext : function-extensionality) + where ```
Imports @@ -10,35 +15,35 @@ module univalent-combinatorics.cartesian-product-types where open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.decidable-equality +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.decidable-equality funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.torsorial-type-families +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-dependent-pair-types +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.double-counting funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/classical-finite-types.lagda.md b/src/univalent-combinatorics/classical-finite-types.lagda.md index 95091e94ec..ae4640280d 100644 --- a/src/univalent-combinatorics/classical-finite-types.lagda.md +++ b/src/univalent-combinatorics/classical-finite-types.lagda.md @@ -1,22 +1,27 @@ # The classical definition of the standard finite types ```agda -module univalent-combinatorics.classical-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.classical-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/complements-isolated-elements.lagda.md b/src/univalent-combinatorics/complements-isolated-elements.lagda.md index add3d8ff3f..c1e8c0d982 100644 --- a/src/univalent-combinatorics/complements-isolated-elements.lagda.md +++ b/src/univalent-combinatorics/complements-isolated-elements.lagda.md @@ -1,7 +1,12 @@ # Complements of isolated elements of finite types ```agda -module univalent-combinatorics.complements-isolated-elements where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.complements-isolated-elements + (funext : function-extensionality) + where ```
Imports @@ -10,16 +15,16 @@ module univalent-combinatorics.complements-isolated-elements where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.identity-types -open import foundation.isolated-elements -open import foundation.maybe -open import foundation.propositional-truncations +open import foundation.equivalences funext +open import foundation.equivalences funext-maybe +open import foundation.identity-types funext +open import foundation.isolated-elements funext +open import foundation.maybe funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/coproduct-types.lagda.md b/src/univalent-combinatorics/coproduct-types.lagda.md index 03c7063c2b..c5627f13ec 100644 --- a/src/univalent-combinatorics/coproduct-types.lagda.md +++ b/src/univalent-combinatorics/coproduct-types.lagda.md @@ -1,7 +1,12 @@ # Coproducts of finite types ```agda -module univalent-combinatorics.coproduct-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.coproduct-types + (funext : function-extensionality) + where ```
Imports @@ -11,27 +16,26 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-propositional-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.type-arithmetic-coproduct-types -open import foundation.type-arithmetic-empty-type +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-empty-type funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-decidable-subtypes +open import univalent-combinatorics.double-counting funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md index 2dc4eea133..b432300747 100644 --- a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md @@ -1,9 +1,14 @@ # Counting the elements of decidable subtypes ```agda -module univalent-combinatorics.counting-decidable-subtypes where +open import foundation.function-extensionality-axiom -open import foundation.decidable-subtypes public +module + univalent-combinatorics.counting-decidable-subtypes + (funext : function-extensionality) + where + +open import foundation.decidable-subtypes funext public ```
Imports @@ -11,31 +16,31 @@ open import foundation.decidable-subtypes public ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-embeddings -open import foundation.decidable-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-embeddings funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.subtypes -open import foundation.type-arithmetic-coproduct-types -open import foundation.type-arithmetic-empty-type +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.propositional-maps funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md index ce45d38d86..833c714a44 100644 --- a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md @@ -1,44 +1,49 @@ # Counting the elements of dependent pair types ```agda -module univalent-combinatorics.counting-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.counting-dependent-pair-types + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.sums-of-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.sections -open import foundation.torsorial-type-families +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.sections funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.double-counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/counting-maybe.lagda.md b/src/univalent-combinatorics/counting-maybe.lagda.md index a69e71d84a..cda5aaa6fe 100644 --- a/src/univalent-combinatorics/counting-maybe.lagda.md +++ b/src/univalent-combinatorics/counting-maybe.lagda.md @@ -1,7 +1,12 @@ # Counting the elements in Maybe ```agda -module univalent-combinatorics.counting-maybe where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.counting-maybe + (funext : function-extensionality) + where ```
Imports @@ -10,14 +15,14 @@ module univalent-combinatorics.counting-maybe where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences-maybe +open import foundation.equivalences-maybe funext open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.maybe -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.counting funext ```
diff --git a/src/univalent-combinatorics/counting.lagda.md b/src/univalent-combinatorics/counting.lagda.md index b9c4fa6d19..2fb9d291fa 100644 --- a/src/univalent-combinatorics/counting.lagda.md +++ b/src/univalent-combinatorics/counting.lagda.md @@ -1,7 +1,12 @@ # Counting in type theory ```agda -module univalent-combinatorics.counting where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.counting + (funext : function-extensionality) + where ```
Imports @@ -9,25 +14,25 @@ module univalent-combinatorics.counting where ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/cubes.lagda.md b/src/univalent-combinatorics/cubes.lagda.md index 658ef99b5f..b9610c82ae 100644 --- a/src/univalent-combinatorics/cubes.lagda.md +++ b/src/univalent-combinatorics/cubes.lagda.md @@ -1,7 +1,12 @@ # Cubes ```agda -module univalent-combinatorics.cubes where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.cubes + (funext : function-extensionality) + where ```
Imports @@ -12,8 +17,8 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.complements-isolated-elements -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.complements-isolated-elements funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/cycle-partitions.lagda.md b/src/univalent-combinatorics/cycle-partitions.lagda.md index 2b24b1903a..470d724f08 100644 --- a/src/univalent-combinatorics/cycle-partitions.lagda.md +++ b/src/univalent-combinatorics/cycle-partitions.lagda.md @@ -1,7 +1,12 @@ # Cycle partitions of finite types ```agda -module univalent-combinatorics.cycle-partitions where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.cycle-partitions + (funext : function-extensionality) + where ```
Imports @@ -10,11 +15,11 @@ module univalent-combinatorics.cycle-partitions where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences +open import foundation.equivalences funext open import foundation.universe-levels -open import univalent-combinatorics.cyclic-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cyclic-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md b/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md index f1c5ab49c3..58f05e8f3e 100644 --- a/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md +++ b/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md @@ -1,41 +1,46 @@ # Cycle prime decompositions of natural numbers ```agda -module univalent-combinatorics.cycle-prime-decomposition-natural-numbers where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.cycle-prime-decomposition-natural-numbers + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.decidable-total-order-natural-numbers -open import elementary-number-theory.fundamental-theorem-of-arithmetic -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.decidable-total-order-natural-numbers funext +open import elementary-number-theory.fundamental-theorem-of-arithmetic funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.permutations-standard-finite-types funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.contractible-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.iterated-cartesian-product-types +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.iterated-cartesian-product-types funext open import foundation.transport-along-identifications -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.iterated-cartesian-products-concrete-groups +open import group-theory.concrete-groups funext +open import group-theory.iterated-cartesian-products-concrete-groups funext -open import lists.arrays -open import lists.concatenation-lists -open import lists.functoriality-lists -open import lists.permutation-lists -open import lists.sort-by-insertion-lists +open import lists.arrays funext +open import lists.concatenation-lists funext +open import lists.functoriality-lists funext +open import lists.permutation-lists funext +open import lists.sort-by-insertion-lists funext -open import univalent-combinatorics.cyclic-finite-types +open import univalent-combinatorics.cyclic-finite-types funext ```
diff --git a/src/univalent-combinatorics/cyclic-finite-types.lagda.md b/src/univalent-combinatorics/cyclic-finite-types.lagda.md index da2741d64a..2ef8352d0f 100644 --- a/src/univalent-combinatorics/cyclic-finite-types.lagda.md +++ b/src/univalent-combinatorics/cyclic-finite-types.lagda.md @@ -1,52 +1,57 @@ # Cyclic finite types ```agda -module univalent-combinatorics.cyclic-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.cyclic-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-integers funext open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.modular-arithmetic funext-standard-finite-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.standard-cyclic-groups +open import elementary-number-theory.standard-cyclic-groups funext -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.mere-equality -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.mere-equality funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.concrete-groups -open import group-theory.groups -open import group-theory.isomorphisms-groups +open import group-theory.concrete-groups funext +open import group-theory.groups funext +open import group-theory.isomorphisms-groups funext -open import higher-group-theory.higher-groups +open import higher-group-theory.higher-groups funext -open import structured-types.equivalences-types-equipped-with-endomorphisms -open import structured-types.mere-equivalences-types-equipped-with-endomorphisms +open import structured-types.equivalences-types-equipped-with-endomorphisms funext +open import structured-types.mere-equivalences-types-equipped-with-endomorphisms funext open import structured-types.pointed-types -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext -open import synthetic-homotopy-theory.groups-of-loops-in-1-types -open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.groups-of-loops-in-1-types funext +open import synthetic-homotopy-theory.loop-spaces funext ```
diff --git a/src/univalent-combinatorics/de-morgans-law.lagda.md b/src/univalent-combinatorics/de-morgans-law.lagda.md index bca666f108..e473843725 100644 --- a/src/univalent-combinatorics/de-morgans-law.lagda.md +++ b/src/univalent-combinatorics/de-morgans-law.lagda.md @@ -1,7 +1,12 @@ # De Morgan's law for finite families of propositions ```agda -module univalent-combinatorics.de-morgans-law where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.de-morgans-law + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,24 @@ module univalent-combinatorics.de-morgans-law where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-dependent-pair-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-dependent-pair-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.existential-quantification -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.negation +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.existential-quantification funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.negation funext open import foundation.unit-type open import foundation.universe-levels -open import logic.de-morgan-propositions -open import logic.de-morgan-types +open import logic.de-morgan-propositions funext +open import logic.de-morgan-types funext -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md b/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md index 5f6cfff00c..6f87159d65 100644 --- a/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md +++ b/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md @@ -1,9 +1,14 @@ # Decidable dependent function types ```agda -module univalent-combinatorics.decidable-dependent-function-types where +open import foundation.function-extensionality-axiom -open import elementary-number-theory.decidable-dependent-function-types public +module + univalent-combinatorics.decidable-dependent-function-types + (funext : function-extensionality) + where + +open import elementary-number-theory.decidable-dependent-function-types funext public ```
Imports @@ -11,21 +16,21 @@ open import elementary-number-theory.decidable-dependent-function-types public ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-choice -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.finite-choice funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md b/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md index 9e48dbc5b3..1a269b2a0b 100644 --- a/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md @@ -1,7 +1,12 @@ # Decidability of dependent pair types ```agda -module univalent-combinatorics.decidable-dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.decidable-dependent-pair-types + (funext : function-extensionality) + where ```
Imports @@ -9,18 +14,18 @@ module univalent-combinatorics.decidable-dependent-pair-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-dependent-pair-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-dependent-pair-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md index 46f0521430..c2e6e2550b 100644 --- a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md +++ b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md @@ -1,7 +1,12 @@ # Decidable equivalence relations on finite types ```agda -module univalent-combinatorics.decidable-equivalence-relations where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.decidable-equivalence-relations + (funext : function-extensionality) + where ```
Imports @@ -9,32 +14,32 @@ module univalent-combinatorics.decidable-equivalence-relations where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types -open import foundation.decidable-equality -open import foundation.decidable-equivalence-relations -open import foundation.decidable-relations -open import foundation.decidable-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-pair-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-equivalence-relations funext +open import foundation.decidable-relations funext +open import foundation.decidable-types funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.function-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.surjective-maps +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.function-types funext +open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.surjective-maps funext ```
diff --git a/src/univalent-combinatorics/decidable-propositions.lagda.md b/src/univalent-combinatorics/decidable-propositions.lagda.md index c825d693f8..7ac0edffed 100644 --- a/src/univalent-combinatorics/decidable-propositions.lagda.md +++ b/src/univalent-combinatorics/decidable-propositions.lagda.md @@ -1,9 +1,14 @@ # Decidable propositions ```agda -module univalent-combinatorics.decidable-propositions where +open import foundation.function-extensionality-axiom -open import foundation.decidable-propositions public +module + univalent-combinatorics.decidable-propositions + (funext : function-extensionality) + where + +open import foundation.decidable-propositions funext public ```
Imports @@ -11,17 +16,17 @@ open import foundation.decidable-propositions public ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/decidable-subtypes.lagda.md b/src/univalent-combinatorics/decidable-subtypes.lagda.md index d7b83a688c..0a1f5e0f1a 100644 --- a/src/univalent-combinatorics/decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/decidable-subtypes.lagda.md @@ -1,37 +1,42 @@ # Decidable subtypes of finite types ```agda -module univalent-combinatorics.decidable-subtypes where +open import foundation.function-extensionality-axiom -open import foundation.decidable-subtypes public +module + univalent-combinatorics.decidable-subtypes + (funext : function-extensionality) + where + +open import foundation.decidable-subtypes funext public ```
Imports ```agda -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.decidable-propositions -open import foundation.embeddings -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.subtypes +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.decidable-propositions funext +open import foundation.embeddings funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.subtypes funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.decidable-dependent-pair-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.function-types +open import univalent-combinatorics.decidable-dependent-pair-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.function-types funext ```
diff --git a/src/univalent-combinatorics/dedekind-finite-sets.lagda.md b/src/univalent-combinatorics/dedekind-finite-sets.lagda.md index f3d73ff2db..6f39fb33a8 100644 --- a/src/univalent-combinatorics/dedekind-finite-sets.lagda.md +++ b/src/univalent-combinatorics/dedekind-finite-sets.lagda.md @@ -1,17 +1,22 @@ # Dedekind finite sets ```agda -module univalent-combinatorics.dedekind-finite-sets where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.dedekind-finite-sets + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equivalences -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics/dependent-function-types.lagda.md b/src/univalent-combinatorics/dependent-function-types.lagda.md index f8354b654c..8f23e0cc17 100644 --- a/src/univalent-combinatorics/dependent-function-types.lagda.md +++ b/src/univalent-combinatorics/dependent-function-types.lagda.md @@ -1,7 +1,12 @@ # Counting the elements of dependent function types ```agda -module univalent-combinatorics.dependent-function-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.dependent-function-types + (funext : function-extensionality) + where ```
Imports @@ -9,28 +14,28 @@ module univalent-combinatorics.dependent-function-types where ```agda open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers +open import elementary-number-theory.products-of-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.equivalences -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.dependent-universal-property-equivalences funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.unit-type -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-choice -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.finite-choice funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/dependent-pair-types.lagda.md b/src/univalent-combinatorics/dependent-pair-types.lagda.md index ce7fef9510..b96958a432 100644 --- a/src/univalent-combinatorics/dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/dependent-pair-types.lagda.md @@ -1,7 +1,12 @@ # Dependent pair types of finite types ```agda -module univalent-combinatorics.dependent-pair-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.dependent-pair-types + (funext : function-extensionality) + where open import foundation.dependent-pair-types public ``` @@ -10,33 +15,33 @@ open import foundation.dependent-pair-types public ```agda open import foundation.complements -open import foundation.decidable-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sections -open import foundation.sets -open import foundation.subtypes -open import foundation.torsorial-type-families +open import foundation.decidable-types funext +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sections funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-choice -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-dependent-pair-types +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-choice funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md index 3eb65dbffb..58fb7fa268 100644 --- a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md @@ -1,24 +1,29 @@ # Finite discrete Σ-decompositions ```agda -module univalent-combinatorics.discrete-sigma-decompositions where +open import foundation.function-extensionality-axiom -open import foundation.discrete-sigma-decompositions public +module + univalent-combinatorics.discrete-sigma-decompositions + (funext : function-extensionality) + where + +open import foundation.discrete-sigma-decompositions funext public ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.subtypes funext open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.sigma-decompositions +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.sigma-decompositions funext ```
diff --git a/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md b/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md index 64609a61a2..2f692573f5 100644 --- a/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md +++ b/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md @@ -1,7 +1,12 @@ # Distributivity of set truncation over finite products ```agda -module univalent-combinatorics.distributivity-of-set-truncation-over-finite-products where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.distributivity-of-set-truncation-over-finite-products + (funext : function-extensionality) + where ```
Imports @@ -10,37 +15,38 @@ module univalent-combinatorics.distributivity-of-set-truncation-over-finite-prod open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-function-types -open import foundation.functoriality-set-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.postcomposition-functions -open import foundation.precomposition-dependent-functions -open import foundation.precomposition-functions -open import foundation.propositional-truncations -open import foundation.set-truncations -open import foundation.sets +open import foundation.dependent-universal-property-equivalences funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-function-types funext +open import foundation.functoriality-set-truncation funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.postcomposition-functions funext +open import foundation.precomposition-dependent-functions funext +open import foundation.precomposition-functions funext +open import foundation.propositional-truncations funext +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-equivalences -open import foundation.universal-property-maybe +open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-equivalences funext +open import foundation.universal-property-maybe funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/double-counting.lagda.md b/src/univalent-combinatorics/double-counting.lagda.md index a6a55dcc85..0796893310 100644 --- a/src/univalent-combinatorics/double-counting.lagda.md +++ b/src/univalent-combinatorics/double-counting.lagda.md @@ -1,19 +1,24 @@ # Double counting ```agda -module univalent-combinatorics.double-counting where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.double-counting + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md b/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md index 458ec1b433..a01863918c 100644 --- a/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md @@ -1,29 +1,34 @@ # Embeddings between standard finite types ```agda -module univalent-combinatorics.embeddings-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.embeddings-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.repeating-element-standard-finite-type +open import elementary-number-theory.repeating-element-standard-finite-type funext open import foundation.action-on-identifications-functions -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/embeddings.lagda.md b/src/univalent-combinatorics/embeddings.lagda.md index e9776b2416..6bb8b115df 100644 --- a/src/univalent-combinatorics/embeddings.lagda.md +++ b/src/univalent-combinatorics/embeddings.lagda.md @@ -1,9 +1,14 @@ # Embeddings ```agda -module univalent-combinatorics.embeddings where +open import foundation.function-extensionality-axiom -open import foundation.embeddings public +module + univalent-combinatorics.embeddings + (funext : function-extensionality) + where + +open import foundation.embeddings funext public ```
Imports @@ -11,22 +16,22 @@ open import foundation.embeddings public ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types -open import foundation.decidable-embeddings -open import foundation.decidable-types +open import foundation.coproduct-types funext +open import foundation.decidable-embeddings funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.injective-maps -open import univalent-combinatorics.retracts-of-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.injective-maps funext +open import univalent-combinatorics.retracts-of-finite-types funext ```
diff --git a/src/univalent-combinatorics/equality-finite-types.lagda.md b/src/univalent-combinatorics/equality-finite-types.lagda.md index 220051d0d8..9c027320b0 100644 --- a/src/univalent-combinatorics/equality-finite-types.lagda.md +++ b/src/univalent-combinatorics/equality-finite-types.lagda.md @@ -1,7 +1,12 @@ # Equality in finite types ```agda -module univalent-combinatorics.equality-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.equality-finite-types + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module univalent-combinatorics.equality-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-equality +open import foundation.decidable-equality funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositional-truncations +open import foundation.identity-types funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/equality-standard-finite-types.lagda.md b/src/univalent-combinatorics/equality-standard-finite-types.lagda.md index 637b3cf66a..891c79f055 100644 --- a/src/univalent-combinatorics/equality-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/equality-standard-finite-types.lagda.md @@ -1,38 +1,43 @@ # Equality in the standard finite types ```agda -module univalent-combinatorics.equality-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.equality-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.apartness-relations -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.apartness-relations funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.discrete-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.functoriality-coproduct-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositions -open import foundation.set-truncations -open import foundation.tight-apartness-relations +open import foundation.discrete-types funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.functoriality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositions funext +open import foundation.set-truncations funext +open import foundation.tight-apartness-relations funext open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.decidable-propositions +open import foundation-core.decidable-propositions funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/equivalences-cubes.lagda.md b/src/univalent-combinatorics/equivalences-cubes.lagda.md index c4971042e6..6263dcf25b 100644 --- a/src/univalent-combinatorics/equivalences-cubes.lagda.md +++ b/src/univalent-combinatorics/equivalences-cubes.lagda.md @@ -1,7 +1,12 @@ # Equivalences of cubes ```agda -module univalent-combinatorics.equivalences-cubes where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.equivalences-cubes + (funext : function-extensionality) + where ```
Imports @@ -10,20 +15,20 @@ module univalent-combinatorics.equivalences-cubes where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalence-extensionality -open import foundation.equivalences -open import foundation.function-types +open import foundation.equality-dependent-function-types funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle -open import foundation.torsorial-type-families +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.cubes -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cubes funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md b/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md index b7044ed428..0cdceeda4d 100644 --- a/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md @@ -1,26 +1,31 @@ # Equivalences between standard finite types ```agda -module univalent-combinatorics.equivalences-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.equivalences-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.contractible-types -open import foundation.equivalences -open import foundation.functoriality-cartesian-product-types -open import foundation.type-arithmetic-empty-type +open import foundation.contractible-types funext +open import foundation.equivalences funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-unit-type funext -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/equivalences.lagda.md b/src/univalent-combinatorics/equivalences.lagda.md index 6b439ee5a4..61d17ec54d 100644 --- a/src/univalent-combinatorics/equivalences.lagda.md +++ b/src/univalent-combinatorics/equivalences.lagda.md @@ -1,21 +1,26 @@ # Equivalences between finite types ```agda -module univalent-combinatorics.equivalences where +open import foundation.function-extensionality-axiom -open import foundation.equivalences public +module + univalent-combinatorics.equivalences + (funext : function-extensionality) + where + +open import foundation.equivalences funext public ```
Imports ```agda -open import foundation.decidable-types +open import foundation.decidable-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.embeddings -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.surjective-maps +open import univalent-combinatorics.embeddings funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.surjective-maps funext ```
diff --git a/src/univalent-combinatorics/ferrers-diagrams.lagda.md b/src/univalent-combinatorics/ferrers-diagrams.lagda.md index 034b26e3ad..24b5ad25ec 100644 --- a/src/univalent-combinatorics/ferrers-diagrams.lagda.md +++ b/src/univalent-combinatorics/ferrers-diagrams.lagda.md @@ -1,28 +1,33 @@ # Ferrers diagrams (unlabeled partitions) ```agda -module univalent-combinatorics.ferrers-diagrams where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.ferrers-diagrams + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types -open import foundation.equivalences +open import foundation.equality-dependent-function-types funext +open import foundation.equivalences funext open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.identity-types funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families -open import foundation.univalence +open import foundation.torsorial-type-families funext +open import foundation.univalence funext open import foundation.universe-levels -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/fibers-of-maps.lagda.md b/src/univalent-combinatorics/fibers-of-maps.lagda.md index 31ba87543e..204431e7c5 100644 --- a/src/univalent-combinatorics/fibers-of-maps.lagda.md +++ b/src/univalent-combinatorics/fibers-of-maps.lagda.md @@ -1,39 +1,44 @@ # Fibers of maps between finite types ```agda -module univalent-combinatorics.fibers-of-maps where +open import foundation.function-extensionality-axiom -open import foundation.fibers-of-maps public +module + univalent-combinatorics.fibers-of-maps + (funext : function-extensionality) + where + +open import foundation.fibers-of-maps funext public ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.sums-of-natural-numbers - -open import foundation.decidable-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.functoriality-dependent-pair-types -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sections -open import foundation.torsorial-type-families +open import elementary-number-theory.sums-of-natural-numbers funext + +open import foundation.decidable-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sections funext +open import foundation.torsorial-type-families funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-dependent-pair-types +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.double-counting funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/finite-choice.lagda.md b/src/univalent-combinatorics/finite-choice.lagda.md index 9446a425cb..291f0f0366 100644 --- a/src/univalent-combinatorics/finite-choice.lagda.md +++ b/src/univalent-combinatorics/finite-choice.lagda.md @@ -1,39 +1,44 @@ # Finite choice ```agda -module univalent-combinatorics.finite-choice where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.finite-choice + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext -open import foundation.coproduct-types -open import foundation.decidable-embeddings +open import foundation.coproduct-types funext +open import foundation.decidable-embeddings funext open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences -open import foundation.empty-types -open import foundation.equivalences -open import foundation.fiber-inclusions -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.hilberts-epsilon-operators -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.dependent-universal-property-equivalences funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.fiber-inclusions funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.hilberts-epsilon-operators funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.unit-type -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-unit-type +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-decidable-subtypes +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/finite-types.lagda.md b/src/univalent-combinatorics/finite-types.lagda.md index ca162f16ce..339fa34cf1 100644 --- a/src/univalent-combinatorics/finite-types.lagda.md +++ b/src/univalent-combinatorics/finite-types.lagda.md @@ -1,50 +1,55 @@ # Finite types ```agda -module univalent-combinatorics.finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.1-types +open import foundation.0-connected-types funext +open import foundation.1-types funext open import foundation.action-on-identifications-functions -open import foundation.connected-components-universes -open import foundation.contractible-types -open import foundation.decidable-types +open import foundation.connected-components-universes funext +open import foundation.contractible-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-coproduct-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels -open import foundation.raising-universe-levels-unit-type -open import foundation.sets -open import foundation.subtypes -open import foundation.subuniverses +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-coproduct-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels funext-unit-type +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.subuniverses funext open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type +open import foundation.type-arithmetic-empty-type funext open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation-core.torsorial-type-families -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/finitely-many-connected-components.lagda.md b/src/univalent-combinatorics/finitely-many-connected-components.lagda.md index b2d49dc3a5..28b1c1f582 100644 --- a/src/univalent-combinatorics/finitely-many-connected-components.lagda.md +++ b/src/univalent-combinatorics/finitely-many-connected-components.lagda.md @@ -1,7 +1,12 @@ # Finiteness of the type of connected components ```agda -module univalent-combinatorics.finitely-many-connected-components where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.finitely-many-connected-components + (funext : function-extensionality) + where ```
Imports @@ -9,28 +14,28 @@ module univalent-combinatorics.finitely-many-connected-components where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.0-connected-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-set-truncation -open import foundation.mere-equivalences -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.set-truncations -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-set-truncation funext +open import foundation.mere-equivalences funext +open import foundation.propositions funext +open import foundation.retracts-of-types funext +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.retracts-of-finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.retracts-of-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/finitely-presented-types.lagda.md b/src/univalent-combinatorics/finitely-presented-types.lagda.md index 6cc22a250a..55119541dc 100644 --- a/src/univalent-combinatorics/finitely-presented-types.lagda.md +++ b/src/univalent-combinatorics/finitely-presented-types.lagda.md @@ -1,7 +1,12 @@ # Finitely presented types ```agda -module univalent-combinatorics.finitely-presented-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.finitely-presented-types + (funext : function-extensionality) + where ```
Imports @@ -10,20 +15,20 @@ module univalent-combinatorics.finitely-presented-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.fibers-of-maps -open import foundation.function-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.set-presented-types -open import foundation.set-truncations -open import foundation.subtypes +open import foundation.equivalences funext +open import foundation.fibers-of-maps funext +open import foundation.function-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.set-presented-types funext +open import foundation.set-truncations funext +open import foundation.subtypes funext open import foundation.universe-levels -open import univalent-combinatorics.finite-choice -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-choice funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finitely-many-connected-components funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/function-types.lagda.md b/src/univalent-combinatorics/function-types.lagda.md index f461d7df2d..58065ca575 100644 --- a/src/univalent-combinatorics/function-types.lagda.md +++ b/src/univalent-combinatorics/function-types.lagda.md @@ -1,28 +1,33 @@ # Finite function types ```agda -module univalent-combinatorics.function-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.function-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.exponentiation-natural-numbers funext open import foundation.action-on-identifications-binary-functions -open import foundation.equivalences -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.sets funext open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/image-of-maps.lagda.md b/src/univalent-combinatorics/image-of-maps.lagda.md index db8cf058d7..29c4d08f51 100644 --- a/src/univalent-combinatorics/image-of-maps.lagda.md +++ b/src/univalent-combinatorics/image-of-maps.lagda.md @@ -1,25 +1,30 @@ # The image of a map ```agda -module univalent-combinatorics.image-of-maps where +open import foundation.function-extensionality-axiom -open import foundation.images public +module + univalent-combinatorics.image-of-maps + (funext : function-extensionality) + where + +open import foundation.images funext public ```
Imports ```agda -open import foundation.decidable-equality -open import foundation.decidable-types -open import foundation.fibers-of-maps -open import foundation.propositional-truncations -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.decidable-equality funext +open import foundation.decidable-types funext +open import foundation.fibers-of-maps funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/inequality-types-with-counting.lagda.md b/src/univalent-combinatorics/inequality-types-with-counting.lagda.md index 137bb6bd70..8d41ab02c3 100644 --- a/src/univalent-combinatorics/inequality-types-with-counting.lagda.md +++ b/src/univalent-combinatorics/inequality-types-with-counting.lagda.md @@ -1,23 +1,28 @@ # Inequality on types equipped with a counting ```agda -module univalent-combinatorics.inequality-types-with-counting where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.inequality-types-with-counting + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.sets funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/inhabited-finite-types.lagda.md b/src/univalent-combinatorics/inhabited-finite-types.lagda.md index f6ad56cab3..9a5a1370bb 100644 --- a/src/univalent-combinatorics/inhabited-finite-types.lagda.md +++ b/src/univalent-combinatorics/inhabited-finite-types.lagda.md @@ -1,7 +1,12 @@ # Inhabited finite types ```agda -module univalent-combinatorics.inhabited-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.inhabited-finite-types + (funext : function-extensionality) + where ```
Imports @@ -9,20 +14,20 @@ module univalent-combinatorics.inhabited-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-function-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositions -open import foundation.subtypes -open import foundation.subuniverses +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.propositions funext +open import foundation.subtypes funext +open import foundation.subuniverses funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/injective-maps.lagda.md b/src/univalent-combinatorics/injective-maps.lagda.md index b848851cf0..5484df2631 100644 --- a/src/univalent-combinatorics/injective-maps.lagda.md +++ b/src/univalent-combinatorics/injective-maps.lagda.md @@ -1,21 +1,26 @@ # Injective maps between finite types ```agda -module univalent-combinatorics.injective-maps where +open import foundation.function-extensionality-axiom -open import foundation.injective-maps public +module + univalent-combinatorics.injective-maps + (funext : function-extensionality) + where + +open import foundation.injective-maps funext public ```
Imports ```agda -open import foundation.decidable-types -open import foundation.identity-types +open import foundation.decidable-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.decidable-dependent-function-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/involution-standard-finite-types.lagda.md b/src/univalent-combinatorics/involution-standard-finite-types.lagda.md index 72c2a01a68..da1786dca0 100644 --- a/src/univalent-combinatorics/involution-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/involution-standard-finite-types.lagda.md @@ -1,20 +1,25 @@ # An involution on the standard finite types ```agda -module univalent-combinatorics.involution-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.involution-standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.identity-types -open import foundation.involutions +open import foundation.identity-types funext +open import foundation.involutions funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/isotopies-latin-squares.lagda.md b/src/univalent-combinatorics/isotopies-latin-squares.lagda.md index 58d4aa23c2..0669cddad2 100644 --- a/src/univalent-combinatorics/isotopies-latin-squares.lagda.md +++ b/src/univalent-combinatorics/isotopies-latin-squares.lagda.md @@ -1,18 +1,23 @@ # Isotopies of Latin squares ```agda -module univalent-combinatorics.isotopies-latin-squares where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.isotopies-latin-squares + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.identity-types funext open import foundation.universe-levels -open import univalent-combinatorics.latin-squares +open import univalent-combinatorics.latin-squares funext ```
diff --git a/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md b/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md index 7de999ba15..be407d4dd4 100644 --- a/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md +++ b/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md @@ -1,7 +1,12 @@ # Kuratowski finite sets ```agda -module univalent-combinatorics.kuratowski-finite-sets where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.kuratowski-finite-sets + (funext : function-extensionality) + where ```
Imports @@ -9,19 +14,19 @@ module univalent-combinatorics.kuratowski-finite-sets where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-equality +open import foundation.decidable-equality funext open import foundation.dependent-pair-types -open import foundation.existential-quantification -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets -open import foundation.surjective-maps +open import foundation.existential-quantification funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext +open import foundation.surjective-maps funext open import foundation.universe-levels -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.image-of-maps -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.image-of-maps funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/latin-squares.lagda.md b/src/univalent-combinatorics/latin-squares.lagda.md index 228092c29d..036fc113ef 100644 --- a/src/univalent-combinatorics/latin-squares.lagda.md +++ b/src/univalent-combinatorics/latin-squares.lagda.md @@ -1,7 +1,12 @@ # Latin squares ```agda -module univalent-combinatorics.latin-squares where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.latin-squares + (funext : function-extensionality) + where ```
Imports @@ -9,7 +14,7 @@ module univalent-combinatorics.latin-squares where ```agda open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.inhabited-types +open import foundation.inhabited-types funext open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics/locally-finite-types.lagda.md b/src/univalent-combinatorics/locally-finite-types.lagda.md index 273e1cd35b..38d067338a 100644 --- a/src/univalent-combinatorics/locally-finite-types.lagda.md +++ b/src/univalent-combinatorics/locally-finite-types.lagda.md @@ -1,7 +1,12 @@ # Locally finite types ```agda -module univalent-combinatorics.locally-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.locally-finite-types + (funext : function-extensionality) + where ```
Imports @@ -9,33 +14,33 @@ module univalent-combinatorics.locally-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-equality -open import foundation.dependent-universal-property-equivalences -open import foundation.empty-types +open import foundation.1-types funext +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-equality funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.empty-types funext open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-coproduct-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-unit-type +open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-unit-type funext open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cartesian-product-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md b/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md index f88ff5969a..7b2a53d9e4 100644 --- a/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md +++ b/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md @@ -1,7 +1,12 @@ # The groupoid of main classes of Latin hypercubes ```agda -module univalent-combinatorics.main-classes-of-latin-hypercubes where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.main-classes-of-latin-hypercubes + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,24 @@ module univalent-combinatorics.main-classes-of-latin-hypercubes where ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types -open import foundation.contractible-types -open import foundation.decidable-propositions +open import foundation.1-types funext +open import foundation.contractible-types funext +open import foundation.decidable-propositions funext open import foundation.dependent-pair-types -open import foundation.inhabited-types -open import foundation.mere-equivalences -open import foundation.products-unordered-tuples-of-types -open import foundation.set-truncations +open import foundation.inhabited-types funext +open import foundation.mere-equivalences funext +open import foundation.products-unordered-tuples-of-types funext +open import foundation.set-truncations funext open import foundation.universe-levels -open import foundation.unordered-tuples - -open import univalent-combinatorics.complements-isolated-elements -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.dependent-function-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import foundation.unordered-tuples funext + +open import univalent-combinatorics.complements-isolated-elements funext +open import univalent-combinatorics.decidable-subtypes funext +open import univalent-combinatorics.dependent-function-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.pi-finite-types funext +open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.untruncated-pi-finite-types funext ```
diff --git a/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md b/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md index 0f3d9410e3..6ed8beda4a 100644 --- a/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md +++ b/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md @@ -1,7 +1,12 @@ # The groupoid of main classes of Latin squares ```agda -module univalent-combinatorics.main-classes-of-latin-squares where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.main-classes-of-latin-squares + (funext : function-extensionality) + where ```
Imports @@ -9,15 +14,15 @@ module univalent-combinatorics.main-classes-of-latin-squares where ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types -open import foundation.mere-equivalences -open import foundation.set-truncations +open import foundation.1-types funext +open import foundation.mere-equivalences funext +open import foundation.set-truncations funext open import foundation.universe-levels -open import univalent-combinatorics.main-classes-of-latin-hypercubes -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import univalent-combinatorics.main-classes-of-latin-hypercubes funext +open import univalent-combinatorics.pi-finite-types funext +open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.untruncated-pi-finite-types funext ```
diff --git a/src/univalent-combinatorics/maybe.lagda.md b/src/univalent-combinatorics/maybe.lagda.md index 7ba870c33e..2d15938771 100644 --- a/src/univalent-combinatorics/maybe.lagda.md +++ b/src/univalent-combinatorics/maybe.lagda.md @@ -1,7 +1,12 @@ # The maybe monad on finite types ```agda -module univalent-combinatorics.maybe where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.maybe + (funext : function-extensionality) + where open import foundation-core.maybe public ``` @@ -13,8 +18,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/necklaces.lagda.md b/src/univalent-combinatorics/necklaces.lagda.md index 49abdc1f29..e0e6cf6141 100644 --- a/src/univalent-combinatorics/necklaces.lagda.md +++ b/src/univalent-combinatorics/necklaces.lagda.md @@ -1,7 +1,12 @@ # Necklaces ```agda -module univalent-combinatorics.necklaces where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.necklaces + (funext : function-extensionality) + where ```
Imports @@ -10,19 +15,20 @@ module univalent-combinatorics.necklaces where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext open import foundation.structure-identity-principle open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext -open import univalent-combinatorics.cyclic-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cyclic-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md index bd5ea5ce14..fdc2717588 100644 --- a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md +++ b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md @@ -3,66 +3,71 @@ ```agda {-# OPTIONS --lossy-unification #-} -module univalent-combinatorics.orientations-complete-undirected-graph where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.orientations-complete-undirected-graph + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers -open import elementary-number-theory.distance-natural-numbers -open import elementary-number-theory.inequality-natural-numbers -open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.congruence-natural-numbers funext +open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.transpositions +open import finite-group-theory.transpositions funext open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types -open import foundation.coproduct-types -open import foundation.decidable-equivalence-relations -open import foundation.decidable-propositions -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-equivalence-relations funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-extensionality -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-extensionality-axiom -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-propositional-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.intersections-subtypes -open import foundation.involutions -open import foundation.logical-equivalences -open import foundation.mere-equivalences -open import foundation.negated-equality -open import foundation.negation -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalence-classes funext +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.intersections-subtypes funext +open import foundation.involutions funext +open import foundation.logical-equivalences funext +open import foundation.mere-equivalences funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.2-element-decidable-subtypes -open import univalent-combinatorics.2-element-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.symmetric-difference +open import univalent-combinatorics.2-element-decidable-subtypes funext +open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.decidable-subtypes funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.symmetric-difference funext ```
diff --git a/src/univalent-combinatorics/orientations-cubes.lagda.md b/src/univalent-combinatorics/orientations-cubes.lagda.md index 9d6c029313..86bcf7a0ee 100644 --- a/src/univalent-combinatorics/orientations-cubes.lagda.md +++ b/src/univalent-combinatorics/orientations-cubes.lagda.md @@ -1,7 +1,12 @@ # Orientations of cubes ```agda -module univalent-combinatorics.orientations-cubes where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.orientations-cubes + (funext : function-extensionality) + where ```
Imports @@ -9,16 +14,16 @@ module univalent-combinatorics.orientations-cubes where ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types -open import foundation.iterating-functions +open import foundation.identity-types funext +open import foundation.iterating-functions funext open import foundation.universe-levels -open import univalent-combinatorics.cubes -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.function-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.cubes funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.function-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/partitions.lagda.md b/src/univalent-combinatorics/partitions.lagda.md index 1d697a9f42..582d042732 100644 --- a/src/univalent-combinatorics/partitions.lagda.md +++ b/src/univalent-combinatorics/partitions.lagda.md @@ -1,7 +1,12 @@ # Partitions of finite types ```agda -module univalent-combinatorics.partitions where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.partitions + (funext : function-extensionality) + where ```
Imports @@ -9,25 +14,25 @@ module univalent-combinatorics.partitions where ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations -open import foundation.cartesian-product-types +open import foundation.binary-relations funext +open import foundation.cartesian-product-types funext open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.equivalence-extensionality funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.structure-identity-principle open import foundation.type-arithmetic-cartesian-product-types open import foundation.universe-levels -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/petri-nets.lagda.md b/src/univalent-combinatorics/petri-nets.lagda.md index 0c3f656649..ff80e0f343 100644 --- a/src/univalent-combinatorics/petri-nets.lagda.md +++ b/src/univalent-combinatorics/petri-nets.lagda.md @@ -1,17 +1,22 @@ # Petri-nets ```agda -module univalent-combinatorics.petri-nets where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.petri-nets + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/pi-finite-types.lagda.md b/src/univalent-combinatorics/pi-finite-types.lagda.md index 5632fede24..7a5dad66d3 100644 --- a/src/univalent-combinatorics/pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/pi-finite-types.lagda.md @@ -1,7 +1,12 @@ # π-finite types ```agda -module univalent-combinatorics.pi-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.pi-finite-types + (funext : function-extensionality) + where ```
Imports @@ -10,16 +15,16 @@ module univalent-combinatorics.pi-finite-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.set-truncations -open import foundation.truncated-types +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.set-truncations funext +open import foundation.truncated-types funext open import foundation.truncation-levels open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.untruncated-pi-finite-types +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finitely-many-connected-components funext +open import univalent-combinatorics.untruncated-pi-finite-types funext ```
diff --git a/src/univalent-combinatorics/pigeonhole-principle.lagda.md b/src/univalent-combinatorics/pigeonhole-principle.lagda.md index 8c52386070..4a2db4566c 100644 --- a/src/univalent-combinatorics/pigeonhole-principle.lagda.md +++ b/src/univalent-combinatorics/pigeonhole-principle.lagda.md @@ -1,39 +1,44 @@ # The pigeonhole principle ```agda -module univalent-combinatorics.pigeonhole-principle where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.pigeonhole-principle + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.pairs-of-distinct-elements -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.pairs-of-distinct-elements funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import univalent-combinatorics.counting -open import univalent-combinatorics.embeddings-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.repetitions-of-values -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.embeddings-standard-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.repetitions-of-values funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/quotients-finite-types.lagda.md b/src/univalent-combinatorics/quotients-finite-types.lagda.md index 0566bd152d..9e537936a7 100644 --- a/src/univalent-combinatorics/quotients-finite-types.lagda.md +++ b/src/univalent-combinatorics/quotients-finite-types.lagda.md @@ -1,7 +1,12 @@ # Quotients of finite types ```agda -module univalent-combinatorics.quotients-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.quotients-finite-types + (funext : function-extensionality) + where ```
Imports @@ -10,10 +15,10 @@ module univalent-combinatorics.quotients-finite-types where open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.decidable-equivalence-relations -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.image-of-maps +open import univalent-combinatorics.decidable-equivalence-relations funext +open import univalent-combinatorics.decidable-subtypes funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.image-of-maps funext ```
diff --git a/src/univalent-combinatorics/ramsey-theory.lagda.md b/src/univalent-combinatorics/ramsey-theory.lagda.md index c5e0cc22ff..5bd7e24cab 100644 --- a/src/univalent-combinatorics/ramsey-theory.lagda.md +++ b/src/univalent-combinatorics/ramsey-theory.lagda.md @@ -1,7 +1,12 @@ # Ramsey theory ```agda -module univalent-combinatorics.ramsey-theory where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.ramsey-theory + (funext : function-extensionality) + where ```
Imports @@ -10,14 +15,14 @@ module univalent-combinatorics.ramsey-theory where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types -open import foundation.propositions +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/repetitions-of-values.lagda.md b/src/univalent-combinatorics/repetitions-of-values.lagda.md index 49862e4292..4d8eaeb72a 100644 --- a/src/univalent-combinatorics/repetitions-of-values.lagda.md +++ b/src/univalent-combinatorics/repetitions-of-values.lagda.md @@ -1,29 +1,34 @@ # Repetitions of values ```agda -module univalent-combinatorics.repetitions-of-values where +open import foundation.function-extensionality-axiom -open import foundation.repetitions-of-values public +module + univalent-combinatorics.repetitions-of-values + (funext : function-extensionality) + where + +open import foundation.repetitions-of-values funext public ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types - -open import foundation.cartesian-product-types -open import foundation.decidable-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation - -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.decidable-propositions -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.standard-finite-types +open import elementary-number-theory.well-ordering-principle-standard-finite-types funext + +open import foundation.cartesian-product-types funext +open import foundation.decidable-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext + +open import univalent-combinatorics.decidable-dependent-function-types funext +open import univalent-combinatorics.decidable-propositions funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/retracts-of-finite-types.lagda.md b/src/univalent-combinatorics/retracts-of-finite-types.lagda.md index d7b3d888e4..9325219a95 100644 --- a/src/univalent-combinatorics/retracts-of-finite-types.lagda.md +++ b/src/univalent-combinatorics/retracts-of-finite-types.lagda.md @@ -1,7 +1,12 @@ # Retracts of finite types ```agda -module univalent-combinatorics.retracts-of-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.retracts-of-finite-types + (funext : function-extensionality) + where ```
Imports @@ -9,23 +14,23 @@ module univalent-combinatorics.retracts-of-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-embeddings -open import foundation.decidable-maps +open import foundation.decidable-embeddings funext +open import foundation.decidable-maps funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.fibers-of-maps -open import foundation.functoriality-propositional-truncation -open import foundation.injective-maps -open import foundation.retractions -open import foundation.retracts-of-types +open import foundation.embeddings funext +open import foundation.fibers-of-maps funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.injective-maps funext +open import foundation.retractions funext +open import foundation.retracts-of-types funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-decidable-subtypes +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/riffle-shuffles.lagda.md b/src/univalent-combinatorics/riffle-shuffles.lagda.md index f4c76c4499..d90a493132 100644 --- a/src/univalent-combinatorics/riffle-shuffles.lagda.md +++ b/src/univalent-combinatorics/riffle-shuffles.lagda.md @@ -1,30 +1,35 @@ # Riffle shuffles ```agda -module univalent-combinatorics.riffle-shuffles where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.riffle-shuffles + (funext : function-extensionality) + where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.inequality-standard-finite-types funext open import elementary-number-theory.natural-numbers -open import foundation.automorphisms -open import foundation.conjunction +open import foundation.automorphisms funext +open import foundation.conjunction funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types +open import foundation.equivalences funext +open import foundation.function-types funext open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.propositions -open import order-theory.order-preserving-maps-posets -open import order-theory.posets +open import order-theory.order-preserving-maps-posets funext +open import order-theory.posets funext -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/sequences-finite-types.lagda.md b/src/univalent-combinatorics/sequences-finite-types.lagda.md index e9cd8106af..adf47ad2d2 100644 --- a/src/univalent-combinatorics/sequences-finite-types.lagda.md +++ b/src/univalent-combinatorics/sequences-finite-types.lagda.md @@ -1,36 +1,41 @@ # Sequences of elements in finite types ```agda -module univalent-combinatorics.sequences-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.sequences-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.decidable-types +open import elementary-number-theory.decidable-types funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.well-ordering-principle-natural-numbers funext open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.pairs-of-distinct-elements -open import foundation.repetitions-of-values -open import foundation.repetitions-sequences +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.pairs-of-distinct-elements funext +open import foundation.repetitions-of-values funext +open import foundation.repetitions-sequences funext open import foundation.sequences -open import foundation.sets +open import foundation.sets funext open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-standard-finite-types -open import univalent-combinatorics.pigeonhole-principle -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.equality-standard-finite-types funext +open import univalent-combinatorics.pigeonhole-principle funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md b/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md index afd05cac1d..3f1c446949 100644 --- a/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md +++ b/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md @@ -3,32 +3,37 @@ ```agda {-# OPTIONS --lossy-unification #-} -module univalent-combinatorics.set-quotients-of-index-two where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.set-quotients-of-index-two + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.commuting-squares-of-maps funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.function-types -open import foundation.functoriality-set-quotients -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.logical-equivalences -open import foundation.reflecting-maps-equivalence-relations -open import foundation.sets -open import foundation.universal-property-set-quotients +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.functoriality-set-quotients funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.logical-equivalences funext +open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.sets funext +open import foundation.universal-property-set-quotients funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/sigma-decompositions.lagda.md b/src/univalent-combinatorics/sigma-decompositions.lagda.md index 3fe2f92b9c..c66bdbea12 100644 --- a/src/univalent-combinatorics/sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/sigma-decompositions.lagda.md @@ -1,37 +1,42 @@ # Finite Σ-decompositions of finite types ```agda -module univalent-combinatorics.sigma-decompositions where +open import foundation.function-extensionality-axiom -open import foundation.sigma-decompositions public +module + univalent-combinatorics.sigma-decompositions + (funext : function-extensionality) + where + +open import foundation.sigma-decompositions funext public ```
Imports ```agda -open import foundation.cartesian-product-types -open import foundation.dependent-universal-property-equivalences -open import foundation.embeddings -open import foundation.equivalences -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.logical-equivalences -open import foundation.propositions -open import foundation.relaxed-sigma-decompositions -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.cartesian-product-types funext +open import foundation.dependent-universal-property-equivalences funext +open import foundation.embeddings funext +open import foundation.equivalences funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.logical-equivalences funext +open import foundation.propositions funext +open import foundation.relaxed-sigma-decompositions funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import univalent-combinatorics.decidable-equivalence-relations -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types -open import univalent-combinatorics.type-duality +open import univalent-combinatorics.decidable-equivalence-relations funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.inhabited-finite-types funext +open import univalent-combinatorics.type-duality funext ```
diff --git a/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md b/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md index 9cadf867c1..ed8b0ed481 100644 --- a/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md @@ -1,7 +1,12 @@ # Skipping elements in standard finite types ```agda -module univalent-combinatorics.skipping-element-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.skipping-element-standard-finite-types + (funext : function-extensionality) + where ```
Imports @@ -10,16 +15,16 @@ module univalent-combinatorics.skipping-element-standard-finite-types where open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.equality-coproduct-types -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.sets +open import foundation.embeddings funext +open import foundation.equality-coproduct-types funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.sets funext open import foundation.unit-type -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/small-types.lagda.md b/src/univalent-combinatorics/small-types.lagda.md index 3a8347ad4a..bc7632d841 100644 --- a/src/univalent-combinatorics/small-types.lagda.md +++ b/src/univalent-combinatorics/small-types.lagda.md @@ -1,9 +1,14 @@ # Small types ```agda -module univalent-combinatorics.small-types where +open import foundation.function-extensionality-axiom -open import foundation.small-types public +module + univalent-combinatorics.small-types + (funext : function-extensionality) + where + +open import foundation.small-types funext public ```
Imports @@ -12,11 +17,11 @@ open import foundation.small-types public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositional-truncations +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md b/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md index b310a181ee..7dc802a3d5 100644 --- a/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md +++ b/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md @@ -1,7 +1,12 @@ # Standard finite pruned trees ```agda -module univalent-combinatorics.standard-finite-pruned-trees where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.standard-finite-pruned-trees + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/standard-finite-trees.lagda.md b/src/univalent-combinatorics/standard-finite-trees.lagda.md index 9ef39e079f..30c5fc220a 100644 --- a/src/univalent-combinatorics/standard-finite-trees.lagda.md +++ b/src/univalent-combinatorics/standard-finite-trees.lagda.md @@ -1,23 +1,28 @@ # Standard finite trees ```agda -module univalent-combinatorics.standard-finite-trees where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.standard-finite-trees + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.maximum-natural-numbers +open import elementary-number-theory.maximum-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.sums-of-natural-numbers +open import elementary-number-theory.sums-of-natural-numbers funext -open import foundation.cartesian-product-types -open import foundation.empty-types -open import foundation.identity-types +open import foundation.cartesian-product-types funext +open import foundation.empty-types funext +open import foundation.identity-types funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/standard-finite-types.lagda.md b/src/univalent-combinatorics/standard-finite-types.lagda.md index 31d90d106c..830dbb9253 100644 --- a/src/univalent-combinatorics/standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/standard-finite-types.lagda.md @@ -1,45 +1,50 @@ # The standard finite types ```agda -module univalent-combinatorics.standard-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.standard-finite-types + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers -open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers funext open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers funext -open import foundation.action-on-higher-identifications-functions +open import foundation.action-on-higher-identifications-functions funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-types +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalence-injective-type-families -open import foundation.equivalences -open import foundation.equivalences-maybe -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.injective-maps -open import foundation.negated-equality -open import foundation.negation -open import foundation.noncontractible-types -open import foundation.preunivalent-type-families -open import foundation.raising-universe-levels -open import foundation.retractions -open import foundation.sets +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equality-coproduct-types funext +open import foundation.equivalence-injective-type-families funext +open import foundation.equivalences funext +open import foundation.equivalences funext-maybe +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.injective-maps funext +open import foundation.negated-equality funext +open import foundation.negation funext +open import foundation.noncontractible-types funext +open import foundation.preunivalent-type-families funext +open import foundation.raising-universe-levels funext +open import foundation.retractions funext +open import foundation.sets funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms funext ```
diff --git a/src/univalent-combinatorics/steiner-systems.lagda.md b/src/univalent-combinatorics/steiner-systems.lagda.md index 5c3a9d87d2..750c1417a8 100644 --- a/src/univalent-combinatorics/steiner-systems.lagda.md +++ b/src/univalent-combinatorics/steiner-systems.lagda.md @@ -1,7 +1,12 @@ # Steiner systems ```agda -module univalent-combinatorics.steiner-systems where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.steiner-systems + (funext : function-extensionality) + where ```
Imports @@ -9,12 +14,12 @@ module univalent-combinatorics.steiner-systems where ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types -open import foundation.decidable-subtypes +open import foundation.contractible-types funext +open import foundation.decidable-subtypes funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/steiner-triple-systems.lagda.md b/src/univalent-combinatorics/steiner-triple-systems.lagda.md index 2ac3dd0658..f49d924235 100644 --- a/src/univalent-combinatorics/steiner-triple-systems.lagda.md +++ b/src/univalent-combinatorics/steiner-triple-systems.lagda.md @@ -1,7 +1,12 @@ # Steiner triple systems ```agda -module univalent-combinatorics.steiner-triple-systems where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.steiner-triple-systems + (funext : function-extensionality) + where ```
Imports @@ -11,7 +16,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.steiner-systems +open import univalent-combinatorics.steiner-systems funext ```
diff --git a/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md b/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md index 6fff4532d6..7808ac541f 100644 --- a/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md +++ b/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md @@ -1,9 +1,14 @@ # Combinatorial identities of sums of natural numbers ```agda -module univalent-combinatorics.sums-of-natural-numbers where +open import foundation.function-extensionality-axiom -open import elementary-number-theory.sums-of-natural-numbers public +module + univalent-combinatorics.sums-of-natural-numbers + (funext : function-extensionality) + where + +open import elementary-number-theory.sums-of-natural-numbers funext public ```
Imports @@ -12,14 +17,14 @@ open import elementary-number-theory.sums-of-natural-numbers public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.double-counting -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-dependent-pair-types +open import univalent-combinatorics.double-counting funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/surjective-maps.lagda.md b/src/univalent-combinatorics/surjective-maps.lagda.md index 2ebd5851c5..2ccd55ee6c 100644 --- a/src/univalent-combinatorics/surjective-maps.lagda.md +++ b/src/univalent-combinatorics/surjective-maps.lagda.md @@ -1,9 +1,14 @@ # Surjective maps between finite types ```agda -module univalent-combinatorics.surjective-maps where +open import foundation.function-extensionality-axiom -open import foundation.surjective-maps public +module + univalent-combinatorics.surjective-maps + (funext : function-extensionality) + where + +open import foundation.surjective-maps funext public ```
Imports @@ -11,26 +16,26 @@ open import foundation.surjective-maps public ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.decidable-embeddings -open import foundation.decidable-equality -open import foundation.decidable-types +open import foundation.cartesian-product-types funext +open import foundation.decidable-embeddings funext +open import foundation.decidable-equality funext +open import foundation.decidable-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.logical-equivalences -open import foundation.propositional-truncations -open import foundation.propositions +open import foundation.equivalences funext +open import foundation.logical-equivalences funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.decidable-dependent-function-types -open import univalent-combinatorics.embeddings -open import univalent-combinatorics.fibers-of-maps -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-decidable-subtypes +open import univalent-combinatorics.counting-dependent-pair-types funext +open import univalent-combinatorics.decidable-dependent-function-types funext +open import univalent-combinatorics.embeddings funext +open import univalent-combinatorics.fibers-of-maps funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/symmetric-difference.lagda.md b/src/univalent-combinatorics/symmetric-difference.lagda.md index 1a75f29a9a..668a97902e 100644 --- a/src/univalent-combinatorics/symmetric-difference.lagda.md +++ b/src/univalent-combinatorics/symmetric-difference.lagda.md @@ -1,9 +1,14 @@ # Symmetric difference of finite subtypes ```agda -module univalent-combinatorics.symmetric-difference where +open import foundation.function-extensionality-axiom -open import foundation.symmetric-difference public +module + univalent-combinatorics.symmetric-difference + (funext : function-extensionality) + where + +open import foundation.symmetric-difference funext public ```
Imports @@ -14,18 +19,18 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.identity-types -open import foundation.intersections-subtypes -open import foundation.mere-equivalences -open import foundation.propositional-truncations +open import foundation.equivalences funext +open import foundation.identity-types funext +open import foundation.intersections-subtypes funext +open import foundation.mere-equivalences funext +open import foundation.propositional-truncations funext open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.decidable-subtypes -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.decidable-subtypes funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md index 5816c35f0e..7be0c392ba 100644 --- a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md @@ -1,25 +1,30 @@ # Finite trivial Σ-decompositions ```agda -module univalent-combinatorics.trivial-sigma-decompositions where +open import foundation.function-extensionality-axiom -open import foundation.trivial-sigma-decompositions public +module + univalent-combinatorics.trivial-sigma-decompositions + (funext : function-extensionality) + where + +open import foundation.trivial-sigma-decompositions funext public ```
Imports ```agda -open import foundation.contractible-types +open import foundation.contractible-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.inhabited-types -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.subtypes +open import foundation.identity-types funext +open import foundation.inhabited-types funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.subtypes funext open import foundation.universe-levels -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.sigma-decompositions +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.sigma-decompositions funext ```
diff --git a/src/univalent-combinatorics/type-duality.lagda.md b/src/univalent-combinatorics/type-duality.lagda.md index fc008806c9..2caecdc9f2 100644 --- a/src/univalent-combinatorics/type-duality.lagda.md +++ b/src/univalent-combinatorics/type-duality.lagda.md @@ -1,34 +1,39 @@ # Type duality of finite types ```agda -module univalent-combinatorics.type-duality where +open import foundation.function-extensionality-axiom -open import foundation.type-duality public +module + univalent-combinatorics.type-duality + (funext : function-extensionality) + where + +open import foundation.type-duality funext public ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.full-subtypes -open import foundation.functoriality-dependent-function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.inhabited-types -open import foundation.postcomposition-functions -open import foundation.propositions -open import foundation.structure -open import foundation.structured-type-duality -open import foundation.surjective-maps +open import foundation.equivalences funext +open import foundation.full-subtypes funext +open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.inhabited-types funext +open import foundation.postcomposition-functions funext +open import foundation.propositions funext +open import foundation.structure funext +open import foundation.structure funextd-type-duality +open import foundation.surjective-maps funext open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice +open import foundation.type-theoretic-principle-of-choice funext open import foundation.universe-levels -open import univalent-combinatorics.fibers-of-maps -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.inhabited-finite-types +open import univalent-combinatorics.fibers-of-maps funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.inhabited-finite-types funext ```
diff --git a/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md b/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md index f4335a963a..9df90df19e 100644 --- a/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module univalent-combinatorics.unbounded-pi-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.unbounded-pi-finite-types + (funext : function-extensionality) + where ```
Imports @@ -11,30 +16,30 @@ module univalent-combinatorics.unbounded-pi-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equivalences -open import foundation.function-types -open import foundation.identity-types -open import foundation.maybe -open import foundation.retracts-of-types -open import foundation.set-truncations -open import foundation.sets +open import foundation.empty-types funext +open import foundation.equality-coproduct-types funext +open import foundation.equivalences funext +open import foundation.function-types funext +open import foundation.identity-types funext +open import foundation.maybe funext +open import foundation.retracts-of-types funext +open import foundation.set-truncations funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.function-types -open import univalent-combinatorics.pi-finite-types -open import univalent-combinatorics.standard-finite-types -open import univalent-combinatorics.untruncated-pi-finite-types +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finitely-many-connected-components funext +open import univalent-combinatorics.function-types funext +open import univalent-combinatorics.pi-finite-types funext +open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.untruncated-pi-finite-types funext ```
diff --git a/src/univalent-combinatorics/unions-subtypes.lagda.md b/src/univalent-combinatorics/unions-subtypes.lagda.md index 9649925534..7a655035e7 100644 --- a/src/univalent-combinatorics/unions-subtypes.lagda.md +++ b/src/univalent-combinatorics/unions-subtypes.lagda.md @@ -1,25 +1,30 @@ # Unions of finite subtypes ```agda -module univalent-combinatorics.unions-subtypes where +open import foundation.function-extensionality-axiom -open import foundation.unions-subtypes public +module + univalent-combinatorics.unions-subtypes + (funext : function-extensionality) + where + +open import foundation.unions-subtypes funext public ```
Imports ```agda -open import foundation.decidable-equality -open import foundation.propositional-truncations -open import foundation.subtypes +open import foundation.decidable-equality funext +open import foundation.propositional-truncations funext +open import foundation.subtypes funext open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.counting-decidable-subtypes -open import univalent-combinatorics.counting-dependent-pair-types -open import univalent-combinatorics.embeddings -open import univalent-combinatorics.finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.counting funext-decidable-subtypes +open import univalent-combinatorics.counting-dependent-pair-types funext +open import univalent-combinatorics.embeddings funext +open import univalent-combinatorics.finite-types funext ```
diff --git a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md index 707c60a123..84710f4720 100644 --- a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md @@ -1,7 +1,12 @@ # The universal property of the standard finite types ```agda -module univalent-combinatorics.universal-property-standard-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.universal-property-standard-finite-types + (funext : function-extensionality) + where ```
Imports @@ -9,24 +14,25 @@ module univalent-combinatorics.universal-property-standard-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types -open import foundation.contractible-types -open import foundation.coproduct-types +open import foundation.cartesian-product-types funext +open import foundation.contractible-types funext +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-cartesian-product-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.raising-universe-levels-unit-type +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-cartesian-product-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type -open import foundation.universal-property-contractible-types -open import foundation.universal-property-empty-type -open import foundation.universal-property-maybe +open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-empty-type funext +open import foundation.universal-property-maybe funext open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md index 63f9ba773a..5bf89ff1f4 100644 --- a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md @@ -1,7 +1,12 @@ # Untruncated π-finite types ```agda -module univalent-combinatorics.untruncated-pi-finite-types where +open import foundation.function-extensionality-axiom + +module + univalent-combinatorics.untruncated-pi-finite-types + (funext : function-extensionality) + where ```
Imports @@ -9,54 +14,55 @@ module univalent-combinatorics.untruncated-pi-finite-types where ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types +open import foundation.0-connected-types funext open import foundation.action-on-identifications-functions -open import foundation.contractible-types -open import foundation.coproduct-types -open import foundation.decidable-propositions -open import foundation.decidable-types -open import foundation.dependent-identifications -open import foundation.embeddings -open import foundation.empty-types -open import foundation.equality-coproduct-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.fiber-inclusions -open import foundation.function-extensionality -open import foundation.function-types -open import foundation.functoriality-dependent-pair-types -open import foundation.functoriality-set-truncation -open import foundation.homotopies -open import foundation.identity-types -open import foundation.logical-equivalences -open import foundation.maybe -open import foundation.mere-equality -open import foundation.propositional-extensionality -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.retracts-of-types -open import foundation.set-presented-types -open import foundation.set-truncations -open import foundation.sets -open import foundation.subtypes -open import foundation.surjective-maps +open import foundation.contractible-types funext +open import foundation.coproduct-types funext +open import foundation.decidable-propositions funext +open import foundation.decidable-types funext +open import foundation.dependent-identifications funext +open import foundation.embeddings funext +open import foundation.empty-types funext +open import foundation.equality-coproduct-types funext +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.fiber-inclusions funext +open import foundation.function-extensionality funext + +open import foundation.function-types funext +open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-set-truncation funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.logical-equivalences funext +open import foundation.maybe funext +open import foundation.mere-equality funext +open import foundation.propositional-extensionality funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.retracts-of-types funext +open import foundation.set-presented-types funext +open import foundation.set-truncations funext +open import foundation.sets funext +open import foundation.subtypes funext +open import foundation.surjective-maps funext open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-coproduct-types funext open import foundation.unit-type -open import foundation.univalence +open import foundation.univalence funext open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import univalent-combinatorics.coproduct-types -open import univalent-combinatorics.counting -open import univalent-combinatorics.dependent-pair-types -open import univalent-combinatorics.equality-finite-types -open import univalent-combinatorics.finite-types -open import univalent-combinatorics.finitely-many-connected-components -open import univalent-combinatorics.finitely-presented-types -open import univalent-combinatorics.function-types -open import univalent-combinatorics.image-of-maps -open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.coproduct-types funext +open import univalent-combinatorics.counting funext +open import univalent-combinatorics.dependent-pair-types funext +open import univalent-combinatorics.equality-finite-types funext +open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finitely-many-connected-components funext +open import univalent-combinatorics.finitely-presented-types funext +open import univalent-combinatorics.function-types funext +open import univalent-combinatorics.image-of-maps funext +open import univalent-combinatorics.standard-finite-types funext ```
diff --git a/src/universal-algebra.lagda.md b/src/universal-algebra.lagda.md index 183927520e..7cebf27d63 100644 --- a/src/universal-algebra.lagda.md +++ b/src/universal-algebra.lagda.md @@ -3,17 +3,22 @@ ## Modules in the universal algebra namespace ```agda -module universal-algebra where +open import foundation.function-extensionality-axiom -open import universal-algebra.abstract-equations-over-signatures public -open import universal-algebra.algebraic-theories public -open import universal-algebra.algebraic-theory-of-groups public -open import universal-algebra.algebras-of-theories public -open import universal-algebra.congruences public -open import universal-algebra.homomorphisms-of-algebras public -open import universal-algebra.kernels public -open import universal-algebra.models-of-signatures public -open import universal-algebra.quotient-algebras public -open import universal-algebra.signatures public -open import universal-algebra.terms-over-signatures public +module + universal-algebra + (funext : function-extensionality) + where + +open import universal-algebra.abstract-equations-over-signatures funext public +open import universal-algebra.algebraic-theories funext public +open import universal-algebra.algebraic-theory-of-groups funext public +open import universal-algebra.algebras-of-theories funext public +open import universal-algebra.congruences funext public +open import universal-algebra.homomorphisms-of-algebras funext public +open import universal-algebra.kernels funext public +open import universal-algebra.models-of-signatures funext public +open import universal-algebra.quotient-algebras funext public +open import universal-algebra.signatures funext public +open import universal-algebra.terms-over-signatures funext public ``` diff --git a/src/universal-algebra/abstract-equations-over-signatures.lagda.md b/src/universal-algebra/abstract-equations-over-signatures.lagda.md index 836403a525..770bb41412 100644 --- a/src/universal-algebra/abstract-equations-over-signatures.lagda.md +++ b/src/universal-algebra/abstract-equations-over-signatures.lagda.md @@ -1,18 +1,23 @@ # Abstract equations over signatures ```agda -module universal-algebra.abstract-equations-over-signatures where +open import foundation.function-extensionality-axiom + +module + universal-algebra.abstract-equations-over-signatures + (funext : function-extensionality) + where ```
Imports ```agda -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types open import foundation.universe-levels -open import universal-algebra.signatures -open import universal-algebra.terms-over-signatures +open import universal-algebra.signatures funext +open import universal-algebra.terms-over-signatures funext ```
diff --git a/src/universal-algebra/algebraic-theories.lagda.md b/src/universal-algebra/algebraic-theories.lagda.md index bff4ee1bee..4b2d3d6ee8 100644 --- a/src/universal-algebra/algebraic-theories.lagda.md +++ b/src/universal-algebra/algebraic-theories.lagda.md @@ -1,7 +1,12 @@ # Algebraic theories ```agda -module universal-algebra.algebraic-theories where +open import foundation.function-extensionality-axiom + +module + universal-algebra.algebraic-theories + (funext : function-extensionality) + where ```
Imports @@ -10,8 +15,8 @@ module universal-algebra.algebraic-theories where open import foundation.dependent-pair-types open import foundation.universe-levels -open import universal-algebra.abstract-equations-over-signatures -open import universal-algebra.signatures +open import universal-algebra.abstract-equations-over-signatures funext +open import universal-algebra.signatures funext ```
diff --git a/src/universal-algebra/algebraic-theory-of-groups.lagda.md b/src/universal-algebra/algebraic-theory-of-groups.lagda.md index 719d008255..72922812fe 100644 --- a/src/universal-algebra/algebraic-theory-of-groups.lagda.md +++ b/src/universal-algebra/algebraic-theory-of-groups.lagda.md @@ -1,7 +1,12 @@ # Algebraic theory of groups ```agda -module universal-algebra.algebraic-theory-of-groups where +open import foundation.function-extensionality-axiom + +module + universal-algebra.algebraic-theory-of-groups + (funext : function-extensionality) + where ```
Imports @@ -10,21 +15,22 @@ module universal-algebra.algebraic-theory-of-groups where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types -open import foundation.equivalences -open import foundation.function-extensionality -open import foundation.identity-types -open import foundation.propositions +open import foundation.equality-dependent-pair-types funext +open import foundation.equivalences funext +open import foundation.function-extensionality funext + +open import foundation.identity-types funext +open import foundation.propositions funext open import foundation.universe-levels -open import group-theory.groups +open import group-theory.groups funext -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.signatures -open import universal-algebra.terms-over-signatures +open import universal-algebra.algebraic-theories funext +open import universal-algebra.algebras-of-theories funext +open import universal-algebra.signatures funext +open import universal-algebra.terms-over-signatures funext ```
diff --git a/src/universal-algebra/algebras-of-theories.lagda.md b/src/universal-algebra/algebras-of-theories.lagda.md index 3ae5fa65d3..26d2ae744a 100644 --- a/src/universal-algebra/algebras-of-theories.lagda.md +++ b/src/universal-algebra/algebras-of-theories.lagda.md @@ -1,23 +1,28 @@ # Algebras ```agda -module universal-algebra.algebras-of-theories where +open import foundation.function-extensionality-axiom + +module + universal-algebra.algebras-of-theories + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.propositions -open import foundation.sets +open import foundation.identity-types funext +open import foundation.propositions funext +open import foundation.sets funext open import foundation.universe-levels -open import universal-algebra.abstract-equations-over-signatures -open import universal-algebra.algebraic-theories -open import universal-algebra.models-of-signatures -open import universal-algebra.signatures -open import universal-algebra.terms-over-signatures +open import universal-algebra.abstract-equations-over-signatures funext +open import universal-algebra.algebraic-theories funext +open import universal-algebra.models-of-signatures funext +open import universal-algebra.signatures funext +open import universal-algebra.terms-over-signatures funext ```
diff --git a/src/universal-algebra/congruences.lagda.md b/src/universal-algebra/congruences.lagda.md index d8951087da..3c4752f535 100644 --- a/src/universal-algebra/congruences.lagda.md +++ b/src/universal-algebra/congruences.lagda.md @@ -1,7 +1,12 @@ # Congruences ```agda -module universal-algebra.congruences where +open import foundation.function-extensionality-axiom + +module + universal-algebra.congruences + (funext : function-extensionality) + where ```
Imports @@ -9,19 +14,19 @@ module universal-algebra.congruences where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type +open import foundation.equivalence-relations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.signatures +open import universal-algebra.algebraic-theories funext +open import universal-algebra.algebras-of-theories funext +open import universal-algebra.signatures funext ```
diff --git a/src/universal-algebra/homomorphisms-of-algebras.lagda.md b/src/universal-algebra/homomorphisms-of-algebras.lagda.md index f8c7ad948a..5022e0770a 100644 --- a/src/universal-algebra/homomorphisms-of-algebras.lagda.md +++ b/src/universal-algebra/homomorphisms-of-algebras.lagda.md @@ -1,22 +1,27 @@ # Homomorphisms of algebras ```agda -module universal-algebra.homomorphisms-of-algebras where +open import foundation.function-extensionality-axiom + +module + universal-algebra.homomorphisms-of-algebras + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.signatures +open import universal-algebra.algebraic-theories funext +open import universal-algebra.algebras-of-theories funext +open import universal-algebra.signatures funext ```
diff --git a/src/universal-algebra/kernels.lagda.md b/src/universal-algebra/kernels.lagda.md index e8c0fe6128..1244c039df 100644 --- a/src/universal-algebra/kernels.lagda.md +++ b/src/universal-algebra/kernels.lagda.md @@ -1,7 +1,12 @@ # Kernels of homomorphisms of algebras ```agda -module universal-algebra.kernels where +open import foundation.function-extensionality-axiom + +module + universal-algebra.kernels + (funext : function-extensionality) + where ```
Imports @@ -11,20 +16,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-relations +open import foundation.binary-relations funext open import foundation.dependent-pair-types -open import foundation.equivalence-relations -open import foundation.identity-types +open import foundation.equivalence-relations funext +open import foundation.identity-types funext open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.congruences -open import universal-algebra.homomorphisms-of-algebras -open import universal-algebra.signatures +open import universal-algebra.algebraic-theories funext +open import universal-algebra.algebras-of-theories funext +open import universal-algebra.congruences funext +open import universal-algebra.homomorphisms-of-algebras funext +open import universal-algebra.signatures funext ```
diff --git a/src/universal-algebra/models-of-signatures.lagda.md b/src/universal-algebra/models-of-signatures.lagda.md index 18b796de52..913e6b9245 100644 --- a/src/universal-algebra/models-of-signatures.lagda.md +++ b/src/universal-algebra/models-of-signatures.lagda.md @@ -1,19 +1,24 @@ # Models of signatures ```agda -module universal-algebra.models-of-signatures where +open import foundation.function-extensionality-axiom + +module + universal-algebra.models-of-signatures + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.sets +open import foundation.sets funext open import foundation.universe-levels -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import universal-algebra.signatures +open import universal-algebra.signatures funext ```
diff --git a/src/universal-algebra/quotient-algebras.lagda.md b/src/universal-algebra/quotient-algebras.lagda.md index 94bfede7ee..80538a4370 100644 --- a/src/universal-algebra/quotient-algebras.lagda.md +++ b/src/universal-algebra/quotient-algebras.lagda.md @@ -1,7 +1,12 @@ # Quotient algebras ```agda -module universal-algebra.quotient-algebras where +open import foundation.function-extensionality-axiom + +module + universal-algebra.quotient-algebras + (funext : function-extensionality) + where ```
Imports @@ -10,28 +15,28 @@ module universal-algebra.quotient-algebras where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalence-classes -open import foundation.equivalence-relations -open import foundation.equivalences -open import foundation.functoriality-propositional-truncation -open import foundation.multivariable-functoriality-set-quotients -open import foundation.multivariable-operations -open import foundation.propositional-truncations -open import foundation.propositions -open import foundation.raising-universe-levels-unit-type -open import foundation.set-quotients -open import foundation.sets +open import foundation.equivalence-classes funext +open import foundation.equivalence-relations funext +open import foundation.equivalences funext +open import foundation.functoriality-propositional-truncation funext +open import foundation.multivariable-functoriality-set-quotients funext +open import foundation.multivariable-operations funext +open import foundation.propositional-truncations funext +open import foundation.propositions funext +open import foundation.raising-universe-levels-unit-type funext +open import foundation.set-quotients funext +open import foundation.sets funext open import foundation.unit-type open import foundation.universe-levels -open import foundation.vectors-set-quotients +open import foundation.vectors-set-quotients funext -open import linear-algebra.vectors +open import linear-algebra.vectors funext -open import universal-algebra.algebraic-theories -open import universal-algebra.algebras-of-theories -open import universal-algebra.congruences -open import universal-algebra.models-of-signatures -open import universal-algebra.signatures +open import universal-algebra.algebraic-theories funext +open import universal-algebra.algebras-of-theories funext +open import universal-algebra.congruences funext +open import universal-algebra.models-of-signatures funext +open import universal-algebra.signatures funext ```
diff --git a/src/universal-algebra/signatures.lagda.md b/src/universal-algebra/signatures.lagda.md index e5b118ac6b..b8ab455575 100644 --- a/src/universal-algebra/signatures.lagda.md +++ b/src/universal-algebra/signatures.lagda.md @@ -1,7 +1,12 @@ # Signatures ```agda -module universal-algebra.signatures where +open import foundation.function-extensionality-axiom + +module + universal-algebra.signatures + (funext : function-extensionality) + where ```
Imports @@ -9,10 +14,10 @@ module universal-algebra.signatures where ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.embeddings -open import foundation.identity-types +open import foundation.embeddings funext +open import foundation.identity-types funext open import foundation.universe-levels ``` diff --git a/src/universal-algebra/terms-over-signatures.lagda.md b/src/universal-algebra/terms-over-signatures.lagda.md index 6ecf7d9351..eb6177ad78 100644 --- a/src/universal-algebra/terms-over-signatures.lagda.md +++ b/src/universal-algebra/terms-over-signatures.lagda.md @@ -1,32 +1,37 @@ # Terms over signatures ```agda -module universal-algebra.terms-over-signatures where +open import foundation.function-extensionality-axiom + +module + universal-algebra.terms-over-signatures + (funext : function-extensionality) + where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.equality-natural-numbers funext open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types +open import foundation.coproduct-types funext open import foundation.dependent-pair-types -open import foundation.identity-types -open import foundation.raising-universe-levels-unit-type +open import foundation.identity-types funext +open import foundation.raising-universe-levels-unit-type funext open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.functoriality-vectors -open import linear-algebra.vectors +open import linear-algebra.functoriality-vectors funext +open import linear-algebra.vectors funext open import lists.lists -open import lists.lists-discrete-types +open import lists.lists-discrete-types funext -open import universal-algebra.models-of-signatures -open import universal-algebra.signatures +open import universal-algebra.models-of-signatures funext +open import universal-algebra.signatures funext ```
diff --git a/src/wild-category-theory.lagda.md b/src/wild-category-theory.lagda.md index 72cf1254d2..f1ba794c86 100644 --- a/src/wild-category-theory.lagda.md +++ b/src/wild-category-theory.lagda.md @@ -11,14 +11,19 @@ ## Modules in the wild category theory namespace ```agda -module wild-category-theory where +open import foundation.function-extensionality-axiom -open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories public -open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories public -open import wild-category-theory.colax-functors-noncoherent-large-omega-precategories public -open import wild-category-theory.colax-functors-noncoherent-omega-precategories public -open import wild-category-theory.maps-noncoherent-large-omega-precategories public -open import wild-category-theory.maps-noncoherent-omega-precategories public -open import wild-category-theory.noncoherent-large-omega-precategories public -open import wild-category-theory.noncoherent-omega-precategories public +module + wild-category-theory + (funext : function-extensionality) + where + +open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories funext public +open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories funext public +open import wild-category-theory.colax-functors-noncoherent-large-omega-precategories funext public +open import wild-category-theory.colax-functors-noncoherent-omega-precategories funext public +open import wild-category-theory.maps-noncoherent-large-omega-precategories funext public +open import wild-category-theory.maps-noncoherent-omega-precategories funext public +open import wild-category-theory.noncoherent-large-omega-precategories funext public +open import wild-category-theory.noncoherent-omega-precategories funext public ``` diff --git a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md index 303c5653ac..fa0ef4498c 100644 --- a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories where +open import foundation.function-extensionality-axiom + +module + wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories + (funext : function-extensionality) + where ```
Imports @@ -12,8 +17,8 @@ module wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega- open import foundation.dependent-pair-types open import foundation.universe-levels -open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories -open import wild-category-theory.noncoherent-large-omega-precategories +open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories funext +open import wild-category-theory.noncoherent-large-omega-precategories funext ```
diff --git a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md index c2494822ea..bb5d2d6d5d 100644 --- a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md @@ -3,7 +3,12 @@ ```agda {-# OPTIONS --guardedness #-} -module wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories where +open import foundation.function-extensionality-axiom + +module + wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories + (funext : function-extensionality) + where ```
Imports @@ -12,7 +17,7 @@ module wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precat open import foundation.dependent-pair-types open import foundation.universe-levels -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories funext ```
diff --git a/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md index 714375f4a2..ffa76f6cfd 100644 --- a/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md @@ -3,28 +3,33 @@ ```agda {-# OPTIONS --guardedness #-} -module wild-category-theory.colax-functors-noncoherent-large-omega-precategories where +open import foundation.function-extensionality-axiom + +module + wild-category-theory.colax-functors-noncoherent-large-omega-precategories + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.large-colax-reflexive-globular-maps -open import globular-types.large-colax-transitive-globular-maps -open import globular-types.large-globular-maps - -open import wild-category-theory.colax-functors-noncoherent-omega-precategories -open import wild-category-theory.maps-noncoherent-large-omega-precategories -open import wild-category-theory.maps-noncoherent-omega-precategories -open import wild-category-theory.noncoherent-large-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import globular-types.large-colax-reflexive-globular-maps funext +open import globular-types.large-colax-transitive-globular-maps funext +open import globular-types.large-globular-maps funext + +open import wild-category-theory.colax-functors-noncoherent-omega-precategories funext +open import wild-category-theory.maps-noncoherent-large-omega-precategories funext +open import wild-category-theory.maps-noncoherent-omega-precategories funext +open import wild-category-theory.noncoherent-large-omega-precategories funext +open import wild-category-theory.noncoherent-omega-precategories funext ```
diff --git a/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md index 8bb9dc1251..8f8081b6d4 100644 --- a/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md @@ -3,25 +3,30 @@ ```agda {-# OPTIONS --guardedness #-} -module wild-category-theory.colax-functors-noncoherent-omega-precategories where +open import foundation.function-extensionality-axiom + +module + wild-category-theory.colax-functors-noncoherent-omega-precategories + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.colax-reflexive-globular-maps -open import globular-types.colax-transitive-globular-maps -open import globular-types.globular-maps +open import globular-types.colax-reflexive-globular-maps funext +open import globular-types.colax-transitive-globular-maps funext +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.reflexive-globular-types +open import globular-types.reflexive-globular-types funext -open import wild-category-theory.maps-noncoherent-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.maps-noncoherent-omega-precategories funext +open import wild-category-theory.noncoherent-omega-precategories funext ```
diff --git a/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md index e7adea0a47..780d53ef40 100644 --- a/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md @@ -3,25 +3,30 @@ ```agda {-# OPTIONS --guardedness #-} -module wild-category-theory.maps-noncoherent-large-omega-precategories where +open import foundation.function-extensionality-axiom + +module + wild-category-theory.maps-noncoherent-large-omega-precategories + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types -open import globular-types.large-globular-maps +open import globular-types.large-globular-maps funext open import globular-types.large-globular-types -open import wild-category-theory.maps-noncoherent-omega-precategories -open import wild-category-theory.noncoherent-large-omega-precategories -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.maps-noncoherent-omega-precategories funext +open import wild-category-theory.noncoherent-large-omega-precategories funext +open import wild-category-theory.noncoherent-omega-precategories funext ```
diff --git a/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md index 2573be3c1a..7a97c32298 100644 --- a/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md @@ -3,21 +3,26 @@ ```agda {-# OPTIONS --guardedness #-} -module wild-category-theory.maps-noncoherent-omega-precategories where +open import foundation.function-extensionality-axiom + +module + wild-category-theory.maps-noncoherent-omega-precategories + (funext : function-extensionality) + where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.identity-types +open import foundation.function-types funext +open import foundation.identity-types funext open import foundation.universe-levels -open import globular-types.globular-maps +open import globular-types.globular-maps funext open import globular-types.globular-types -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories funext ```
diff --git a/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md index d40fa26fd8..931351bc8d 100644 --- a/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md @@ -3,31 +3,36 @@ ```agda {-# OPTIONS --guardedness #-} -module wild-category-theory.noncoherent-large-omega-precategories where +open import foundation.function-extensionality-axiom + +module + wild-category-theory.noncoherent-large-omega-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.large-reflexive-globular-types -open import globular-types.large-transitive-globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.large-reflexive-globular-types funext +open import globular-types.large-transitive-globular-types funext +open import globular-types.reflexive-globular-types funext +open import globular-types.transitive-globular-types funext -open import wild-category-theory.noncoherent-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories funext ```
diff --git a/src/wild-category-theory/noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/noncoherent-omega-precategories.lagda.md index 648d1f464f..3546a35dc9 100644 --- a/src/wild-category-theory/noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/noncoherent-omega-precategories.lagda.md @@ -3,27 +3,32 @@ ```agda {-# OPTIONS --guardedness #-} -module wild-category-theory.noncoherent-omega-precategories where +open import foundation.function-extensionality-axiom + +module + wild-category-theory.noncoherent-omega-precategories + (funext : function-extensionality) + where ```
Imports ```agda -open import category-theory.precategories +open import category-theory.precategories funext open import foundation.action-on-identifications-binary-functions -open import foundation.cartesian-product-types +open import foundation.cartesian-product-types funext open import foundation.dependent-pair-types -open import foundation.function-types -open import foundation.homotopies -open import foundation.identity-types -open import foundation.sets -open import foundation.strictly-involutive-identity-types +open import foundation.function-types funext +open import foundation.homotopies funext +open import foundation.identity-types funext +open import foundation.sets funext +open import foundation.strictly-involutive-identity-types funext open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.reflexive-globular-types -open import globular-types.transitive-globular-types +open import globular-types.reflexive-globular-types funext +open import globular-types.transitive-globular-types funext ```
From 63b3fa38ad3c94f2f21c9f67358df671f4deb76b Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Fri, 21 Mar 2025 11:52:52 +0000 Subject: [PATCH 29/39] Revert "depostulate funext" This reverts commit f402d8e7f598831a852d69072ec438a3dcdb1568. --- scripts/add_funext_parameter.py | 17 +- src/category-theory.lagda.md | 325 ++++--- .../adjunctions-large-categories.lagda.md | 23 +- .../adjunctions-large-precategories.lagda.md | 19 +- .../anafunctors-categories.lagda.md | 15 +- .../anafunctors-precategories.lagda.md | 19 +- .../augmented-simplex-category.lagda.md | 21 +- src/category-theory/categories.lagda.md | 39 +- ...rs-from-small-to-large-categories.lagda.md | 37 +- .../category-of-functors.lagda.md | 29 +- .../category-of-maps-categories.lagda.md | 43 +- ...ps-from-small-to-large-categories.lagda.md | 37 +- ...-morphisms-in-large-precategories.lagda.md | 11 +- ...res-of-morphisms-in-precategories.lagda.md | 11 +- ...ares-of-morphisms-in-set-magmoids.lagda.md | 11 +- ...les-of-morphisms-in-precategories.lagda.md | 13 +- ...gles-of-morphisms-in-set-magmoids.lagda.md | 11 +- .../complete-precategories.lagda.md | 17 +- ...ations-on-binary-families-of-sets.lagda.md | 24 +- .../cones-precategories.lagda.md | 64 +- ...nservative-functors-precategories.lagda.md | 17 +- .../constant-functors.lagda.md | 35 +- .../copresheaf-categories.lagda.md | 61 +- .../coproducts-in-precategories.lagda.md | 21 +- src/category-theory/cores-categories.lagda.md | 25 +- .../cores-precategories.lagda.md | 35 +- .../coslice-precategories.lagda.md | 15 +- ...ion-operations-over-precategories.lagda.md | 31 +- .../dependent-products-of-categories.lagda.md | 32 +- ...dent-products-of-large-categories.lagda.md | 30 +- ...t-products-of-large-precategories.lagda.md | 29 +- ...pendent-products-of-precategories.lagda.md | 31 +- .../discrete-categories.lagda.md | 15 +- .../displayed-precategories.lagda.md | 39 +- .../embedding-maps-precategories.lagda.md | 17 +- 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...discrete-reflexive-globular-types.lagda.md | 17 +- .../empty-globular-types.lagda.md | 9 +- .../equality-globular-types.lagda.md | 17 +- .../exponentials-globular-types.lagda.md | 11 +- .../fibers-globular-maps.lagda.md | 15 +- .../globular-equivalences.lagda.md | 15 +- src/globular-types/globular-maps.lagda.md | 11 +- ...rge-colax-reflexive-globular-maps.lagda.md | 17 +- ...ge-colax-transitive-globular-maps.lagda.md | 17 +- .../large-globular-maps.lagda.md | 13 +- ...large-lax-reflexive-globular-maps.lagda.md | 17 +- ...arge-lax-transitive-globular-maps.lagda.md | 17 +- .../large-reflexive-globular-maps.lagda.md | 17 +- .../large-reflexive-globular-types.lagda.md | 15 +- .../large-symmetric-globular-types.lagda.md | 11 +- .../large-transitive-globular-maps.lagda.md | 19 +- .../large-transitive-globular-types.lagda.md | 11 +- .../lax-reflexive-globular-maps.lagda.md | 11 +- .../lax-transitive-globular-maps.lagda.md | 11 +- .../points-globular-types.lagda.md | 9 +- .../points-reflexive-globular-types.lagda.md | 11 +- ...ns-binary-families-globular-types.lagda.md | 13 +- ...families-reflexive-globular-types.lagda.md | 15 +- ...xtensions-families-globular-types.lagda.md | 13 +- ...families-reflexive-globular-types.lagda.md | 19 +- ...oducts-families-of-globular-types.lagda.md | 9 +- .../reflexive-globular-equivalences.lagda.md | 21 +- .../reflexive-globular-maps.lagda.md | 13 +- .../reflexive-globular-types.lagda.md | 13 +- ...sections-dependent-globular-types.lagda.md | 9 +- .../superglobular-types.lagda.md | 17 +- .../symmetric-globular-types.lagda.md | 11 +- .../terminal-globular-types.lagda.md | 11 +- .../transitive-globular-maps.lagda.md | 13 +- .../transitive-globular-types.lagda.md | 13 +- .../unit-reflexive-globular-type.lagda.md | 9 +- .../universal-globular-type.lagda.md | 13 +- ...universal-reflexive-globular-type.lagda.md | 9 +- src/graph-theory.lagda.md | 163 ++-- .../acyclic-undirected-graphs.lagda.md | 13 +- ...-change-dependent-directed-graphs.lagda.md | 13 +- ...change-dependent-reflexive-graphs.lagda.md | 19 +- ...artesian-products-directed-graphs.lagda.md | 13 +- ...rtesian-products-reflexive-graphs.lagda.md | 21 +- .../circuits-undirected-graphs.lagda.md | 13 +- .../closed-walks-undirected-graphs.lagda.md | 13 +- .../complete-bipartite-graphs.lagda.md | 25 +- .../complete-multipartite-graphs.lagda.md | 23 +- .../complete-undirected-graphs.lagda.md | 13 +- .../connected-undirected-graphs.lagda.md | 15 +- .../cycles-undirected-graphs.lagda.md | 13 +- .../dependent-directed-graphs.lagda.md | 9 +- ...ependent-products-directed-graphs.lagda.md | 27 +- ...pendent-products-reflexive-graphs.lagda.md | 51 +- .../dependent-reflexive-graphs.lagda.md | 13 +- .../dependent-sums-directed-graphs.lagda.md | 17 +- .../dependent-sums-reflexive-graphs.lagda.md | 35 +- .../directed-graph-duality.lagda.md | 31 +- ...tructures-on-standard-finite-sets.lagda.md | 9 +- src/graph-theory/directed-graphs.lagda.md | 13 +- ...screte-dependent-reflexive-graphs.lagda.md | 15 +- .../discrete-directed-graphs.lagda.md | 27 +- .../discrete-reflexive-graphs.lagda.md | 15 +- .../displayed-large-reflexive-graphs.lagda.md | 9 +- .../edge-coloured-undirected-graphs.lagda.md | 15 +- .../embeddings-directed-graphs.lagda.md | 15 +- .../embeddings-undirected-graphs.lagda.md | 15 +- .../enriched-undirected-graphs.lagda.md | 25 +- ...alences-dependent-directed-graphs.lagda.md | 25 +- ...lences-dependent-reflexive-graphs.lagda.md | 27 +- .../equivalences-directed-graphs.lagda.md | 39 +- ...lences-enriched-undirected-graphs.lagda.md | 29 +- .../equivalences-reflexive-graphs.lagda.md | 17 +- .../equivalences-undirected-graphs.lagda.md | 35 +- ...lerian-circuits-undirected-graphs.lagda.md | 17 +- ...thful-morphisms-undirected-graphs.lagda.md | 15 +- .../fibers-directed-graphs.lagda.md | 29 +- .../fibers-morphisms-directed-graphs.lagda.md | 27 +- ...fibers-morphisms-reflexive-graphs.lagda.md | 39 +- src/graph-theory/finite-graphs.lagda.md | 21 +- ...ic-realizations-undirected-graphs.lagda.md | 17 +- .../higher-directed-graphs.lagda.md | 17 +- src/graph-theory/hypergraphs.lagda.md | 9 +- .../internal-hom-directed-graphs.lagda.md | 21 +- .../large-higher-directed-graphs.lagda.md | 21 +- src/graph-theory/matchings.lagda.md | 21 +- ...re-equivalences-undirected-graphs.lagda.md | 15 +- ...rphisms-dependent-directed-graphs.lagda.md | 13 +- .../morphisms-directed-graphs.lagda.md | 25 +- .../morphisms-reflexive-graphs.lagda.md | 29 +- .../morphisms-undirected-graphs.lagda.md | 31 +- .../neighbors-undirected-graphs.lagda.md | 25 +- .../orientations-undirected-graphs.lagda.md | 11 +- .../paths-undirected-graphs.lagda.md | 13 +- src/graph-theory/polygons.lagda.md | 29 +- ...g-universe-levels-directed-graphs.lagda.md | 17 +- ...reflecting-maps-undirected-graphs.lagda.md | 15 +- src/graph-theory/reflexive-graphs.lagda.md | 13 +- .../regular-undirected-graphs.lagda.md | 15 +- ...ections-dependent-directed-graphs.lagda.md | 23 +- ...ctions-dependent-reflexive-graphs.lagda.md | 31 +- .../simple-undirected-graphs.lagda.md | 19 +- ...merism-enriched-undirected-graphs.lagda.md | 15 +- .../terminal-directed-graphs.lagda.md | 15 +- .../terminal-reflexive-graphs.lagda.md | 19 +- ...thful-morphisms-undirected-graphs.lagda.md | 15 +- .../trails-directed-graphs.lagda.md | 13 +- .../trails-undirected-graphs.lagda.md | 17 +- ...tructures-on-standard-finite-sets.lagda.md | 11 +- src/graph-theory/undirected-graphs.lagda.md | 15 +- .../universal-directed-graph.lagda.md | 17 +- .../universal-reflexive-graph.lagda.md | 15 +- src/graph-theory/vertex-covers.lagda.md | 21 +- src/graph-theory/voltage-graphs.lagda.md | 11 +- .../walks-directed-graphs.lagda.md | 41 +- .../walks-undirected-graphs.lagda.md | 37 +- ...-displayed-large-reflexive-graphs.lagda.md | 13 +- src/group-theory.lagda.md | 399 ++++---- src/group-theory/abelian-groups.lagda.md | 63 +- .../abelianization-groups.lagda.md | 57 +- ...tion-homomorphisms-abelian-groups.lagda.md | 17 +- src/group-theory/automorphism-groups.lagda.md | 27 +- ...cartesian-products-abelian-groups.lagda.md | 21 +- ...artesian-products-concrete-groups.lagda.md | 35 +- .../cartesian-products-groups.lagda.md | 19 +- .../cartesian-products-monoids.lagda.md | 17 +- .../cartesian-products-semigroups.lagda.md | 13 +- .../category-of-abelian-groups.lagda.md | 23 +- .../category-of-group-actions.lagda.md | 27 +- src/group-theory/category-of-groups.lagda.md | 23 +- .../category-of-orbits-groups.lagda.md | 33 +- .../category-of-semigroups.lagda.md | 23 +- src/group-theory/cayleys-theorem.lagda.md | 23 +- src/group-theory/centers-groups.lagda.md | 21 +- src/group-theory/centers-monoids.lagda.md | 19 +- src/group-theory/centers-semigroups.lagda.md | 19 +- .../central-elements-groups.lagda.md | 19 +- .../central-elements-monoids.lagda.md | 15 +- .../central-elements-semigroups.lagda.md | 15 +- .../centralizer-subgroups.lagda.md | 23 +- .../characteristic-subgroups.lagda.md | 17 +- src/group-theory/commutative-monoids.lagda.md | 19 +- .../commutator-subgroups.lagda.md | 39 +- .../commutators-of-elements-groups.lagda.md | 17 +- .../commuting-elements-groups.lagda.md | 15 +- .../commuting-elements-monoids.lagda.md | 15 +- .../commuting-elements-semigroups.lagda.md | 15 +- ...ng-squares-of-group-homomorphisms.lagda.md | 13 +- .../concrete-group-actions.lagda.md | 13 +- src/group-theory/concrete-groups.lagda.md | 35 +- src/group-theory/concrete-monoids.lagda.md | 19 +- ...ngruence-relations-abelian-groups.lagda.md | 23 +- ...nce-relations-commutative-monoids.lagda.md | 23 +- .../congruence-relations-groups.lagda.md | 25 +- .../congruence-relations-monoids.lagda.md | 23 +- .../congruence-relations-semigroups.lagda.md | 21 +- .../conjugation-concrete-groups.lagda.md | 19 +- src/group-theory/conjugation.lagda.md | 39 +- ...ushforward-concrete-group-actions.lagda.md | 11 +- src/group-theory/cores-monoids.lagda.md | 33 +- src/group-theory/cyclic-groups.lagda.md | 27 +- src/group-theory/decidable-subgroups.lagda.md | 37 +- ...dependent-products-abelian-groups.lagda.md | 24 +- ...dent-products-commutative-monoids.lagda.md | 20 +- .../dependent-products-groups.lagda.md | 22 +- .../dependent-products-monoids.lagda.md | 20 +- .../dependent-products-semigroups.lagda.md | 16 +- .../dihedral-group-construction.lagda.md | 23 +- src/group-theory/dihedral-groups.lagda.md | 13 +- src/group-theory/e8-lattice.lagda.md | 15 +- .../elements-of-finite-order-groups.lagda.md | 23 +- .../embeddings-abelian-groups.lagda.md | 17 +- src/group-theory/embeddings-groups.lagda.md | 15 +- ...endomorphism-rings-abelian-groups.lagda.md | 15 +- src/group-theory/epimorphisms-groups.lagda.md | 19 +- ...uivalences-concrete-group-actions.lagda.md | 31 +- .../equivalences-concrete-groups.lagda.md | 21 +- .../equivalences-group-actions.lagda.md | 37 +- .../equivalences-semigroups.lagda.md | 30 +- .../exponents-abelian-groups.lagda.md | 15 +- src/group-theory/exponents-groups.lagda.md | 19 +- .../free-concrete-group-actions.lagda.md | 19 +- .../free-groups-with-one-generator.lagda.md | 31 +- src/group-theory/full-subgroups.lagda.md | 23 +- src/group-theory/full-subsemigroups.lagda.md | 25 +- .../function-abelian-groups.lagda.md | 21 +- .../function-commutative-monoids.lagda.md | 17 +- src/group-theory/function-groups.lagda.md | 19 +- src/group-theory/function-monoids.lagda.md | 17 +- src/group-theory/function-semigroups.lagda.md | 15 +- .../functoriality-quotient-groups.lagda.md | 29 +- src/group-theory/furstenberg-groups.lagda.md | 15 +- .../generating-elements-groups.lagda.md | 75 +- .../generating-sets-groups.lagda.md | 15 +- src/group-theory/group-actions.lagda.md | 26 +- src/group-theory/groups.lagda.md | 48 +- .../homomorphisms-abelian-groups.lagda.md | 29 +- ...homomorphisms-commutative-monoids.lagda.md | 21 +- ...omorphisms-concrete-group-actions.lagda.md | 30 +- .../homomorphisms-concrete-groups.lagda.md | 21 +- ...homomorphisms-generated-subgroups.lagda.md | 53 +- .../homomorphisms-group-actions.lagda.md | 31 +- ...ps-equipped-with-normal-subgroups.lagda.md | 23 +- .../homomorphisms-groups.lagda.md | 25 +- .../homomorphisms-monoids.lagda.md | 27 +- .../homomorphisms-semigroups.lagda.md | 25 +- .../homotopy-automorphism-groups.lagda.md | 15 +- .../images-of-group-homomorphisms.lagda.md | 37 +- ...images-of-semigroup-homomorphisms.lagda.md | 35 +- ...tiples-of-elements-abelian-groups.lagda.md | 23 +- ...integer-powers-of-elements-groups.lagda.md | 31 +- ...sections-subgroups-abelian-groups.lagda.md | 15 +- .../intersections-subgroups-groups.lagda.md | 19 +- src/group-theory/inverse-semigroups.lagda.md | 17 +- .../invertible-elements-monoids.lagda.md | 29 +- .../isomorphisms-abelian-groups.lagda.md | 31 +- .../isomorphisms-concrete-groups.lagda.md | 13 +- .../isomorphisms-group-actions.lagda.md | 40 +- src/group-theory/isomorphisms-groups.lagda.md | 39 +- .../isomorphisms-monoids.lagda.md | 27 +- .../isomorphisms-semigroups.lagda.md | 36 +- ...artesian-products-concrete-groups.lagda.md | 49 +- ...nels-homomorphisms-abelian-groups.lagda.md | 19 +- ...els-homomorphisms-concrete-groups.lagda.md | 25 +- .../kernels-homomorphisms-groups.lagda.md | 25 +- src/group-theory/large-semigroups.lagda.md | 13 +- src/group-theory/loop-groups-sets.lagda.md | 48 +- ...uivalences-concrete-group-actions.lagda.md | 21 +- .../mere-equivalences-group-actions.lagda.md | 17 +- ...ultiplication-commutative-monoids.lagda.md | 23 +- .../minkowski-multiplication-monoids.lagda.md | 23 +- ...nkowski-multiplication-semigroups.lagda.md | 33 +- src/group-theory/monoid-actions.lagda.md | 18 +- src/group-theory/monoids.lagda.md | 21 +- .../monomorphisms-concrete-groups.lagda.md | 15 +- .../monomorphisms-groups.lagda.md | 19 +- ...tiples-of-elements-abelian-groups.lagda.md | 15 +- src/group-theory/nontrivial-groups.lagda.md | 41 +- .../normal-closures-subgroups.lagda.md | 39 +- .../normal-cores-subgroups.lagda.md | 37 +- .../normal-subgroups-concrete-groups.lagda.md | 15 +- src/group-theory/normal-subgroups.lagda.md | 49 +- ...al-submonoids-commutative-monoids.lagda.md | 41 +- src/group-theory/normal-submonoids.lagda.md | 39 +- .../normalizer-subgroups.lagda.md | 29 +- .../nullifying-group-homomorphisms.lagda.md | 27 +- src/group-theory/opposite-groups.lagda.md | 15 +- src/group-theory/opposite-semigroups.lagda.md | 13 +- ...tabilizer-theorem-concrete-groups.lagda.md | 15 +- .../orbits-concrete-group-actions.lagda.md | 15 +- .../orbits-group-actions.lagda.md | 13 +- .../orders-of-elements-groups.lagda.md | 21 +- src/group-theory/perfect-cores.lagda.md | 15 +- src/group-theory/perfect-groups.lagda.md | 15 +- src/group-theory/perfect-subgroups.lagda.md | 15 +- ...s-of-elements-commutative-monoids.lagda.md | 17 +- .../powers-of-elements-groups.lagda.md | 19 +- .../powers-of-elements-monoids.lagda.md | 17 +- ...recategory-of-commutative-monoids.lagda.md | 17 +- .../precategory-of-concrete-groups.lagda.md | 13 +- .../precategory-of-group-actions.lagda.md | 17 +- .../precategory-of-groups.lagda.md | 17 +- .../precategory-of-monoids.lagda.md | 19 +- ...category-of-orbits-monoid-actions.lagda.md | 25 +- .../precategory-of-semigroups.lagda.md | 13 +- .../principal-group-actions.lagda.md | 13 +- ...principal-torsors-concrete-groups.lagda.md | 11 +- .../products-of-elements-monoids.lagda.md | 13 +- ...s-of-elements-commutative-monoids.lagda.md | 17 +- src/group-theory/pullbacks-subgroups.lagda.md | 39 +- .../pullbacks-subsemigroups.lagda.md | 31 +- .../quotient-groups-concrete-groups.lagda.md | 39 +- src/group-theory/quotient-groups.lagda.md | 55 +- .../quotients-abelian-groups.lagda.md | 43 +- .../rational-commutative-monoids.lagda.md | 19 +- ...esentations-monoids-precategories.lagda.md | 19 +- ...nce-relations-commutative-monoids.lagda.md | 25 +- ...ated-congruence-relations-monoids.lagda.md | 25 +- src/group-theory/semigroups.lagda.md | 11 +- src/group-theory/sheargroups.lagda.md | 13 +- .../shriek-concrete-group-actions.lagda.md | 21 +- ...zer-groups-concrete-group-actions.lagda.md | 27 +- src/group-theory/stabilizer-groups.lagda.md | 13 +- .../subgroups-abelian-groups.lagda.md | 51 +- .../subgroups-concrete-groups.lagda.md | 43 +- ...oups-generated-by-elements-groups.lagda.md | 39 +- ...ed-by-families-of-elements-groups.lagda.md | 37 +- ...roups-generated-by-subsets-groups.lagda.md | 71 +- src/group-theory/subgroups.lagda.md | 67 +- .../submonoids-commutative-monoids.lagda.md | 29 +- src/group-theory/submonoids.lagda.md | 27 +- src/group-theory/subsemigroups.lagda.md | 41 +- .../subsets-abelian-groups.lagda.md | 21 +- .../subsets-commutative-monoids.lagda.md | 17 +- src/group-theory/subsets-groups.lagda.md | 17 +- src/group-theory/subsets-monoids.lagda.md | 17 +- src/group-theory/subsets-semigroups.lagda.md | 25 +- ...on-functor-concrete-group-actions.lagda.md | 13 +- ...ubstitution-functor-group-actions.lagda.md | 35 +- .../surjective-group-homomorphisms.lagda.md | 21 +- ...urjective-semigroup-homomorphisms.lagda.md | 19 +- .../symmetric-concrete-groups.lagda.md | 19 +- src/group-theory/symmetric-groups.lagda.md | 38 +- .../torsion-elements-groups.lagda.md | 21 +- src/group-theory/torsion-free-groups.lagda.md | 39 +- src/group-theory/torsors.lagda.md | 53 +- ...transitive-concrete-group-actions.lagda.md | 37 +- .../transitive-group-actions.lagda.md | 19 +- .../trivial-concrete-groups.lagda.md | 17 +- .../trivial-group-homomorphisms.lagda.md | 17 +- src/group-theory/trivial-groups.lagda.md | 27 +- src/group-theory/trivial-subgroups.lagda.md | 13 +- ...s-of-elements-commutative-monoids.lagda.md | 11 +- .../wild-representations-monoids.lagda.md | 17 +- src/higher-group-theory.lagda.md | 57 +- .../abelian-higher-groups.lagda.md | 23 +- .../automorphism-groups.lagda.md | 25 +- .../cartesian-products-higher-groups.lagda.md | 25 +- src/higher-group-theory/conjugation.lagda.md | 19 +- .../cyclic-higher-groups.lagda.md | 17 +- .../deloopable-groups.lagda.md | 11 +- .../deloopable-h-spaces.lagda.md | 13 +- .../deloopable-types.lagda.md | 21 +- .../eilenberg-mac-lane-spaces.lagda.md | 27 +- .../equivalences-higher-groups.lagda.md | 27 +- ...fixed-points-higher-group-actions.lagda.md | 11 +- .../free-higher-group-actions.lagda.md | 29 +- .../higher-group-actions.lagda.md | 11 +- .../higher-groups.lagda.md | 27 +- ...omomorphisms-higher-group-actions.lagda.md | 22 +- .../homomorphisms-higher-groups.lagda.md | 19 +- .../integers-higher-group.lagda.md | 11 +- ...-cartesian-products-higher-groups.lagda.md | 41 +- ...rated-deloopings-of-pointed-types.lagda.md | 15 +- .../orbits-higher-group-actions.lagda.md | 11 +- .../small-higher-groups.lagda.md | 33 +- .../subgroups-higher-groups.lagda.md | 17 +- .../symmetric-higher-groups.lagda.md | 15 +- .../transitive-higher-group-actions.lagda.md | 27 +- .../trivial-higher-groups.lagda.md | 17 +- src/linear-algebra.lagda.md | 41 +- src/linear-algebra/constant-matrices.lagda.md | 11 +- src/linear-algebra/constant-vectors.lagda.md | 9 +- .../diagonal-matrices-on-rings.lagda.md | 19 +- .../functoriality-matrices.lagda.md | 11 +- .../functoriality-vectors.lagda.md | 19 +- src/linear-algebra/matrices-on-rings.lagda.md | 21 +- src/linear-algebra/matrices.lagda.md | 15 +- .../scalar-multiplication-matrices.lagda.md | 11 +- ...r-multiplication-vectors-on-rings.lagda.md | 23 +- .../scalar-multiplication-vectors.lagda.md | 11 +- .../transposition-matrices.lagda.md | 15 +- .../vectors-on-commutative-rings.lagda.md | 21 +- .../vectors-on-commutative-semirings.lagda.md | 21 +- .../vectors-on-euclidean-domains.lagda.md | 30 +- src/linear-algebra/vectors-on-rings.lagda.md | 30 +- .../vectors-on-semirings.lagda.md | 26 +- src/linear-algebra/vectors.lagda.md | 41 +- src/lists.lagda.md | 43 +- src/lists/arrays.lagda.md | 29 +- src/lists/concatenation-lists.lagda.md | 17 +- src/lists/equality-lists.lagda.md | 37 +- src/lists/flattening-lists.lagda.md | 15 +- src/lists/functoriality-lists.lagda.md | 29 +- src/lists/lists-discrete-types.lagda.md | 29 +- src/lists/permutation-lists.lagda.md | 27 +- src/lists/permutation-vectors.lagda.md | 35 +- src/lists/predicates-on-lists.lagda.md | 11 +- src/lists/quicksort-lists.lagda.md | 19 +- src/lists/reversing-lists.lagda.md | 17 +- src/lists/sort-by-insertion-lists.lagda.md | 23 +- src/lists/sort-by-insertion-vectors.lagda.md | 31 +- src/lists/sorted-lists.lagda.md | 19 +- src/lists/sorted-vectors.lagda.md | 27 +- src/lists/sorting-algorithms-lists.lagda.md | 25 +- src/lists/sorting-algorithms-vectors.lagda.md | 21 +- ...ersal-property-lists-wild-monoids.lagda.md | 23 +- src/literature.lagda.md | 19 +- src/literature/100-theorems.lagda.md | 41 +- src/literature/1000plus-theorems.lagda.md | 49 +- ...otents-in-intensional-type-theory.lagda.md | 109 +-- ...roduction-to-homotopy-type-theory.lagda.md | 774 ++++++++++------ src/literature/oeis.lagda.md | 49 +- ...-colimits-in-homotopy-type-theory.lagda.md | 50 +- src/logic.lagda.md | 39 +- .../complements-de-morgan-subtypes.lagda.md | 35 +- .../complements-decidable-subtypes.lagda.md | 37 +- ...s-double-negation-stable-subtypes.lagda.md | 29 +- src/logic/de-morgan-embeddings.lagda.md | 51 +- src/logic/de-morgan-maps.lagda.md | 53 +- src/logic/de-morgan-propositions.lagda.md | 57 +- src/logic/de-morgan-subtypes.lagda.md | 39 +- src/logic/de-morgan-types.lagda.md | 47 +- src/logic/de-morgans-law.lagda.md | 33 +- .../double-negation-eliminating-maps.lagda.md | 37 +- .../double-negation-elimination.lagda.md | 25 +- ...double-negation-stable-embeddings.lagda.md | 47 +- .../double-negation-stable-subtypes.lagda.md | 41 +- ...iality-existential-quantification.lagda.md | 9 +- 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+- .../isometries-metric-spaces.lagda.md | 42 +- .../isometries-premetric-spaces.lagda.md | 34 +- ...pproximations-in-premetric-spaces.lagda.md | 23 +- ...-approximations-in-a-metric-space.lagda.md | 17 +- ...-approximations-in-a-metric-space.lagda.md | 15 +- ...l-numbers-with-open-neighborhoods.lagda.md | 51 +- .../metric-space-of-rational-numbers.lagda.md | 67 +- src/metric-spaces/metric-spaces.lagda.md | 45 +- src/metric-spaces/metric-structures.lagda.md | 31 +- .../monotonic-premetric-structures.lagda.md | 13 +- .../ordering-premetric-structures.lagda.md | 23 +- ...ry-of-metric-spaces-and-functions.lagda.md | 17 +- ...y-of-metric-spaces-and-isometries.lagda.md | 28 +- ...metric-spaces-and-short-functions.lagda.md | 32 +- src/metric-spaces/premetric-spaces.lagda.md | 27 +- .../premetric-structures.lagda.md | 40 +- .../pseudometric-spaces.lagda.md | 37 +- .../pseudometric-structures.lagda.md | 27 +- .../reflexive-premetric-structures.lagda.md | 31 +- 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+- .../order-preserving-maps-posets.lagda.md | 27 +- .../order-preserving-maps-preorders.lagda.md | 23 +- src/order-theory/ordinals.lagda.md | 27 +- src/order-theory/posets.lagda.md | 31 +- .../powers-of-large-locales.lagda.md | 29 +- ...ategory-of-decidable-total-orders.lagda.md | 17 +- .../precategory-of-finite-posets.lagda.md | 17 +- ...recategory-of-finite-total-orders.lagda.md | 17 +- ...-of-inhabited-finite-total-orders.lagda.md | 17 +- .../precategory-of-posets.lagda.md | 15 +- .../precategory-of-total-orders.lagda.md | 17 +- src/order-theory/preorders.lagda.md | 27 +- ...principal-lower-sets-large-posets.lagda.md | 19 +- ...principal-upper-sets-large-posets.lagda.md | 19 +- ...e-galois-connections-large-posets.lagda.md | 15 +- src/order-theory/resizing-posets.lagda.md | 41 +- src/order-theory/resizing-preorders.lagda.md | 31 +- .../resizing-suplattices.lagda.md | 39 +- ...milarity-of-elements-large-posets.lagda.md | 23 +- ...arity-of-elements-large-preorders.lagda.md | 15 +- 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| 43 +- ...perations-global-function-classes.lagda.md | 15 +- .../factorization-operations.lagda.md | 9 +- ...izations-of-maps-function-classes.lagda.md | 35 +- ...s-of-maps-global-function-classes.lagda.md | 37 +- .../factorizations-of-maps.lagda.md | 23 +- .../families-of-types-local-at-maps.lagda.md | 17 +- .../fiberwise-orthogonal-maps.lagda.md | 31 +- .../function-classes.lagda.md | 31 +- .../functoriality-higher-modalities.lagda.md | 32 +- ...alizations-at-global-subuniverses.lagda.md | 34 +- .../functoriality-pullback-hom.lagda.md | 15 +- ...ty-reflective-global-subuniverses.lagda.md | 23 +- .../global-function-classes.lagda.md | 23 +- .../higher-modalities.lagda.md | 39 +- .../identity-modality.lagda.md | 17 +- .../large-lawvere-tierney-topologies.lagda.md | 19 +- .../lawvere-tierney-topologies.lagda.md | 25 +- .../lifting-operations.lagda.md | 17 +- .../lifting-structures-on-squares.lagda.md | 49 +- .../lifts-families-of-elements.lagda.md | 19 +- .../lifts-maps.lagda.md | 31 +- ...alizations-at-global-subuniverses.lagda.md | 68 +- .../localizations-at-maps.lagda.md | 13 +- .../localizations-at-subuniverses.lagda.md | 13 +- .../locally-small-modal-operators.lagda.md | 11 +- .../maps-local-at-maps.lagda.md | 21 +- .../mere-lifting-properties.lagda.md | 13 +- .../modal-induction.lagda.md | 36 +- .../modal-operators.lagda.md | 17 +- .../modal-subuniverse-induction.lagda.md | 31 +- .../null-families-of-types.lagda.md | 19 +- .../null-maps.lagda.md | 51 +- .../null-types.lagda.md | 60 +- .../open-modalities.lagda.md | 29 +- .../orthogonal-factorization-systems.lagda.md | 37 +- .../orthogonal-maps.lagda.md | 84 +- ...sition-lifts-families-of-elements.lagda.md | 35 +- .../pullback-hom.lagda.md | 61 +- .../raise-modalities.lagda.md | 17 +- .../reflective-global-subuniverses.lagda.md | 31 +- .../reflective-modalities.lagda.md | 11 +- .../reflective-subuniverses.lagda.md | 23 +- .../sigma-closed-modalities.lagda.md | 13 +- 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.../standard-finite-trees.lagda.md | 19 +- .../standard-finite-types.lagda.md | 57 +- .../steiner-systems.lagda.md | 13 +- .../steiner-triple-systems.lagda.md | 9 +- .../sums-of-natural-numbers.lagda.md | 19 +- .../surjective-maps.lagda.md | 41 +- .../symmetric-difference.lagda.md | 27 +- .../trivial-sigma-decompositions.lagda.md | 25 +- .../type-duality.lagda.md | 39 +- .../unbounded-pi-finite-types.lagda.md | 47 +- .../unions-subtypes.lagda.md | 27 +- ...al-property-standard-finite-types.lagda.md | 36 +- .../untruncated-pi-finite-types.lagda.md | 92 +- src/universal-algebra.lagda.md | 29 +- ...bstract-equations-over-signatures.lagda.md | 13 +- .../algebraic-theories.lagda.md | 11 +- .../algebraic-theory-of-groups.lagda.md | 30 +- .../algebras-of-theories.lagda.md | 23 +- src/universal-algebra/congruences.lagda.md | 23 +- .../homomorphisms-of-algebras.lagda.md | 19 +- src/universal-algebra/kernels.lagda.md | 27 +- .../models-of-signatures.lagda.md | 13 +- .../quotient-algebras.lagda.md | 43 +- src/universal-algebra/signatures.lagda.md | 13 +- .../terms-over-signatures.lagda.md | 25 +- src/wild-category-theory.lagda.md | 23 +- ...oherent-large-omega-precategories.lagda.md | 11 +- ...n-noncoherent-omega-precategories.lagda.md | 9 +- ...oherent-large-omega-precategories.lagda.md | 31 +- ...s-noncoherent-omega-precategories.lagda.md | 23 +- ...oherent-large-omega-precategories.lagda.md | 21 +- ...s-noncoherent-omega-precategories.lagda.md | 15 +- ...oherent-large-omega-precategories.lagda.md | 29 +- .../noncoherent-omega-precategories.lagda.md | 25 +- 2097 files changed, 22015 insertions(+), 32398 deletions(-) diff --git a/scripts/add_funext_parameter.py b/scripts/add_funext_parameter.py index c71172b522..078f9f42f3 100644 --- a/scripts/add_funext_parameter.py +++ b/scripts/add_funext_parameter.py @@ -68,18 +68,13 @@ def modify_file_content(file_path, module_name, dependent_modules): # Add funext parameter to module declaration if needed if not has_funext_param: - # Extract module name and any existing parameters/declarations - module_name_match = re.match(r'^module\s+([^\s\(]+)', line) - if module_name_match: - module_name = module_name_match.group(1) - # Create multi-line declaration with indentation - updated_lines.append("module") - updated_lines.append(" " + module_name) - updated_lines.append(" " + FUNEXT_PARAM) - updated_lines.append(" where") + if "where" in line: + # If there's a 'where' clause, put parameters before it + updated_line = re.sub(r'(\s+where)', f" {FUNEXT_PARAM}\\1", line) else: - # Fallback if we can't parse the module name correctly - updated_lines.append(line) + # Otherwise, add at the end + updated_line = line.rstrip() + f" {FUNEXT_PARAM} where" + updated_lines.append(updated_line) else: updated_lines.append(line) else: diff --git a/src/category-theory.lagda.md b/src/category-theory.lagda.md index b8f906a0d5..5d426bb25d 100644 --- a/src/category-theory.lagda.md +++ b/src/category-theory.lagda.md @@ -11,170 +11,165 @@ ## Modules in the category theory namespace ```agda -open import foundation.function-extensionality-axiom +module category-theory where -module - category-theory - (funext : function-extensionality) - where - -open import category-theory.adjunctions-large-categories funext public -open import category-theory.adjunctions-large-precategories funext public -open import category-theory.anafunctors-categories funext public -open import category-theory.anafunctors-precategories funext public -open import category-theory.augmented-simplex-category funext public -open import category-theory.categories funext public -open import category-theory.category-of-functors funext public -open import category-theory.category-of-functors-from-small-to-large-categories funext public -open import category-theory.category-of-maps-categories funext public -open import category-theory.category-of-maps-from-small-to-large-categories funext public -open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext public -open import category-theory.commuting-squares-of-morphisms-in-precategories funext public -open import category-theory.commuting-squares-of-morphisms-in-set-magmoids funext public -open import category-theory.commuting-triangles-of-morphisms-in-precategories funext public -open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids funext public -open import category-theory.complete-precategories funext public -open import category-theory.composition-operations-on-binary-families-of-sets funext public -open import category-theory.cones-precategories funext public -open import category-theory.conservative-functors-precategories funext public -open import category-theory.constant-functors funext public -open import category-theory.copresheaf-categories funext public -open import category-theory.coproducts-in-precategories funext public -open import category-theory.cores-categories funext public -open import category-theory.cores-precategories funext public -open import category-theory.coslice-precategories funext public -open import category-theory.dependent-composition-operations-over-precategories funext public -open import category-theory.dependent-products-of-categories funext public -open import category-theory.dependent-products-of-large-categories funext public -open import category-theory.dependent-products-of-large-precategories funext public -open import category-theory.dependent-products-of-precategories funext public -open import category-theory.discrete-categories funext public -open import category-theory.displayed-precategories funext public -open import category-theory.embedding-maps-precategories funext public -open import category-theory.embeddings-precategories funext public -open import category-theory.endomorphisms-in-categories funext public -open import category-theory.endomorphisms-in-precategories funext public -open import category-theory.epimorphisms-in-large-precategories funext public -open import category-theory.equivalences-of-categories funext public -open import category-theory.equivalences-of-large-precategories funext public -open import category-theory.equivalences-of-precategories funext public -open import category-theory.essential-fibers-of-functors-precategories funext public -open import category-theory.essentially-injective-functors-precategories funext public -open import category-theory.essentially-surjective-functors-precategories funext public -open import category-theory.exponential-objects-precategories funext public -open import category-theory.extensions-of-functors-precategories funext public -open import category-theory.faithful-functors-precategories funext public -open import category-theory.faithful-maps-precategories funext public -open import category-theory.full-functors-precategories funext public -open import category-theory.full-large-subcategories funext public -open import category-theory.full-large-subprecategories funext public -open import category-theory.full-maps-precategories funext public -open import category-theory.full-subcategories funext public -open import category-theory.full-subprecategories funext public -open import category-theory.fully-faithful-functors-precategories funext public -open import category-theory.fully-faithful-maps-precategories funext public -open import category-theory.function-categories funext public -open import category-theory.function-precategories funext public -open import category-theory.functors-categories funext public -open import category-theory.functors-from-small-to-large-categories funext public -open import category-theory.functors-from-small-to-large-precategories funext public -open import category-theory.functors-large-categories funext public -open import category-theory.functors-large-precategories funext public -open import category-theory.functors-nonunital-precategories funext public -open import category-theory.functors-precategories funext public -open import category-theory.functors-set-magmoids funext public -open import category-theory.gaunt-categories funext public -open import category-theory.groupoids funext public -open import category-theory.homotopies-natural-transformations-large-precategories funext public -open import category-theory.indiscrete-precategories funext public -open import category-theory.initial-category funext public -open import category-theory.initial-objects-large-categories funext public -open import category-theory.initial-objects-large-precategories funext public -open import category-theory.initial-objects-precategories funext public -open import category-theory.isomorphism-induction-categories funext public -open import category-theory.isomorphism-induction-precategories funext public -open import category-theory.isomorphisms-in-categories funext public -open import category-theory.isomorphisms-in-large-categories funext public -open import category-theory.isomorphisms-in-large-precategories funext public -open import category-theory.isomorphisms-in-precategories funext public -open import category-theory.isomorphisms-in-subprecategories funext public -open import category-theory.large-categories funext public -open import category-theory.large-function-categories funext public -open import category-theory.large-function-precategories funext public -open import category-theory.large-precategories funext public -open import category-theory.large-subcategories funext public -open import category-theory.large-subprecategories funext public -open import category-theory.limits-precategories funext public -open import category-theory.maps-categories funext public -open import category-theory.maps-from-small-to-large-categories funext public -open import category-theory.maps-from-small-to-large-precategories funext public -open import category-theory.maps-precategories funext public -open import category-theory.maps-set-magmoids funext public -open import category-theory.monads-on-categories funext public -open import category-theory.monads-on-precategories funext public -open import category-theory.monomorphisms-in-large-precategories funext public -open import category-theory.natural-isomorphisms-functors-categories funext public -open import category-theory.natural-isomorphisms-functors-large-precategories funext public -open import category-theory.natural-isomorphisms-functors-precategories funext public -open import category-theory.natural-isomorphisms-maps-categories funext public -open import category-theory.natural-isomorphisms-maps-precategories funext public -open import category-theory.natural-numbers-object-precategories funext public -open import category-theory.natural-transformations-functors-categories funext public -open import category-theory.natural-transformations-functors-from-small-to-large-categories funext public -open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext public -open import category-theory.natural-transformations-functors-large-categories funext public -open import category-theory.natural-transformations-functors-large-precategories funext public -open import category-theory.natural-transformations-functors-precategories funext public -open import category-theory.natural-transformations-maps-categories funext public -open import category-theory.natural-transformations-maps-from-small-to-large-precategories funext public -open import category-theory.natural-transformations-maps-precategories funext public -open import category-theory.nonunital-precategories funext public -open import category-theory.one-object-precategories funext public -open import category-theory.opposite-categories funext public -open import category-theory.opposite-large-precategories funext public -open import category-theory.opposite-precategories funext public -open import category-theory.opposite-preunivalent-categories funext public -open import category-theory.opposite-strongly-preunivalent-categories funext public -open import category-theory.pointed-endofunctors-categories funext public -open import category-theory.pointed-endofunctors-precategories funext public -open import category-theory.precategories funext public -open import category-theory.precategory-of-elements-of-a-presheaf funext public -open import category-theory.precategory-of-functors funext public -open import category-theory.precategory-of-functors-from-small-to-large-precategories funext public -open import category-theory.precategory-of-maps-from-small-to-large-precategories funext public -open import category-theory.precategory-of-maps-precategories funext public -open import category-theory.pregroupoids funext public -open import category-theory.presheaf-categories funext public -open import category-theory.preunivalent-categories funext public -open import category-theory.products-in-precategories funext public -open import category-theory.products-of-precategories funext public -open import category-theory.pseudomonic-functors-precategories funext public -open import category-theory.pullbacks-in-precategories funext public -open import category-theory.replete-subprecategories funext public -open import category-theory.representable-functors-categories funext public -open import category-theory.representable-functors-large-precategories funext public -open import category-theory.representable-functors-precategories funext public -open import category-theory.representing-arrow-category funext public -open import category-theory.restrictions-functors-cores-precategories funext public -open import category-theory.right-extensions-precategories funext public -open import category-theory.right-kan-extensions-precategories funext public -open import category-theory.rigid-objects-categories funext public -open import category-theory.rigid-objects-precategories funext public -open import category-theory.set-magmoids funext public -open import category-theory.sieves-in-categories funext public -open import category-theory.simplex-category funext public -open import category-theory.slice-precategories funext public -open import category-theory.split-essentially-surjective-functors-precategories funext public -open import category-theory.strict-categories funext public -open import category-theory.strongly-preunivalent-categories funext public -open import category-theory.structure-equivalences-set-magmoids funext public -open import category-theory.subcategories funext public -open import category-theory.subprecategories funext public -open import category-theory.subterminal-precategories funext public -open import category-theory.terminal-category funext public -open import category-theory.terminal-objects-precategories funext public -open import category-theory.wide-subcategories funext public -open import category-theory.wide-subprecategories funext public -open import category-theory.yoneda-lemma-categories funext public -open import category-theory.yoneda-lemma-precategories funext public +open import category-theory.adjunctions-large-categories public +open import category-theory.adjunctions-large-precategories public +open import category-theory.anafunctors-categories public +open import category-theory.anafunctors-precategories public +open import category-theory.augmented-simplex-category public +open import category-theory.categories public +open import category-theory.category-of-functors public +open import category-theory.category-of-functors-from-small-to-large-categories public +open import category-theory.category-of-maps-categories public +open import category-theory.category-of-maps-from-small-to-large-categories public +open import category-theory.commuting-squares-of-morphisms-in-large-precategories public +open import category-theory.commuting-squares-of-morphisms-in-precategories public +open import category-theory.commuting-squares-of-morphisms-in-set-magmoids public +open import category-theory.commuting-triangles-of-morphisms-in-precategories public +open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids public +open import category-theory.complete-precategories public +open import category-theory.composition-operations-on-binary-families-of-sets public +open import category-theory.cones-precategories public +open import category-theory.conservative-functors-precategories public +open import category-theory.constant-functors public +open import category-theory.copresheaf-categories public +open import category-theory.coproducts-in-precategories public +open import category-theory.cores-categories public +open import category-theory.cores-precategories public +open import category-theory.coslice-precategories public +open import category-theory.dependent-composition-operations-over-precategories public +open import category-theory.dependent-products-of-categories public +open import category-theory.dependent-products-of-large-categories public +open import category-theory.dependent-products-of-large-precategories public +open import category-theory.dependent-products-of-precategories public +open import category-theory.discrete-categories public +open import category-theory.displayed-precategories public +open import category-theory.embedding-maps-precategories public +open import category-theory.embeddings-precategories public +open import category-theory.endomorphisms-in-categories public +open import category-theory.endomorphisms-in-precategories public +open import category-theory.epimorphisms-in-large-precategories public +open import category-theory.equivalences-of-categories public +open import category-theory.equivalences-of-large-precategories public +open import category-theory.equivalences-of-precategories public +open import category-theory.essential-fibers-of-functors-precategories public +open import category-theory.essentially-injective-functors-precategories public +open import category-theory.essentially-surjective-functors-precategories public +open import category-theory.exponential-objects-precategories public +open import category-theory.extensions-of-functors-precategories public +open import category-theory.faithful-functors-precategories public +open import category-theory.faithful-maps-precategories public +open import category-theory.full-functors-precategories public +open import category-theory.full-large-subcategories public +open import category-theory.full-large-subprecategories public +open import category-theory.full-maps-precategories public +open import category-theory.full-subcategories public +open import category-theory.full-subprecategories public +open import category-theory.fully-faithful-functors-precategories public +open import category-theory.fully-faithful-maps-precategories public +open import category-theory.function-categories public +open import category-theory.function-precategories public +open import category-theory.functors-categories public +open import category-theory.functors-from-small-to-large-categories public +open import category-theory.functors-from-small-to-large-precategories public +open import category-theory.functors-large-categories public +open import category-theory.functors-large-precategories public +open import category-theory.functors-nonunital-precategories public +open import category-theory.functors-precategories public +open import category-theory.functors-set-magmoids public +open import category-theory.gaunt-categories public +open import category-theory.groupoids public +open import category-theory.homotopies-natural-transformations-large-precategories public +open import category-theory.indiscrete-precategories public +open import category-theory.initial-category public +open import category-theory.initial-objects-large-categories public +open import category-theory.initial-objects-large-precategories public +open import category-theory.initial-objects-precategories public +open import category-theory.isomorphism-induction-categories public +open import category-theory.isomorphism-induction-precategories public +open import category-theory.isomorphisms-in-categories public +open import category-theory.isomorphisms-in-large-categories public +open import category-theory.isomorphisms-in-large-precategories public +open import category-theory.isomorphisms-in-precategories public +open import category-theory.isomorphisms-in-subprecategories public +open import category-theory.large-categories public +open import category-theory.large-function-categories public +open import category-theory.large-function-precategories public +open import category-theory.large-precategories public +open import category-theory.large-subcategories public +open import category-theory.large-subprecategories public +open import category-theory.limits-precategories public +open import category-theory.maps-categories public +open import category-theory.maps-from-small-to-large-categories public +open import category-theory.maps-from-small-to-large-precategories public +open import category-theory.maps-precategories public +open import category-theory.maps-set-magmoids public +open import category-theory.monads-on-categories public +open import category-theory.monads-on-precategories public +open import category-theory.monomorphisms-in-large-precategories public +open import category-theory.natural-isomorphisms-functors-categories public +open import category-theory.natural-isomorphisms-functors-large-precategories public +open import category-theory.natural-isomorphisms-functors-precategories public +open import category-theory.natural-isomorphisms-maps-categories public +open import category-theory.natural-isomorphisms-maps-precategories public +open import category-theory.natural-numbers-object-precategories public +open import category-theory.natural-transformations-functors-categories public +open import category-theory.natural-transformations-functors-from-small-to-large-categories public +open import category-theory.natural-transformations-functors-from-small-to-large-precategories public +open import category-theory.natural-transformations-functors-large-categories public +open import category-theory.natural-transformations-functors-large-precategories public +open import category-theory.natural-transformations-functors-precategories public +open import category-theory.natural-transformations-maps-categories public +open import category-theory.natural-transformations-maps-from-small-to-large-precategories public +open import category-theory.natural-transformations-maps-precategories public +open import category-theory.nonunital-precategories public +open import category-theory.one-object-precategories public +open import category-theory.opposite-categories public +open import category-theory.opposite-large-precategories public +open import category-theory.opposite-precategories public +open import category-theory.opposite-preunivalent-categories public +open import category-theory.opposite-strongly-preunivalent-categories public +open import category-theory.pointed-endofunctors-categories public +open import category-theory.pointed-endofunctors-precategories public +open import category-theory.precategories public +open import category-theory.precategory-of-elements-of-a-presheaf public +open import category-theory.precategory-of-functors public +open import category-theory.precategory-of-functors-from-small-to-large-precategories public +open import category-theory.precategory-of-maps-from-small-to-large-precategories public +open import category-theory.precategory-of-maps-precategories public +open import category-theory.pregroupoids public +open import category-theory.presheaf-categories public +open import category-theory.preunivalent-categories public +open import category-theory.products-in-precategories public +open import category-theory.products-of-precategories public +open import category-theory.pseudomonic-functors-precategories public +open import category-theory.pullbacks-in-precategories public +open import category-theory.replete-subprecategories public +open import category-theory.representable-functors-categories public +open import category-theory.representable-functors-large-precategories public +open import category-theory.representable-functors-precategories public +open import category-theory.representing-arrow-category public +open import category-theory.restrictions-functors-cores-precategories public +open import category-theory.right-extensions-precategories public +open import category-theory.right-kan-extensions-precategories public +open import category-theory.rigid-objects-categories public +open import category-theory.rigid-objects-precategories public +open import category-theory.set-magmoids public +open import category-theory.sieves-in-categories public +open import category-theory.simplex-category public +open import category-theory.slice-precategories public +open import category-theory.split-essentially-surjective-functors-precategories public +open import category-theory.strict-categories public +open import category-theory.strongly-preunivalent-categories public +open import category-theory.structure-equivalences-set-magmoids public +open import category-theory.subcategories public +open import category-theory.subprecategories public +open import category-theory.subterminal-precategories public +open import category-theory.terminal-category public +open import category-theory.terminal-objects-precategories public +open import category-theory.wide-subcategories public +open import category-theory.wide-subprecategories public +open import category-theory.yoneda-lemma-categories public +open import category-theory.yoneda-lemma-precategories public ``` diff --git a/src/category-theory/adjunctions-large-categories.lagda.md b/src/category-theory/adjunctions-large-categories.lagda.md index 68df714e49..a8adbd3bcd 100644 --- a/src/category-theory/adjunctions-large-categories.lagda.md +++ b/src/category-theory/adjunctions-large-categories.lagda.md @@ -1,25 +1,20 @@ # Adjunctions between large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.adjunctions-large-categories - (funext : function-extensionality) - where +module category-theory.adjunctions-large-categories where ```
Imports ```agda -open import category-theory.adjunctions-large-precategories funext -open import category-theory.functors-large-categories funext -open import category-theory.large-categories funext -open import category-theory.natural-transformations-functors-large-categories funext - -open import foundation.commuting-squares-of-maps funext -open import foundation.equivalences funext -open import foundation.identity-types funext +open import category-theory.adjunctions-large-precategories +open import category-theory.functors-large-categories +open import category-theory.large-categories +open import category-theory.natural-transformations-functors-large-categories + +open import foundation.commuting-squares-of-maps +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/adjunctions-large-precategories.lagda.md b/src/category-theory/adjunctions-large-precategories.lagda.md index 56d22070c7..ac473c743e 100644 --- a/src/category-theory/adjunctions-large-precategories.lagda.md +++ b/src/category-theory/adjunctions-large-precategories.lagda.md @@ -1,25 +1,20 @@ # Adjunctions between large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.adjunctions-large-precategories - (funext : function-extensionality) - where +module category-theory.adjunctions-large-precategories where ```
Imports ```agda -open import category-theory.functors-large-precategories funext -open import category-theory.large-precategories funext -open import category-theory.natural-transformations-functors-large-precategories funext +open import category-theory.functors-large-precategories +open import category-theory.large-precategories +open import category-theory.natural-transformations-functors-large-precategories open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.commuting-squares-of-maps +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/anafunctors-categories.lagda.md b/src/category-theory/anafunctors-categories.lagda.md index eb7973d591..447086f3eb 100644 --- a/src/category-theory/anafunctors-categories.lagda.md +++ b/src/category-theory/anafunctors-categories.lagda.md @@ -1,23 +1,18 @@ # Anafunctors between categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.anafunctors-categories - (funext : function-extensionality) - where +module category-theory.anafunctors-categories where ```
Imports ```agda -open import category-theory.anafunctors-precategories funext -open import category-theory.categories funext -open import category-theory.functors-categories funext +open import category-theory.anafunctors-precategories +open import category-theory.categories +open import category-theory.functors-categories open import foundation.dependent-pair-types -open import foundation.propositional-truncations funext +open import foundation.propositional-truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/anafunctors-precategories.lagda.md b/src/category-theory/anafunctors-precategories.lagda.md index 5854692528..105714a8a5 100644 --- a/src/category-theory/anafunctors-precategories.lagda.md +++ b/src/category-theory/anafunctors-precategories.lagda.md @@ -1,26 +1,21 @@ # Anafunctors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.anafunctors-precategories - (funext : function-extensionality) - where +module category-theory.anafunctors-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels ``` diff --git a/src/category-theory/augmented-simplex-category.lagda.md b/src/category-theory/augmented-simplex-category.lagda.md index 696f77dfa2..9c59e0e7b2 100644 --- a/src/category-theory/augmented-simplex-category.lagda.md +++ b/src/category-theory/augmented-simplex-category.lagda.md @@ -1,30 +1,25 @@ # The augmented simplex category ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.augmented-simplex-category - (funext : function-extensionality) - where +module category-theory.augmented-simplex-category where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.precategories funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.precategories -open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.inequality-standard-finite-types open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets funext +open import order-theory.order-preserving-maps-posets ```
diff --git a/src/category-theory/categories.lagda.md b/src/category-theory/categories.lagda.md index a2bf9538d5..42f12c7076 100644 --- a/src/category-theory/categories.lagda.md +++ b/src/category-theory/categories.lagda.md @@ -1,35 +1,30 @@ # Categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.categories - (funext : function-extensionality) - where +module category-theory.categories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.nonunital-precategories funext -open import category-theory.precategories funext -open import category-theory.preunivalent-categories funext -open import category-theory.strongly-preunivalent-categories funext - -open import foundation.1-types funext -open import foundation.cartesian-product-types funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.isomorphisms-in-precategories +open import category-theory.nonunital-precategories +open import category-theory.precategories +open import category-theory.preunivalent-categories +open import category-theory.strongly-preunivalent-categories + +open import foundation.1-types +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.surjective-maps funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.surjective-maps open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md b/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md index 179923ac1c..a79a1fe316 100644 --- a/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/category-of-functors-from-small-to-large-categories.lagda.md @@ -1,32 +1,27 @@ # The category of functors and natural transformations from small to large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.category-of-functors-from-small-to-large-categories - (funext : function-extensionality) - where +module category-theory.category-of-functors-from-small-to-large-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.category-of-functors funext -open import category-theory.functors-from-small-to-large-categories funext -open import category-theory.functors-from-small-to-large-precategories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.natural-isomorphisms-functors-categories funext -open import category-theory.natural-isomorphisms-functors-precategories funext -open import category-theory.precategories funext -open import category-theory.precategory-of-functors-from-small-to-large-precategories funext - -open import foundation.equivalences funext -open import foundation.identity-types funext +open import category-theory.categories +open import category-theory.category-of-functors +open import category-theory.functors-from-small-to-large-categories +open import category-theory.functors-from-small-to-large-precategories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.natural-isomorphisms-functors-categories +open import category-theory.natural-isomorphisms-functors-precategories +open import category-theory.precategories +open import category-theory.precategory-of-functors-from-small-to-large-precategories + +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-functors.lagda.md b/src/category-theory/category-of-functors.lagda.md index fdcd59fb84..c2486d1ff0 100644 --- a/src/category-theory/category-of-functors.lagda.md +++ b/src/category-theory/category-of-functors.lagda.md @@ -1,30 +1,25 @@ # The category of functors and natural transformations between two categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.category-of-functors - (funext : function-extensionality) - where +module category-theory.category-of-functors where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.category-of-maps-categories funext -open import category-theory.functors-categories funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.natural-isomorphisms-functors-categories funext -open import category-theory.natural-isomorphisms-functors-precategories funext -open import category-theory.precategories funext -open import category-theory.precategory-of-functors funext +open import category-theory.categories +open import category-theory.category-of-maps-categories +open import category-theory.functors-categories +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-categories +open import category-theory.natural-isomorphisms-functors-categories +open import category-theory.natural-isomorphisms-functors-precategories +open import category-theory.precategories +open import category-theory.precategory-of-functors open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-maps-categories.lagda.md b/src/category-theory/category-of-maps-categories.lagda.md index ba64359ccb..1226b6f854 100644 --- a/src/category-theory/category-of-maps-categories.lagda.md +++ b/src/category-theory/category-of-maps-categories.lagda.md @@ -1,39 +1,34 @@ # The category of maps and natural transformations between two categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.category-of-maps-categories - (funext : function-extensionality) - where +module category-theory.category-of-maps-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.commuting-squares-of-morphisms-in-precategories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.maps-categories funext -open import category-theory.maps-precategories funext -open import category-theory.natural-isomorphisms-maps-categories funext -open import category-theory.natural-isomorphisms-maps-precategories funext -open import category-theory.natural-transformations-maps-precategories funext -open import category-theory.precategories funext -open import category-theory.precategory-of-maps-precategories funext +open import category-theory.categories +open import category-theory.commuting-squares-of-morphisms-in-precategories +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.maps-categories +open import category-theory.maps-precategories +open import category-theory.natural-isomorphisms-maps-categories +open import category-theory.natural-isomorphisms-maps-precategories +open import category-theory.natural-transformations-maps-precategories +open import category-theory.precategories +open import category-theory.precategory-of-maps-precategories open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext -open import foundation.univalence funext +open import foundation.type-theoretic-principle-of-choice +open import foundation.univalence open import foundation.universe-levels ``` diff --git a/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md b/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md index c05df315a2..bf67d50b0e 100644 --- a/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md +++ b/src/category-theory/category-of-maps-from-small-to-large-categories.lagda.md @@ -1,32 +1,27 @@ # The category of maps and natural transformations from small to large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.category-of-maps-from-small-to-large-categories - (funext : function-extensionality) - where +module category-theory.category-of-maps-from-small-to-large-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.category-of-maps-categories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.maps-from-small-to-large-categories funext -open import category-theory.maps-from-small-to-large-precategories funext -open import category-theory.natural-isomorphisms-maps-categories funext -open import category-theory.natural-isomorphisms-maps-precategories funext -open import category-theory.precategories funext -open import category-theory.precategory-of-maps-from-small-to-large-precategories funext - -open import foundation.equivalences funext -open import foundation.identity-types funext +open import category-theory.categories +open import category-theory.category-of-maps-categories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.maps-from-small-to-large-categories +open import category-theory.maps-from-small-to-large-precategories +open import category-theory.natural-isomorphisms-maps-categories +open import category-theory.natural-isomorphisms-maps-precategories +open import category-theory.precategories +open import category-theory.precategory-of-maps-from-small-to-large-precategories + +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md b/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md index e5b09d42d1..3e6f636e0b 100644 --- a/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md +++ b/src/category-theory/commuting-squares-of-morphisms-in-large-precategories.lagda.md @@ -1,20 +1,15 @@ # Commuting squares of morphisms in large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.commuting-squares-of-morphisms-in-large-precategories - (funext : function-extensionality) - where +module category-theory.commuting-squares-of-morphisms-in-large-precategories where ```
Imports ```agda -open import category-theory.large-precategories funext +open import category-theory.large-precategories -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md b/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md index 2e66fd64eb..9fce14c311 100644 --- a/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md +++ b/src/category-theory/commuting-squares-of-morphisms-in-precategories.lagda.md @@ -1,19 +1,14 @@ # Commuting squares of morphisms in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.commuting-squares-of-morphisms-in-precategories - (funext : function-extensionality) - where +module category-theory.commuting-squares-of-morphisms-in-precategories where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-set-magmoids funext -open import category-theory.precategories funext +open import category-theory.commuting-squares-of-morphisms-in-set-magmoids +open import category-theory.precategories open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md b/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md index 99bd887dfd..9bcce6ed57 100644 --- a/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md +++ b/src/category-theory/commuting-squares-of-morphisms-in-set-magmoids.lagda.md @@ -1,20 +1,15 @@ # Commuting squares of morphisms in set-magmoids ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.commuting-squares-of-morphisms-in-set-magmoids - (funext : function-extensionality) - where +module category-theory.commuting-squares-of-morphisms-in-set-magmoids where ```
Imports ```agda -open import category-theory.set-magmoids funext +open import category-theory.set-magmoids -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md b/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md index a765cfded2..7ba7f47e35 100644 --- a/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md +++ b/src/category-theory/commuting-triangles-of-morphisms-in-precategories.lagda.md @@ -1,21 +1,16 @@ # Commuting triangles of morphisms in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.commuting-triangles-of-morphisms-in-precategories - (funext : function-extensionality) - where +module category-theory.commuting-triangles-of-morphisms-in-precategories where ```
Imports ```agda -open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids funext -open import category-theory.precategories funext +open import category-theory.commuting-triangles-of-morphisms-in-set-magmoids +open import category-theory.precategories -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md b/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md index 68fef1e45c..3e43a6c09f 100644 --- a/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md +++ b/src/category-theory/commuting-triangles-of-morphisms-in-set-magmoids.lagda.md @@ -1,20 +1,15 @@ # Commuting triangles of morphisms in set-magmoids ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.commuting-triangles-of-morphisms-in-set-magmoids - (funext : function-extensionality) - where +module category-theory.commuting-triangles-of-morphisms-in-set-magmoids where ```
Imports ```agda -open import category-theory.set-magmoids funext +open import category-theory.set-magmoids -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/complete-precategories.lagda.md b/src/category-theory/complete-precategories.lagda.md index b54d1c7eaf..aed7151ba7 100644 --- a/src/category-theory/complete-precategories.lagda.md +++ b/src/category-theory/complete-precategories.lagda.md @@ -1,22 +1,17 @@ # Complete precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.complete-precategories - (funext : function-extensionality) - where +module category-theory.complete-precategories where ```
Imports ```agda -open import category-theory.cones-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.limits-precategories funext -open import category-theory.precategories funext -open import category-theory.terminal-objects-precategories funext +open import category-theory.cones-precategories +open import category-theory.functors-precategories +open import category-theory.limits-precategories +open import category-theory.precategories +open import category-theory.terminal-objects-precategories open import foundation.universe-levels ``` diff --git a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md index 87c06e6b9b..49fbe79018 100644 --- a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md +++ b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md @@ -1,27 +1,21 @@ # Composition operations on binary families of sets ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.composition-operations-on-binary-families-of-sets - (funext : function-extensionality) - where +module category-theory.composition-operations-on-binary-families-of-sets where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/cones-precategories.lagda.md b/src/category-theory/cones-precategories.lagda.md index d011e081f3..12df81dc10 100644 --- a/src/category-theory/cones-precategories.lagda.md +++ b/src/category-theory/cones-precategories.lagda.md @@ -1,51 +1,45 @@ # Cones in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.cones-precategories - (funext : function-extensionality) - where +module category-theory.cones-precategories where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories funext -open import category-theory.commuting-triangles-of-morphisms-in-precategories funext -open import category-theory.constant-functors funext -open import category-theory.functors-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext -open import category-theory.precategory-of-functors funext -open import category-theory.right-extensions-precategories funext -open import category-theory.terminal-category funext +open import category-theory.commuting-squares-of-morphisms-in-precategories +open import category-theory.commuting-triangles-of-morphisms-in-precategories +open import category-theory.constant-functors +open import category-theory.functors-precategories +open import category-theory.maps-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories +open import category-theory.precategory-of-functors +open import category-theory.right-extensions-precategories +open import category-theory.terminal-category open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.dependent-identifications funext +open import foundation.contractible-types +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.multivariable-homotopies funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.multivariable-homotopies +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.sets open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/conservative-functors-precategories.lagda.md b/src/category-theory/conservative-functors-precategories.lagda.md index 394a60d3f4..e3b24903e9 100644 --- a/src/category-theory/conservative-functors-precategories.lagda.md +++ b/src/category-theory/conservative-functors-precategories.lagda.md @@ -1,24 +1,19 @@ # Conservative functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.conservative-functors-precategories - (funext : function-extensionality) - where +module category-theory.conservative-functors-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext +open import foundation.iterated-dependent-product-types +open import foundation.propositions open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/constant-functors.lagda.md b/src/category-theory/constant-functors.lagda.md index 18678afffa..a07c37b14b 100644 --- a/src/category-theory/constant-functors.lagda.md +++ b/src/category-theory/constant-functors.lagda.md @@ -1,33 +1,28 @@ # Constant functors ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.constant-functors - (funext : function-extensionality) - where +module category-theory.constant-functors where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-categories funext -open import category-theory.functors-large-categories funext -open import category-theory.functors-large-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext -open import category-theory.precategory-of-functors funext +open import category-theory.categories +open import category-theory.functors-categories +open import category-theory.functors-large-categories +open import category-theory.functors-large-precategories +open import category-theory.functors-precategories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories +open import category-theory.precategory-of-functors open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/copresheaf-categories.lagda.md b/src/category-theory/copresheaf-categories.lagda.md index d19c4d335e..71e72eff00 100644 --- a/src/category-theory/copresheaf-categories.lagda.md +++ b/src/category-theory/copresheaf-categories.lagda.md @@ -1,46 +1,41 @@ # Copresheaf categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.copresheaf-categories - (funext : function-extensionality) - where +module category-theory.copresheaf-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.category-of-functors-from-small-to-large-categories funext -open import category-theory.constant-functors funext -open import category-theory.functors-from-small-to-large-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.initial-objects-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext -open import category-theory.precategory-of-functors-from-small-to-large-precategories funext -open import category-theory.terminal-objects-precategories funext - -open import foundation.category-of-sets funext -open import foundation.commuting-squares-of-maps funext +open import category-theory.categories +open import category-theory.category-of-functors-from-small-to-large-categories +open import category-theory.constant-functors +open import category-theory.functors-from-small-to-large-precategories +open import category-theory.functors-precategories +open import category-theory.initial-objects-precategories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.natural-transformations-functors-from-small-to-large-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories +open import category-theory.precategory-of-functors-from-small-to-large-precategories +open import category-theory.terminal-objects-precategories + +open import foundation.category-of-sets +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.empty-types funext +open import foundation.empty-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/coproducts-in-precategories.lagda.md b/src/category-theory/coproducts-in-precategories.lagda.md index 618ec80bb4..89a697bd01 100644 --- a/src/category-theory/coproducts-in-precategories.lagda.md +++ b/src/category-theory/coproducts-in-precategories.lagda.md @@ -1,28 +1,23 @@ # Coproducts in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.coproducts-in-precategories - (funext : function-extensionality) - where +module category-theory.coproducts-in-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions open import foundation.telescopes -open import foundation.uniqueness-quantification funext +open import foundation.uniqueness-quantification open import foundation.universe-levels ``` diff --git a/src/category-theory/cores-categories.lagda.md b/src/category-theory/cores-categories.lagda.md index 0736e55876..d8577944ab 100644 --- a/src/category-theory/cores-categories.lagda.md +++ b/src/category-theory/cores-categories.lagda.md @@ -1,28 +1,23 @@ # Cores of categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.cores-categories - (funext : function-extensionality) - where +module category-theory.cores-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.cores-precategories funext -open import category-theory.groupoids funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.precategories funext -open import category-theory.pregroupoids funext -open import category-theory.subcategories funext -open import category-theory.wide-subcategories funext +open import category-theory.categories +open import category-theory.cores-precategories +open import category-theory.groupoids +open import category-theory.isomorphisms-in-categories +open import category-theory.precategories +open import category-theory.pregroupoids +open import category-theory.subcategories +open import category-theory.wide-subcategories open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels ``` diff --git a/src/category-theory/cores-precategories.lagda.md b/src/category-theory/cores-precategories.lagda.md index 5d2bb04329..210c08f99c 100644 --- a/src/category-theory/cores-precategories.lagda.md +++ b/src/category-theory/cores-precategories.lagda.md @@ -1,33 +1,28 @@ # Cores of precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.cores-precategories - (funext : function-extensionality) - where +module category-theory.cores-precategories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext -open import category-theory.pregroupoids funext -open import category-theory.replete-subprecategories funext -open import category-theory.subprecategories funext -open import category-theory.wide-subprecategories funext - -open import foundation.contractible-types funext +open import category-theory.categories +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories +open import category-theory.pregroupoids +open import category-theory.replete-subprecategories +open import category-theory.subprecategories +open import category-theory.wide-subprecategories + +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/coslice-precategories.lagda.md b/src/category-theory/coslice-precategories.lagda.md index d782a63d8b..b47a0de89f 100644 --- a/src/category-theory/coslice-precategories.lagda.md +++ b/src/category-theory/coslice-precategories.lagda.md @@ -1,21 +1,16 @@ # Coslice precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.coslice-precategories - (funext : function-extensionality) - where +module category-theory.coslice-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.opposite-precategories funext -open import category-theory.precategories funext -open import category-theory.slice-precategories funext +open import category-theory.functors-precategories +open import category-theory.opposite-precategories +open import category-theory.precategories +open import category-theory.slice-precategories open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md index 1b9dc2998c..cd698e7403 100644 --- a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md +++ b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md @@ -1,33 +1,28 @@ # Dependent composition operations over precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.dependent-composition-operations-over-precategories - (funext : function-extensionality) - where +module category-theory.dependent-composition-operations-over-precategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.nonunital-precategories funext -open import category-theory.precategories funext -open import category-theory.set-magmoids funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.nonunital-precategories +open import category-theory.precategories +open import category-theory.set-magmoids -open import foundation.cartesian-product-types funext -open import foundation.dependent-identifications funext +open import foundation.cartesian-product-types +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-categories.lagda.md b/src/category-theory/dependent-products-of-categories.lagda.md index 337fd902f2..64742bf6c0 100644 --- a/src/category-theory/dependent-products-of-categories.lagda.md +++ b/src/category-theory/dependent-products-of-categories.lagda.md @@ -1,32 +1,26 @@ # Dependent products of categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.dependent-products-of-categories - (funext : function-extensionality) - where +module category-theory.dependent-products-of-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.dependent-products-of-precategories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.dependent-products-of-precategories +open import category-theory.isomorphisms-in-categories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-large-categories.lagda.md b/src/category-theory/dependent-products-of-large-categories.lagda.md index b2c8aaa9e4..d674d884ab 100644 --- a/src/category-theory/dependent-products-of-large-categories.lagda.md +++ b/src/category-theory/dependent-products-of-large-categories.lagda.md @@ -1,29 +1,23 @@ # Dependent products of large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.dependent-products-of-large-categories - (funext : function-extensionality) - where +module category-theory.dependent-products-of-large-categories where ```
Imports ```agda -open import category-theory.dependent-products-of-large-precategories funext -open import category-theory.isomorphisms-in-large-categories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext - -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-dependent-function-types funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import category-theory.dependent-products-of-large-precategories +open import category-theory.isomorphisms-in-large-categories +open import category-theory.large-categories +open import category-theory.large-precategories + +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.functoriality-dependent-function-types +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-large-precategories.lagda.md b/src/category-theory/dependent-products-of-large-precategories.lagda.md index 4b9c0f9a9c..4eacbea052 100644 --- a/src/category-theory/dependent-products-of-large-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-large-precategories.lagda.md @@ -1,30 +1,25 @@ # Dependent products of large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.dependent-products-of-large-precategories - (funext : function-extensionality) - where +module category-theory.dependent-products-of-large-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-precategories funext +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/dependent-products-of-precategories.lagda.md b/src/category-theory/dependent-products-of-precategories.lagda.md index bd1380b147..e4f7e693fb 100644 --- a/src/category-theory/dependent-products-of-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-precategories.lagda.md @@ -1,31 +1,26 @@ # Dependent products of precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.dependent-products-of-precategories - (funext : function-extensionality) - where +module category-theory.dependent-products-of-precategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/discrete-categories.lagda.md b/src/category-theory/discrete-categories.lagda.md index 936de3d80c..f4a10cea33 100644 --- a/src/category-theory/discrete-categories.lagda.md +++ b/src/category-theory/discrete-categories.lagda.md @@ -1,23 +1,18 @@ # Discrete categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.discrete-categories - (funext : function-extensionality) - where +module category-theory.discrete-categories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/displayed-precategories.lagda.md b/src/category-theory/displayed-precategories.lagda.md index ac5e3a734c..959ce0871a 100644 --- a/src/category-theory/displayed-precategories.lagda.md +++ b/src/category-theory/displayed-precategories.lagda.md @@ -1,36 +1,31 @@ # Displayed precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.displayed-precategories - (funext : function-extensionality) - where +module category-theory.displayed-precategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.dependent-composition-operations-over-precategories funext -open import category-theory.nonunital-precategories funext -open import category-theory.precategories funext -open import category-theory.set-magmoids funext - -open import foundation.cartesian-product-types funext -open import foundation.dependent-identifications funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.dependent-composition-operations-over-precategories +open import category-theory.nonunital-precategories +open import category-theory.precategories +open import category-theory.set-magmoids + +open import foundation.cartesian-product-types +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.equality-dependent-pair-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.subsingleton-induction open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/embedding-maps-precategories.lagda.md b/src/category-theory/embedding-maps-precategories.lagda.md index 604e51de46..469ee2913d 100644 --- a/src/category-theory/embedding-maps-precategories.lagda.md +++ b/src/category-theory/embedding-maps-precategories.lagda.md @@ -1,24 +1,19 @@ # Embedding maps between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.embedding-maps-precategories - (funext : function-extensionality) - where +module category-theory.embedding-maps-precategories where ```
Imports ```agda -open import category-theory.fully-faithful-maps-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext +open import category-theory.fully-faithful-maps-precategories +open import category-theory.maps-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/embeddings-precategories.lagda.md b/src/category-theory/embeddings-precategories.lagda.md index fd576ef7f2..39ffe2e71f 100644 --- a/src/category-theory/embeddings-precategories.lagda.md +++ b/src/category-theory/embeddings-precategories.lagda.md @@ -1,24 +1,19 @@ # Embeddings between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.embeddings-precategories - (funext : function-extensionality) - where +module category-theory.embeddings-precategories where ```
Imports ```agda -open import category-theory.embedding-maps-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext +open import category-theory.embedding-maps-precategories +open import category-theory.functors-precategories +open import category-theory.maps-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/endomorphisms-in-categories.lagda.md b/src/category-theory/endomorphisms-in-categories.lagda.md index 2ac8aafdfe..91a32f4441 100644 --- a/src/category-theory/endomorphisms-in-categories.lagda.md +++ b/src/category-theory/endomorphisms-in-categories.lagda.md @@ -1,26 +1,21 @@ # Endomorphisms in categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.endomorphisms-in-categories - (funext : function-extensionality) - where +module category-theory.endomorphisms-in-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.endomorphisms-in-precategories funext +open import category-theory.categories +open import category-theory.endomorphisms-in-precategories -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/category-theory/endomorphisms-in-precategories.lagda.md b/src/category-theory/endomorphisms-in-precategories.lagda.md index 46949de770..75cac02bde 100644 --- a/src/category-theory/endomorphisms-in-precategories.lagda.md +++ b/src/category-theory/endomorphisms-in-precategories.lagda.md @@ -1,26 +1,21 @@ # Endomorphisms in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.endomorphisms-in-precategories - (funext : function-extensionality) - where +module category-theory.endomorphisms-in-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/category-theory/epimorphisms-in-large-precategories.lagda.md b/src/category-theory/epimorphisms-in-large-precategories.lagda.md index d773b7e7af..d03cd93b4a 100644 --- a/src/category-theory/epimorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/epimorphisms-in-large-precategories.lagda.md @@ -1,23 +1,18 @@ # Epimorphism in large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.epimorphisms-in-large-precategories - (funext : function-extensionality) - where +module category-theory.epimorphisms-in-large-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-precategories funext +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-precategories -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/equivalences-of-categories.lagda.md b/src/category-theory/equivalences-of-categories.lagda.md index 52959660f3..3f49dba3f0 100644 --- a/src/category-theory/equivalences-of-categories.lagda.md +++ b/src/category-theory/equivalences-of-categories.lagda.md @@ -1,20 +1,15 @@ # Equivalences between categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.equivalences-of-categories - (funext : function-extensionality) - where +module category-theory.equivalences-of-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.equivalences-of-precategories funext -open import category-theory.functors-categories funext +open import category-theory.categories +open import category-theory.equivalences-of-precategories +open import category-theory.functors-categories open import foundation.universe-levels ``` diff --git a/src/category-theory/equivalences-of-large-precategories.lagda.md b/src/category-theory/equivalences-of-large-precategories.lagda.md index f10b1cd6c6..c6dd8e5fb5 100644 --- a/src/category-theory/equivalences-of-large-precategories.lagda.md +++ b/src/category-theory/equivalences-of-large-precategories.lagda.md @@ -1,20 +1,15 @@ # Equivalences between large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.equivalences-of-large-precategories - (funext : function-extensionality) - where +module category-theory.equivalences-of-large-precategories where ```
Imports ```agda -open import category-theory.functors-large-precategories funext -open import category-theory.large-precategories funext -open import category-theory.natural-isomorphisms-functors-large-precategories funext +open import category-theory.functors-large-precategories +open import category-theory.large-precategories +open import category-theory.natural-isomorphisms-functors-large-precategories open import foundation.universe-levels ``` diff --git a/src/category-theory/equivalences-of-precategories.lagda.md b/src/category-theory/equivalences-of-precategories.lagda.md index e85229fdcd..5478d066df 100644 --- a/src/category-theory/equivalences-of-precategories.lagda.md +++ b/src/category-theory/equivalences-of-precategories.lagda.md @@ -1,22 +1,17 @@ # Equivalences between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.equivalences-of-precategories - (funext : function-extensionality) - where +module category-theory.equivalences-of-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.natural-isomorphisms-functors-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.natural-isomorphisms-functors-precategories +open import category-theory.precategories -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/essential-fibers-of-functors-precategories.lagda.md b/src/category-theory/essential-fibers-of-functors-precategories.lagda.md index 9874faeef6..f0bdaf07fc 100644 --- a/src/category-theory/essential-fibers-of-functors-precategories.lagda.md +++ b/src/category-theory/essential-fibers-of-functors-precategories.lagda.md @@ -1,20 +1,15 @@ # Essential fibers of functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.essential-fibers-of-functors-precategories - (funext : function-extensionality) - where +module category-theory.essential-fibers-of-functors-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/essentially-injective-functors-precategories.lagda.md b/src/category-theory/essentially-injective-functors-precategories.lagda.md index f8610a8048..db632862bb 100644 --- a/src/category-theory/essentially-injective-functors-precategories.lagda.md +++ b/src/category-theory/essentially-injective-functors-precategories.lagda.md @@ -1,20 +1,15 @@ # Essentially injective functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.essentially-injective-functors-precategories - (funext : function-extensionality) - where +module category-theory.essentially-injective-functors-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/essentially-surjective-functors-precategories.lagda.md b/src/category-theory/essentially-surjective-functors-precategories.lagda.md index 8618911aa0..da79c73d46 100644 --- a/src/category-theory/essentially-surjective-functors-precategories.lagda.md +++ b/src/category-theory/essentially-surjective-functors-precategories.lagda.md @@ -1,24 +1,19 @@ # Essentially surjective functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.essentially-surjective-functors-precategories - (funext : function-extensionality) - where +module category-theory.essentially-surjective-functors-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.propositions funext +open import foundation.existential-quantification +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/exponential-objects-precategories.lagda.md b/src/category-theory/exponential-objects-precategories.lagda.md index c921eebd63..e2fad05451 100644 --- a/src/category-theory/exponential-objects-precategories.lagda.md +++ b/src/category-theory/exponential-objects-precategories.lagda.md @@ -1,24 +1,19 @@ # Exponential objects in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.exponential-objects-precategories - (funext : function-extensionality) - where +module category-theory.exponential-objects-precategories where ```
Imports ```agda -open import category-theory.precategories funext -open import category-theory.products-in-precategories funext +open import category-theory.precategories +open import category-theory.products-in-precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.uniqueness-quantification funext +open import foundation.identity-types +open import foundation.uniqueness-quantification open import foundation.universe-levels ``` diff --git a/src/category-theory/extensions-of-functors-precategories.lagda.md b/src/category-theory/extensions-of-functors-precategories.lagda.md index 96951fec22..bf91bbfdb8 100644 --- a/src/category-theory/extensions-of-functors-precategories.lagda.md +++ b/src/category-theory/extensions-of-functors-precategories.lagda.md @@ -1,22 +1,17 @@ # Extensions of functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.extensions-of-functors-precategories - (funext : function-extensionality) - where +module category-theory.extensions-of-functors-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/faithful-functors-precategories.lagda.md b/src/category-theory/faithful-functors-precategories.lagda.md index 7ba9a01752..8c6ea55099 100644 --- a/src/category-theory/faithful-functors-precategories.lagda.md +++ b/src/category-theory/faithful-functors-precategories.lagda.md @@ -1,27 +1,22 @@ # Faithful functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.faithful-functors-precategories - (funext : function-extensionality) - where +module category-theory.faithful-functors-precategories where ```
Imports ```agda -open import category-theory.faithful-maps-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.faithful-maps-precategories +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/faithful-maps-precategories.lagda.md b/src/category-theory/faithful-maps-precategories.lagda.md index ed9eda0477..092f8cb396 100644 --- a/src/category-theory/faithful-maps-precategories.lagda.md +++ b/src/category-theory/faithful-maps-precategories.lagda.md @@ -1,29 +1,24 @@ # Faithful maps between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.faithful-maps-precategories - (funext : function-extensionality) - where +module category-theory.faithful-maps-precategories where ```
Imports ```agda -open import category-theory.maps-precategories funext -open import category-theory.precategories funext +open import category-theory.maps-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.injective-maps funext -open import foundation.iterated-dependent-product-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.injective-maps +open import foundation.iterated-dependent-product-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/full-functors-precategories.lagda.md b/src/category-theory/full-functors-precategories.lagda.md index 38af28bd71..6fcd4a2690 100644 --- a/src/category-theory/full-functors-precategories.lagda.md +++ b/src/category-theory/full-functors-precategories.lagda.md @@ -1,24 +1,19 @@ # Full functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.full-functors-precategories - (funext : function-extensionality) - where +module category-theory.full-functors-precategories where ```
Imports ```agda -open import category-theory.full-maps-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.precategories funext +open import category-theory.full-maps-precategories +open import category-theory.functors-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/full-large-subcategories.lagda.md b/src/category-theory/full-large-subcategories.lagda.md index 829d410f66..4b96c679d6 100644 --- a/src/category-theory/full-large-subcategories.lagda.md +++ b/src/category-theory/full-large-subcategories.lagda.md @@ -1,26 +1,21 @@ # Full large subcategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.full-large-subcategories - (funext : function-extensionality) - where +module category-theory.full-large-subcategories where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.functors-large-categories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext - -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import category-theory.full-large-subprecategories +open import category-theory.functors-large-categories +open import category-theory.large-categories +open import category-theory.large-precategories + +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/full-large-subprecategories.lagda.md b/src/category-theory/full-large-subprecategories.lagda.md index 3b5a435a5f..a3789dd83e 100644 --- a/src/category-theory/full-large-subprecategories.lagda.md +++ b/src/category-theory/full-large-subprecategories.lagda.md @@ -1,31 +1,26 @@ # Full large subprecategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.full-large-subprecategories - (funext : function-extensionality) - where +module category-theory.full-large-subprecategories where ```
Imports ```agda -open import category-theory.functors-large-precategories funext -open import category-theory.isomorphisms-in-large-categories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext +open import category-theory.functors-large-precategories +open import category-theory.isomorphisms-in-large-categories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-categories +open import category-theory.large-precategories -open import foundation.function-types funext +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/full-maps-precategories.lagda.md b/src/category-theory/full-maps-precategories.lagda.md index 8de930dcbe..0e88643319 100644 --- a/src/category-theory/full-maps-precategories.lagda.md +++ b/src/category-theory/full-maps-precategories.lagda.md @@ -1,25 +1,20 @@ # Full maps between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.full-maps-precategories - (funext : function-extensionality) - where +module category-theory.full-maps-precategories where ```
Imports ```agda -open import category-theory.maps-precategories funext -open import category-theory.precategories funext +open import category-theory.maps-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.surjective-maps funext +open import foundation.function-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.surjective-maps open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/full-subcategories.lagda.md b/src/category-theory/full-subcategories.lagda.md index e84e529f1e..a1921d9182 100644 --- a/src/category-theory/full-subcategories.lagda.md +++ b/src/category-theory/full-subcategories.lagda.md @@ -1,33 +1,28 @@ # Full subcategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.full-subcategories - (funext : function-extensionality) - where +module category-theory.full-subcategories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.embeddings-precategories funext -open import category-theory.full-subprecategories funext -open import category-theory.fully-faithful-functors-precategories funext -open import category-theory.functors-categories funext -open import category-theory.maps-categories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.embeddings-precategories +open import category-theory.full-subprecategories +open import category-theory.fully-faithful-functors-precategories +open import category-theory.functors-categories +open import category-theory.maps-categories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/full-subprecategories.lagda.md b/src/category-theory/full-subprecategories.lagda.md index f2e0014c57..7d2faeebad 100644 --- a/src/category-theory/full-subprecategories.lagda.md +++ b/src/category-theory/full-subprecategories.lagda.md @@ -1,38 +1,33 @@ # Full subprecategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.full-subprecategories - (funext : function-extensionality) - where +module category-theory.full-subprecategories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.embeddings-precategories funext -open import category-theory.fully-faithful-functors-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.embeddings-precategories +open import category-theory.fully-faithful-functors-precategories +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.maps-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/fully-faithful-functors-precategories.lagda.md b/src/category-theory/fully-faithful-functors-precategories.lagda.md index 11f167d8bc..a0de4952c0 100644 --- a/src/category-theory/fully-faithful-functors-precategories.lagda.md +++ b/src/category-theory/fully-faithful-functors-precategories.lagda.md @@ -1,37 +1,32 @@ # Fully faithful functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.fully-faithful-functors-precategories - (funext : function-extensionality) - where +module category-theory.fully-faithful-functors-precategories where ```
Imports ```agda -open import category-theory.conservative-functors-precategories funext -open import category-theory.essentially-injective-functors-precategories funext -open import category-theory.faithful-functors-precategories funext -open import category-theory.full-functors-precategories funext -open import category-theory.fully-faithful-maps-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext -open import category-theory.pseudomonic-functors-precategories funext +open import category-theory.conservative-functors-precategories +open import category-theory.essentially-injective-functors-precategories +open import category-theory.faithful-functors-precategories +open import category-theory.full-functors-precategories +open import category-theory.fully-faithful-maps-precategories +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories +open import category-theory.pseudomonic-functors-precategories open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.universe-levels ``` diff --git a/src/category-theory/fully-faithful-maps-precategories.lagda.md b/src/category-theory/fully-faithful-maps-precategories.lagda.md index 92ee592d08..2317e1536a 100644 --- a/src/category-theory/fully-faithful-maps-precategories.lagda.md +++ b/src/category-theory/fully-faithful-maps-precategories.lagda.md @@ -1,28 +1,23 @@ # Fully faithful maps between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.fully-faithful-maps-precategories - (funext : function-extensionality) - where +module category-theory.fully-faithful-maps-precategories where ```
Imports ```agda -open import category-theory.faithful-maps-precategories funext -open import category-theory.full-maps-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext +open import category-theory.faithful-maps-precategories +open import category-theory.full-maps-precategories +open import category-theory.maps-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.surjective-maps funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.surjective-maps open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/function-categories.lagda.md b/src/category-theory/function-categories.lagda.md index 218e640473..2e86a66718 100644 --- a/src/category-theory/function-categories.lagda.md +++ b/src/category-theory/function-categories.lagda.md @@ -1,27 +1,22 @@ # Function categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.function-categories - (funext : function-extensionality) - where +module category-theory.function-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.dependent-products-of-categories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.precategories funext - -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import category-theory.categories +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.dependent-products-of-categories +open import category-theory.isomorphisms-in-categories +open import category-theory.precategories + +open import foundation.equivalences +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/function-precategories.lagda.md b/src/category-theory/function-precategories.lagda.md index 6b641f53b1..64506a827d 100644 --- a/src/category-theory/function-precategories.lagda.md +++ b/src/category-theory/function-precategories.lagda.md @@ -1,26 +1,21 @@ # Function precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.function-precategories - (funext : function-extensionality) - where +module category-theory.function-precategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.dependent-products-of-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext - -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.dependent-products-of-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories + +open import foundation.equivalences +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-categories.lagda.md b/src/category-theory/functors-categories.lagda.md index 2cd5b37963..8b751210a5 100644 --- a/src/category-theory/functors-categories.lagda.md +++ b/src/category-theory/functors-categories.lagda.md @@ -1,27 +1,22 @@ # Functors between categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.functors-categories - (funext : function-extensionality) - where +module category-theory.functors-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.maps-categories funext - -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import category-theory.categories +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-categories +open import category-theory.maps-categories + +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-from-small-to-large-categories.lagda.md b/src/category-theory/functors-from-small-to-large-categories.lagda.md index 78186e0cab..0194f3b8dd 100644 --- a/src/category-theory/functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/functors-from-small-to-large-categories.lagda.md @@ -1,26 +1,21 @@ # Functors from small to large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.functors-from-small-to-large-categories - (funext : function-extensionality) - where +module category-theory.functors-from-small-to-large-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-from-small-to-large-precategories funext -open import category-theory.large-categories funext -open import category-theory.maps-from-small-to-large-categories funext - -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import category-theory.categories +open import category-theory.functors-from-small-to-large-precategories +open import category-theory.large-categories +open import category-theory.maps-from-small-to-large-categories + +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-from-small-to-large-precategories.lagda.md b/src/category-theory/functors-from-small-to-large-precategories.lagda.md index 1b3550e637..0565ce0d40 100644 --- a/src/category-theory/functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/functors-from-small-to-large-precategories.lagda.md @@ -1,28 +1,23 @@ # Functors from small to large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.functors-from-small-to-large-precategories - (funext : function-extensionality) - where +module category-theory.functors-from-small-to-large-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.large-precategories funext -open import category-theory.maps-from-small-to-large-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.large-precategories +open import category-theory.maps-from-small-to-large-precategories +open import category-theory.precategories -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-large-categories.lagda.md b/src/category-theory/functors-large-categories.lagda.md index 913247188b..450779039d 100644 --- a/src/category-theory/functors-large-categories.lagda.md +++ b/src/category-theory/functors-large-categories.lagda.md @@ -1,21 +1,16 @@ # Functors between large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.functors-large-categories - (funext : function-extensionality) - where +module category-theory.functors-large-categories where ```
Imports ```agda -open import category-theory.functors-large-precategories funext -open import category-theory.large-categories funext +open import category-theory.functors-large-precategories +open import category-theory.large-categories -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-large-precategories.lagda.md b/src/category-theory/functors-large-precategories.lagda.md index 0df8ba1c61..0c4d15795a 100644 --- a/src/category-theory/functors-large-precategories.lagda.md +++ b/src/category-theory/functors-large-precategories.lagda.md @@ -1,22 +1,17 @@ # Functors between large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.functors-large-precategories - (funext : function-extensionality) - where +module category-theory.functors-large-precategories where ```
Imports ```agda -open import category-theory.large-precategories funext +open import category-theory.large-precategories open import foundation.action-on-identifications-functions -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-nonunital-precategories.lagda.md b/src/category-theory/functors-nonunital-precategories.lagda.md index d88e97598c..a0a49b2b51 100644 --- a/src/category-theory/functors-nonunital-precategories.lagda.md +++ b/src/category-theory/functors-nonunital-precategories.lagda.md @@ -1,26 +1,21 @@ # Functors between nonunital precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.functors-nonunital-precategories - (funext : function-extensionality) - where +module category-theory.functors-nonunital-precategories where ```
Imports ```agda -open import category-theory.functors-set-magmoids funext -open import category-theory.maps-set-magmoids funext -open import category-theory.nonunital-precategories funext +open import category-theory.functors-set-magmoids +open import category-theory.maps-set-magmoids +open import category-theory.nonunital-precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-precategories.lagda.md b/src/category-theory/functors-precategories.lagda.md index 2b2728683e..0a9c7a225e 100644 --- a/src/category-theory/functors-precategories.lagda.md +++ b/src/category-theory/functors-precategories.lagda.md @@ -1,32 +1,27 @@ # Functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.functors-precategories - (funext : function-extensionality) - where +module category-theory.functors-precategories where ```
Imports ```agda -open import category-theory.functors-set-magmoids funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.opposite-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-set-magmoids +open import category-theory.isomorphisms-in-precategories +open import category-theory.maps-precategories +open import category-theory.opposite-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/functors-set-magmoids.lagda.md b/src/category-theory/functors-set-magmoids.lagda.md index 97029a1f12..340252ac73 100644 --- a/src/category-theory/functors-set-magmoids.lagda.md +++ b/src/category-theory/functors-set-magmoids.lagda.md @@ -1,30 +1,25 @@ # Functors between set-magmoids ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.functors-set-magmoids - (funext : function-extensionality) - where +module category-theory.functors-set-magmoids where ```
Imports ```agda -open import category-theory.maps-set-magmoids funext -open import category-theory.set-magmoids funext +open import category-theory.maps-set-magmoids +open import category-theory.set-magmoids open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.subtypes open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/gaunt-categories.lagda.md b/src/category-theory/gaunt-categories.lagda.md index 6c789ddccc..01853cf160 100644 --- a/src/category-theory/gaunt-categories.lagda.md +++ b/src/category-theory/gaunt-categories.lagda.md @@ -1,35 +1,30 @@ # Gaunt categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.gaunt-categories - (funext : function-extensionality) - where +module category-theory.gaunt-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.isomorphism-induction-categories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.nonunital-precategories funext -open import category-theory.precategories funext -open import category-theory.rigid-objects-categories funext -open import category-theory.strict-categories funext -open import category-theory.strongly-preunivalent-categories funext - -open import foundation.cartesian-product-types funext +open import category-theory.categories +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.isomorphism-induction-categories +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.nonunital-precategories +open import category-theory.precategories +open import category-theory.rigid-objects-categories +open import category-theory.strict-categories +open import category-theory.strongly-preunivalent-categories + +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.surjective-maps funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.surjective-maps open import foundation.universe-levels ``` diff --git a/src/category-theory/groupoids.lagda.md b/src/category-theory/groupoids.lagda.md index 1925e1a593..b137946933 100644 --- a/src/category-theory/groupoids.lagda.md +++ b/src/category-theory/groupoids.lagda.md @@ -1,38 +1,33 @@ # Groupoids ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.groupoids - (funext : function-extensionality) - where +module category-theory.groupoids where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-categories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext -open import category-theory.pregroupoids funext - -open import foundation.1-types funext -open import foundation.contractible-types funext +open import category-theory.categories +open import category-theory.functors-categories +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories +open import category-theory.pregroupoids + +open import foundation.1-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.iterated-dependent-pair-types -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.telescopes -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md b/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md index 960d9ef36d..1359d2abd4 100644 --- a/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md +++ b/src/category-theory/homotopies-natural-transformations-large-precategories.lagda.md @@ -1,23 +1,18 @@ # Homotopies of natural transformations in large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.homotopies-natural-transformations-large-precategories - (funext : function-extensionality) - where +module category-theory.homotopies-natural-transformations-large-precategories where ```
Imports ```agda -open import category-theory.functors-large-precategories funext -open import category-theory.large-precategories funext -open import category-theory.natural-transformations-functors-large-precategories funext +open import category-theory.functors-large-precategories +open import category-theory.large-precategories +open import category-theory.natural-transformations-functors-large-precategories -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/indiscrete-precategories.lagda.md b/src/category-theory/indiscrete-precategories.lagda.md index 7fa6bbe805..7692b84a17 100644 --- a/src/category-theory/indiscrete-precategories.lagda.md +++ b/src/category-theory/indiscrete-precategories.lagda.md @@ -1,33 +1,28 @@ # Indiscrete precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.indiscrete-precategories - (funext : function-extensionality) - where +module category-theory.indiscrete-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext -open import category-theory.pregroupoids funext -open import category-theory.preunivalent-categories funext -open import category-theory.strict-categories funext -open import category-theory.subterminal-precategories funext - -open import foundation.contractible-types funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories +open import category-theory.pregroupoids +open import category-theory.preunivalent-categories +open import category-theory.strict-categories +open import category-theory.subterminal-precategories + +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/initial-category.lagda.md b/src/category-theory/initial-category.lagda.md index 3f22a06c30..c24a71c44d 100644 --- a/src/category-theory/initial-category.lagda.md +++ b/src/category-theory/initial-category.lagda.md @@ -1,30 +1,25 @@ # The initial category ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.initial-category - (funext : function-extensionality) - where +module category-theory.initial-category where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-precategories funext -open import category-theory.gaunt-categories funext -open import category-theory.indiscrete-precategories funext -open import category-theory.precategories funext -open import category-theory.strict-categories funext -open import category-theory.strongly-preunivalent-categories funext - -open import foundation.contractible-types funext +open import category-theory.categories +open import category-theory.functors-precategories +open import category-theory.gaunt-categories +open import category-theory.indiscrete-precategories +open import category-theory.precategories +open import category-theory.strict-categories +open import category-theory.strongly-preunivalent-categories + +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-large-categories.lagda.md b/src/category-theory/initial-objects-large-categories.lagda.md index 83cf196a6b..8dce8c764a 100644 --- a/src/category-theory/initial-objects-large-categories.lagda.md +++ b/src/category-theory/initial-objects-large-categories.lagda.md @@ -1,19 +1,14 @@ # Initial objects of large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.initial-objects-large-categories - (funext : function-extensionality) - where +module category-theory.initial-objects-large-categories where ```
Imports ```agda -open import category-theory.initial-objects-large-precategories funext -open import category-theory.large-categories funext +open import category-theory.initial-objects-large-precategories +open import category-theory.large-categories open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-large-precategories.lagda.md b/src/category-theory/initial-objects-large-precategories.lagda.md index ecdb68c72c..c49900291d 100644 --- a/src/category-theory/initial-objects-large-precategories.lagda.md +++ b/src/category-theory/initial-objects-large-precategories.lagda.md @@ -1,20 +1,15 @@ # Initial objects of large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.initial-objects-large-precategories - (funext : function-extensionality) - where +module category-theory.initial-objects-large-precategories where ```
Imports ```agda -open import category-theory.large-precategories funext +open import category-theory.large-precategories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-precategories.lagda.md b/src/category-theory/initial-objects-precategories.lagda.md index fa087769b5..dac1af8fa9 100644 --- a/src/category-theory/initial-objects-precategories.lagda.md +++ b/src/category-theory/initial-objects-precategories.lagda.md @@ -1,23 +1,18 @@ # Initial objects in a precategory ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.initial-objects-precategories - (funext : function-extensionality) - where +module category-theory.initial-objects-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.propositions open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/category-theory/isomorphism-induction-categories.lagda.md b/src/category-theory/isomorphism-induction-categories.lagda.md index 1544c21f60..a23461c24d 100644 --- a/src/category-theory/isomorphism-induction-categories.lagda.md +++ b/src/category-theory/isomorphism-induction-categories.lagda.md @@ -1,29 +1,24 @@ # Isomorphism induction in categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.isomorphism-induction-categories - (funext : function-extensionality) - where +module category-theory.isomorphism-induction-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphism-induction-precategories funext -open import category-theory.isomorphisms-in-categories funext +open import category-theory.categories +open import category-theory.isomorphism-induction-precategories +open import category-theory.isomorphisms-in-categories -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.sections funext -open import foundation.universal-property-identity-systems funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.sections +open import foundation.universal-property-identity-systems open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphism-induction-precategories.lagda.md b/src/category-theory/isomorphism-induction-precategories.lagda.md index 8271e97e37..60acd05355 100644 --- a/src/category-theory/isomorphism-induction-precategories.lagda.md +++ b/src/category-theory/isomorphism-induction-precategories.lagda.md @@ -1,27 +1,22 @@ # Isomorphism induction in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.isomorphism-induction-precategories - (funext : function-extensionality) - where +module category-theory.isomorphism-induction-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.function-types funext +open import foundation.function-types open import foundation.identity-systems -open import foundation.identity-types funext -open import foundation.sections funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.sections +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-categories.lagda.md b/src/category-theory/isomorphisms-in-categories.lagda.md index c4aa6b8119..a0f12490f9 100644 --- a/src/category-theory/isomorphisms-in-categories.lagda.md +++ b/src/category-theory/isomorphisms-in-categories.lagda.md @@ -1,30 +1,25 @@ # Isomorphisms in categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.isomorphisms-in-categories - (funext : function-extensionality) - where +module category-theory.isomorphisms-in-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-precategories funext +open import category-theory.categories +open import category-theory.isomorphisms-in-precategories open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-large-categories.lagda.md b/src/category-theory/isomorphisms-in-large-categories.lagda.md index 2616747086..e6f13cb68a 100644 --- a/src/category-theory/isomorphisms-in-large-categories.lagda.md +++ b/src/category-theory/isomorphisms-in-large-categories.lagda.md @@ -1,30 +1,25 @@ # Isomorphisms in large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.isomorphisms-in-large-categories - (funext : function-extensionality) - where +module category-theory.isomorphisms-in-large-categories where ```
Imports ```agda -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-categories funext +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-categories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-large-precategories.lagda.md b/src/category-theory/isomorphisms-in-large-precategories.lagda.md index 4a7d4fe8b4..065f4abe1e 100644 --- a/src/category-theory/isomorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/isomorphisms-in-large-precategories.lagda.md @@ -1,33 +1,28 @@ # Isomorphisms in large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.isomorphisms-in-large-precategories - (funext : function-extensionality) - where +module category-theory.isomorphisms-in-large-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.large-precategories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.large-precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-precategories.lagda.md b/src/category-theory/isomorphisms-in-precategories.lagda.md index e689424c05..31a63e5d4f 100644 --- a/src/category-theory/isomorphisms-in-precategories.lagda.md +++ b/src/category-theory/isomorphisms-in-precategories.lagda.md @@ -1,32 +1,27 @@ # Isomorphisms in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.isomorphisms-in-precategories - (funext : function-extensionality) - where +module category-theory.isomorphisms-in-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/isomorphisms-in-subprecategories.lagda.md b/src/category-theory/isomorphisms-in-subprecategories.lagda.md index 65ebc536f6..e0d8560de0 100644 --- a/src/category-theory/isomorphisms-in-subprecategories.lagda.md +++ b/src/category-theory/isomorphisms-in-subprecategories.lagda.md @@ -1,26 +1,21 @@ # Isomorphisms in subprecategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.isomorphisms-in-subprecategories - (funext : function-extensionality) - where +module category-theory.isomorphisms-in-subprecategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext -open import category-theory.subprecategories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories +open import category-theory.subprecategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/large-categories.lagda.md b/src/category-theory/large-categories.lagda.md index 8c97282fc8..b798eee311 100644 --- a/src/category-theory/large-categories.lagda.md +++ b/src/category-theory/large-categories.lagda.md @@ -1,29 +1,24 @@ # Large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.large-categories - (funext : function-extensionality) - where +module category-theory.large-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/large-function-categories.lagda.md b/src/category-theory/large-function-categories.lagda.md index 311b63bd30..dedadafc7f 100644 --- a/src/category-theory/large-function-categories.lagda.md +++ b/src/category-theory/large-function-categories.lagda.md @@ -1,25 +1,20 @@ # Large function categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.large-function-categories - (funext : function-extensionality) - where +module category-theory.large-function-categories where ```
Imports ```agda -open import category-theory.dependent-products-of-large-categories funext -open import category-theory.isomorphisms-in-large-categories funext -open import category-theory.large-categories funext - -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import category-theory.dependent-products-of-large-categories +open import category-theory.isomorphisms-in-large-categories +open import category-theory.large-categories + +open import foundation.equivalences +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/large-function-precategories.lagda.md b/src/category-theory/large-function-precategories.lagda.md index d0abcda17c..e7b592b608 100644 --- a/src/category-theory/large-function-precategories.lagda.md +++ b/src/category-theory/large-function-precategories.lagda.md @@ -1,25 +1,20 @@ # Large function precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.large-function-precategories - (funext : function-extensionality) - where +module category-theory.large-function-precategories where ```
Imports ```agda -open import category-theory.dependent-products-of-large-precategories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-precategories funext - -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import category-theory.dependent-products-of-large-precategories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-precategories + +open import foundation.equivalences +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/large-precategories.lagda.md b/src/category-theory/large-precategories.lagda.md index 2fd1c17181..4220dda23e 100644 --- a/src/category-theory/large-precategories.lagda.md +++ b/src/category-theory/large-precategories.lagda.md @@ -1,26 +1,21 @@ # Large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.large-precategories - (funext : function-extensionality) - where +module category-theory.large-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/large-subcategories.lagda.md b/src/category-theory/large-subcategories.lagda.md index 1ef32e660a..375f57780d 100644 --- a/src/category-theory/large-subcategories.lagda.md +++ b/src/category-theory/large-subcategories.lagda.md @@ -1,19 +1,14 @@ # Large subcategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.large-subcategories - (funext : function-extensionality) - where +module category-theory.large-subcategories where ```
Imports ```agda -open import category-theory.large-categories funext -open import category-theory.large-subprecategories funext +open import category-theory.large-categories +open import category-theory.large-subprecategories open import foundation.universe-levels ``` diff --git a/src/category-theory/large-subprecategories.lagda.md b/src/category-theory/large-subprecategories.lagda.md index 8999179f6b..935a5ad81c 100644 --- a/src/category-theory/large-subprecategories.lagda.md +++ b/src/category-theory/large-subprecategories.lagda.md @@ -1,24 +1,19 @@ # Large subprecategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.large-subprecategories - (funext : function-extensionality) - where +module category-theory.large-subprecategories where ```
Imports ```agda -open import category-theory.large-precategories funext +open import category-theory.large-precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/limits-precategories.lagda.md b/src/category-theory/limits-precategories.lagda.md index 28b6294ba7..60015d9a58 100644 --- a/src/category-theory/limits-precategories.lagda.md +++ b/src/category-theory/limits-precategories.lagda.md @@ -1,36 +1,30 @@ # Limits in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.limits-precategories - (funext : function-extensionality) - where +module category-theory.limits-precategories where ```
Imports ```agda -open import category-theory.cones-precategories funext -open import category-theory.constant-functors funext -open import category-theory.functors-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext -open import category-theory.right-extensions-precategories funext -open import category-theory.right-kan-extensions-precategories funext -open import category-theory.terminal-category funext +open import category-theory.cones-precategories +open import category-theory.constant-functors +open import category-theory.functors-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories +open import category-theory.right-extensions-precategories +open import category-theory.right-kan-extensions-precategories +open import category-theory.terminal-category open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/maps-categories.lagda.md b/src/category-theory/maps-categories.lagda.md index b1aa76cca9..ac264b5160 100644 --- a/src/category-theory/maps-categories.lagda.md +++ b/src/category-theory/maps-categories.lagda.md @@ -1,24 +1,19 @@ # Maps between categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.maps-categories - (funext : function-extensionality) - where +module category-theory.maps-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.maps-precategories funext +open import category-theory.categories +open import category-theory.maps-precategories -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-from-small-to-large-categories.lagda.md b/src/category-theory/maps-from-small-to-large-categories.lagda.md index f3f7d35642..9f96fbd611 100644 --- a/src/category-theory/maps-from-small-to-large-categories.lagda.md +++ b/src/category-theory/maps-from-small-to-large-categories.lagda.md @@ -1,24 +1,19 @@ # Maps from small to large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.maps-from-small-to-large-categories - (funext : function-extensionality) - where +module category-theory.maps-from-small-to-large-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.large-categories funext -open import category-theory.maps-from-small-to-large-precategories funext +open import category-theory.categories +open import category-theory.large-categories +open import category-theory.maps-from-small-to-large-precategories -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-from-small-to-large-precategories.lagda.md b/src/category-theory/maps-from-small-to-large-precategories.lagda.md index a5b9b49af3..e577f98972 100644 --- a/src/category-theory/maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/maps-from-small-to-large-precategories.lagda.md @@ -1,24 +1,19 @@ # Maps from small to large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.maps-from-small-to-large-precategories - (funext : function-extensionality) - where +module category-theory.maps-from-small-to-large-precategories where ```
Imports ```agda -open import category-theory.large-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext +open import category-theory.large-precategories +open import category-theory.maps-precategories +open import category-theory.precategories -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-precategories.lagda.md b/src/category-theory/maps-precategories.lagda.md index 3f3f8945f8..ba08c41d5c 100644 --- a/src/category-theory/maps-precategories.lagda.md +++ b/src/category-theory/maps-precategories.lagda.md @@ -1,34 +1,29 @@ # Maps between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.maps-precategories - (funext : function-extensionality) - where +module category-theory.maps-precategories where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories funext -open import category-theory.maps-set-magmoids funext -open import category-theory.precategories funext +open import category-theory.commuting-squares-of-morphisms-in-precategories +open import category-theory.maps-set-magmoids +open import category-theory.precategories open import foundation.binary-transport -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/category-theory/maps-set-magmoids.lagda.md b/src/category-theory/maps-set-magmoids.lagda.md index 6ac02f5ba3..33d9842d6b 100644 --- a/src/category-theory/maps-set-magmoids.lagda.md +++ b/src/category-theory/maps-set-magmoids.lagda.md @@ -1,24 +1,19 @@ # Maps between set-magmoids ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.maps-set-magmoids - (funext : function-extensionality) - where +module category-theory.maps-set-magmoids where ```
Imports ```agda -open import category-theory.set-magmoids funext +open import category-theory.set-magmoids open import foundation.action-on-identifications-functions open import foundation.commuting-pentagons-of-identifications open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/monads-on-categories.lagda.md b/src/category-theory/monads-on-categories.lagda.md index 36446e0cd1..c09db9468b 100644 --- a/src/category-theory/monads-on-categories.lagda.md +++ b/src/category-theory/monads-on-categories.lagda.md @@ -1,25 +1,20 @@ # Monads on categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.monads-on-categories - (funext : function-extensionality) - where +module category-theory.monads-on-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-categories funext -open import category-theory.monads-on-precategories funext -open import category-theory.natural-transformations-functors-categories funext -open import category-theory.pointed-endofunctors-categories funext +open import category-theory.categories +open import category-theory.functors-categories +open import category-theory.monads-on-precategories +open import category-theory.natural-transformations-functors-categories +open import category-theory.pointed-endofunctors-categories open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/category-theory/monads-on-precategories.lagda.md b/src/category-theory/monads-on-precategories.lagda.md index b573ed161a..63225d5d66 100644 --- a/src/category-theory/monads-on-precategories.lagda.md +++ b/src/category-theory/monads-on-precategories.lagda.md @@ -1,24 +1,19 @@ # Monads on precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.monads-on-precategories - (funext : function-extensionality) - where +module category-theory.monads-on-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.pointed-endofunctors-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.pointed-endofunctors-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/category-theory/monomorphisms-in-large-precategories.lagda.md b/src/category-theory/monomorphisms-in-large-precategories.lagda.md index 1a37bacbeb..73ce9e3886 100644 --- a/src/category-theory/monomorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/monomorphisms-in-large-precategories.lagda.md @@ -1,23 +1,18 @@ # Monomorphisms in large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.monomorphisms-in-large-precategories - (funext : function-extensionality) - where +module category-theory.monomorphisms-in-large-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-precategories funext +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-precategories -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-functors-categories.lagda.md b/src/category-theory/natural-isomorphisms-functors-categories.lagda.md index e6d9ac88b2..f8f8894aea 100644 --- a/src/category-theory/natural-isomorphisms-functors-categories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-categories.lagda.md @@ -1,31 +1,26 @@ # Natural isomorphisms between functors between categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-isomorphisms-functors-categories - (funext : function-extensionality) - where +module category-theory.natural-isomorphisms-functors-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-categories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.natural-isomorphisms-functors-precategories funext -open import category-theory.natural-transformations-functors-categories funext +open import category-theory.categories +open import category-theory.functors-categories +open import category-theory.isomorphisms-in-categories +open import category-theory.natural-isomorphisms-functors-precategories +open import category-theory.natural-transformations-functors-categories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md b/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md index 43804b0b8a..edaf9fc991 100644 --- a/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-large-precategories.lagda.md @@ -1,22 +1,17 @@ # Natural isomorphisms between functors between large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-isomorphisms-functors-large-precategories - (funext : function-extensionality) - where +module category-theory.natural-isomorphisms-functors-large-precategories where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext -open import category-theory.functors-large-precategories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-precategories funext -open import category-theory.natural-transformations-functors-large-precategories funext +open import category-theory.commuting-squares-of-morphisms-in-large-precategories +open import category-theory.functors-large-precategories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-precategories +open import category-theory.natural-transformations-functors-large-precategories open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md b/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md index d592d9efc9..35a1b71552 100644 --- a/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md @@ -1,31 +1,26 @@ # Natural isomorphisms between functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-isomorphisms-functors-precategories - (funext : function-extensionality) - where +module category-theory.natural-isomorphisms-functors-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.natural-isomorphisms-maps-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.natural-isomorphisms-maps-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-maps-categories.lagda.md b/src/category-theory/natural-isomorphisms-maps-categories.lagda.md index 96c80943dc..571c2723dc 100644 --- a/src/category-theory/natural-isomorphisms-maps-categories.lagda.md +++ b/src/category-theory/natural-isomorphisms-maps-categories.lagda.md @@ -1,31 +1,26 @@ # Natural isomorphisms between maps between categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-isomorphisms-maps-categories - (funext : function-extensionality) - where +module category-theory.natural-isomorphisms-maps-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.maps-categories funext -open import category-theory.natural-isomorphisms-maps-precategories funext -open import category-theory.natural-transformations-maps-categories funext +open import category-theory.categories +open import category-theory.isomorphisms-in-categories +open import category-theory.maps-categories +open import category-theory.natural-isomorphisms-maps-precategories +open import category-theory.natural-transformations-maps-categories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md b/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md index 9e37fc5cec..1e2ff1ccc6 100644 --- a/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md @@ -1,32 +1,27 @@ # Natural isomorphisms between maps between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-isomorphisms-maps-precategories - (funext : function-extensionality) - where +module category-theory.natural-isomorphisms-maps-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.natural-transformations-maps-precategories funext -open import category-theory.precategories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.maps-precategories +open import category-theory.natural-transformations-maps-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-numbers-object-precategories.lagda.md b/src/category-theory/natural-numbers-object-precategories.lagda.md index 099b1d7c40..33cad6e351 100644 --- a/src/category-theory/natural-numbers-object-precategories.lagda.md +++ b/src/category-theory/natural-numbers-object-precategories.lagda.md @@ -1,25 +1,20 @@ # Natural numbers object in a precategory ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-numbers-object-precategories - (funext : function-extensionality) - where +module category-theory.natural-numbers-object-precategories where ```
Imports ```agda -open import category-theory.precategories funext -open import category-theory.terminal-objects-precategories funext +open import category-theory.precategories +open import category-theory.terminal-objects-precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.uniqueness-quantification funext +open import foundation.identity-types +open import foundation.uniqueness-quantification open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-categories.lagda.md b/src/category-theory/natural-transformations-functors-categories.lagda.md index dd8224542e..31ddf1de0b 100644 --- a/src/category-theory/natural-transformations-functors-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-categories.lagda.md @@ -1,27 +1,22 @@ # Natural transformations between functors between categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-transformations-functors-categories - (funext : function-extensionality) - where +module category-theory.natural-transformations-functors-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-categories funext -open import category-theory.natural-transformations-functors-precategories funext - -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import category-theory.categories +open import category-theory.functors-categories +open import category-theory.natural-transformations-functors-precategories + +open import foundation.embeddings +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md b/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md index 3803c379d3..229103a8d2 100644 --- a/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md @@ -1,29 +1,24 @@ # Natural transformations between functors from small to large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-transformations-functors-from-small-to-large-categories - (funext : function-extensionality) - where +module category-theory.natural-transformations-functors-from-small-to-large-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-from-small-to-large-categories funext -open import category-theory.large-categories funext -open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext +open import category-theory.categories +open import category-theory.functors-from-small-to-large-categories +open import category-theory.large-categories +open import category-theory.natural-transformations-functors-from-small-to-large-precategories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md b/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md index 3a098e3a76..bde1b382d5 100644 --- a/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md @@ -1,30 +1,25 @@ # Natural transformations between functors from small to large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-transformations-functors-from-small-to-large-precategories - (funext : function-extensionality) - where +module category-theory.natural-transformations-functors-from-small-to-large-precategories where ```
Imports ```agda -open import category-theory.functors-from-small-to-large-precategories funext -open import category-theory.large-precategories funext -open import category-theory.natural-transformations-maps-from-small-to-large-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-from-small-to-large-precategories +open import category-theory.large-precategories +open import category-theory.natural-transformations-maps-from-small-to-large-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-large-categories.lagda.md b/src/category-theory/natural-transformations-functors-large-categories.lagda.md index bef3e409ff..756ae5d8b1 100644 --- a/src/category-theory/natural-transformations-functors-large-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-large-categories.lagda.md @@ -1,20 +1,15 @@ # Natural transformations between functors between large categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-transformations-functors-large-categories - (funext : function-extensionality) - where +module category-theory.natural-transformations-functors-large-categories where ```
Imports ```agda -open import category-theory.functors-large-categories funext -open import category-theory.large-categories funext -open import category-theory.natural-transformations-functors-large-precategories funext +open import category-theory.functors-large-categories +open import category-theory.large-categories +open import category-theory.natural-transformations-functors-large-precategories open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-large-precategories.lagda.md b/src/category-theory/natural-transformations-functors-large-precategories.lagda.md index 7fe4223bf3..40e89cd14c 100644 --- a/src/category-theory/natural-transformations-functors-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-large-precategories.lagda.md @@ -1,23 +1,18 @@ # Natural transformations between functors between large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-transformations-functors-large-precategories - (funext : function-extensionality) - where +module category-theory.natural-transformations-functors-large-precategories where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext -open import category-theory.functors-large-precategories funext -open import category-theory.large-precategories funext +open import category-theory.commuting-squares-of-morphisms-in-large-precategories +open import category-theory.functors-large-precategories +open import category-theory.large-precategories open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-functors-precategories.lagda.md b/src/category-theory/natural-transformations-functors-precategories.lagda.md index ad3c27d02d..7076ad1387 100644 --- a/src/category-theory/natural-transformations-functors-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-precategories.lagda.md @@ -1,31 +1,26 @@ # Natural transformations between functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-transformations-functors-precategories - (funext : function-extensionality) - where +module category-theory.natural-transformations-functors-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.natural-transformations-maps-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.natural-transformations-maps-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-maps-categories.lagda.md b/src/category-theory/natural-transformations-maps-categories.lagda.md index 2555c2a17e..04e78aa05e 100644 --- a/src/category-theory/natural-transformations-maps-categories.lagda.md +++ b/src/category-theory/natural-transformations-maps-categories.lagda.md @@ -1,27 +1,22 @@ # Natural transformations between maps between categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-transformations-maps-categories - (funext : function-extensionality) - where +module category-theory.natural-transformations-maps-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.maps-categories funext -open import category-theory.natural-transformations-maps-precategories funext - -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import category-theory.categories +open import category-theory.maps-categories +open import category-theory.natural-transformations-maps-precategories + +open import foundation.embeddings +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md b/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md index 6414fa06b0..3158288d63 100644 --- a/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md @@ -1,35 +1,29 @@ # Natural transformations between maps from small to large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-transformations-maps-from-small-to-large-precategories - (funext : function-extensionality) - where +module category-theory.natural-transformations-maps-from-small-to-large-precategories where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-large-precategories funext -open import category-theory.large-precategories funext -open import category-theory.maps-from-small-to-large-precategories funext -open import category-theory.precategories funext +open import category-theory.commuting-squares-of-morphisms-in-large-precategories +open import category-theory.large-precategories +open import category-theory.maps-from-small-to-large-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/natural-transformations-maps-precategories.lagda.md b/src/category-theory/natural-transformations-maps-precategories.lagda.md index daa31f9058..57b61936ce 100644 --- a/src/category-theory/natural-transformations-maps-precategories.lagda.md +++ b/src/category-theory/natural-transformations-maps-precategories.lagda.md @@ -1,34 +1,28 @@ # Natural transformations between maps between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.natural-transformations-maps-precategories - (funext : function-extensionality) - where +module category-theory.natural-transformations-maps-precategories where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext +open import category-theory.commuting-squares-of-morphisms-in-precategories +open import category-theory.maps-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/nonunital-precategories.lagda.md b/src/category-theory/nonunital-precategories.lagda.md index 3815b716ee..32f4782eab 100644 --- a/src/category-theory/nonunital-precategories.lagda.md +++ b/src/category-theory/nonunital-precategories.lagda.md @@ -1,27 +1,22 @@ # Nonunital precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.nonunital-precategories - (funext : function-extensionality) - where +module category-theory.nonunital-precategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.set-magmoids funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.set-magmoids -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.truncated-types funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/one-object-precategories.lagda.md b/src/category-theory/one-object-precategories.lagda.md index 0b720fecf7..76dbd98741 100644 --- a/src/category-theory/one-object-precategories.lagda.md +++ b/src/category-theory/one-object-precategories.lagda.md @@ -1,29 +1,24 @@ # One object precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.one-object-precategories - (funext : function-extensionality) - where +module category-theory.one-object-precategories where ```
Imports ```agda -open import category-theory.endomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.endomorphisms-in-precategories +open import category-theory.precategories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import group-theory.monoids funext +open import group-theory.monoids ```
diff --git a/src/category-theory/opposite-categories.lagda.md b/src/category-theory/opposite-categories.lagda.md index 8282520eaf..8eefb6735c 100644 --- a/src/category-theory/opposite-categories.lagda.md +++ b/src/category-theory/opposite-categories.lagda.md @@ -1,29 +1,24 @@ # Opposite categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.opposite-categories - (funext : function-extensionality) - where +module category-theory.opposite-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.opposite-precategories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.opposite-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.involutions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.involutions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-large-precategories.lagda.md b/src/category-theory/opposite-large-precategories.lagda.md index 67a2047114..99647dd2de 100644 --- a/src/category-theory/opposite-large-precategories.lagda.md +++ b/src/category-theory/opposite-large-precategories.lagda.md @@ -1,27 +1,22 @@ # Opposite large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.opposite-large-precategories - (funext : function-extensionality) - where +module category-theory.opposite-large-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-precategories funext +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types open import foundation.large-identity-types -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-precategories.lagda.md b/src/category-theory/opposite-precategories.lagda.md index 287c9cb8ea..d349bfe93e 100644 --- a/src/category-theory/opposite-precategories.lagda.md +++ b/src/category-theory/opposite-precategories.lagda.md @@ -1,27 +1,22 @@ # Opposite precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.opposite-precategories - (funext : function-extensionality) - where +module category-theory.opposite-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.involutions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.involutions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-preunivalent-categories.lagda.md b/src/category-theory/opposite-preunivalent-categories.lagda.md index 834a7bb0ee..4ea17ae265 100644 --- a/src/category-theory/opposite-preunivalent-categories.lagda.md +++ b/src/category-theory/opposite-preunivalent-categories.lagda.md @@ -1,30 +1,25 @@ # Opposite preunivalent categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.opposite-preunivalent-categories - (funext : function-extensionality) - where +module category-theory.opposite-preunivalent-categories where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.opposite-precategories funext -open import category-theory.precategories funext -open import category-theory.preunivalent-categories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.opposite-precategories +open import category-theory.precategories +open import category-theory.preunivalent-categories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.involutions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.identity-types +open import foundation.involutions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md b/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md index 6bd809ff2d..131c39a411 100644 --- a/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md +++ b/src/category-theory/opposite-strongly-preunivalent-categories.lagda.md @@ -1,31 +1,26 @@ # Opposite strongly preunivalent categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.opposite-strongly-preunivalent-categories - (funext : function-extensionality) - where +module category-theory.opposite-strongly-preunivalent-categories where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.opposite-precategories funext -open import category-theory.precategories funext -open import category-theory.strongly-preunivalent-categories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.opposite-precategories +open import category-theory.precategories +open import category-theory.strongly-preunivalent-categories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.involutions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.involutions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/pointed-endofunctors-categories.lagda.md b/src/category-theory/pointed-endofunctors-categories.lagda.md index 53871fb02c..f5d7468bb0 100644 --- a/src/category-theory/pointed-endofunctors-categories.lagda.md +++ b/src/category-theory/pointed-endofunctors-categories.lagda.md @@ -1,24 +1,19 @@ # Pointed endofunctors on categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.pointed-endofunctors-categories - (funext : function-extensionality) - where +module category-theory.pointed-endofunctors-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-categories funext -open import category-theory.natural-transformations-functors-categories funext -open import category-theory.pointed-endofunctors-precategories funext +open import category-theory.categories +open import category-theory.functors-categories +open import category-theory.natural-transformations-functors-categories +open import category-theory.pointed-endofunctors-precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/pointed-endofunctors-precategories.lagda.md b/src/category-theory/pointed-endofunctors-precategories.lagda.md index 142b06c157..2472a4dab6 100644 --- a/src/category-theory/pointed-endofunctors-precategories.lagda.md +++ b/src/category-theory/pointed-endofunctors-precategories.lagda.md @@ -1,23 +1,18 @@ # Pointed endofunctors ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.pointed-endofunctors-precategories - (funext : function-extensionality) - where +module category-theory.pointed-endofunctors-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/precategories.lagda.md b/src/category-theory/precategories.lagda.md index 8e570f19be..1eb71cad75 100644 --- a/src/category-theory/precategories.lagda.md +++ b/src/category-theory/precategories.lagda.md @@ -1,30 +1,25 @@ # Precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.precategories - (funext : function-extensionality) - where +module category-theory.precategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.nonunital-precategories funext -open import category-theory.set-magmoids funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.nonunital-precategories +open import category-theory.set-magmoids open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.truncated-types funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md b/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md index 2bf8efad92..2e36074e3f 100644 --- a/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md +++ b/src/category-theory/precategory-of-elements-of-a-presheaf.lagda.md @@ -1,28 +1,23 @@ # Precategory of elements of a presheaf ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.precategory-of-elements-of-a-presheaf - (funext : function-extensionality) - where +module category-theory.precategory-of-elements-of-a-presheaf where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.opposite-precategories funext -open import category-theory.precategories funext -open import category-theory.presheaf-categories funext +open import category-theory.functors-precategories +open import category-theory.opposite-precategories +open import category-theory.precategories +open import category-theory.presheaf-categories open import foundation.action-on-identifications-functions -open import foundation.category-of-sets funext +open import foundation.category-of-sets open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md b/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md index 5b44085f1c..6494609f6b 100644 --- a/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/precategory-of-functors-from-small-to-large-precategories.lagda.md @@ -1,24 +1,19 @@ # The precategory of functors and natural transformations from small to large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.precategory-of-functors-from-small-to-large-precategories - (funext : function-extensionality) - where +module category-theory.precategory-of-functors-from-small-to-large-precategories where ```
Imports ```agda -open import category-theory.functors-from-small-to-large-precategories funext -open import category-theory.large-precategories funext -open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-from-small-to-large-precategories +open import category-theory.large-precategories +open import category-theory.natural-transformations-functors-from-small-to-large-precategories +open import category-theory.precategories -open import foundation.identity-types funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-functors.lagda.md b/src/category-theory/precategory-of-functors.lagda.md index 6bf104119d..17626c170b 100644 --- a/src/category-theory/precategory-of-functors.lagda.md +++ b/src/category-theory/precategory-of-functors.lagda.md @@ -1,31 +1,27 @@ # The precategory of functors and natural transformations between two precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.precategory-of-functors - (funext : function-extensionality) - where +module category-theory.precategory-of-functors where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.natural-isomorphisms-functors-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.natural-isomorphisms-functors-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md b/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md index 61c129fc2c..7c755df183 100644 --- a/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/precategory-of-maps-from-small-to-large-precategories.lagda.md @@ -1,24 +1,19 @@ # The precategory of maps and natural transformations from a small to a large precategory ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.precategory-of-maps-from-small-to-large-precategories - (funext : function-extensionality) - where +module category-theory.precategory-of-maps-from-small-to-large-precategories where ```
Imports ```agda -open import category-theory.large-precategories funext -open import category-theory.maps-from-small-to-large-precategories funext -open import category-theory.natural-transformations-maps-from-small-to-large-precategories funext -open import category-theory.precategories funext +open import category-theory.large-precategories +open import category-theory.maps-from-small-to-large-precategories +open import category-theory.natural-transformations-maps-from-small-to-large-precategories +open import category-theory.precategories -open import foundation.identity-types funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/precategory-of-maps-precategories.lagda.md b/src/category-theory/precategory-of-maps-precategories.lagda.md index 2205fd36a1..cc303bf840 100644 --- a/src/category-theory/precategory-of-maps-precategories.lagda.md +++ b/src/category-theory/precategory-of-maps-precategories.lagda.md @@ -1,31 +1,27 @@ # The precategory of maps and natural transformations between two precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.precategory-of-maps-precategories - (funext : function-extensionality) - where +module category-theory.precategory-of-maps-precategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.natural-isomorphisms-maps-precategories funext -open import category-theory.natural-transformations-maps-precategories funext -open import category-theory.precategories funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.isomorphisms-in-precategories +open import category-theory.maps-precategories +open import category-theory.natural-isomorphisms-maps-precategories +open import category-theory.natural-transformations-maps-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/pregroupoids.lagda.md b/src/category-theory/pregroupoids.lagda.md index 7c814fc725..6acee12a3c 100644 --- a/src/category-theory/pregroupoids.lagda.md +++ b/src/category-theory/pregroupoids.lagda.md @@ -1,27 +1,22 @@ # Pregroupoids ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.pregroupoids - (funext : function-extensionality) - where +module category-theory.pregroupoids where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/category-theory/presheaf-categories.lagda.md b/src/category-theory/presheaf-categories.lagda.md index c9a5810d45..40467e0a41 100644 --- a/src/category-theory/presheaf-categories.lagda.md +++ b/src/category-theory/presheaf-categories.lagda.md @@ -1,33 +1,29 @@ # Presheaf categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.presheaf-categories - (funext : function-extensionality) - where +module category-theory.presheaf-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.copresheaf-categories funext -open import category-theory.functors-from-small-to-large-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext -open import category-theory.opposite-precategories funext -open import category-theory.precategories funext - -open import foundation.category-of-sets funext -open import foundation.commuting-squares-of-maps funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import category-theory.categories +open import category-theory.copresheaf-categories +open import category-theory.functors-from-small-to-large-precategories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.natural-transformations-functors-from-small-to-large-precategories +open import category-theory.opposite-precategories +open import category-theory.precategories + +open import foundation.category-of-sets +open import foundation.commuting-squares-of-maps +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/preunivalent-categories.lagda.md b/src/category-theory/preunivalent-categories.lagda.md index 898eba8f06..15f683b862 100644 --- a/src/category-theory/preunivalent-categories.lagda.md +++ b/src/category-theory/preunivalent-categories.lagda.md @@ -1,29 +1,24 @@ # Preunivalent categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.preunivalent-categories - (funext : function-extensionality) - where +module category-theory.preunivalent-categories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories -open import foundation.1-types funext -open import foundation.cartesian-product-types funext +open import foundation.1-types +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.embeddings +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/products-in-precategories.lagda.md b/src/category-theory/products-in-precategories.lagda.md index aa4f2d3e53..69fc1f4b93 100644 --- a/src/category-theory/products-in-precategories.lagda.md +++ b/src/category-theory/products-in-precategories.lagda.md @@ -1,28 +1,23 @@ # Products in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.products-in-precategories - (funext : function-extensionality) - where +module category-theory.products-in-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions open import foundation.telescopes -open import foundation.uniqueness-quantification funext +open import foundation.uniqueness-quantification open import foundation.universe-levels ``` diff --git a/src/category-theory/products-of-precategories.lagda.md b/src/category-theory/products-of-precategories.lagda.md index 4e3142f3b7..cb52fdd0e6 100644 --- a/src/category-theory/products-of-precategories.lagda.md +++ b/src/category-theory/products-of-precategories.lagda.md @@ -1,24 +1,19 @@ # Products of precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.products-of-precategories - (funext : function-extensionality) - where +module category-theory.products-of-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/category-theory/pseudomonic-functors-precategories.lagda.md b/src/category-theory/pseudomonic-functors-precategories.lagda.md index 0e5844dfc0..f5127417ad 100644 --- a/src/category-theory/pseudomonic-functors-precategories.lagda.md +++ b/src/category-theory/pseudomonic-functors-precategories.lagda.md @@ -1,32 +1,27 @@ # Pseudomonic functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.pseudomonic-functors-precategories - (funext : function-extensionality) - where +module category-theory.pseudomonic-functors-precategories where ```
Imports ```agda -open import category-theory.conservative-functors-precategories funext -open import category-theory.faithful-functors-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.conservative-functors-precategories +open import category-theory.faithful-functors-precategories +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.surjective-maps funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.iterated-dependent-product-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.surjective-maps open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/pullbacks-in-precategories.lagda.md b/src/category-theory/pullbacks-in-precategories.lagda.md index e76c9ee00e..2ade1aec32 100644 --- a/src/category-theory/pullbacks-in-precategories.lagda.md +++ b/src/category-theory/pullbacks-in-precategories.lagda.md @@ -1,28 +1,23 @@ # Pullbacks in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.pullbacks-in-precategories - (funext : function-extensionality) - where +module category-theory.pullbacks-in-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions open import foundation.telescopes -open import foundation.uniqueness-quantification funext +open import foundation.uniqueness-quantification open import foundation.universe-levels ``` diff --git a/src/category-theory/replete-subprecategories.lagda.md b/src/category-theory/replete-subprecategories.lagda.md index 3aa5392461..4f15777ab4 100644 --- a/src/category-theory/replete-subprecategories.lagda.md +++ b/src/category-theory/replete-subprecategories.lagda.md @@ -1,32 +1,27 @@ # Replete subprecategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.replete-subprecategories - (funext : function-extensionality) - where +module category-theory.replete-subprecategories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphism-induction-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.isomorphisms-in-subprecategories funext -open import category-theory.precategories funext -open import category-theory.subprecategories funext +open import category-theory.categories +open import category-theory.isomorphism-induction-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.isomorphisms-in-subprecategories +open import category-theory.precategories +open import category-theory.subprecategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.iterated-dependent-product-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.subsingleton-induction -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.telescopes open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/category-theory/representable-functors-categories.lagda.md b/src/category-theory/representable-functors-categories.lagda.md index 4ee0500283..22014d5f9d 100644 --- a/src/category-theory/representable-functors-categories.lagda.md +++ b/src/category-theory/representable-functors-categories.lagda.md @@ -1,23 +1,18 @@ # Representable functors between categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.representable-functors-categories - (funext : function-extensionality) - where +module category-theory.representable-functors-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.functors-categories funext -open import category-theory.natural-transformations-functors-categories funext -open import category-theory.representable-functors-precategories funext +open import category-theory.categories +open import category-theory.functors-categories +open import category-theory.natural-transformations-functors-categories +open import category-theory.representable-functors-precategories -open import foundation.category-of-sets funext +open import foundation.category-of-sets open import foundation.universe-levels ``` diff --git a/src/category-theory/representable-functors-large-precategories.lagda.md b/src/category-theory/representable-functors-large-precategories.lagda.md index c97b3fcd49..6a88be63e6 100644 --- a/src/category-theory/representable-functors-large-precategories.lagda.md +++ b/src/category-theory/representable-functors-large-precategories.lagda.md @@ -1,27 +1,21 @@ # Representable functors between large precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.representable-functors-large-precategories - (funext : function-extensionality) - where +module category-theory.representable-functors-large-precategories where ```
Imports ```agda -open import category-theory.functors-large-precategories funext -open import category-theory.large-precategories funext -open import category-theory.natural-transformations-functors-large-precategories funext - -open import foundation.category-of-sets funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.sets funext +open import category-theory.functors-large-precategories +open import category-theory.large-precategories +open import category-theory.natural-transformations-functors-large-precategories + +open import foundation.category-of-sets +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/category-theory/representable-functors-precategories.lagda.md b/src/category-theory/representable-functors-precategories.lagda.md index c3d76c7d8c..64efc53409 100644 --- a/src/category-theory/representable-functors-precategories.lagda.md +++ b/src/category-theory/representable-functors-precategories.lagda.md @@ -1,31 +1,25 @@ # Representable functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.representable-functors-precategories - (funext : function-extensionality) - where +module category-theory.representable-functors-precategories where ```
Imports ```agda -open import category-theory.copresheaf-categories funext -open import category-theory.functors-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.opposite-precategories funext -open import category-theory.precategories funext - -open import foundation.category-of-sets funext +open import category-theory.copresheaf-categories +open import category-theory.functors-precategories +open import category-theory.maps-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.opposite-precategories +open import category-theory.precategories + +open import foundation.category-of-sets open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/category-theory/representing-arrow-category.lagda.md b/src/category-theory/representing-arrow-category.lagda.md index 537b9433a1..a4259a4611 100644 --- a/src/category-theory/representing-arrow-category.lagda.md +++ b/src/category-theory/representing-arrow-category.lagda.md @@ -1,28 +1,23 @@ # The representing arrow category ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.representing-arrow-category - (funext : function-extensionality) - where +module category-theory.representing-arrow-category where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/restrictions-functors-cores-precategories.lagda.md b/src/category-theory/restrictions-functors-cores-precategories.lagda.md index b72a053e50..1463265b07 100644 --- a/src/category-theory/restrictions-functors-cores-precategories.lagda.md +++ b/src/category-theory/restrictions-functors-cores-precategories.lagda.md @@ -1,28 +1,23 @@ # Restrictions of functors to cores of precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.restrictions-functors-cores-precategories - (funext : function-extensionality) - where +module category-theory.restrictions-functors-cores-precategories where ```
Imports ```agda -open import category-theory.cores-precategories funext -open import category-theory.faithful-functors-precategories funext -open import category-theory.fully-faithful-functors-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext -open import category-theory.pseudomonic-functors-precategories funext +open import category-theory.cores-precategories +open import category-theory.faithful-functors-precategories +open import category-theory.fully-faithful-functors-precategories +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.maps-precategories +open import category-theory.precategories +open import category-theory.pseudomonic-functors-precategories open import foundation.dependent-pair-types -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/right-extensions-precategories.lagda.md b/src/category-theory/right-extensions-precategories.lagda.md index 75abfbc96c..4c3828347f 100644 --- a/src/category-theory/right-extensions-precategories.lagda.md +++ b/src/category-theory/right-extensions-precategories.lagda.md @@ -1,48 +1,42 @@ # Right extensions in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.right-extensions-precategories - (funext : function-extensionality) - where +module category-theory.right-extensions-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext +open import category-theory.functors-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories -open import foundation.action-on-equivalences-functions funext +open import foundation.action-on-equivalences-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.dependent-identifications funext +open import foundation.contractible-types +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.multivariable-homotopies funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.multivariable-homotopies +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.sets open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types ```
diff --git a/src/category-theory/right-kan-extensions-precategories.lagda.md b/src/category-theory/right-kan-extensions-precategories.lagda.md index a65d47a0e0..1af7fd92a1 100644 --- a/src/category-theory/right-kan-extensions-precategories.lagda.md +++ b/src/category-theory/right-kan-extensions-precategories.lagda.md @@ -1,25 +1,20 @@ # Right Kan extensions in precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.right-kan-extensions-precategories - (funext : function-extensionality) - where +module category-theory.right-kan-extensions-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext -open import category-theory.right-extensions-precategories funext +open import category-theory.functors-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories +open import category-theory.right-extensions-precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/rigid-objects-categories.lagda.md b/src/category-theory/rigid-objects-categories.lagda.md index 2e46ffd311..ed69843f56 100644 --- a/src/category-theory/rigid-objects-categories.lagda.md +++ b/src/category-theory/rigid-objects-categories.lagda.md @@ -1,21 +1,16 @@ # Rigid objects in a category ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.rigid-objects-categories - (funext : function-extensionality) - where +module category-theory.rigid-objects-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.rigid-objects-precategories funext +open import category-theory.categories +open import category-theory.rigid-objects-precategories -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/rigid-objects-precategories.lagda.md b/src/category-theory/rigid-objects-precategories.lagda.md index ec3f5c6779..356a7f517a 100644 --- a/src/category-theory/rigid-objects-precategories.lagda.md +++ b/src/category-theory/rigid-objects-precategories.lagda.md @@ -1,23 +1,18 @@ # Rigid objects in a precategory ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.rigid-objects-precategories - (funext : function-extensionality) - where +module category-theory.rigid-objects-precategories where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/set-magmoids.lagda.md b/src/category-theory/set-magmoids.lagda.md index 1a02bc7788..ec501dc223 100644 --- a/src/category-theory/set-magmoids.lagda.md +++ b/src/category-theory/set-magmoids.lagda.md @@ -1,24 +1,19 @@ # Set-magmoids ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.set-magmoids - (funext : function-extensionality) - where +module category-theory.set-magmoids where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext +open import category-theory.composition-operations-on-binary-families-of-sets -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.truncated-types funext +open import foundation.propositions +open import foundation.sets +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels ``` diff --git a/src/category-theory/sieves-in-categories.lagda.md b/src/category-theory/sieves-in-categories.lagda.md index 753490b423..1bab198afa 100644 --- a/src/category-theory/sieves-in-categories.lagda.md +++ b/src/category-theory/sieves-in-categories.lagda.md @@ -1,21 +1,16 @@ # Sieves in categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.sieves-in-categories - (funext : function-extensionality) - where +module category-theory.sieves-in-categories where ```
Imports ```agda -open import category-theory.categories funext +open import category-theory.categories -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/simplex-category.lagda.md b/src/category-theory/simplex-category.lagda.md index b6b19eb689..aa311fa6b6 100644 --- a/src/category-theory/simplex-category.lagda.md +++ b/src/category-theory/simplex-category.lagda.md @@ -1,30 +1,25 @@ # The simplex category ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.simplex-category - (funext : function-extensionality) - where +module category-theory.simplex-category where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.precategories funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.precategories -open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.inequality-standard-finite-types open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets funext +open import order-theory.order-preserving-maps-posets ```
diff --git a/src/category-theory/slice-precategories.lagda.md b/src/category-theory/slice-precategories.lagda.md index e5f3489be9..9443a721e1 100644 --- a/src/category-theory/slice-precategories.lagda.md +++ b/src/category-theory/slice-precategories.lagda.md @@ -1,39 +1,34 @@ # Slice precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.slice-precategories - (funext : function-extensionality) - where +module category-theory.slice-precategories where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.precategories funext -open import category-theory.products-in-precategories funext -open import category-theory.pullbacks-in-precategories funext -open import category-theory.terminal-objects-precategories funext +open import category-theory.functors-precategories +open import category-theory.precategories +open import category-theory.products-in-precategories +open import category-theory.pullbacks-in-precategories +open import category-theory.terminal-objects-precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md b/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md index 4d946c0b1c..d62ed8e8fe 100644 --- a/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md +++ b/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md @@ -1,37 +1,32 @@ # Split essentially surjective functors between precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.split-essentially-surjective-functors-precategories - (funext : function-extensionality) - where +module category-theory.split-essentially-surjective-functors-precategories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.cores-precategories funext -open import category-theory.essential-fibers-of-functors-precategories funext -open import category-theory.essentially-surjective-functors-precategories funext -open import category-theory.fully-faithful-functors-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext -open import category-theory.pseudomonic-functors-precategories funext - -open import foundation.contractible-types funext +open import category-theory.categories +open import category-theory.cores-precategories +open import category-theory.essential-fibers-of-functors-precategories +open import category-theory.essentially-surjective-functors-precategories +open import category-theory.fully-faithful-functors-precategories +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories +open import category-theory.pseudomonic-functors-precategories + +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.retracts-of-types funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.retracts-of-types +open import foundation.sections open import foundation.universe-levels ``` diff --git a/src/category-theory/strict-categories.lagda.md b/src/category-theory/strict-categories.lagda.md index 0d6e92e185..549eed68e0 100644 --- a/src/category-theory/strict-categories.lagda.md +++ b/src/category-theory/strict-categories.lagda.md @@ -1,31 +1,26 @@ # Strict categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.strict-categories - (funext : function-extensionality) - where +module category-theory.strict-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.nonunital-precategories funext -open import category-theory.precategories funext -open import category-theory.strongly-preunivalent-categories funext - -open import foundation.cartesian-product-types funext +open import category-theory.categories +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.isomorphisms-in-precategories +open import category-theory.nonunital-precategories +open import category-theory.precategories +open import category-theory.strongly-preunivalent-categories + +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/strongly-preunivalent-categories.lagda.md b/src/category-theory/strongly-preunivalent-categories.lagda.md index 565c7dd197..8ba02ef3ba 100644 --- a/src/category-theory/strongly-preunivalent-categories.lagda.md +++ b/src/category-theory/strongly-preunivalent-categories.lagda.md @@ -1,33 +1,28 @@ # Strongly preunivalent categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.strongly-preunivalent-categories - (funext : function-extensionality) - where +module category-theory.strongly-preunivalent-categories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext -open import category-theory.preunivalent-categories funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories +open import category-theory.preunivalent-categories -open import foundation.1-types funext -open import foundation.cartesian-product-types funext +open import foundation.1-types +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositional-maps funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.structured-equality-duality funext +open import foundation.embeddings +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositional-maps +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.structured-equality-duality open import foundation.universe-levels ``` diff --git a/src/category-theory/structure-equivalences-set-magmoids.lagda.md b/src/category-theory/structure-equivalences-set-magmoids.lagda.md index f95ae67773..38be07d265 100644 --- a/src/category-theory/structure-equivalences-set-magmoids.lagda.md +++ b/src/category-theory/structure-equivalences-set-magmoids.lagda.md @@ -1,31 +1,26 @@ # Structure equivalences between set-magmoids ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.structure-equivalences-set-magmoids - (funext : function-extensionality) - where +module category-theory.structure-equivalences-set-magmoids where ```
Imports ```agda -open import category-theory.functors-set-magmoids funext -open import category-theory.set-magmoids funext +open import category-theory.functors-set-magmoids +open import category-theory.set-magmoids -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions open import foundation.telescopes open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels ``` diff --git a/src/category-theory/subcategories.lagda.md b/src/category-theory/subcategories.lagda.md index 76c0a91b65..cb8cf062cf 100644 --- a/src/category-theory/subcategories.lagda.md +++ b/src/category-theory/subcategories.lagda.md @@ -1,41 +1,36 @@ # Subcategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.subcategories - (funext : function-extensionality) - where +module category-theory.subcategories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.faithful-functors-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.isomorphisms-in-subprecategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext -open import category-theory.replete-subprecategories funext -open import category-theory.subprecategories funext - -open import foundation.contractible-types funext +open import category-theory.categories +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.faithful-functors-precategories +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.isomorphisms-in-subprecategories +open import category-theory.maps-precategories +open import category-theory.precategories +open import category-theory.replete-subprecategories +open import category-theory.subprecategories + +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/category-theory/subprecategories.lagda.md b/src/category-theory/subprecategories.lagda.md index 1950bce6fe..9d2ff28504 100644 --- a/src/category-theory/subprecategories.lagda.md +++ b/src/category-theory/subprecategories.lagda.md @@ -1,31 +1,26 @@ # Subprecategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.subprecategories - (funext : function-extensionality) - where +module category-theory.subprecategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.faithful-functors-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.faithful-functors-precategories +open import category-theory.functors-precategories +open import category-theory.maps-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/category-theory/subterminal-precategories.lagda.md b/src/category-theory/subterminal-precategories.lagda.md index 2f3b16a735..a85c94a746 100644 --- a/src/category-theory/subterminal-precategories.lagda.md +++ b/src/category-theory/subterminal-precategories.lagda.md @@ -1,37 +1,32 @@ # Subterminal precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.subterminal-precategories - (funext : function-extensionality) - where +module category-theory.subterminal-precategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.fully-faithful-functors-precategories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext -open import category-theory.pregroupoids funext -open import category-theory.strict-categories funext -open import category-theory.terminal-category funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.fully-faithful-functors-precategories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories +open import category-theory.pregroupoids +open import category-theory.strict-categories +open import category-theory.terminal-category open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/terminal-category.lagda.md b/src/category-theory/terminal-category.lagda.md index 2991a64e6b..a8a8284077 100644 --- a/src/category-theory/terminal-category.lagda.md +++ b/src/category-theory/terminal-category.lagda.md @@ -1,37 +1,32 @@ # The terminal category ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.terminal-category - (funext : function-extensionality) - where +module category-theory.terminal-category where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.constant-functors funext -open import category-theory.functors-categories funext -open import category-theory.functors-precategories funext -open import category-theory.gaunt-categories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext -open import category-theory.strict-categories funext -open import category-theory.strongly-preunivalent-categories funext +open import category-theory.categories +open import category-theory.constant-functors +open import category-theory.functors-categories +open import category-theory.functors-precategories +open import category-theory.gaunt-categories +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories +open import category-theory.strict-categories +open import category-theory.strongly-preunivalent-categories open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/category-theory/terminal-objects-precategories.lagda.md b/src/category-theory/terminal-objects-precategories.lagda.md index 7e38ccc0e6..5a1fcb7d9c 100644 --- a/src/category-theory/terminal-objects-precategories.lagda.md +++ b/src/category-theory/terminal-objects-precategories.lagda.md @@ -1,23 +1,18 @@ # Terminal objects in a precategory ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.terminal-objects-precategories - (funext : function-extensionality) - where +module category-theory.terminal-objects-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/category-theory/wide-subcategories.lagda.md b/src/category-theory/wide-subcategories.lagda.md index 3da939955a..7c10b8b282 100644 --- a/src/category-theory/wide-subcategories.lagda.md +++ b/src/category-theory/wide-subcategories.lagda.md @@ -1,40 +1,35 @@ # Wide subcategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.wide-subcategories - (funext : function-extensionality) - where +module category-theory.wide-subcategories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.faithful-functors-precategories funext -open import category-theory.functors-categories funext -open import category-theory.isomorphisms-in-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.maps-categories funext -open import category-theory.precategories funext -open import category-theory.subcategories funext -open import category-theory.wide-subprecategories funext - -open import foundation.contractible-types funext +open import category-theory.categories +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.faithful-functors-precategories +open import category-theory.functors-categories +open import category-theory.isomorphisms-in-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.maps-categories +open import category-theory.precategories +open import category-theory.subcategories +open import category-theory.wide-subprecategories + +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/wide-subprecategories.lagda.md b/src/category-theory/wide-subprecategories.lagda.md index 3b207a863e..9c22aab29a 100644 --- a/src/category-theory/wide-subprecategories.lagda.md +++ b/src/category-theory/wide-subprecategories.lagda.md @@ -1,33 +1,28 @@ # Wide subprecategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.wide-subprecategories - (funext : function-extensionality) - where +module category-theory.wide-subprecategories where ```
Imports ```agda -open import category-theory.composition-operations-on-binary-families-of-sets funext -open import category-theory.faithful-functors-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.maps-precategories funext -open import category-theory.precategories funext -open import category-theory.subprecategories funext +open import category-theory.composition-operations-on-binary-families-of-sets +open import category-theory.faithful-functors-precategories +open import category-theory.functors-precategories +open import category-theory.maps-precategories +open import category-theory.precategories +open import category-theory.subprecategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes open import foundation.telescopes open import foundation.unit-type open import foundation.universe-levels diff --git a/src/category-theory/yoneda-lemma-categories.lagda.md b/src/category-theory/yoneda-lemma-categories.lagda.md index 28206236ba..3548e0a58d 100644 --- a/src/category-theory/yoneda-lemma-categories.lagda.md +++ b/src/category-theory/yoneda-lemma-categories.lagda.md @@ -1,25 +1,20 @@ # The Yoneda lemma for categories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.yoneda-lemma-categories - (funext : function-extensionality) - where +module category-theory.yoneda-lemma-categories where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.copresheaf-categories funext -open import category-theory.natural-transformations-functors-from-small-to-large-categories funext -open import category-theory.representable-functors-categories funext -open import category-theory.yoneda-lemma-precategories funext - -open import foundation.category-of-sets funext -open import foundation.equivalences funext +open import category-theory.categories +open import category-theory.copresheaf-categories +open import category-theory.natural-transformations-functors-from-small-to-large-categories +open import category-theory.representable-functors-categories +open import category-theory.yoneda-lemma-precategories + +open import foundation.category-of-sets +open import foundation.equivalences open import foundation.universe-levels ``` diff --git a/src/category-theory/yoneda-lemma-precategories.lagda.md b/src/category-theory/yoneda-lemma-precategories.lagda.md index 0185ca898e..1181e89b5f 100644 --- a/src/category-theory/yoneda-lemma-precategories.lagda.md +++ b/src/category-theory/yoneda-lemma-precategories.lagda.md @@ -1,33 +1,28 @@ # The Yoneda lemma for precategories ```agda -open import foundation.function-extensionality-axiom - -module - category-theory.yoneda-lemma-precategories - (funext : function-extensionality) - where +module category-theory.yoneda-lemma-precategories where ```
Imports ```agda -open import category-theory.copresheaf-categories funext -open import category-theory.functors-from-small-to-large-precategories funext -open import category-theory.natural-transformations-functors-from-small-to-large-precategories funext -open import category-theory.precategories funext -open import category-theory.representable-functors-precategories funext +open import category-theory.copresheaf-categories +open import category-theory.functors-from-small-to-large-precategories +open import category-theory.natural-transformations-functors-from-small-to-large-precategories +open import category-theory.precategories +open import category-theory.representable-functors-precategories open import foundation.action-on-identifications-functions -open import foundation.category-of-sets funext +open import foundation.category-of-sets open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/commutative-algebra.lagda.md b/src/commutative-algebra.lagda.md index 39c7e4aa6d..7719d0d4d2 100644 --- a/src/commutative-algebra.lagda.md +++ b/src/commutative-algebra.lagda.md @@ -3,67 +3,62 @@ ## Modules in the commutative algebra namespace ```agda -open import foundation.function-extensionality-axiom +module commutative-algebra where -module - commutative-algebra - (funext : function-extensionality) - where - -open import commutative-algebra.binomial-theorem-commutative-rings funext public -open import commutative-algebra.binomial-theorem-commutative-semirings funext public -open import commutative-algebra.boolean-rings funext public -open import commutative-algebra.category-of-commutative-rings funext public -open import commutative-algebra.commutative-rings funext public -open import commutative-algebra.commutative-semirings funext public -open import commutative-algebra.dependent-products-commutative-rings funext public -open import commutative-algebra.dependent-products-commutative-semirings funext public -open import commutative-algebra.discrete-fields funext public -open import commutative-algebra.eisenstein-integers funext public -open import commutative-algebra.euclidean-domains funext public -open import commutative-algebra.full-ideals-commutative-rings funext public -open import commutative-algebra.function-commutative-rings funext public -open import commutative-algebra.function-commutative-semirings funext public -open import commutative-algebra.gaussian-integers funext public -open import commutative-algebra.groups-of-units-commutative-rings funext public -open import commutative-algebra.homomorphisms-commutative-rings funext public -open import commutative-algebra.homomorphisms-commutative-semirings funext public -open import commutative-algebra.ideals-commutative-rings funext public -open import commutative-algebra.ideals-commutative-semirings funext public -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext public -open import commutative-algebra.integer-multiples-of-elements-commutative-rings funext public -open import commutative-algebra.integral-domains funext public -open import commutative-algebra.intersections-ideals-commutative-rings funext public -open import commutative-algebra.intersections-radical-ideals-commutative-rings funext public -open import commutative-algebra.invertible-elements-commutative-rings funext public -open import commutative-algebra.isomorphisms-commutative-rings funext public -open import commutative-algebra.joins-ideals-commutative-rings funext public -open import commutative-algebra.joins-radical-ideals-commutative-rings funext public -open import commutative-algebra.local-commutative-rings funext public +open import commutative-algebra.binomial-theorem-commutative-rings public +open import commutative-algebra.binomial-theorem-commutative-semirings public +open import commutative-algebra.boolean-rings public +open import commutative-algebra.category-of-commutative-rings public +open import commutative-algebra.commutative-rings public +open import commutative-algebra.commutative-semirings public +open import commutative-algebra.dependent-products-commutative-rings public +open import commutative-algebra.dependent-products-commutative-semirings public +open import commutative-algebra.discrete-fields public +open import commutative-algebra.eisenstein-integers public +open import commutative-algebra.euclidean-domains public +open import commutative-algebra.full-ideals-commutative-rings public +open import commutative-algebra.function-commutative-rings public +open import commutative-algebra.function-commutative-semirings public +open import commutative-algebra.gaussian-integers public +open import commutative-algebra.groups-of-units-commutative-rings public +open import commutative-algebra.homomorphisms-commutative-rings public +open import commutative-algebra.homomorphisms-commutative-semirings public +open import commutative-algebra.ideals-commutative-rings public +open import commutative-algebra.ideals-commutative-semirings public +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings public +open import commutative-algebra.integer-multiples-of-elements-commutative-rings public +open import commutative-algebra.integral-domains public +open import commutative-algebra.intersections-ideals-commutative-rings public +open import commutative-algebra.intersections-radical-ideals-commutative-rings public +open import commutative-algebra.invertible-elements-commutative-rings public +open import commutative-algebra.isomorphisms-commutative-rings public +open import commutative-algebra.joins-ideals-commutative-rings public +open import commutative-algebra.joins-radical-ideals-commutative-rings public +open import commutative-algebra.local-commutative-rings public open import commutative-algebra.maximal-ideals-commutative-rings public -open import commutative-algebra.multiples-of-elements-commutative-rings funext public -open import commutative-algebra.nilradical-commutative-rings funext public -open import commutative-algebra.nilradicals-commutative-semirings funext public -open import commutative-algebra.poset-of-ideals-commutative-rings funext public -open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext public -open import commutative-algebra.powers-of-elements-commutative-rings funext public -open import commutative-algebra.powers-of-elements-commutative-semirings funext public -open import commutative-algebra.precategory-of-commutative-rings funext public -open import commutative-algebra.precategory-of-commutative-semirings funext public -open import commutative-algebra.prime-ideals-commutative-rings funext public -open import commutative-algebra.products-commutative-rings funext public -open import commutative-algebra.products-ideals-commutative-rings funext public -open import commutative-algebra.products-radical-ideals-commutative-rings funext public -open import commutative-algebra.products-subsets-commutative-rings funext public -open import commutative-algebra.radical-ideals-commutative-rings funext public -open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings funext public -open import commutative-algebra.radicals-of-ideals-commutative-rings funext public -open import commutative-algebra.subsets-commutative-rings funext public -open import commutative-algebra.subsets-commutative-semirings funext public -open import commutative-algebra.sums-commutative-rings funext public -open import commutative-algebra.sums-commutative-semirings funext public -open import commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups funext public -open import commutative-algebra.trivial-commutative-rings funext public -open import commutative-algebra.zariski-locale funext public -open import commutative-algebra.zariski-topology funext public +open import commutative-algebra.multiples-of-elements-commutative-rings public +open import commutative-algebra.nilradical-commutative-rings public +open import commutative-algebra.nilradicals-commutative-semirings public +open import commutative-algebra.poset-of-ideals-commutative-rings public +open import commutative-algebra.poset-of-radical-ideals-commutative-rings public +open import commutative-algebra.powers-of-elements-commutative-rings public +open import commutative-algebra.powers-of-elements-commutative-semirings public +open import commutative-algebra.precategory-of-commutative-rings public +open import commutative-algebra.precategory-of-commutative-semirings public +open import commutative-algebra.prime-ideals-commutative-rings public +open import commutative-algebra.products-commutative-rings public +open import commutative-algebra.products-ideals-commutative-rings public +open import commutative-algebra.products-radical-ideals-commutative-rings public +open import commutative-algebra.products-subsets-commutative-rings public +open import commutative-algebra.radical-ideals-commutative-rings public +open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings public +open import commutative-algebra.radicals-of-ideals-commutative-rings public +open import commutative-algebra.subsets-commutative-rings public +open import commutative-algebra.subsets-commutative-semirings public +open import commutative-algebra.sums-commutative-rings public +open import commutative-algebra.sums-commutative-semirings public +open import commutative-algebra.transporting-commutative-ring-structure-isomorphisms-abelian-groups public +open import commutative-algebra.trivial-commutative-rings public +open import commutative-algebra.zariski-locale public +open import commutative-algebra.zariski-topology public ``` diff --git a/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md b/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md index 66ed617765..2e3e0a4f5e 100644 --- a/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md +++ b/src/commutative-algebra/binomial-theorem-commutative-rings.lagda.md @@ -1,36 +1,31 @@ # The binomial theorem in commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.binomial-theorem-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.binomial-theorem-commutative-rings where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-semirings funext -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.powers-of-elements-commutative-rings funext -open import commutative-algebra.sums-commutative-rings funext +open import commutative-algebra.binomial-theorem-commutative-semirings +open import commutative-algebra.commutative-rings +open import commutative-algebra.powers-of-elements-commutative-rings +open import commutative-algebra.sums-commutative-rings open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients funext -open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.binomial-coefficients +open import elementary-number-theory.distance-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.vectors-on-commutative-rings funext +open import linear-algebra.vectors-on-commutative-rings -open import ring-theory.binomial-theorem-rings funext +open import ring-theory.binomial-theorem-rings -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md b/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md index f5de2dcc09..3bbda32f19 100644 --- a/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md +++ b/src/commutative-algebra/binomial-theorem-commutative-semirings.lagda.md @@ -1,35 +1,30 @@ # The binomial theorem in commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.binomial-theorem-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.binomial-theorem-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext -open import commutative-algebra.powers-of-elements-commutative-semirings funext -open import commutative-algebra.sums-commutative-semirings funext +open import commutative-algebra.commutative-semirings +open import commutative-algebra.powers-of-elements-commutative-semirings +open import commutative-algebra.sums-commutative-semirings open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients funext -open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.binomial-coefficients +open import elementary-number-theory.distance-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.vectors-on-commutative-semirings funext +open import linear-algebra.vectors-on-commutative-semirings -open import ring-theory.binomial-theorem-semirings funext +open import ring-theory.binomial-theorem-semirings -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/commutative-algebra/boolean-rings.lagda.md b/src/commutative-algebra/boolean-rings.lagda.md index 0d0a00364b..6ae1075b5d 100644 --- a/src/commutative-algebra/boolean-rings.lagda.md +++ b/src/commutative-algebra/boolean-rings.lagda.md @@ -1,23 +1,18 @@ # Boolean rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.boolean-rings - (funext : function-extensionality) - where +module commutative-algebra.boolean-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import foundation.dependent-pair-types open import foundation.universe-levels -open import ring-theory.idempotent-elements-rings funext +open import ring-theory.idempotent-elements-rings ```
diff --git a/src/commutative-algebra/category-of-commutative-rings.lagda.md b/src/commutative-algebra/category-of-commutative-rings.lagda.md index a4cb09a777..c3fd89fa48 100644 --- a/src/commutative-algebra/category-of-commutative-rings.lagda.md +++ b/src/commutative-algebra/category-of-commutative-rings.lagda.md @@ -1,22 +1,17 @@ # The category of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.category-of-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.category-of-commutative-rings where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.large-categories funext +open import category-theory.categories +open import category-theory.large-categories -open import commutative-algebra.isomorphisms-commutative-rings funext -open import commutative-algebra.precategory-of-commutative-rings funext +open import commutative-algebra.isomorphisms-commutative-rings +open import commutative-algebra.precategory-of-commutative-rings open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/commutative-rings.lagda.md b/src/commutative-algebra/commutative-rings.lagda.md index 0d09b9357c..06b3e5d600 100644 --- a/src/commutative-algebra/commutative-rings.lagda.md +++ b/src/commutative-algebra/commutative-rings.lagda.md @@ -1,52 +1,47 @@ # Commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps open import foundation.interchange-law -open import foundation.involutions funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.involutions +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import ring-theory.rings funext -open import ring-theory.semirings funext +open import ring-theory.rings +open import ring-theory.semirings ```
diff --git a/src/commutative-algebra/commutative-semirings.lagda.md b/src/commutative-algebra/commutative-semirings.lagda.md index f08205268f..9f261db26a 100644 --- a/src/commutative-algebra/commutative-semirings.lagda.md +++ b/src/commutative-algebra/commutative-semirings.lagda.md @@ -1,12 +1,7 @@ # Commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.commutative-semirings where ```
Imports @@ -16,17 +11,17 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets open import foundation.telescopes open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext +open import group-theory.commutative-monoids +open import group-theory.monoids -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/commutative-algebra/dependent-products-commutative-rings.lagda.md b/src/commutative-algebra/dependent-products-commutative-rings.lagda.md index ce74483af8..45881aecf1 100644 --- a/src/commutative-algebra/dependent-products-commutative-rings.lagda.md +++ b/src/commutative-algebra/dependent-products-commutative-rings.lagda.md @@ -1,30 +1,25 @@ # Dependent products of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.dependent-products-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.dependent-products-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.dependent-products-commutative-monoids funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.dependent-products-commutative-monoids -open import ring-theory.dependent-products-rings funext -open import ring-theory.rings funext +open import ring-theory.dependent-products-rings +open import ring-theory.rings ```
diff --git a/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md b/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md index 1bd7ed4d4d..abcf6a837e 100644 --- a/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md +++ b/src/commutative-algebra/dependent-products-commutative-semirings.lagda.md @@ -1,29 +1,24 @@ # Dependent products of commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.dependent-products-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.dependent-products-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.dependent-products-commutative-monoids funext +open import group-theory.commutative-monoids +open import group-theory.dependent-products-commutative-monoids -open import ring-theory.dependent-products-semirings funext -open import ring-theory.semirings funext +open import ring-theory.dependent-products-semirings +open import ring-theory.semirings ```
diff --git a/src/commutative-algebra/discrete-fields.lagda.md b/src/commutative-algebra/discrete-fields.lagda.md index 674e77107c..6943d29b4b 100644 --- a/src/commutative-algebra/discrete-fields.lagda.md +++ b/src/commutative-algebra/discrete-fields.lagda.md @@ -1,22 +1,17 @@ # Discrete fields ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.discrete-fields - (funext : function-extensionality) - where +module commutative-algebra.discrete-fields where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import foundation.universe-levels -open import ring-theory.division-rings funext +open import ring-theory.division-rings ```
diff --git a/src/commutative-algebra/eisenstein-integers.lagda.md b/src/commutative-algebra/eisenstein-integers.lagda.md index 44c469260e..d0120575cd 100644 --- a/src/commutative-algebra/eisenstein-integers.lagda.md +++ b/src/commutative-algebra/eisenstein-integers.lagda.md @@ -1,37 +1,32 @@ # The Eisenstein integers ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.eisenstein-integers - (funext : function-extensionality) - where +module commutative-algebra.eisenstein-integers where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.semigroups -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/commutative-algebra/euclidean-domains.lagda.md b/src/commutative-algebra/euclidean-domains.lagda.md index 178d7dad95..abd586d5ef 100644 --- a/src/commutative-algebra/euclidean-domains.lagda.md +++ b/src/commutative-algebra/euclidean-domains.lagda.md @@ -1,56 +1,51 @@ # Euclidean domains ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.euclidean-domains - (funext : function-extensionality) - where +module commutative-algebra.euclidean-domains where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.commutative-semirings funext -open import commutative-algebra.integral-domains funext -open import commutative-algebra.trivial-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-semirings +open import commutative-algebra.integral-domains +open import commutative-algebra.trivial-commutative-rings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps open import foundation.interchange-law -open import foundation.involutions funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.involutions +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import ring-theory.rings funext -open import ring-theory.semirings funext +open import ring-theory.rings +open import ring-theory.semirings ```
diff --git a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md index 4df1509d28..762bbd4709 100644 --- a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md @@ -1,33 +1,28 @@ # Full ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.full-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.full-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.poset-of-ideals-commutative-rings funext -open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext -open import commutative-algebra.radical-ideals-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.poset-of-ideals-commutative-rings +open import commutative-algebra.poset-of-radical-ideals-commutative-rings +open import commutative-algebra.radical-ideals-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import order-theory.top-elements-large-posets funext +open import order-theory.top-elements-large-posets -open import ring-theory.full-ideals-rings funext +open import ring-theory.full-ideals-rings ```
diff --git a/src/commutative-algebra/function-commutative-rings.lagda.md b/src/commutative-algebra/function-commutative-rings.lagda.md index a740285c39..fb7920277a 100644 --- a/src/commutative-algebra/function-commutative-rings.lagda.md +++ b/src/commutative-algebra/function-commutative-rings.lagda.md @@ -1,28 +1,23 @@ # Function commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.function-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.function-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.dependent-products-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.dependent-products-commutative-rings -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/commutative-algebra/function-commutative-semirings.lagda.md b/src/commutative-algebra/function-commutative-semirings.lagda.md index 005e2833de..186bc1dbc1 100644 --- a/src/commutative-algebra/function-commutative-semirings.lagda.md +++ b/src/commutative-algebra/function-commutative-semirings.lagda.md @@ -1,27 +1,22 @@ # Function commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.function-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.function-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext -open import commutative-algebra.dependent-products-commutative-semirings funext +open import commutative-algebra.commutative-semirings +open import commutative-algebra.dependent-products-commutative-semirings -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.commutative-monoids funext +open import group-theory.commutative-monoids -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/commutative-algebra/gaussian-integers.lagda.md b/src/commutative-algebra/gaussian-integers.lagda.md index 6529b2c3b0..2cbe987830 100644 --- a/src/commutative-algebra/gaussian-integers.lagda.md +++ b/src/commutative-algebra/gaussian-integers.lagda.md @@ -1,38 +1,33 @@ # The Gaussian integers ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.gaussian-integers - (funext : function-extensionality) - where +module commutative-algebra.gaussian-integers where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.difference-integers +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.semigroups -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md b/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md index f9e0b103be..f3fcd5aac1 100644 --- a/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md +++ b/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md @@ -1,39 +1,34 @@ # The group of multiplicative units of a commutative ring ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.groups-of-units-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.groups-of-units-commutative-rings where ```
Imports ```agda -open import category-theory.functors-large-precategories funext +open import category-theory.functors-large-precategories -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.homomorphisms-commutative-rings funext -open import commutative-algebra.precategory-of-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.homomorphisms-commutative-rings +open import commutative-algebra.precategory-of-commutative-rings open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.category-of-abelian-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext -open import group-theory.submonoids funext +open import group-theory.abelian-groups +open import group-theory.category-of-abelian-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-monoids +open import group-theory.monoids +open import group-theory.semigroups +open import group-theory.submonoids -open import ring-theory.groups-of-units-rings funext +open import ring-theory.groups-of-units-rings ```
diff --git a/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md b/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md index 0bf8ee831f..284d752ce5 100644 --- a/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md +++ b/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md @@ -1,32 +1,27 @@ # Homomorphisms of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.homomorphisms-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.homomorphisms-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.homomorphisms-commutative-semirings funext -open import commutative-algebra.invertible-elements-commutative-rings funext - -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.homomorphisms-commutative-semirings +open import commutative-algebra.invertible-elements-commutative-rings + +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.homomorphisms-monoids funext +open import group-theory.homomorphisms-abelian-groups +open import group-theory.homomorphisms-monoids -open import ring-theory.homomorphisms-rings funext +open import ring-theory.homomorphisms-rings ```
diff --git a/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md b/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md index b7e95ceecd..c5ee3254af 100644 --- a/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md +++ b/src/commutative-algebra/homomorphisms-commutative-semirings.lagda.md @@ -1,29 +1,24 @@ # Homomorphisms of commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.homomorphisms-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.homomorphisms-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.homomorphisms-commutative-monoids funext -open import group-theory.homomorphisms-monoids funext +open import group-theory.homomorphisms-commutative-monoids +open import group-theory.homomorphisms-monoids -open import ring-theory.homomorphisms-semirings funext +open import ring-theory.homomorphisms-semirings ```
diff --git a/src/commutative-algebra/ideals-commutative-rings.lagda.md b/src/commutative-algebra/ideals-commutative-rings.lagda.md index ad2e40878a..90f082cc86 100644 --- a/src/commutative-algebra/ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/ideals-commutative-rings.lagda.md @@ -1,34 +1,29 @@ # Ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.powers-of-elements-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.powers-of-elements-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.universe-levels -open import ring-theory.ideals-rings funext -open import ring-theory.left-ideals-rings funext -open import ring-theory.right-ideals-rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.ideals-rings +open import ring-theory.left-ideals-rings +open import ring-theory.right-ideals-rings +open import ring-theory.subsets-rings ```
diff --git a/src/commutative-algebra/ideals-commutative-semirings.lagda.md b/src/commutative-algebra/ideals-commutative-semirings.lagda.md index 44111aa66d..8fb7d4a127 100644 --- a/src/commutative-algebra/ideals-commutative-semirings.lagda.md +++ b/src/commutative-algebra/ideals-commutative-semirings.lagda.md @@ -1,26 +1,21 @@ # Ideals of commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.ideals-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.ideals-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext -open import commutative-algebra.subsets-commutative-semirings funext +open import commutative-algebra.commutative-semirings +open import commutative-algebra.subsets-commutative-semirings open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import ring-theory.ideals-semirings funext +open import ring-theory.ideals-semirings ```
diff --git a/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md b/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md index 6705ffb22d..c057c98271 100644 --- a/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/ideals-generated-by-subsets-commutative-rings.lagda.md @@ -1,29 +1,24 @@ # Ideals generated by subsets of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.ideals-generated-by-subsets-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.ideals-generated-by-subsets-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.poset-of-ideals-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.poset-of-ideals-commutative-rings +open import commutative-algebra.subsets-commutative-rings -open import foundation.identity-types funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.subtypes open import foundation.universe-levels -open import lists.concatenation-lists funext +open import lists.concatenation-lists -open import ring-theory.ideals-generated-by-subsets-rings funext +open import ring-theory.ideals-generated-by-subsets-rings ```
diff --git a/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md b/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md index 9f26a8c364..ea8f228c18 100644 --- a/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/integer-multiples-of-elements-commutative-rings.lagda.md @@ -1,32 +1,27 @@ # Integer multiples of elements of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.integer-multiples-of-elements-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.integer-multiples-of-elements-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.homomorphisms-commutative-rings funext -open import commutative-algebra.multiples-of-elements-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.homomorphisms-commutative-rings +open import commutative-algebra.multiples-of-elements-commutative-rings -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.homomorphisms-abelian-groups -open import ring-theory.integer-multiples-of-elements-rings funext +open import ring-theory.integer-multiples-of-elements-rings ```
diff --git a/src/commutative-algebra/integral-domains.lagda.md b/src/commutative-algebra/integral-domains.lagda.md index f74ed26a29..d960d94053 100644 --- a/src/commutative-algebra/integral-domains.lagda.md +++ b/src/commutative-algebra/integral-domains.lagda.md @@ -1,53 +1,48 @@ # Integral domains ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.integral-domains - (funext : function-extensionality) - where +module commutative-algebra.integral-domains where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.commutative-semirings funext -open import commutative-algebra.trivial-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-semirings +open import commutative-algebra.trivial-commutative-rings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps open import foundation.interchange-law -open import foundation.involutions funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.involutions +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import ring-theory.rings funext -open import ring-theory.semirings funext +open import ring-theory.rings +open import ring-theory.semirings ```
diff --git a/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md b/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md index 7c65b17989..6846baf280 100644 --- a/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/intersections-ideals-commutative-rings.lagda.md @@ -1,30 +1,25 @@ # Intersections of ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.intersections-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.intersections-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.poset-of-ideals-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.poset-of-ideals-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import foundation.dependent-pair-types -open import foundation.intersections-subtypes funext -open import foundation.subtypes funext +open import foundation.intersections-subtypes +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets -open import ring-theory.intersections-ideals-rings funext +open import ring-theory.intersections-ideals-rings ```
diff --git a/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md index 657fd20b20..1bf031cb1c 100644 --- a/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/intersections-radical-ideals-commutative-rings.lagda.md @@ -1,39 +1,34 @@ # Intersections of radical ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.intersections-radical-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.intersections-radical-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.full-ideals-commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.intersections-ideals-commutative-rings funext -open import commutative-algebra.poset-of-ideals-commutative-rings funext -open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext -open import commutative-algebra.powers-of-elements-commutative-rings funext -open import commutative-algebra.products-ideals-commutative-rings funext -open import commutative-algebra.products-radical-ideals-commutative-rings funext -open import commutative-algebra.radical-ideals-commutative-rings funext -open import commutative-algebra.radicals-of-ideals-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.full-ideals-commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.intersections-ideals-commutative-rings +open import commutative-algebra.poset-of-ideals-commutative-rings +open import commutative-algebra.poset-of-radical-ideals-commutative-rings +open import commutative-algebra.powers-of-elements-commutative-rings +open import commutative-algebra.products-ideals-commutative-rings +open import commutative-algebra.products-radical-ideals-commutative-rings +open import commutative-algebra.radical-ideals-commutative-rings +open import commutative-algebra.radicals-of-ideals-commutative-rings open import elementary-number-theory.addition-natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-meet-semilattices funext +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-meet-semilattices ```
diff --git a/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md b/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md index 832a92a546..ebc4116027 100644 --- a/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md @@ -1,26 +1,21 @@ # Invertible elements in commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.invertible-elements-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.invertible-elements-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import ring-theory.invertible-elements-rings funext +open import ring-theory.invertible-elements-rings ```
diff --git a/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md b/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md index 97956b6146..663583921f 100644 --- a/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md +++ b/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md @@ -1,38 +1,33 @@ # Isomorphisms of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.isomorphisms-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.isomorphisms-commutative-rings where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.homomorphisms-commutative-rings funext -open import commutative-algebra.invertible-elements-commutative-rings funext -open import commutative-algebra.precategory-of-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.homomorphisms-commutative-rings +open import commutative-algebra.invertible-elements-commutative-rings +open import commutative-algebra.precategory-of-commutative-rings open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.isomorphisms-abelian-groups funext +open import group-theory.isomorphisms-abelian-groups -open import ring-theory.isomorphisms-rings funext +open import ring-theory.isomorphisms-rings ```
diff --git a/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md b/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md index 1378574e66..52deaa9ff9 100644 --- a/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/joins-ideals-commutative-rings.lagda.md @@ -1,33 +1,28 @@ # Joins of ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.joins-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.joins-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext -open import commutative-algebra.poset-of-ideals-commutative-rings funext -open import commutative-algebra.products-ideals-commutative-rings funext -open import commutative-algebra.products-subsets-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings +open import commutative-algebra.poset-of-ideals-commutative-rings +open import commutative-algebra.products-ideals-commutative-rings +open import commutative-algebra.products-subsets-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.subtypes funext -open import foundation.unions-subtypes funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.subtypes +open import foundation.unions-subtypes open import foundation.universe-levels -open import ring-theory.joins-ideals-rings funext +open import ring-theory.joins-ideals-rings ```
diff --git a/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md index cd8406084f..3cd6e927ed 100644 --- a/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/joins-radical-ideals-commutative-rings.lagda.md @@ -1,36 +1,31 @@ # Joins of radical ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.joins-radical-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.joins-radical-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.intersections-radical-ideals-commutative-rings funext -open import commutative-algebra.joins-ideals-commutative-rings funext -open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext -open import commutative-algebra.products-ideals-commutative-rings funext -open import commutative-algebra.products-radical-ideals-commutative-rings funext -open import commutative-algebra.radical-ideals-commutative-rings funext -open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings funext -open import commutative-algebra.radicals-of-ideals-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.intersections-radical-ideals-commutative-rings +open import commutative-algebra.joins-ideals-commutative-rings +open import commutative-algebra.poset-of-radical-ideals-commutative-rings +open import commutative-algebra.products-ideals-commutative-rings +open import commutative-algebra.products-radical-ideals-commutative-rings +open import commutative-algebra.radical-ideals-commutative-rings +open import commutative-algebra.radical-ideals-generated-by-subsets-commutative-rings +open import commutative-algebra.radicals-of-ideals-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets ```
diff --git a/src/commutative-algebra/local-commutative-rings.lagda.md b/src/commutative-algebra/local-commutative-rings.lagda.md index 741dffe391..9de71b60fc 100644 --- a/src/commutative-algebra/local-commutative-rings.lagda.md +++ b/src/commutative-algebra/local-commutative-rings.lagda.md @@ -1,26 +1,21 @@ # Local commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.local-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.local-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import ring-theory.local-rings funext -open import ring-theory.rings funext +open import ring-theory.local-rings +open import ring-theory.rings ```
diff --git a/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md b/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md index 580c5524d9..9121d62200 100644 --- a/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/multiples-of-elements-commutative-rings.lagda.md @@ -1,27 +1,22 @@ # Multiples of elements in commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.multiples-of-elements-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.multiples-of-elements-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.multiples-of-elements-rings funext +open import ring-theory.multiples-of-elements-rings ```
diff --git a/src/commutative-algebra/nilradical-commutative-rings.lagda.md b/src/commutative-algebra/nilradical-commutative-rings.lagda.md index fbfe8ca6fe..e8cae03fe9 100644 --- a/src/commutative-algebra/nilradical-commutative-rings.lagda.md +++ b/src/commutative-algebra/nilradical-commutative-rings.lagda.md @@ -1,30 +1,25 @@ # Nilradical of a commutative ring ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.nilradical-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.nilradical-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.prime-ideals-commutative-rings funext -open import commutative-algebra.radical-ideals-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.prime-ideals-commutative-rings +open import commutative-algebra.radical-ideals-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels -open import ring-theory.nilpotent-elements-rings funext +open import ring-theory.nilpotent-elements-rings ```
diff --git a/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md b/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md index a56e881c9c..994c83bc29 100644 --- a/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md +++ b/src/commutative-algebra/nilradicals-commutative-semirings.lagda.md @@ -1,25 +1,20 @@ # The nilradical of a commutative semiring ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.nilradicals-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.nilradicals-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext -open import commutative-algebra.subsets-commutative-semirings funext +open import commutative-algebra.commutative-semirings +open import commutative-algebra.subsets-commutative-semirings -open import foundation.existential-quantification funext -open import foundation.identity-types funext +open import foundation.existential-quantification +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.nilpotent-elements-semirings funext +open import ring-theory.nilpotent-elements-semirings ```
diff --git a/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md b/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md index de63dc2a43..4b5b4c589f 100644 --- a/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md @@ -1,28 +1,23 @@ # The poset of ideals of a commutative ring ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.poset-of-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.poset-of-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext +open import order-theory.large-posets +open import order-theory.large-preorders -open import ring-theory.poset-of-ideals-rings funext +open import ring-theory.poset-of-ideals-rings ```
diff --git a/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md index 4c2e24e6f6..79e6803732 100644 --- a/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md @@ -1,31 +1,26 @@ # The poset of radical ideals of a commutative ring ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.poset-of-radical-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.poset-of-radical-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.poset-of-ideals-commutative-rings funext -open import commutative-algebra.radical-ideals-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.poset-of-ideals-commutative-rings +open import commutative-algebra.radical-ideals-commutative-rings -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.similarity-of-elements-large-posets ```
diff --git a/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md b/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md index 0e44f2a90a..9cd508163f 100644 --- a/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/powers-of-elements-commutative-rings.lagda.md @@ -1,28 +1,23 @@ # Powers of elements in commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.powers-of-elements-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.powers-of-elements-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers funext +open import elementary-number-theory.parity-natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.powers-of-elements-rings funext +open import ring-theory.powers-of-elements-rings ```
diff --git a/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md b/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md index e551a299b3..0bda772d1a 100644 --- a/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md +++ b/src/commutative-algebra/powers-of-elements-commutative-semirings.lagda.md @@ -1,26 +1,21 @@ # Powers of elements in commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.powers-of-elements-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.powers-of-elements-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.powers-of-elements-semirings funext +open import ring-theory.powers-of-elements-semirings ```
diff --git a/src/commutative-algebra/precategory-of-commutative-rings.lagda.md b/src/commutative-algebra/precategory-of-commutative-rings.lagda.md index ef537ea59d..51c54f1c3f 100644 --- a/src/commutative-algebra/precategory-of-commutative-rings.lagda.md +++ b/src/commutative-algebra/precategory-of-commutative-rings.lagda.md @@ -1,26 +1,21 @@ # The precategory of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.precategory-of-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.precategory-of-commutative-rings where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.full-large-subprecategories +open import category-theory.large-precategories +open import category-theory.precategories -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import foundation.universe-levels -open import ring-theory.precategory-of-rings funext +open import ring-theory.precategory-of-rings ```
diff --git a/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md b/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md index a7a4a16402..e0239a074f 100644 --- a/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md +++ b/src/commutative-algebra/precategory-of-commutative-semirings.lagda.md @@ -1,26 +1,21 @@ # The precategory of commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.precategory-of-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.precategory-of-commutative-semirings where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.full-large-subprecategories +open import category-theory.large-precategories +open import category-theory.precategories -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings open import foundation.universe-levels -open import ring-theory.precategory-of-semirings funext +open import ring-theory.precategory-of-semirings ```
diff --git a/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md b/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md index 09636d11ab..de9a327c13 100644 --- a/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md @@ -1,34 +1,29 @@ # Prime ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.prime-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.prime-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.full-ideals-commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.powers-of-elements-commutative-rings funext -open import commutative-algebra.radical-ideals-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.full-ideals-commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.powers-of-elements-commutative-rings +open import commutative-algebra.radical-ideals-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.disjunction +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import ring-theory.subsets-rings funext +open import ring-theory.subsets-rings ```
diff --git a/src/commutative-algebra/products-commutative-rings.lagda.md b/src/commutative-algebra/products-commutative-rings.lagda.md index 4518d26d3c..dee1a7ee38 100644 --- a/src/commutative-algebra/products-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-commutative-rings.lagda.md @@ -1,31 +1,26 @@ # Products of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.products-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.products-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.semigroups -open import ring-theory.products-rings funext -open import ring-theory.rings funext +open import ring-theory.products-rings +open import ring-theory.rings ```
diff --git a/src/commutative-algebra/products-ideals-commutative-rings.lagda.md b/src/commutative-algebra/products-ideals-commutative-rings.lagda.md index 91245efc37..9e1a2d1173 100644 --- a/src/commutative-algebra/products-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-ideals-commutative-rings.lagda.md @@ -1,33 +1,28 @@ # Products of ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.products-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.products-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext -open import commutative-algebra.poset-of-ideals-commutative-rings funext -open import commutative-algebra.products-subsets-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings +open import commutative-algebra.poset-of-ideals-commutative-rings +open import commutative-algebra.products-subsets-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels open import lists.lists -open import ring-theory.products-ideals-rings funext +open import ring-theory.products-ideals-rings ```
diff --git a/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md index e88c46f9ba..f112058f6d 100644 --- a/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-radical-ideals-commutative-rings.lagda.md @@ -1,32 +1,27 @@ # Products of radical ideals of a commutative ring ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.products-radical-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.products-radical-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext -open import commutative-algebra.powers-of-elements-commutative-rings funext -open import commutative-algebra.products-ideals-commutative-rings funext -open import commutative-algebra.radical-ideals-commutative-rings funext -open import commutative-algebra.radicals-of-ideals-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.poset-of-radical-ideals-commutative-rings +open import commutative-algebra.powers-of-elements-commutative-rings +open import commutative-algebra.products-ideals-commutative-rings +open import commutative-algebra.radical-ideals-commutative-rings +open import commutative-algebra.radicals-of-ideals-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/products-subsets-commutative-rings.lagda.md b/src/commutative-algebra/products-subsets-commutative-rings.lagda.md index 1615bcdbce..9bad16cb22 100644 --- a/src/commutative-algebra/products-subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/products-subsets-commutative-rings.lagda.md @@ -1,26 +1,21 @@ # Products of subsets of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.products-subsets-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.products-subsets-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.subsets-commutative-rings -open import foundation.identity-types funext -open import foundation.subtypes funext -open import foundation.unions-subtypes funext +open import foundation.identity-types +open import foundation.subtypes +open import foundation.unions-subtypes open import foundation.universe-levels -open import ring-theory.products-subsets-rings funext +open import ring-theory.products-subsets-rings ```
diff --git a/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md index a8662f9e6b..f087226bc9 100644 --- a/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md @@ -1,31 +1,26 @@ # Radical ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.radical-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.radical-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.powers-of-elements-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.powers-of-elements-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md b/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md index d01ca8f870..9c09b474bf 100644 --- a/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/radical-ideals-generated-by-subsets-commutative-rings.lagda.md @@ -9,14 +9,14 @@ module
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.ideals-generated-by-subsets-commutative-rings funext -open import commutative-algebra.radical-ideals-commutative-rings funext -open import commutative-algebra.radicals-of-ideals-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext - -open import foundation.subtypes funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.ideals-generated-by-subsets-commutative-rings +open import commutative-algebra.radical-ideals-commutative-rings +open import commutative-algebra.radicals-of-ideals-commutative-rings +open import commutative-algebra.subsets-commutative-rings + +open import foundation.subtypes open import foundation.universe-levels ``` @@ -34,12 +34,7 @@ containing `S`. ### The universal property of the radical ideal generated by a subset ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {l1 l2 l3 : Level} (A : Commutative-Ring l1) (S : subset-Commutative-Ring l2 A) (I : radical-ideal-Commutative-Ring l3 A) diff --git a/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md b/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md index 283714df24..13a2f12ae2 100644 --- a/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md @@ -1,42 +1,37 @@ # Radicals of ideals of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.radicals-of-ideals-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.radicals-of-ideals-commutative-rings where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-rings funext -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.ideals-commutative-rings funext -open import commutative-algebra.poset-of-ideals-commutative-rings funext -open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext -open import commutative-algebra.powers-of-elements-commutative-rings funext -open import commutative-algebra.radical-ideals-commutative-rings funext -open import commutative-algebra.subsets-commutative-rings funext +open import commutative-algebra.binomial-theorem-commutative-rings +open import commutative-algebra.commutative-rings +open import commutative-algebra.ideals-commutative-rings +open import commutative-algebra.poset-of-ideals-commutative-rings +open import commutative-algebra.poset-of-radical-ideals-commutative-rings +open import commutative-algebra.powers-of-elements-commutative-rings +open import commutative-algebra.radical-ideals-commutative-rings +open import commutative-algebra.subsets-commutative-rings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.galois-connections-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.reflective-galois-connections-large-posets funext +open import order-theory.galois-connections-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.reflective-galois-connections-large-posets ```
diff --git a/src/commutative-algebra/subsets-commutative-rings.lagda.md b/src/commutative-algebra/subsets-commutative-rings.lagda.md index 0197c79c0b..fd7c2d204e 100644 --- a/src/commutative-algebra/subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/subsets-commutative-rings.lagda.md @@ -1,29 +1,24 @@ # Subsets of commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.subsets-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.subsets-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings -open import foundation.identity-types funext -open import foundation.propositional-extensionality funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositional-extensionality +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.subgroups-abelian-groups funext +open import group-theory.subgroups-abelian-groups -open import ring-theory.subsets-rings funext +open import ring-theory.subsets-rings ```
diff --git a/src/commutative-algebra/subsets-commutative-semirings.lagda.md b/src/commutative-algebra/subsets-commutative-semirings.lagda.md index 993233e06b..73f9932341 100644 --- a/src/commutative-algebra/subsets-commutative-semirings.lagda.md +++ b/src/commutative-algebra/subsets-commutative-semirings.lagda.md @@ -1,26 +1,21 @@ # Subsets of commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.subsets-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.subsets-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import ring-theory.subsets-semirings funext +open import ring-theory.subsets-semirings ```
diff --git a/src/commutative-algebra/sums-commutative-rings.lagda.md b/src/commutative-algebra/sums-commutative-rings.lagda.md index e320adfe0e..f26a86e6db 100644 --- a/src/commutative-algebra/sums-commutative-rings.lagda.md +++ b/src/commutative-algebra/sums-commutative-rings.lagda.md @@ -1,37 +1,32 @@ # Sums in commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.sums-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.sums-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.coproduct-types +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors funext -open import linear-algebra.vectors funext-on-commutative-rings +open import linear-algebra.vectors +open import linear-algebra.vectors-on-commutative-rings -open import ring-theory.sums-rings funext +open import ring-theory.sums-rings -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/commutative-algebra/sums-commutative-semirings.lagda.md b/src/commutative-algebra/sums-commutative-semirings.lagda.md index 7b3da31ad7..16eaf02de8 100644 --- a/src/commutative-algebra/sums-commutative-semirings.lagda.md +++ b/src/commutative-algebra/sums-commutative-semirings.lagda.md @@ -1,34 +1,29 @@ # Sums in commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.sums-commutative-semirings - (funext : function-extensionality) - where +module commutative-algebra.sums-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.vectors funext -open import linear-algebra.vectors funext-on-commutative-semirings +open import linear-algebra.vectors +open import linear-algebra.vectors-on-commutative-semirings -open import ring-theory.sums-semirings funext +open import ring-theory.sums-semirings -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md b/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md index bdbc75dc63..d504ae3dbc 100644 --- a/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md +++ b/src/commutative-algebra/transporting-commutative-ring-structure-isomorphisms-abelian-groups.lagda.md @@ -9,23 +9,23 @@ module
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.homomorphisms-commutative-rings funext -open import commutative-algebra.isomorphisms-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.homomorphisms-commutative-rings +open import commutative-algebra.isomorphisms-commutative-rings open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.isomorphisms-abelian-groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.isomorphisms-abelian-groups +open import group-theory.semigroups -open import ring-theory.homomorphisms-rings funext -open import ring-theory.rings funext -open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups funext +open import ring-theory.homomorphisms-rings +open import ring-theory.rings +open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups ```
@@ -48,12 +48,7 @@ transported ring structure. ### Transporting the multiplicative structure of a commutative ring along an isomorphism of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {l1 l2 : Level} (A : Commutative-Ring l1) (B : Ab l2) (f : iso-Ab (ab-Commutative-Ring A) B) where diff --git a/src/commutative-algebra/trivial-commutative-rings.lagda.md b/src/commutative-algebra/trivial-commutative-rings.lagda.md index 2f4cf74b79..8aa4781e63 100644 --- a/src/commutative-algebra/trivial-commutative-rings.lagda.md +++ b/src/commutative-algebra/trivial-commutative-rings.lagda.md @@ -1,36 +1,31 @@ # Trivial commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.trivial-commutative-rings - (funext : function-extensionality) - where +module commutative-algebra.trivial-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.isomorphisms-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.isomorphisms-commutative-rings -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.structure-identity-principle open import foundation.unit-type open import foundation.universe-levels open import foundation-core.identity-types -open import group-theory.abelian-groups funext -open import group-theory.trivial-groups funext +open import group-theory.abelian-groups +open import group-theory.trivial-groups -open import ring-theory.rings funext -open import ring-theory.trivial-rings funext +open import ring-theory.rings +open import ring-theory.trivial-rings ```
diff --git a/src/commutative-algebra/zariski-locale.lagda.md b/src/commutative-algebra/zariski-locale.lagda.md index 0a7fa646a8..512b67f821 100644 --- a/src/commutative-algebra/zariski-locale.lagda.md +++ b/src/commutative-algebra/zariski-locale.lagda.md @@ -1,26 +1,21 @@ # The Zariski locale ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.zariski-locale - (funext : function-extensionality) - where +module commutative-algebra.zariski-locale where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.intersections-radical-ideals-commutative-rings funext -open import commutative-algebra.joins-radical-ideals-commutative-rings funext -open import commutative-algebra.poset-of-radical-ideals-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.intersections-radical-ideals-commutative-rings +open import commutative-algebra.joins-radical-ideals-commutative-rings +open import commutative-algebra.poset-of-radical-ideals-commutative-rings open import foundation.universe-levels -open import order-theory.large-frames funext -open import order-theory.large-locales funext +open import order-theory.large-frames +open import order-theory.large-locales ```
diff --git a/src/commutative-algebra/zariski-topology.lagda.md b/src/commutative-algebra/zariski-topology.lagda.md index 3f5f0dd52c..b3bbbec25c 100644 --- a/src/commutative-algebra/zariski-topology.lagda.md +++ b/src/commutative-algebra/zariski-topology.lagda.md @@ -1,24 +1,19 @@ # The Zariski topology on the set of prime ideals of a commutative ring ```agda -open import foundation.function-extensionality-axiom - -module - commutative-algebra.zariski-topology - (funext : function-extensionality) - where +module commutative-algebra.zariski-topology where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.prime-ideals-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.prime-ideals-commutative-rings -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/domain-theory.lagda.md b/src/domain-theory.lagda.md index a2853d3ac7..5e1cb84b7f 100644 --- a/src/domain-theory.lagda.md +++ b/src/domain-theory.lagda.md @@ -3,20 +3,15 @@ ## Modules in the domain theory namespace ```agda -open import foundation.function-extensionality-axiom +module domain-theory where -module - domain-theory - (funext : function-extensionality) - where - -open import domain-theory.directed-complete-posets funext public -open import domain-theory.directed-families-posets funext public -open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets funext public -open import domain-theory.kleenes-fixed-point-theorem-posets funext public -open import domain-theory.omega-complete-posets funext public -open import domain-theory.omega-continuous-maps-omega-complete-posets funext public -open import domain-theory.omega-continuous-maps-posets funext public -open import domain-theory.reindexing-directed-families-posets funext public -open import domain-theory.scott-continuous-maps-posets funext public +open import domain-theory.directed-complete-posets public +open import domain-theory.directed-families-posets public +open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets public +open import domain-theory.kleenes-fixed-point-theorem-posets public +open import domain-theory.omega-complete-posets public +open import domain-theory.omega-continuous-maps-omega-complete-posets public +open import domain-theory.omega-continuous-maps-posets public +open import domain-theory.reindexing-directed-families-posets public +open import domain-theory.scott-continuous-maps-posets public ``` diff --git a/src/domain-theory/directed-complete-posets.lagda.md b/src/domain-theory/directed-complete-posets.lagda.md index fb840536f4..2225aeff51 100644 --- a/src/domain-theory/directed-complete-posets.lagda.md +++ b/src/domain-theory/directed-complete-posets.lagda.md @@ -1,30 +1,25 @@ # Directed complete posets ```agda -open import foundation.function-extensionality-axiom - -module - domain-theory.directed-complete-posets - (funext : function-extensionality) - where +module domain-theory.directed-complete-posets where ```
Imports ```agda -open import domain-theory.directed-families-posets funext +open import domain-theory.directed-families-posets -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets funext -open import order-theory.posets funext +open import order-theory.least-upper-bounds-posets +open import order-theory.posets ```
diff --git a/src/domain-theory/directed-families-posets.lagda.md b/src/domain-theory/directed-families-posets.lagda.md index dd3523c946..0b192c1b84 100644 --- a/src/domain-theory/directed-families-posets.lagda.md +++ b/src/domain-theory/directed-families-posets.lagda.md @@ -1,34 +1,29 @@ # Directed families in posets ```agda -open import foundation.function-extensionality-axiom - -module - domain-theory.directed-families-posets - (funext : function-extensionality) - where +module domain-theory.directed-families-posets where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext +open import foundation.cartesian-product-types +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.surjective-maps funext -open import foundation.universal-quantification funext +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.surjective-maps +open import foundation.universal-quantification open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md b/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md index de4056d860..0e760554ec 100644 --- a/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md +++ b/src/domain-theory/kleenes-fixed-point-theorem-omega-complete-posets.lagda.md @@ -1,46 +1,41 @@ # Kleene's fixed point theorem for ω-complete posets ```agda -open import foundation.function-extensionality-axiom - -module - domain-theory.kleenes-fixed-point-theorem-omega-complete-posets - (funext : function-extensionality) - where +module domain-theory.kleenes-fixed-point-theorem-omega-complete-posets where ```
Imports ```agda -open import domain-theory.directed-families-posets funext -open import domain-theory.kleenes-fixed-point-theorem-posets funext -open import domain-theory.omega-complete-posets funext -open import domain-theory.omega-continuous-maps-omega-complete-posets funext -open import domain-theory.omega-continuous-maps-posets funext - -open import elementary-number-theory.decidable-total-order-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import domain-theory.directed-families-posets +open import domain-theory.kleenes-fixed-point-theorem-posets +open import domain-theory.omega-complete-posets +open import domain-theory.omega-continuous-maps-omega-complete-posets +open import domain-theory.omega-continuous-maps-posets + +open import elementary-number-theory.decidable-total-order-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.iterating-functions funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.iterating-functions +open import foundation.logical-equivalences +open import foundation.propositional-truncations open import foundation.universe-levels -open import order-theory.bottom-elements-posets funext -open import order-theory.chains-posets funext -open import order-theory.inflattices funext -open import order-theory.inhabited-chains-posets funext -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext -open import order-theory.suplattices funext -open import order-theory.upper-bounds-posets funext +open import order-theory.bottom-elements-posets +open import order-theory.chains-posets +open import order-theory.inflattices +open import order-theory.inhabited-chains-posets +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.posets +open import order-theory.suplattices +open import order-theory.upper-bounds-posets ```
diff --git a/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md b/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md index 34cbc88b25..8a3518c188 100644 --- a/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md +++ b/src/domain-theory/kleenes-fixed-point-theorem-posets.lagda.md @@ -1,43 +1,38 @@ # Kleene's fixed point theorem for posets ```agda -open import foundation.function-extensionality-axiom - -module - domain-theory.kleenes-fixed-point-theorem-posets - (funext : function-extensionality) - where +module domain-theory.kleenes-fixed-point-theorem-posets where ```
Imports ```agda -open import domain-theory.directed-families-posets funext -open import domain-theory.omega-continuous-maps-posets funext +open import domain-theory.directed-families-posets +open import domain-theory.omega-continuous-maps-posets -open import elementary-number-theory.decidable-total-order-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.decidable-total-order-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.iterating-functions funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.iterating-functions +open import foundation.logical-equivalences +open import foundation.propositional-truncations open import foundation.universe-levels -open import order-theory.bottom-elements-posets funext -open import order-theory.chains-posets funext -open import order-theory.inflattices funext -open import order-theory.inhabited-chains-posets funext -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext -open import order-theory.suplattices funext -open import order-theory.upper-bounds-posets funext +open import order-theory.bottom-elements-posets +open import order-theory.chains-posets +open import order-theory.inflattices +open import order-theory.inhabited-chains-posets +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.posets +open import order-theory.suplattices +open import order-theory.upper-bounds-posets ```
diff --git a/src/domain-theory/omega-complete-posets.lagda.md b/src/domain-theory/omega-complete-posets.lagda.md index cbae88df54..612e60affb 100644 --- a/src/domain-theory/omega-complete-posets.lagda.md +++ b/src/domain-theory/omega-complete-posets.lagda.md @@ -1,34 +1,29 @@ # ω-Complete posets ```agda -open import foundation.function-extensionality-axiom - -module - domain-theory.omega-complete-posets - (funext : function-extensionality) - where +module domain-theory.omega-complete-posets where ```
Imports ```agda -open import elementary-number-theory.decidable-total-order-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.decidable-total-order-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext -open import order-theory.upper-bounds-posets funext +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.posets +open import order-theory.upper-bounds-posets ```
diff --git a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md index 36d6a284bf..60ce16827f 100644 --- a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md @@ -1,48 +1,43 @@ # ω-Continuous maps between ω-complete posets ```agda -open import foundation.function-extensionality-axiom - -module - domain-theory.omega-continuous-maps-omega-complete-posets - (funext : function-extensionality) - where +module domain-theory.omega-continuous-maps-omega-complete-posets where ```
Imports ```agda -open import domain-theory.directed-families-posets funext -open import domain-theory.omega-complete-posets funext -open import domain-theory.omega-continuous-maps-posets funext +open import domain-theory.directed-families-posets +open import domain-theory.omega-complete-posets +open import domain-theory.omega-continuous-maps-posets -open import elementary-number-theory.decidable-total-order-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.decidable-total-order-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.booleans funext +open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.evaluation-functions -open import foundation.existential-quantification funext -open import foundation.function-types funext +open import foundation.existential-quantification +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle -open import foundation.surjective-maps funext -open import foundation.torsorial-type-families funext +open import foundation.surjective-maps +open import foundation.torsorial-type-families open import foundation.universe-levels -open import order-theory.join-preserving-maps-posets funext -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.join-preserving-maps-posets +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/domain-theory/omega-continuous-maps-posets.lagda.md b/src/domain-theory/omega-continuous-maps-posets.lagda.md index 179bdc67fd..3781ac426b 100644 --- a/src/domain-theory/omega-continuous-maps-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-posets.lagda.md @@ -1,46 +1,41 @@ # ω-Continuous maps between posets ```agda -open import foundation.function-extensionality-axiom - -module - domain-theory.omega-continuous-maps-posets - (funext : function-extensionality) - where +module domain-theory.omega-continuous-maps-posets where ```
Imports ```agda -open import domain-theory.directed-families-posets funext +open import domain-theory.directed-families-posets -open import elementary-number-theory.decidable-total-order-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.decidable-total-order-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.booleans funext +open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.evaluation-functions -open import foundation.existential-quantification funext -open import foundation.function-types funext +open import foundation.existential-quantification +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle -open import foundation.surjective-maps funext -open import foundation.torsorial-type-families funext +open import foundation.surjective-maps +open import foundation.torsorial-type-families open import foundation.universe-levels -open import order-theory.join-preserving-maps-posets funext -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.join-preserving-maps-posets +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/domain-theory/reindexing-directed-families-posets.lagda.md b/src/domain-theory/reindexing-directed-families-posets.lagda.md index 6484b0d608..28396bf30a 100644 --- a/src/domain-theory/reindexing-directed-families-posets.lagda.md +++ b/src/domain-theory/reindexing-directed-families-posets.lagda.md @@ -1,36 +1,31 @@ # Reindexing directed families in posets ```agda -open import foundation.function-extensionality-axiom - -module - domain-theory.reindexing-directed-families-posets - (funext : function-extensionality) - where +module domain-theory.reindexing-directed-families-posets where ```
Imports ```agda -open import domain-theory.directed-families-posets funext +open import domain-theory.directed-families-posets open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext +open import foundation.cartesian-product-types +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.surjective-maps funext -open import foundation.universal-quantification funext +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.surjective-maps +open import foundation.universal-quantification open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/domain-theory/scott-continuous-maps-posets.lagda.md b/src/domain-theory/scott-continuous-maps-posets.lagda.md index bc2908bab3..bd50ff479e 100644 --- a/src/domain-theory/scott-continuous-maps-posets.lagda.md +++ b/src/domain-theory/scott-continuous-maps-posets.lagda.md @@ -1,43 +1,38 @@ # Scott-continuous maps between posets ```agda -open import foundation.function-extensionality-axiom - -module - domain-theory.scott-continuous-maps-posets - (funext : function-extensionality) - where +module domain-theory.scott-continuous-maps-posets where ```
Imports ```agda -open import domain-theory.directed-families-posets funext -open import domain-theory.reindexing-directed-families-posets funext +open import domain-theory.directed-families-posets +open import domain-theory.reindexing-directed-families-posets -open import foundation.booleans funext +open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.evaluation-functions -open import foundation.existential-quantification funext -open import foundation.function-types funext +open import foundation.existential-quantification +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.small-types funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.small-types +open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle -open import foundation.surjective-maps funext -open import foundation.torsorial-type-families funext +open import foundation.surjective-maps +open import foundation.torsorial-type-families open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/elementary-number-theory.lagda.md b/src/elementary-number-theory.lagda.md index a7cd00c920..11611b1a6a 100644 --- a/src/elementary-number-theory.lagda.md +++ b/src/elementary-number-theory.lagda.md @@ -7,185 +7,180 @@ ## Modules in the elementary number theory namespace ```agda -open import foundation.function-extensionality-axiom +module elementary-number-theory where -module - elementary-number-theory - (funext : function-extensionality) - where - -open import elementary-number-theory.absolute-value-integers funext public +open import elementary-number-theory.absolute-value-integers public open import elementary-number-theory.ackermann-function public -open import elementary-number-theory.addition-integer-fractions funext public -open import elementary-number-theory.addition-integers funext public +open import elementary-number-theory.addition-integer-fractions public +open import elementary-number-theory.addition-integers public open import elementary-number-theory.addition-natural-numbers public -open import elementary-number-theory.addition-positive-and-negative-integers funext public -open import elementary-number-theory.addition-rational-numbers funext public -open import elementary-number-theory.additive-group-of-rational-numbers funext public -open import elementary-number-theory.archimedean-property-integer-fractions funext public -open import elementary-number-theory.archimedean-property-integers funext public -open import elementary-number-theory.archimedean-property-natural-numbers funext public -open import elementary-number-theory.archimedean-property-positive-rational-numbers funext public -open import elementary-number-theory.archimedean-property-rational-numbers funext public -open import elementary-number-theory.arithmetic-functions funext public -open import elementary-number-theory.based-induction-natural-numbers funext public -open import elementary-number-theory.based-strong-induction-natural-numbers funext public -open import elementary-number-theory.bell-numbers funext public -open import elementary-number-theory.bezouts-lemma-integers funext public -open import elementary-number-theory.bezouts-lemma-natural-numbers funext public -open import elementary-number-theory.binomial-coefficients funext public -open import elementary-number-theory.binomial-theorem-integers funext public -open import elementary-number-theory.binomial-theorem-natural-numbers funext public -open import elementary-number-theory.bounded-sums-arithmetic-functions funext public -open import elementary-number-theory.catalan-numbers funext public -open import elementary-number-theory.cofibonacci funext public -open import elementary-number-theory.collatz-bijection funext public -open import elementary-number-theory.collatz-conjecture funext public -open import elementary-number-theory.commutative-semiring-of-natural-numbers funext public -open import elementary-number-theory.conatural-numbers funext public -open import elementary-number-theory.congruence-integers funext public -open import elementary-number-theory.congruence-natural-numbers funext public -open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext public -open import elementary-number-theory.cubes-natural-numbers funext public -open import elementary-number-theory.decidable-dependent-function-types funext public -open import elementary-number-theory.decidable-total-order-integers funext public -open import elementary-number-theory.decidable-total-order-natural-numbers funext public -open import elementary-number-theory.decidable-total-order-rational-numbers funext public -open import elementary-number-theory.decidable-total-order-standard-finite-types funext public -open import elementary-number-theory.decidable-types funext public -open import elementary-number-theory.difference-integers funext public -open import elementary-number-theory.difference-rational-numbers funext public -open import elementary-number-theory.dirichlet-convolution funext public -open import elementary-number-theory.distance-integers funext public -open import elementary-number-theory.distance-natural-numbers funext public -open import elementary-number-theory.divisibility-integers funext public -open import elementary-number-theory.divisibility-modular-arithmetic funext public -open import elementary-number-theory.divisibility-natural-numbers funext public -open import elementary-number-theory.divisibility-standard-finite-types funext public -open import elementary-number-theory.equality-conatural-numbers funext public -open import elementary-number-theory.equality-integers funext public -open import elementary-number-theory.equality-natural-numbers funext public -open import elementary-number-theory.equality-rational-numbers funext public -open import elementary-number-theory.euclid-mullin-sequence funext public -open import elementary-number-theory.euclidean-division-natural-numbers funext public -open import elementary-number-theory.eulers-totient-function funext public -open import elementary-number-theory.exponentiation-natural-numbers funext public -open import elementary-number-theory.factorials funext public +open import elementary-number-theory.addition-positive-and-negative-integers public +open import elementary-number-theory.addition-rational-numbers public +open import elementary-number-theory.additive-group-of-rational-numbers public +open import elementary-number-theory.archimedean-property-integer-fractions public +open import elementary-number-theory.archimedean-property-integers public +open import elementary-number-theory.archimedean-property-natural-numbers public +open import elementary-number-theory.archimedean-property-positive-rational-numbers public +open import elementary-number-theory.archimedean-property-rational-numbers public +open import elementary-number-theory.arithmetic-functions public +open import elementary-number-theory.based-induction-natural-numbers public +open import elementary-number-theory.based-strong-induction-natural-numbers public +open import elementary-number-theory.bell-numbers public +open import elementary-number-theory.bezouts-lemma-integers public +open import elementary-number-theory.bezouts-lemma-natural-numbers public +open import elementary-number-theory.binomial-coefficients public +open import elementary-number-theory.binomial-theorem-integers public +open import elementary-number-theory.binomial-theorem-natural-numbers public +open import elementary-number-theory.bounded-sums-arithmetic-functions public +open import elementary-number-theory.catalan-numbers public +open import elementary-number-theory.cofibonacci public +open import elementary-number-theory.collatz-bijection public +open import elementary-number-theory.collatz-conjecture public +open import elementary-number-theory.commutative-semiring-of-natural-numbers public +open import elementary-number-theory.conatural-numbers public +open import elementary-number-theory.congruence-integers public +open import elementary-number-theory.congruence-natural-numbers public +open import elementary-number-theory.cross-multiplication-difference-integer-fractions public +open import elementary-number-theory.cubes-natural-numbers public +open import elementary-number-theory.decidable-dependent-function-types public +open import elementary-number-theory.decidable-total-order-integers public +open import elementary-number-theory.decidable-total-order-natural-numbers public +open import elementary-number-theory.decidable-total-order-rational-numbers public +open import elementary-number-theory.decidable-total-order-standard-finite-types public +open import elementary-number-theory.decidable-types public +open import elementary-number-theory.difference-integers public +open import elementary-number-theory.difference-rational-numbers public +open import elementary-number-theory.dirichlet-convolution public +open import elementary-number-theory.distance-integers public +open import elementary-number-theory.distance-natural-numbers public +open import elementary-number-theory.divisibility-integers public +open import elementary-number-theory.divisibility-modular-arithmetic public +open import elementary-number-theory.divisibility-natural-numbers public +open import elementary-number-theory.divisibility-standard-finite-types public +open import elementary-number-theory.equality-conatural-numbers public +open import elementary-number-theory.equality-integers public +open import elementary-number-theory.equality-natural-numbers public +open import elementary-number-theory.equality-rational-numbers public +open import elementary-number-theory.euclid-mullin-sequence public +open import elementary-number-theory.euclidean-division-natural-numbers public +open import elementary-number-theory.eulers-totient-function public +open import elementary-number-theory.exponentiation-natural-numbers public +open import elementary-number-theory.factorials public open import elementary-number-theory.falling-factorials public -open import elementary-number-theory.fermat-numbers funext public -open import elementary-number-theory.fibonacci-sequence funext public -open import elementary-number-theory.field-of-rational-numbers funext public -open import elementary-number-theory.finitary-natural-numbers funext public -open import elementary-number-theory.finitely-cyclic-maps funext public -open import elementary-number-theory.fundamental-theorem-of-arithmetic funext public -open import elementary-number-theory.goldbach-conjecture funext public -open import elementary-number-theory.greatest-common-divisor-integers funext public -open import elementary-number-theory.greatest-common-divisor-natural-numbers funext public -open import elementary-number-theory.group-of-integers funext public -open import elementary-number-theory.half-integers funext public -open import elementary-number-theory.hardy-ramanujan-number funext public -open import elementary-number-theory.inclusion-natural-numbers-conatural-numbers funext public -open import elementary-number-theory.inequality-conatural-numbers funext public -open import elementary-number-theory.inequality-integer-fractions funext public -open import elementary-number-theory.inequality-integers funext public -open import elementary-number-theory.inequality-natural-numbers funext public -open import elementary-number-theory.inequality-rational-numbers funext public -open import elementary-number-theory.inequality-standard-finite-types funext public -open import elementary-number-theory.infinite-conatural-numbers funext public -open import elementary-number-theory.infinitude-of-primes funext public -open import elementary-number-theory.initial-segments-natural-numbers funext public -open import elementary-number-theory.integer-fractions funext public +open import elementary-number-theory.fermat-numbers public +open import elementary-number-theory.fibonacci-sequence public +open import elementary-number-theory.field-of-rational-numbers public +open import elementary-number-theory.finitary-natural-numbers public +open import elementary-number-theory.finitely-cyclic-maps public +open import elementary-number-theory.fundamental-theorem-of-arithmetic public +open import elementary-number-theory.goldbach-conjecture public +open import elementary-number-theory.greatest-common-divisor-integers public +open import elementary-number-theory.greatest-common-divisor-natural-numbers public +open import elementary-number-theory.group-of-integers public +open import elementary-number-theory.half-integers public +open import elementary-number-theory.hardy-ramanujan-number public +open import elementary-number-theory.inclusion-natural-numbers-conatural-numbers public +open import elementary-number-theory.inequality-conatural-numbers public +open import elementary-number-theory.inequality-integer-fractions public +open import elementary-number-theory.inequality-integers public +open import elementary-number-theory.inequality-natural-numbers public +open import elementary-number-theory.inequality-rational-numbers public +open import elementary-number-theory.inequality-standard-finite-types public +open import elementary-number-theory.infinite-conatural-numbers public +open import elementary-number-theory.infinitude-of-primes public +open import elementary-number-theory.initial-segments-natural-numbers public +open import elementary-number-theory.integer-fractions public open import elementary-number-theory.integer-partitions public open import elementary-number-theory.integers public -open import elementary-number-theory.jacobi-symbol funext public -open import elementary-number-theory.kolakoski-sequence funext public -open import elementary-number-theory.legendre-symbol funext public -open import elementary-number-theory.lower-bounds-natural-numbers funext public -open import elementary-number-theory.maximum-natural-numbers funext public -open import elementary-number-theory.maximum-standard-finite-types funext public -open import elementary-number-theory.mediant-integer-fractions funext public -open import elementary-number-theory.mersenne-primes funext public -open import elementary-number-theory.minimum-natural-numbers funext public -open import elementary-number-theory.minimum-standard-finite-types funext public -open import elementary-number-theory.modular-arithmetic funext public -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext public -open import elementary-number-theory.monoid-of-natural-numbers-with-addition funext public -open import elementary-number-theory.monoid-of-natural-numbers-with-maximum funext public -open import elementary-number-theory.multiplication-integer-fractions funext public -open import elementary-number-theory.multiplication-integers funext public -open import elementary-number-theory.multiplication-lists-of-natural-numbers funext public +open import elementary-number-theory.jacobi-symbol public +open import elementary-number-theory.kolakoski-sequence public +open import elementary-number-theory.legendre-symbol public +open import elementary-number-theory.lower-bounds-natural-numbers public +open import elementary-number-theory.maximum-natural-numbers public +open import elementary-number-theory.maximum-standard-finite-types public +open import elementary-number-theory.mediant-integer-fractions public +open import elementary-number-theory.mersenne-primes public +open import elementary-number-theory.minimum-natural-numbers public +open import elementary-number-theory.minimum-standard-finite-types public +open import elementary-number-theory.modular-arithmetic public +open import elementary-number-theory.modular-arithmetic-standard-finite-types public +open import elementary-number-theory.monoid-of-natural-numbers-with-addition public +open import elementary-number-theory.monoid-of-natural-numbers-with-maximum public +open import elementary-number-theory.multiplication-integer-fractions public +open import elementary-number-theory.multiplication-integers public +open import elementary-number-theory.multiplication-lists-of-natural-numbers public open import elementary-number-theory.multiplication-natural-numbers public -open import elementary-number-theory.multiplication-positive-and-negative-integers funext public -open import elementary-number-theory.multiplication-rational-numbers funext public -open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers funext public -open import elementary-number-theory.multiplicative-group-of-rational-numbers funext public -open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions funext public -open import elementary-number-theory.multiplicative-monoid-of-natural-numbers funext public -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext public +open import elementary-number-theory.multiplication-positive-and-negative-integers public +open import elementary-number-theory.multiplication-rational-numbers public +open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers public +open import elementary-number-theory.multiplicative-group-of-rational-numbers public +open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions public +open import elementary-number-theory.multiplicative-monoid-of-natural-numbers public +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers public open import elementary-number-theory.multiplicative-units-integers public open import elementary-number-theory.multiplicative-units-standard-cyclic-rings public open import elementary-number-theory.multiset-coefficients public open import elementary-number-theory.natural-numbers public -open import elementary-number-theory.negative-integers funext public -open import elementary-number-theory.nonnegative-integers funext public -open import elementary-number-theory.nonpositive-integers funext public -open import elementary-number-theory.nonzero-integers funext public -open import elementary-number-theory.nonzero-natural-numbers funext public -open import elementary-number-theory.nonzero-rational-numbers funext public -open import elementary-number-theory.ordinal-induction-natural-numbers funext public -open import elementary-number-theory.parity-natural-numbers funext public -open import elementary-number-theory.peano-arithmetic funext public -open import elementary-number-theory.pisano-periods funext public -open import elementary-number-theory.poset-of-natural-numbers-ordered-by-divisibility funext public -open import elementary-number-theory.positive-and-negative-integers funext public -open import elementary-number-theory.positive-conatural-numbers funext public -open import elementary-number-theory.positive-integer-fractions funext public -open import elementary-number-theory.positive-integers funext public -open import elementary-number-theory.positive-rational-numbers funext public -open import elementary-number-theory.powers-integers funext public -open import elementary-number-theory.powers-of-two funext public -open import elementary-number-theory.prime-numbers funext public -open import elementary-number-theory.products-of-natural-numbers funext public -open import elementary-number-theory.proper-divisors-natural-numbers funext public -open import elementary-number-theory.pythagorean-triples funext public -open import elementary-number-theory.rational-numbers funext public -open import elementary-number-theory.reduced-integer-fractions funext public -open import elementary-number-theory.relatively-prime-integers funext public -open import elementary-number-theory.relatively-prime-natural-numbers funext public -open import elementary-number-theory.repeating-element-standard-finite-type funext public -open import elementary-number-theory.retracts-of-natural-numbers funext public -open import elementary-number-theory.ring-of-integers funext public -open import elementary-number-theory.ring-of-rational-numbers funext public -open import elementary-number-theory.sieve-of-eratosthenes funext public -open import elementary-number-theory.square-free-natural-numbers funext public -open import elementary-number-theory.squares-integers funext public -open import elementary-number-theory.squares-modular-arithmetic funext public -open import elementary-number-theory.squares-natural-numbers funext public -open import elementary-number-theory.standard-cyclic-groups funext public -open import elementary-number-theory.standard-cyclic-rings funext public +open import elementary-number-theory.negative-integers public +open import elementary-number-theory.nonnegative-integers public +open import elementary-number-theory.nonpositive-integers public +open import elementary-number-theory.nonzero-integers public +open import elementary-number-theory.nonzero-natural-numbers public +open import elementary-number-theory.nonzero-rational-numbers public +open import elementary-number-theory.ordinal-induction-natural-numbers public +open import elementary-number-theory.parity-natural-numbers public +open import elementary-number-theory.peano-arithmetic public +open import elementary-number-theory.pisano-periods public +open import elementary-number-theory.poset-of-natural-numbers-ordered-by-divisibility public +open import elementary-number-theory.positive-and-negative-integers public +open import elementary-number-theory.positive-conatural-numbers public +open import elementary-number-theory.positive-integer-fractions public +open import elementary-number-theory.positive-integers public +open import elementary-number-theory.positive-rational-numbers public +open import elementary-number-theory.powers-integers public +open import elementary-number-theory.powers-of-two public +open import elementary-number-theory.prime-numbers public +open import elementary-number-theory.products-of-natural-numbers public +open import elementary-number-theory.proper-divisors-natural-numbers public +open import elementary-number-theory.pythagorean-triples public +open import elementary-number-theory.rational-numbers public +open import elementary-number-theory.reduced-integer-fractions public +open import elementary-number-theory.relatively-prime-integers public +open import elementary-number-theory.relatively-prime-natural-numbers public +open import elementary-number-theory.repeating-element-standard-finite-type public +open import elementary-number-theory.retracts-of-natural-numbers public +open import elementary-number-theory.ring-of-integers public +open import elementary-number-theory.ring-of-rational-numbers public +open import elementary-number-theory.sieve-of-eratosthenes public +open import elementary-number-theory.square-free-natural-numbers public +open import elementary-number-theory.squares-integers public +open import elementary-number-theory.squares-modular-arithmetic public +open import elementary-number-theory.squares-natural-numbers public +open import elementary-number-theory.standard-cyclic-groups public +open import elementary-number-theory.standard-cyclic-rings public open import elementary-number-theory.stirling-numbers-of-the-second-kind public -open import elementary-number-theory.strict-inequality-integer-fractions funext public -open import elementary-number-theory.strict-inequality-integers funext public -open import elementary-number-theory.strict-inequality-natural-numbers funext public -open import elementary-number-theory.strict-inequality-rational-numbers funext public -open import elementary-number-theory.strict-inequality-standard-finite-types funext public -open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers funext public -open import elementary-number-theory.strong-induction-natural-numbers funext public -open import elementary-number-theory.sums-of-natural-numbers funext public -open import elementary-number-theory.sylvesters-sequence funext public -open import elementary-number-theory.taxicab-numbers funext public +open import elementary-number-theory.strict-inequality-integer-fractions public +open import elementary-number-theory.strict-inequality-integers public +open import elementary-number-theory.strict-inequality-natural-numbers public +open import elementary-number-theory.strict-inequality-rational-numbers public +open import elementary-number-theory.strict-inequality-standard-finite-types public +open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers public +open import elementary-number-theory.strong-induction-natural-numbers public +open import elementary-number-theory.sums-of-natural-numbers public +open import elementary-number-theory.sylvesters-sequence public +open import elementary-number-theory.taxicab-numbers public open import elementary-number-theory.telephone-numbers public open import elementary-number-theory.triangular-numbers public -open import elementary-number-theory.twin-prime-conjecture funext public -open import elementary-number-theory.type-arithmetic-natural-numbers funext public -open import elementary-number-theory.unit-elements-standard-finite-types funext public -open import elementary-number-theory.unit-fractions-rational-numbers funext public -open import elementary-number-theory.unit-similarity-standard-finite-types funext public -open import elementary-number-theory.universal-property-conatural-numbers funext public -open import elementary-number-theory.universal-property-integers funext public -open import elementary-number-theory.universal-property-natural-numbers funext public -open import elementary-number-theory.upper-bounds-natural-numbers funext public -open import elementary-number-theory.well-ordering-principle-natural-numbers funext public -open import elementary-number-theory.well-ordering-principle-standard-finite-types funext public -open import elementary-number-theory.zero-conatural-numbers funext public +open import elementary-number-theory.twin-prime-conjecture public +open import elementary-number-theory.type-arithmetic-natural-numbers public +open import elementary-number-theory.unit-elements-standard-finite-types public +open import elementary-number-theory.unit-fractions-rational-numbers public +open import elementary-number-theory.unit-similarity-standard-finite-types public +open import elementary-number-theory.universal-property-conatural-numbers public +open import elementary-number-theory.universal-property-integers public +open import elementary-number-theory.universal-property-natural-numbers public +open import elementary-number-theory.upper-bounds-natural-numbers public +open import elementary-number-theory.well-ordering-principle-natural-numbers public +open import elementary-number-theory.well-ordering-principle-standard-finite-types public +open import elementary-number-theory.zero-conatural-numbers public ``` diff --git a/src/elementary-number-theory/absolute-value-integers.lagda.md b/src/elementary-number-theory/absolute-value-integers.lagda.md index d179466116..59455c73a5 100644 --- a/src/elementary-number-theory/absolute-value-integers.lagda.md +++ b/src/elementary-number-theory/absolute-value-integers.lagda.md @@ -1,31 +1,26 @@ # The absolute value function on the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.absolute-value-integers - (funext : function-extensionality) - where +module elementary-number-theory.absolute-value-integers where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.positive-integers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.coproduct-types +open import foundation.function-types +open import foundation.identity-types open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/addition-integer-fractions.lagda.md b/src/elementary-number-theory/addition-integer-fractions.lagda.md index 0facabd85a..2ae01f48aa 100644 --- a/src/elementary-number-theory/addition-integer-fractions.lagda.md +++ b/src/elementary-number-theory/addition-integer-fractions.lagda.md @@ -1,27 +1,22 @@ # Addition on integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.addition-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.addition-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types ```
diff --git a/src/elementary-number-theory/addition-integers.lagda.md b/src/elementary-number-theory/addition-integers.lagda.md index 65ecc00ed3..0074401613 100644 --- a/src/elementary-number-theory/addition-integers.lagda.md +++ b/src/elementary-number-theory/addition-integers.lagda.md @@ -1,12 +1,7 @@ # Addition on the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.addition-integers - (funext : function-extensionality) - where +module elementary-number-theory.addition-integers where ```
Imports @@ -15,23 +10,23 @@ module open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps open import foundation.interchange-law -open import foundation.sets funext +open import foundation.sets open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md b/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md index 70506f226a..cc38778380 100644 --- a/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md +++ b/src/elementary-number-theory/addition-positive-and-negative-integers.lagda.md @@ -1,31 +1,26 @@ # Addition of positive, negative, nonnegative and nonpositive integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.addition-positive-and-negative-integers - (funext : function-extensionality) - where +module elementary-number-theory.addition-positive-and-negative-integers where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers funext -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.nonpositive-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.negative-integers +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonpositive-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/addition-rational-numbers.lagda.md b/src/elementary-number-theory/addition-rational-numbers.lagda.md index 622b9859c3..4bd4afc3d5 100644 --- a/src/elementary-number-theory/addition-rational-numbers.lagda.md +++ b/src/elementary-number-theory/addition-rational-numbers.lagda.md @@ -3,33 +3,28 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.addition-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.addition-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions funext -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-integer-fractions +open import elementary-number-theory.addition-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.reduced-integer-fractions funext +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.reduced-integer-fractions open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps open import foundation.interchange-law -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.retractions +open import foundation.sections ```
diff --git a/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md b/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md index 12d33ba91a..60aeaf1fb9 100644 --- a/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/additive-group-of-rational-numbers.lagda.md @@ -3,28 +3,23 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.additive-group-of-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.additive-group-of-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.rational-numbers open import foundation.dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md b/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md index c531f3ceaf..c28ab250d1 100644 --- a/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md +++ b/src/elementary-number-theory/archimedean-property-integer-fractions.lagda.md @@ -3,32 +3,27 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.archimedean-property-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.archimedean-property-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.archimedean-property-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions funext -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.multiplication-integer-fractions +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.positive-integer-fractions funext -open import elementary-number-theory.strict-inequality-integer-fractions funext -open import elementary-number-theory.strict-inequality-integers funext +open import elementary-number-theory.positive-integer-fractions +open import elementary-number-theory.strict-inequality-integer-fractions +open import elementary-number-theory.strict-inequality-integers open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/archimedean-property-integers.lagda.md b/src/elementary-number-theory/archimedean-property-integers.lagda.md index 41b8505179..21e49492ed 100644 --- a/src/elementary-number-theory/archimedean-property-integers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-integers.lagda.md @@ -1,35 +1,30 @@ # The Archimedean property of the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.archimedean-property-integers - (funext : function-extensionality) - where +module elementary-number-theory.archimedean-property-integers where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-natural-numbers funext +open import elementary-number-theory.archimedean-property-natural-numbers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.strict-inequality-integers funext +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.strict-inequality-integers open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations ```
diff --git a/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md index 2659b1e7f2..a24fbc0a07 100644 --- a/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-natural-numbers.lagda.md @@ -1,25 +1,20 @@ # The Archimedean property of the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.archimedean-property-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.archimedean-property-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.euclidean-division-natural-numbers funext +open import elementary-number-theory.euclidean-division-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.propositional-truncations open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md index 6749dad688..0a61a1bf8e 100644 --- a/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-positive-rational-numbers.lagda.md @@ -3,31 +3,26 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.archimedean-property-positive-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.archimedean-property-positive-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-rational-numbers funext +open import elementary-number-theory.archimedean-property-rational-numbers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-rational-numbers funext +open import elementary-number-theory.multiplication-rational-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers funext -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md b/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md index 131ed344b4..dc4fd7b441 100644 --- a/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md +++ b/src/elementary-number-theory/archimedean-property-rational-numbers.lagda.md @@ -3,33 +3,28 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.archimedean-property-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.archimedean-property-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-integer-fractions funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.archimedean-property-integer-fractions +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions funext -open import elementary-number-theory.multiplication-rational-numbers funext +open import elementary-number-theory.multiplication-integer-fractions +open import elementary-number-theory.multiplication-rational-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-binary-functions open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations ```
diff --git a/src/elementary-number-theory/arithmetic-functions.lagda.md b/src/elementary-number-theory/arithmetic-functions.lagda.md index 58c0a70549..291d7d48e5 100644 --- a/src/elementary-number-theory/arithmetic-functions.lagda.md +++ b/src/elementary-number-theory/arithmetic-functions.lagda.md @@ -1,22 +1,17 @@ # Arithmetic functions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.arithmetic-functions - (funext : function-extensionality) - where +module elementary-number-theory.arithmetic-functions where ```
Imports ```agda -open import elementary-number-theory.nonzero-natural-numbers funext +open import elementary-number-theory.nonzero-natural-numbers open import foundation.universe-levels -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/elementary-number-theory/based-induction-natural-numbers.lagda.md b/src/elementary-number-theory/based-induction-natural-numbers.lagda.md index 72ed796b19..04b3c569a4 100644 --- a/src/elementary-number-theory/based-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/based-induction-natural-numbers.lagda.md @@ -1,22 +1,17 @@ # The based induction principle of the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.based-induction-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.based-induction-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md index 0aa8cdeb28..d355c01418 100644 --- a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md @@ -1,32 +1,27 @@ # Based strong induction for the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.based-strong-induction-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.based-strong-induction-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.based-induction-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.based-induction-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.empty-types funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.universal-property-contractible-types funext +open import foundation.coproduct-types +open import foundation.empty-types +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.universal-property-contractible-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/bell-numbers.lagda.md b/src/elementary-number-theory/bell-numbers.lagda.md index 116971dd11..d824cdd82b 100644 --- a/src/elementary-number-theory/bell-numbers.lagda.md +++ b/src/elementary-number-theory/bell-numbers.lagda.md @@ -1,23 +1,18 @@ # The Bell numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.bell-numbers - (funext : function-extensionality) - where +module elementary-number-theory.bell-numbers where ```
Imports ```agda -open import elementary-number-theory.binomial-coefficients funext +open import elementary-number-theory.binomial-coefficients open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.strong-induction-natural-numbers funext -open import elementary-number-theory.sums-of-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.sums-of-natural-numbers ```
diff --git a/src/elementary-number-theory/bezouts-lemma-integers.lagda.md b/src/elementary-number-theory/bezouts-lemma-integers.lagda.md index ee8aba77b9..1b169fb860 100644 --- a/src/elementary-number-theory/bezouts-lemma-integers.lagda.md +++ b/src/elementary-number-theory/bezouts-lemma-integers.lagda.md @@ -1,42 +1,37 @@ # Bezout's lemma in the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.bezouts-lemma-integers - (funext : function-extensionality) - where +module elementary-number-theory.bezouts-lemma-integers where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers funext -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.addition-integers open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.bezouts-lemma-natural-numbers funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.distance-integers funext -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.divisibility-integers funext -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.greatest-common-divisor-integers funext -open import elementary-number-theory.greatest-common-divisor-natural-numbers funext +open import elementary-number-theory.bezouts-lemma-natural-numbers +open import elementary-number-theory.difference-integers +open import elementary-number-theory.distance-integers +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.divisibility-integers +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.greatest-common-divisor-integers +open import elementary-number-theory.greatest-common-divisor-natural-numbers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md b/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md index a72e10aea8..681142d4bb 100755 --- a/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md +++ b/src/elementary-number-theory/bezouts-lemma-natural-numbers.lagda.md @@ -1,54 +1,49 @@ # Bezout's lemma on the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.bezouts-lemma-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.bezouts-lemma-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers funext -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.addition-integers open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-integers funext -open import elementary-number-theory.distance-integers funext -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.divisibility-modular-arithmetic funext -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.euclidean-division-natural-numbers funext -open import elementary-number-theory.greatest-common-divisor-natural-numbers funext -open import elementary-number-theory.inequality-integers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.congruence-integers +open import elementary-number-theory.distance-integers +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.divisibility-modular-arithmetic +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.euclidean-division-natural-numbers +open import elementary-number-theory.greatest-common-divisor-natural-numbers +open import elementary-number-theory.inequality-integers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.integers -open import elementary-number-theory.lower-bounds-natural-numbers funext -open import elementary-number-theory.modular-arithmetic funext -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.multiplication-positive-and-negative-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.well-ordering-principle-natural-numbers funext +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.well-ordering-principle-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.negation funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.negation open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/binomial-coefficients.lagda.md b/src/elementary-number-theory/binomial-coefficients.lagda.md index 9170cca111..655ad9e203 100644 --- a/src/elementary-number-theory/binomial-coefficients.lagda.md +++ b/src/elementary-number-theory/binomial-coefficients.lagda.md @@ -1,35 +1,30 @@ # The binomial coefficients ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.binomial-coefficients - (funext : function-extensionality) - where +module elementary-number-theory.binomial-coefficients where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.commutative-semiring-of-natural-numbers funext -open import elementary-number-theory.factorials funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.commutative-semiring-of-natural-numbers +open import elementary-number-theory.factorials +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.identity-types -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/binomial-theorem-integers.lagda.md b/src/elementary-number-theory/binomial-theorem-integers.lagda.md index ca4be4bd7b..ec01e91220 100644 --- a/src/elementary-number-theory/binomial-theorem-integers.lagda.md +++ b/src/elementary-number-theory/binomial-theorem-integers.lagda.md @@ -1,33 +1,28 @@ # The binomial theorem for the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.binomial-theorem-integers - (funext : function-extensionality) - where +module elementary-number-theory.binomial-theorem-integers where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-rings funext +open import commutative-algebra.binomial-theorem-commutative-rings -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.distance-natural-numbers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.powers-integers funext -open import elementary-number-theory.ring-of-integers funext +open import elementary-number-theory.powers-integers +open import elementary-number-theory.ring-of-integers -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md b/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md index f1d115118f..08f650294f 100644 --- a/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md +++ b/src/elementary-number-theory/binomial-theorem-natural-numbers.lagda.md @@ -1,32 +1,27 @@ # The binomial theorem for the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.binomial-theorem-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.binomial-theorem-natural-numbers where ```
Imports ```agda -open import commutative-algebra.binomial-theorem-commutative-semirings funext +open import commutative-algebra.binomial-theorem-commutative-semirings open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.commutative-semiring-of-natural-numbers funext -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.exponentiation-natural-numbers funext +open import elementary-number-theory.commutative-semiring-of-natural-numbers +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md b/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md index 9ddaf4ed0b..7e513fd97a 100644 --- a/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md +++ b/src/elementary-number-theory/bounded-sums-arithmetic-functions.lagda.md @@ -1,28 +1,23 @@ # Bounded sums of arithmetic functions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.bounded-sums-arithmetic-functions - (funext : function-extensionality) - where +module elementary-number-theory.bounded-sums-arithmetic-functions where ```
Imports ```agda -open import elementary-number-theory.arithmetic-functions funext +open import elementary-number-theory.arithmetic-functions open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers funext +open import elementary-number-theory.nonzero-natural-numbers -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext -open import foundation.function-types funext +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types +open import foundation.function-types open import foundation.universe-levels -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/elementary-number-theory/catalan-numbers.lagda.md b/src/elementary-number-theory/catalan-numbers.lagda.md index 43cbaf36ac..55257b4c79 100644 --- a/src/elementary-number-theory/catalan-numbers.lagda.md +++ b/src/elementary-number-theory/catalan-numbers.lagda.md @@ -1,26 +1,21 @@ # Catalan numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.catalan-numbers - (funext : function-extensionality) - where +module elementary-number-theory.catalan-numbers where ```
Imports ```agda -open import elementary-number-theory.binomial-coefficients funext -open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.binomial-coefficients +open import elementary-number-theory.distance-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.strong-induction-natural-numbers funext -open import elementary-number-theory.sums-of-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strong-induction-natural-numbers +open import elementary-number-theory.sums-of-natural-numbers -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/cofibonacci.lagda.md b/src/elementary-number-theory/cofibonacci.lagda.md index 18cc9c5dfc..e2a6f001ba 100644 --- a/src/elementary-number-theory/cofibonacci.lagda.md +++ b/src/elementary-number-theory/cofibonacci.lagda.md @@ -1,32 +1,27 @@ # The cofibonacci sequence ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.cofibonacci - (funext : function-extensionality) - where +module elementary-number-theory.cofibonacci where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.fibonacci-sequence funext -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.fibonacci-sequence +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.pisano-periods funext -open import elementary-number-theory.well-ordering-principle-natural-numbers funext +open import elementary-number-theory.pisano-periods +open import elementary-number-theory.well-ordering-principle-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/collatz-bijection.lagda.md b/src/elementary-number-theory/collatz-bijection.lagda.md index 0c1fd19602..8e734174e5 100644 --- a/src/elementary-number-theory/collatz-bijection.lagda.md +++ b/src/elementary-number-theory/collatz-bijection.lagda.md @@ -1,25 +1,20 @@ # The Collatz bijection ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.collatz-bijection - (funext : function-extensionality) - where +module elementary-number-theory.collatz-bijection where ```
Imports ```agda -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.euclidean-division-natural-numbers funext -open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.euclidean-division-natural-numbers +open import elementary-number-theory.modular-arithmetic open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext -open import foundation.identity-types funext +open import foundation.coproduct-types +open import foundation.identity-types ```
diff --git a/src/elementary-number-theory/collatz-conjecture.lagda.md b/src/elementary-number-theory/collatz-conjecture.lagda.md index dbc5791c1c..9c44a48d71 100644 --- a/src/elementary-number-theory/collatz-conjecture.lagda.md +++ b/src/elementary-number-theory/collatz-conjecture.lagda.md @@ -1,22 +1,17 @@ # The Collatz conjecture ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.collatz-conjecture - (funext : function-extensionality) - where +module elementary-number-theory.collatz-conjecture where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md b/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md index 20b714eb16..45f3324d10 100644 --- a/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/commutative-semiring-of-natural-numbers.lagda.md @@ -1,26 +1,21 @@ # The commutative semiring of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.commutative-semiring-of-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.commutative-semiring-of-natural-numbers where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings -open import elementary-number-theory.monoid-of-natural-numbers-with-addition funext +open import elementary-number-theory.monoid-of-natural-numbers-with-addition open import elementary-number-theory.multiplication-natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/elementary-number-theory/conatural-numbers.lagda.md b/src/elementary-number-theory/conatural-numbers.lagda.md index 9eeb51c23d..54310d096a 100644 --- a/src/elementary-number-theory/conatural-numbers.lagda.md +++ b/src/elementary-number-theory/conatural-numbers.lagda.md @@ -3,25 +3,20 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.conatural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.conatural-numbers where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.homotopies +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.retractions +open import foundation.sections open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/congruence-integers.lagda.md b/src/elementary-number-theory/congruence-integers.lagda.md index d35036bd44..9844348d01 100644 --- a/src/elementary-number-theory/congruence-integers.lagda.md +++ b/src/elementary-number-theory/congruence-integers.lagda.md @@ -1,32 +1,27 @@ # The congruence relations on the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.congruence-integers - (funext : function-extensionality) - where +module elementary-number-theory.congruence-integers where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers funext -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.distance-integers funext -open import elementary-number-theory.divisibility-integers funext +open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.addition-integers +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.difference-integers +open import elementary-number-theory.distance-integers +open import elementary-number-theory.divisibility-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/congruence-natural-numbers.lagda.md b/src/elementary-number-theory/congruence-natural-numbers.lagda.md index 97d78b729b..d4c0ff60a4 100644 --- a/src/elementary-number-theory/congruence-natural-numbers.lagda.md +++ b/src/elementary-number-theory/congruence-natural-numbers.lagda.md @@ -1,33 +1,28 @@ # The congruence relations on the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.congruence-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.congruence-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext -open import foundation.coproduct-types funext +open import foundation.binary-relations +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md b/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md index 736039a2bc..38bca51942 100644 --- a/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md +++ b/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md @@ -1,28 +1,23 @@ # The cross-multiplication difference of two integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.cross-multiplication-difference-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.cross-multiplication-difference-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.difference-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions ```
diff --git a/src/elementary-number-theory/cubes-natural-numbers.lagda.md b/src/elementary-number-theory/cubes-natural-numbers.lagda.md index 027f4b150b..491369a597 100644 --- a/src/elementary-number-theory/cubes-natural-numbers.lagda.md +++ b/src/elementary-number-theory/cubes-natural-numbers.lagda.md @@ -1,12 +1,7 @@ # Cubes of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.cubes-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.cubes-natural-numbers where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers funext +open import elementary-number-theory.squares-natural-numbers open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext +open import foundation.fibers-of-maps open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/decidable-dependent-function-types.lagda.md b/src/elementary-number-theory/decidable-dependent-function-types.lagda.md index 93da615aa3..ca2d7fd780 100644 --- a/src/elementary-number-theory/decidable-dependent-function-types.lagda.md +++ b/src/elementary-number-theory/decidable-dependent-function-types.lagda.md @@ -1,14 +1,9 @@ # Decidable dependent function types ```agda -open import foundation.function-extensionality-axiom +module elementary-number-theory.decidable-dependent-function-types where -module - elementary-number-theory.decidable-dependent-function-types - (funext : function-extensionality) - where - -open import foundation.decidable-dependent-function-types funext public +open import foundation.decidable-dependent-function-types public ```
Imports diff --git a/src/elementary-number-theory/decidable-total-order-integers.lagda.md b/src/elementary-number-theory/decidable-total-order-integers.lagda.md index fcc2241128..f4e2772ec7 100644 --- a/src/elementary-number-theory/decidable-total-order-integers.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-integers.lagda.md @@ -1,25 +1,20 @@ # The decidable total order of integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.decidable-total-order-integers - (funext : function-extensionality) - where +module elementary-number-theory.decidable-total-order-integers where ```
Imports ```agda -open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.inequality-integers open import foundation.dependent-pair-types -open import foundation.propositional-truncations funext +open import foundation.propositional-truncations open import foundation.universe-levels -open import order-theory.decidable-total-orders funext -open import order-theory.total-orders funext +open import order-theory.decidable-total-orders +open import order-theory.total-orders ```
diff --git a/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md b/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md index 8517b2c81b..ba6c9d2db7 100644 --- a/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-natural-numbers.lagda.md @@ -1,32 +1,27 @@ # The decidable total order of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.decidable-total-order-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.decidable-total-order-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.propositional-truncations funext +open import foundation.function-types +open import foundation.propositional-truncations open import foundation.unit-type open import foundation.universe-levels -open import order-theory.decidable-total-orders funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.order-preserving-maps-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.total-orders funext +open import order-theory.decidable-total-orders +open import order-theory.order-preserving-maps-posets +open import order-theory.order-preserving-maps-preorders +open import order-theory.posets +open import order-theory.preorders +open import order-theory.total-orders ```
diff --git a/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md b/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md index a0658424a8..3a1b901c63 100644 --- a/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-rational-numbers.lagda.md @@ -1,25 +1,20 @@ # The decidable total order of rational numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.decidable-total-order-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.decidable-total-order-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers open import foundation.dependent-pair-types -open import foundation.propositional-truncations funext +open import foundation.propositional-truncations open import foundation.universe-levels -open import order-theory.decidable-total-orders funext -open import order-theory.total-orders funext +open import order-theory.decidable-total-orders +open import order-theory.total-orders ```
diff --git a/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md b/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md index 528ee3ac94..a33da4e7bb 100644 --- a/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/decidable-total-order-standard-finite-types.lagda.md @@ -1,26 +1,21 @@ # The decidable total order of a standard finite type ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.decidable-total-order-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.decidable-total-order-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.inequality-standard-finite-types open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositional-truncations funext +open import foundation.propositional-truncations open import foundation.universe-levels -open import order-theory.decidable-total-orders funext -open import order-theory.total-orders funext +open import order-theory.decidable-total-orders +open import order-theory.total-orders ```
diff --git a/src/elementary-number-theory/decidable-types.lagda.md b/src/elementary-number-theory/decidable-types.lagda.md index 5857bfabd5..047ada9a91 100644 --- a/src/elementary-number-theory/decidable-types.lagda.md +++ b/src/elementary-number-theory/decidable-types.lagda.md @@ -1,28 +1,23 @@ # Decidable types in elementary number theory ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.decidable-types - (funext : function-extensionality) - where +module elementary-number-theory.decidable-types where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.upper-bounds-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.upper-bounds-natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext +open import foundation.empty-types +open import foundation.function-types open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/difference-integers.lagda.md b/src/elementary-number-theory/difference-integers.lagda.md index e5ade4877e..6cd796526c 100644 --- a/src/elementary-number-theory/difference-integers.lagda.md +++ b/src/elementary-number-theory/difference-integers.lagda.md @@ -1,23 +1,18 @@ # The difference between integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.difference-integers - (funext : function-extensionality) - where +module elementary-number-theory.difference-integers where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.interchange-law ``` diff --git a/src/elementary-number-theory/difference-rational-numbers.lagda.md b/src/elementary-number-theory/difference-rational-numbers.lagda.md index d330660e57..7dbe0779c1 100644 --- a/src/elementary-number-theory/difference-rational-numbers.lagda.md +++ b/src/elementary-number-theory/difference-rational-numbers.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.difference-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.difference-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.rational-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.interchange-law ``` diff --git a/src/elementary-number-theory/dirichlet-convolution.lagda.md b/src/elementary-number-theory/dirichlet-convolution.lagda.md index fd8fb7aa53..0745ebdfe9 100644 --- a/src/elementary-number-theory/dirichlet-convolution.lagda.md +++ b/src/elementary-number-theory/dirichlet-convolution.lagda.md @@ -1,29 +1,24 @@ # Dirichlet convolution ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.dirichlet-convolution - (funext : function-extensionality) - where +module elementary-number-theory.dirichlet-convolution where ```
Imports ```agda -open import elementary-number-theory.arithmetic-functions funext -open import elementary-number-theory.bounded-sums-arithmetic-functions funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.arithmetic-functions +open import elementary-number-theory.bounded-sums-arithmetic-functions +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers funext +open import elementary-number-theory.nonzero-natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/elementary-number-theory/distance-integers.lagda.md b/src/elementary-number-theory/distance-integers.lagda.md index f220847ab9..ee659aed25 100644 --- a/src/elementary-number-theory/distance-integers.lagda.md +++ b/src/elementary-number-theory/distance-integers.lagda.md @@ -1,30 +1,25 @@ # The distance between integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.distance-integers - (funext : function-extensionality) - where +module elementary-number-theory.distance-integers where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.difference-integers +open import elementary-number-theory.distance-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.identity-types funext +open import foundation.coproduct-types +open import foundation.identity-types ```
diff --git a/src/elementary-number-theory/distance-natural-numbers.lagda.md b/src/elementary-number-theory/distance-natural-numbers.lagda.md index c492ecfd41..6026c735da 100644 --- a/src/elementary-number-theory/distance-natural-numbers.lagda.md +++ b/src/elementary-number-theory/distance-natural-numbers.lagda.md @@ -1,29 +1,24 @@ # The distance between natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.distance-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.distance-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/divisibility-integers.lagda.md b/src/elementary-number-theory/divisibility-integers.lagda.md index 95f5d21d39..bed59408c3 100644 --- a/src/elementary-number-theory/divisibility-integers.lagda.md +++ b/src/elementary-number-theory/divisibility-integers.lagda.md @@ -1,42 +1,37 @@ # Divisibility of integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.divisibility-integers - (funext : function-extensionality) - where +module elementary-number-theory.divisibility-integers where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers funext -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.addition-integers +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.nonpositive-integers funext -open import elementary-number-theory.nonzero-integers funext -open import elementary-number-theory.positive-and-negative-integers funext +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonpositive-integers +open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.positive-and-negative-integers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositional-maps funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.negation +open import foundation.propositional-maps +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md b/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md index 880efaa503..6d2a85ab6f 100644 --- a/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md +++ b/src/elementary-number-theory/divisibility-modular-arithmetic.lagda.md @@ -1,29 +1,24 @@ # Divisibility in modular arithmetic ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.divisibility-modular-arithmetic - (funext : function-extensionality) - where +module elementary-number-theory.divisibility-modular-arithmetic where ```
Imports ```agda -open import elementary-number-theory.divisibility-integers funext -open import elementary-number-theory.divisibility-standard-finite-types funext -open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.divisibility-integers +open import elementary-number-theory.divisibility-standard-finite-types +open import elementary-number-theory.modular-arithmetic open import elementary-number-theory.natural-numbers -open import foundation.binary-relations funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.fibers-of-maps funext +open import univalent-combinatorics.fibers-of-maps ```
diff --git a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md index 1058b4042a..a7879e5365 100644 --- a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md +++ b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md @@ -1,38 +1,33 @@ # Divisibility of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.divisibility-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.divisibility-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.logical-equivalences funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-maps funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.logical-equivalences +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-maps +open import foundation.propositions open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md b/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md index f39a9c36f2..0e659d21ac 100644 --- a/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/divisibility-standard-finite-types.lagda.md @@ -1,30 +1,25 @@ # The divisibility relation on the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.divisibility-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.divisibility-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.decidable-dependent-pair-types funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.decidable-dependent-pair-types +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/equality-conatural-numbers.lagda.md b/src/elementary-number-theory/equality-conatural-numbers.lagda.md index 453259bc0a..eb8d842c46 100644 --- a/src/elementary-number-theory/equality-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/equality-conatural-numbers.lagda.md @@ -3,46 +3,41 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.equality-conatural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.equality-conatural-numbers where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers funext +open import elementary-number-theory.conatural-numbers open import foundation.action-on-identifications-functions -open import foundation.coherently-invertible-maps funext -open import foundation.coproduct-types funext +open import foundation.coherently-invertible-maps +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.double-negation funext-stable-equality -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext +open import foundation.double-negation +open import foundation.double-negation-stable-equality +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-coproduct-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negation funext -open import foundation.retractions funext -open import foundation.retracts-of-types funext -open import foundation.sections funext -open import foundation.sets funext -open import foundation.tight-apartness-relations funext -open import foundation.torsorial-type-families funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negation +open import foundation.retractions +open import foundation.retracts-of-types +open import foundation.sections +open import foundation.sets +open import foundation.tight-apartness-relations +open import foundation.torsorial-type-families open import foundation.unit-type open import foundation.universe-levels open import foundation-core.maybe -open import logic.double-negation-elimination funext +open import logic.double-negation-elimination ```
diff --git a/src/elementary-number-theory/equality-integers.lagda.md b/src/elementary-number-theory/equality-integers.lagda.md index 27a164ffea..0ff7538a18 100644 --- a/src/elementary-number-theory/equality-integers.lagda.md +++ b/src/elementary-number-theory/equality-integers.lagda.md @@ -1,37 +1,32 @@ # Equality of integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.equality-integers - (funext : function-extensionality) - where +module elementary-number-theory.equality-integers where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.integers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.discrete-types funext -open import foundation.empty-types funext -open import foundation.equality-coproduct-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.discrete-types +open import foundation.empty-types +open import foundation.equality-coproduct-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.set-truncations funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.set-truncations +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/equality-natural-numbers.lagda.md b/src/elementary-number-theory/equality-natural-numbers.lagda.md index 7403562b0e..bb335e5e58 100644 --- a/src/elementary-number-theory/equality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/equality-natural-numbers.lagda.md @@ -1,12 +1,7 @@ # Equality of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.equality-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.equality-natural-numbers where ```
Imports @@ -15,23 +10,23 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.set-truncations +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.decidable-propositions funext -open import foundation-core.discrete-types funext +open import foundation-core.decidable-propositions +open import foundation-core.discrete-types open import foundation-core.torsorial-type-families ``` diff --git a/src/elementary-number-theory/equality-rational-numbers.lagda.md b/src/elementary-number-theory/equality-rational-numbers.lagda.md index 01f92ec7a6..aaf8ae64f0 100644 --- a/src/elementary-number-theory/equality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/equality-rational-numbers.lagda.md @@ -1,29 +1,24 @@ # Equality of rational numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.equality-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.equality-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.integer-fractions funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.reduced-integer-fractions funext +open import elementary-number-theory.integer-fractions +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.reduced-integer-fractions -open import foundation.decidable-equality funext +open import foundation.decidable-equality open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/euclid-mullin-sequence.lagda.md b/src/elementary-number-theory/euclid-mullin-sequence.lagda.md index 3c4f9bbf82..be53df7a65 100644 --- a/src/elementary-number-theory/euclid-mullin-sequence.lagda.md +++ b/src/elementary-number-theory/euclid-mullin-sequence.lagda.md @@ -1,28 +1,23 @@ # The Euclid–Mullin sequence ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.euclid-mullin-sequence - (funext : function-extensionality) - where +module elementary-number-theory.euclid-mullin-sequence where ```
Imports ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic funext +open import elementary-number-theory.fundamental-theorem-of-arithmetic open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers funext -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.strong-induction-natural-numbers funext +open import elementary-number-theory.products-of-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.strong-induction-natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md b/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md index 18d51a3a30..1ef17f8247 100644 --- a/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md +++ b/src/elementary-number-theory/euclidean-division-natural-numbers.lagda.md @@ -1,32 +1,27 @@ # Euclidean division on the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.euclidean-division-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.euclidean-division-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.identity-types -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/eulers-totient-function.lagda.md b/src/elementary-number-theory/eulers-totient-function.lagda.md index 8870278296..83f8c0970d 100644 --- a/src/elementary-number-theory/eulers-totient-function.lagda.md +++ b/src/elementary-number-theory/eulers-totient-function.lagda.md @@ -1,23 +1,18 @@ # Euler's totient function ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.eulers-totient-function - (funext : function-extensionality) - where +module elementary-number-theory.eulers-totient-function where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.relatively-prime-natural-numbers funext +open import elementary-number-theory.relatively-prime-natural-numbers -open import univalent-combinatorics.decidable-subtypes funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.decidable-subtypes +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md b/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md index cbfbc7dc50..abbf1734ae 100644 --- a/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md +++ b/src/elementary-number-theory/exponentiation-natural-numbers.lagda.md @@ -1,27 +1,22 @@ # Exponentiation of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.exponentiation-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.exponentiation-natural-numbers where ```
Imports ```agda -open import commutative-algebra.powers-of-elements-commutative-semirings funext +open import commutative-algebra.powers-of-elements-commutative-semirings open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.commutative-semiring-of-natural-numbers funext +open import elementary-number-theory.commutative-semiring-of-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers funext +open import elementary-number-theory.products-of-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types ```
diff --git a/src/elementary-number-theory/factorials.lagda.md b/src/elementary-number-theory/factorials.lagda.md index 2a07db5520..05851e426e 100644 --- a/src/elementary-number-theory/factorials.lagda.md +++ b/src/elementary-number-theory/factorials.lagda.md @@ -1,27 +1,22 @@ # Factorials of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.factorials - (funext : function-extensionality) - where +module elementary-number-theory.factorials where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.identity-types ```
diff --git a/src/elementary-number-theory/fermat-numbers.lagda.md b/src/elementary-number-theory/fermat-numbers.lagda.md index e79ab6519b..8a76e9fc21 100644 --- a/src/elementary-number-theory/fermat-numbers.lagda.md +++ b/src/elementary-number-theory/fermat-numbers.lagda.md @@ -1,24 +1,19 @@ # Fermat numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.fermat-numbers - (funext : function-extensionality) - where +module elementary-number-theory.fermat-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers funext +open import elementary-number-theory.exponentiation-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers funext -open import elementary-number-theory.strong-induction-natural-numbers funext +open import elementary-number-theory.products-of-natural-numbers +open import elementary-number-theory.strong-induction-natural-numbers -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/fibonacci-sequence.lagda.md b/src/elementary-number-theory/fibonacci-sequence.lagda.md index 03d39b2446..89af95e039 100644 --- a/src/elementary-number-theory/fibonacci-sequence.lagda.md +++ b/src/elementary-number-theory/fibonacci-sequence.lagda.md @@ -1,27 +1,22 @@ # The Fibonacci sequence ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.fibonacci-sequence - (funext : function-extensionality) - where +module elementary-number-theory.fibonacci-sequence where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.greatest-common-divisor-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.greatest-common-divisor-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.relatively-prime-natural-numbers funext +open import elementary-number-theory.relatively-prime-natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/field-of-rational-numbers.lagda.md b/src/elementary-number-theory/field-of-rational-numbers.lagda.md index 5ed5d9b6be..88e4a88422 100644 --- a/src/elementary-number-theory/field-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/field-of-rational-numbers.lagda.md @@ -1,28 +1,23 @@ # The field of rational numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.field-of-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.field-of-rational-numbers where ```
Imports ```agda -open import commutative-algebra.discrete-fields funext +open import commutative-algebra.discrete-fields -open import elementary-number-theory.multiplicative-group-of-rational-numbers funext -open import elementary-number-theory.nonzero-rational-numbers funext -open import elementary-number-theory.ring-of-rational-numbers funext +open import elementary-number-theory.multiplicative-group-of-rational-numbers +open import elementary-number-theory.nonzero-rational-numbers +open import elementary-number-theory.ring-of-rational-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types -open import ring-theory.division-rings funext +open import ring-theory.division-rings ```
diff --git a/src/elementary-number-theory/finitary-natural-numbers.lagda.md b/src/elementary-number-theory/finitary-natural-numbers.lagda.md index 85a00da121..57acf9d9c0 100644 --- a/src/elementary-number-theory/finitary-natural-numbers.lagda.md +++ b/src/elementary-number-theory/finitary-natural-numbers.lagda.md @@ -1,35 +1,30 @@ # The natural numbers base `k` ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.finitary-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.finitary-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.sets open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/finitely-cyclic-maps.lagda.md b/src/elementary-number-theory/finitely-cyclic-maps.lagda.md index 9e0597c7b4..d70daec324 100644 --- a/src/elementary-number-theory/finitely-cyclic-maps.lagda.md +++ b/src/elementary-number-theory/finitely-cyclic-maps.lagda.md @@ -1,30 +1,25 @@ # Finitely cyclic maps ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.finitely-cyclic-maps - (funext : function-extensionality) - where +module elementary-number-theory.finitely-cyclic-maps where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.iterating-functions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.iterating-functions open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md index 3b2797a025..770e230cd9 100644 --- a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md +++ b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md @@ -1,59 +1,54 @@ # The fundamental theorem of arithmetic ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.fundamental-theorem-of-arithmetic - (funext : function-extensionality) - where +module elementary-number-theory.fundamental-theorem-of-arithmetic where ```
Imports ```agda -open import elementary-number-theory.based-strong-induction-natural-numbers funext -open import elementary-number-theory.bezouts-lemma-integers funext -open import elementary-number-theory.decidable-total-order-natural-numbers funext -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.lower-bounds-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext -open import elementary-number-theory.multiplication-lists-of-natural-numbers funext +open import elementary-number-theory.based-strong-induction-natural-numbers +open import elementary-number-theory.bezouts-lemma-integers +open import elementary-number-theory.decidable-total-order-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.multiplication-lists-of-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers funext -open import elementary-number-theory.relatively-prime-natural-numbers funext -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.well-ordering-principle-natural-numbers funext +open import elementary-number-theory.prime-numbers +open import elementary-number-theory.relatively-prime-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.well-ordering-principle-natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.unit-type open import foundation.universe-levels -open import lists.concatenation-lists funext -open import lists.equality-lists funext -open import lists.functoriality-lists funext +open import lists.concatenation-lists +open import lists.equality-lists +open import lists.functoriality-lists open import lists.lists -open import lists.permutation-lists funext -open import lists.predicates-on-lists funext -open import lists.sort-by-insertion-lists funext -open import lists.sorted-lists funext +open import lists.permutation-lists +open import lists.predicates-on-lists +open import lists.sort-by-insertion-lists +open import lists.sorted-lists ```
diff --git a/src/elementary-number-theory/goldbach-conjecture.lagda.md b/src/elementary-number-theory/goldbach-conjecture.lagda.md index 1642006127..ab096dfab1 100644 --- a/src/elementary-number-theory/goldbach-conjecture.lagda.md +++ b/src/elementary-number-theory/goldbach-conjecture.lagda.md @@ -1,12 +1,7 @@ # The Goldbach conjecture ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.goldbach-conjecture - (funext : function-extensionality) - where +module elementary-number-theory.goldbach-conjecture where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers funext -open import elementary-number-theory.prime-numbers funext -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.parity-natural-numbers +open import elementary-number-theory.prime-numbers +open import elementary-number-theory.strict-inequality-natural-numbers -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md b/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md index 914755108d..fc8abf413d 100644 --- a/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md +++ b/src/elementary-number-theory/greatest-common-divisor-integers.lagda.md @@ -1,37 +1,32 @@ # The greatest common divisor of integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.greatest-common-divisor-integers - (funext : function-extensionality) - where +module elementary-number-theory.greatest-common-divisor-integers where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers funext +open import elementary-number-theory.absolute-value-integers open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-integers funext -open import elementary-number-theory.equality-integers funext -open import elementary-number-theory.greatest-common-divisor-natural-numbers funext +open import elementary-number-theory.divisibility-integers +open import elementary-number-theory.equality-integers +open import elementary-number-theory.greatest-common-divisor-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.logical-equivalences open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md b/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md index 14a8b300b5..13347d69ac 100644 --- a/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md +++ b/src/elementary-number-theory/greatest-common-divisor-natural-numbers.lagda.md @@ -1,40 +1,35 @@ # The greatest common divisor of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.greatest-common-divisor-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.greatest-common-divisor-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.decidable-types funext -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.euclidean-division-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.lower-bounds-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.decidable-types +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.euclidean-division-natural-numbers +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.well-ordering-principle-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.well-ordering-principle-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext +open import foundation.empty-types +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.logical-equivalences open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/group-of-integers.lagda.md b/src/elementary-number-theory/group-of-integers.lagda.md index 711c0db1c8..e1c12a108d 100644 --- a/src/elementary-number-theory/group-of-integers.lagda.md +++ b/src/elementary-number-theory/group-of-integers.lagda.md @@ -1,29 +1,24 @@ # The group of integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.group-of-integers - (funext : function-extensionality) - where +module elementary-number-theory.group-of-integers where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.semigroups -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms ```
diff --git a/src/elementary-number-theory/half-integers.lagda.md b/src/elementary-number-theory/half-integers.lagda.md index 4b18b64680..b62b4ae496 100644 --- a/src/elementary-number-theory/half-integers.lagda.md +++ b/src/elementary-number-theory/half-integers.lagda.md @@ -1,21 +1,16 @@ # The half-integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.half-integers - (funext : function-extensionality) - where +module elementary-number-theory.half-integers where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/hardy-ramanujan-number.lagda.md b/src/elementary-number-theory/hardy-ramanujan-number.lagda.md index 1371f97fa7..9ecffa68bf 100644 --- a/src/elementary-number-theory/hardy-ramanujan-number.lagda.md +++ b/src/elementary-number-theory/hardy-ramanujan-number.lagda.md @@ -1,22 +1,17 @@ # The Hardy-Ramanujan number ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.hardy-ramanujan-number - (funext : function-extensionality) - where +module elementary-number-theory.hardy-ramanujan-number where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.taxicab-numbers funext +open import elementary-number-theory.taxicab-numbers open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md b/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md index 71d6884566..ea3f148c51 100644 --- a/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/inclusion-natural-numbers-conatural-numbers.lagda.md @@ -3,27 +3,22 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.inclusion-natural-numbers-conatural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.inclusion-natural-numbers-conatural-numbers where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers funext -open import elementary-number-theory.infinite-conatural-numbers funext +open import elementary-number-theory.conatural-numbers +open import elementary-number-theory.infinite-conatural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.existential-quantification funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.surjective-maps funext +open import foundation.existential-quantification +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation +open import foundation.surjective-maps open import foundation-core.empty-types open import foundation-core.identity-types diff --git a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md index 7db168ea47..5a90091ea9 100644 --- a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md @@ -3,38 +3,33 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.inequality-conatural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.inequality-conatural-numbers where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers funext +open import elementary-number-theory.conatural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels open import foundation-core.maybe -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/elementary-number-theory/inequality-integer-fractions.lagda.md b/src/elementary-number-theory/inequality-integer-fractions.lagda.md index b0e5112365..e87b85c1c3 100644 --- a/src/elementary-number-theory/inequality-integer-fractions.lagda.md +++ b/src/elementary-number-theory/inequality-integer-fractions.lagda.md @@ -1,42 +1,37 @@ # Inequality on integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.inequality-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.inequality-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions funext -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.addition-positive-and-negative-integers funext -open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.inequality-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-integer-fractions +open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-positive-and-negative-integers +open import elementary-number-theory.cross-multiplication-difference-integer-fractions +open import elementary-number-theory.difference-integers +open import elementary-number-theory.inequality-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.nonpositive-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.strict-inequality-integers funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonpositive-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.strict-inequality-integers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/inequality-integers.lagda.md b/src/elementary-number-theory/inequality-integers.lagda.md index 4b1972f799..1e9c9063f6 100644 --- a/src/elementary-number-theory/inequality-integers.lagda.md +++ b/src/elementary-number-theory/inequality-integers.lagda.md @@ -1,45 +1,40 @@ # Inequality on the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.inequality-integers - (funext : function-extensionality) - where +module elementary-number-theory.inequality-integers where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.addition-positive-and-negative-integers funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-positive-and-negative-integers +open import elementary-number-theory.difference-integers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers funext -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.nonpositive-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.negative-integers +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonpositive-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/elementary-number-theory/inequality-natural-numbers.lagda.md b/src/elementary-number-theory/inequality-natural-numbers.lagda.md index 13c1510b2d..a31c50691d 100644 --- a/src/elementary-number-theory/inequality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-natural-numbers.lagda.md @@ -1,40 +1,35 @@ # Inequality of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.inequality-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.inequality-natural-numbers where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/elementary-number-theory/inequality-rational-numbers.lagda.md b/src/elementary-number-theory/inequality-rational-numbers.lagda.md index 9fa7192e16..c8956f0ff1 100644 --- a/src/elementary-number-theory/inequality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-rational-numbers.lagda.md @@ -1,46 +1,41 @@ # Inequality on the rational numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.inequality-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.inequality-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions funext -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.difference-rational-numbers funext -open import elementary-number-theory.inequality-integer-fractions funext -open import elementary-number-theory.inequality-integers funext -open import elementary-number-theory.integer-fractions funext -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.reduced-integer-fractions funext +open import elementary-number-theory.addition-integer-fractions +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.cross-multiplication-difference-integer-fractions +open import elementary-number-theory.difference-integers +open import elementary-number-theory.difference-rational-numbers +open import elementary-number-theory.inequality-integer-fractions +open import elementary-number-theory.inequality-integers +open import elementary-number-theory.integer-fractions +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.reduced-integer-fractions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/elementary-number-theory/inequality-standard-finite-types.lagda.md b/src/elementary-number-theory/inequality-standard-finite-types.lagda.md index c8f1d75439..d21985ad6f 100644 --- a/src/elementary-number-theory/inequality-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/inequality-standard-finite-types.lagda.md @@ -1,37 +1,32 @@ # Inequality on the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.inequality-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.inequality-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.posets +open import order-theory.preorders -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/infinite-conatural-numbers.lagda.md b/src/elementary-number-theory/infinite-conatural-numbers.lagda.md index fb0d750414..4b5d718a19 100644 --- a/src/elementary-number-theory/infinite-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/infinite-conatural-numbers.lagda.md @@ -3,22 +3,17 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.infinite-conatural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.infinite-conatural-numbers where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers funext -open import elementary-number-theory.equality-conatural-numbers funext +open import elementary-number-theory.conatural-numbers +open import elementary-number-theory.equality-conatural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/elementary-number-theory/infinitude-of-primes.lagda.md b/src/elementary-number-theory/infinitude-of-primes.lagda.md index 9924f6d426..2da5b37a90 100644 --- a/src/elementary-number-theory/infinitude-of-primes.lagda.md +++ b/src/elementary-number-theory/infinitude-of-primes.lagda.md @@ -1,37 +1,32 @@ # The infinitude of primes ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.infinitude-of-primes - (funext : function-extensionality) - where +module elementary-number-theory.infinitude-of-primes where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.factorials funext -open import elementary-number-theory.lower-bounds-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.factorials +open import elementary-number-theory.lower-bounds-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers funext -open import elementary-number-theory.proper-divisors-natural-numbers funext -open import elementary-number-theory.sieve-of-eratosthenes funext -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.well-ordering-principle-natural-numbers funext - -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import elementary-number-theory.prime-numbers +open import elementary-number-theory.proper-divisors-natural-numbers +open import elementary-number-theory.sieve-of-eratosthenes +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.well-ordering-principle-natural-numbers + +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.iterating-functions funext -open import foundation.negation funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.iterating-functions +open import foundation.negation +open import foundation.type-arithmetic-empty-type open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md b/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md index 48663e56ac..9823b2c9a1 100644 --- a/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md +++ b/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md @@ -1,25 +1,20 @@ # Initial segments of the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.initial-segments-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.initial-segments-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.maximum-natural-numbers funext +open import elementary-number-theory.maximum-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/integer-fractions.lagda.md b/src/elementary-number-theory/integer-fractions.lagda.md index b1f2e054a0..c2bc0db1a8 100644 --- a/src/elementary-number-theory/integer-fractions.lagda.md +++ b/src/elementary-number-theory/integer-fractions.lagda.md @@ -1,37 +1,32 @@ # Integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.integer-fractions where ```
Imports ```agda -open import elementary-number-theory.equality-integers funext -open import elementary-number-theory.greatest-common-divisor-integers funext +open import elementary-number-theory.equality-integers +open import elementary-number-theory.greatest-common-divisor-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.nonzero-integers funext -open import elementary-number-theory.positive-integers funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.positive-integers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext -open import foundation.decidable-equality funext +open import foundation.binary-relations +open import foundation.cartesian-product-types +open import foundation.decidable-equality open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalence-relations +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import set-theory.countable-sets funext +open import set-theory.countable-sets ```
diff --git a/src/elementary-number-theory/jacobi-symbol.lagda.md b/src/elementary-number-theory/jacobi-symbol.lagda.md index 077d3a8ba9..b7c291a319 100644 --- a/src/elementary-number-theory/jacobi-symbol.lagda.md +++ b/src/elementary-number-theory/jacobi-symbol.lagda.md @@ -1,27 +1,22 @@ # The Jacobi symbol ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.jacobi-symbol - (funext : function-extensionality) - where +module elementary-number-theory.jacobi-symbol where ```
Imports ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic funext +open import elementary-number-theory.fundamental-theorem-of-arithmetic open import elementary-number-theory.integers -open import elementary-number-theory.legendre-symbol funext -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.legendre-symbol +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers -open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.type-arithmetic-dependent-function-types open import foundation.unit-type -open import lists.functoriality-lists funext +open import lists.functoriality-lists open import lists.lists ``` diff --git a/src/elementary-number-theory/kolakoski-sequence.lagda.md b/src/elementary-number-theory/kolakoski-sequence.lagda.md index a6d3b8b601..602bc2597a 100644 --- a/src/elementary-number-theory/kolakoski-sequence.lagda.md +++ b/src/elementary-number-theory/kolakoski-sequence.lagda.md @@ -1,23 +1,18 @@ # The Kolakoski sequence ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.kolakoski-sequence - (funext : function-extensionality) - where +module elementary-number-theory.kolakoski-sequence where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers funext +open import elementary-number-theory.strong-induction-natural-numbers -open import foundation.booleans funext -open import foundation.cartesian-product-types funext +open import foundation.booleans +open import foundation.cartesian-product-types open import foundation.dependent-pair-types ``` diff --git a/src/elementary-number-theory/legendre-symbol.lagda.md b/src/elementary-number-theory/legendre-symbol.lagda.md index 363d1ba015..57f91cb937 100644 --- a/src/elementary-number-theory/legendre-symbol.lagda.md +++ b/src/elementary-number-theory/legendre-symbol.lagda.md @@ -1,28 +1,23 @@ # The Legendre symbol ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.legendre-symbol - (funext : function-extensionality) - where +module elementary-number-theory.legendre-symbol where ```
Imports ```agda open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.modular-arithmetic open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers funext -open import elementary-number-theory.squares-modular-arithmetic funext +open import elementary-number-theory.prime-numbers +open import elementary-number-theory.squares-modular-arithmetic open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types ```
diff --git a/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md b/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md index 1a69bb4a4b..1a84c70750 100644 --- a/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md +++ b/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md @@ -1,22 +1,17 @@ # Lower bounds of type families over the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.lower-bounds-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.lower-bounds-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/maximum-natural-numbers.lagda.md b/src/elementary-number-theory/maximum-natural-numbers.lagda.md index f463ad2859..97038be80f 100644 --- a/src/elementary-number-theory/maximum-natural-numbers.lagda.md +++ b/src/elementary-number-theory/maximum-natural-numbers.lagda.md @@ -1,31 +1,26 @@ # Maximum on the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.maximum-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.maximum-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type -open import order-theory.least-upper-bounds-posets funext +open import order-theory.least-upper-bounds-posets -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/maximum-standard-finite-types.lagda.md b/src/elementary-number-theory/maximum-standard-finite-types.lagda.md index 825fc31e8b..160a0de610 100644 --- a/src/elementary-number-theory/maximum-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/maximum-standard-finite-types.lagda.md @@ -1,27 +1,22 @@ # Maximum on the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.maximum-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.maximum-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.inequality-standard-finite-types open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.unit-type -open import order-theory.least-upper-bounds-posets funext +open import order-theory.least-upper-bounds-posets -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/mediant-integer-fractions.lagda.md b/src/elementary-number-theory/mediant-integer-fractions.lagda.md index cd4715e9fb..96adcb2df1 100644 --- a/src/elementary-number-theory/mediant-integer-fractions.lagda.md +++ b/src/elementary-number-theory/mediant-integer-fractions.lagda.md @@ -1,26 +1,21 @@ # The mediant fraction of two integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.mediant-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.mediant-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.addition-positive-and-negative-integers funext -open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.integer-fractions funext -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-positive-and-negative-integers +open import elementary-number-theory.cross-multiplication-difference-integer-fractions +open import elementary-number-theory.difference-integers +open import elementary-number-theory.integer-fractions +open import elementary-number-theory.multiplication-integers open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types ```
diff --git a/src/elementary-number-theory/mersenne-primes.lagda.md b/src/elementary-number-theory/mersenne-primes.lagda.md index b3e6ce9262..072edc42fe 100644 --- a/src/elementary-number-theory/mersenne-primes.lagda.md +++ b/src/elementary-number-theory/mersenne-primes.lagda.md @@ -1,25 +1,20 @@ # Mersenne primes ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.mersenne-primes - (funext : function-extensionality) - where +module elementary-number-theory.mersenne-primes where ```
Imports ```agda -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.exponentiation-natural-numbers funext +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers funext +open import elementary-number-theory.prime-numbers -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/minimum-natural-numbers.lagda.md b/src/elementary-number-theory/minimum-natural-numbers.lagda.md index e7e1d4e6be..71d9c60530 100644 --- a/src/elementary-number-theory/minimum-natural-numbers.lagda.md +++ b/src/elementary-number-theory/minimum-natural-numbers.lagda.md @@ -1,31 +1,26 @@ # Minimum on the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.minimum-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.minimum-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type -open import order-theory.greatest-lower-bounds-posets funext +open import order-theory.greatest-lower-bounds-posets -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/minimum-standard-finite-types.lagda.md b/src/elementary-number-theory/minimum-standard-finite-types.lagda.md index b2f09690d3..d2eef65a72 100644 --- a/src/elementary-number-theory/minimum-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/minimum-standard-finite-types.lagda.md @@ -1,27 +1,22 @@ # Minimum on the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.minimum-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.minimum-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.inequality-standard-finite-types open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.unit-type -open import order-theory.greatest-lower-bounds-posets funext +open import order-theory.greatest-lower-bounds-posets -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md b/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md index 6f50697afc..302d0c9537 100644 --- a/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/modular-arithmetic-standard-finite-types.lagda.md @@ -1,42 +1,37 @@ # Modular arithmetic on the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.modular-arithmetic-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.modular-arithmetic-standard-finite-types where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps open import foundation.split-surjective-maps -open import foundation.surjective-maps funext +open import foundation.surjective-maps open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/modular-arithmetic.lagda.md b/src/elementary-number-theory/modular-arithmetic.lagda.md index d58bab9f81..b75b74c017 100644 --- a/src/elementary-number-theory/modular-arithmetic.lagda.md +++ b/src/elementary-number-theory/modular-arithmetic.lagda.md @@ -1,55 +1,50 @@ # Modular arithmetic ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.modular-arithmetic - (funext : function-extensionality) - where +module elementary-number-theory.modular-arithmetic where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers funext -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.congruence-integers funext -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.divisibility-integers funext -open import elementary-number-theory.equality-integers funext -open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.addition-integers +open import elementary-number-theory.congruence-integers +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.divisibility-integers +open import elementary-number-theory.equality-integers +open import elementary-number-theory.inequality-integers open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext +open import elementary-number-theory.nonnegative-integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.discrete-types funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.sets funext -open import foundation.surjective-maps funext +open import foundation.discrete-types +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation +open import foundation.sets +open import foundation.surjective-maps open import foundation.unit-type open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md b/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md index 4835841780..da4c41ed15 100644 --- a/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md +++ b/src/elementary-number-theory/monoid-of-natural-numbers-with-addition.lagda.md @@ -1,26 +1,21 @@ # The monoid of natural numbers with addition ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.monoid-of-natural-numbers-with-addition - (funext : function-extensionality) - where +module elementary-number-theory.monoid-of-natural-numbers-with-addition where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.commutative-monoids +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md b/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md index 5aa7f55c55..ae0b8fe991 100644 --- a/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md +++ b/src/elementary-number-theory/monoid-of-natural-numbers-with-maximum.lagda.md @@ -1,30 +1,25 @@ # The monoid of the natural numbers with maximum ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.monoid-of-natural-numbers-with-maximum - (funext : function-extensionality) - where +module elementary-number-theory.monoid-of-natural-numbers-with-maximum where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.initial-segments-natural-numbers funext -open import elementary-number-theory.maximum-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.initial-segments-natural-numbers +open import elementary-number-theory.maximum-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.normal-submonoids-commutative-monoids funext -open import group-theory.semigroups funext -open import group-theory.submonoids-commutative-monoids funext +open import group-theory.commutative-monoids +open import group-theory.monoids +open import group-theory.normal-submonoids-commutative-monoids +open import group-theory.semigroups +open import group-theory.submonoids-commutative-monoids ```
diff --git a/src/elementary-number-theory/multiplication-integer-fractions.lagda.md b/src/elementary-number-theory/multiplication-integer-fractions.lagda.md index 0463457a12..33ca87b0b6 100644 --- a/src/elementary-number-theory/multiplication-integer-fractions.lagda.md +++ b/src/elementary-number-theory/multiplication-integer-fractions.lagda.md @@ -1,28 +1,23 @@ # Multiplication on integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplication-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.multiplication-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions funext -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-integer-fractions +open import elementary-number-theory.addition-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types ```
diff --git a/src/elementary-number-theory/multiplication-integers.lagda.md b/src/elementary-number-theory/multiplication-integers.lagda.md index 473818289d..41d4dfcc1b 100644 --- a/src/elementary-number-theory/multiplication-integers.lagda.md +++ b/src/elementary-number-theory/multiplication-integers.lagda.md @@ -1,36 +1,31 @@ # Multiplication of integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplication-integers - (funext : function-extensionality) - where +module elementary-number-theory.multiplication-integers where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.difference-integers +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.nonzero-integers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.coproduct-types +open import foundation.embeddings +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps open import foundation.interchange-law -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md b/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md index afe65c6a0b..85b452a28c 100644 --- a/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/multiplication-lists-of-natural-numbers.lagda.md @@ -1,12 +1,7 @@ # Multiplication of the elements of a list of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplication-lists-of-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.multiplication-lists-of-natural-numbers where ```
Imports @@ -16,14 +11,14 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import lists.permutation-lists funext +open import lists.permutation-lists ```
diff --git a/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md b/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md index 9101352d75..a8c0e801c0 100644 --- a/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md +++ b/src/elementary-number-theory/multiplication-positive-and-negative-integers.lagda.md @@ -1,33 +1,28 @@ # Multiplication of positive, negative, nonnegative and nonpositive integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplication-positive-and-negative-integers - (funext : function-extensionality) - where +module elementary-number-theory.multiplication-positive-and-negative-integers where ```
Imports ```agda -open import elementary-number-theory.addition-positive-and-negative-integers funext -open import elementary-number-theory.inequality-integers funext +open import elementary-number-theory.addition-positive-and-negative-integers +open import elementary-number-theory.inequality-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers funext -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.nonpositive-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.strict-inequality-integers funext - -open import foundation.coproduct-types funext +open import elementary-number-theory.negative-integers +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonpositive-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.strict-inequality-integers + +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.identity-types open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/multiplication-rational-numbers.lagda.md b/src/elementary-number-theory/multiplication-rational-numbers.lagda.md index 95e2c69b2b..367d83d9a5 100644 --- a/src/elementary-number-theory/multiplication-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplication-rational-numbers.lagda.md @@ -3,33 +3,28 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplication-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.multiplication-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions funext -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.difference-rational-numbers funext -open import elementary-number-theory.greatest-common-divisor-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-integer-fractions +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.difference-rational-numbers +open import elementary-number-theory.greatest-common-divisor-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions funext -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.reduced-integer-fractions funext +open import elementary-number-theory.multiplication-integer-fractions +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.reduced-integer-fractions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.interchange-law ``` diff --git a/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md b/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md index 15e4a6df69..5c6d0553be 100644 --- a/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-group-of-positive-rational-numbers.lagda.md @@ -3,31 +3,26 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplicative-group-of-positive-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.multiplicative-group-of-positive-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.multiplication-rational-numbers funext -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.multiplication-rational-numbers +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.rational-numbers -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.submonoids funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.submonoids ```
diff --git a/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md b/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md index 70ddff8542..9fd3c96f59 100644 --- a/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-group-of-rational-numbers.lagda.md @@ -3,38 +3,33 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplicative-group-of-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.multiplicative-group-of-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext -open import elementary-number-theory.nonzero-rational-numbers funext -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.ring-of-rational-numbers funext +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers +open import elementary-number-theory.nonzero-rational-numbers +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.ring-of-rational-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.cores-monoids funext -open import group-theory.groups funext -open import group-theory.submonoids-commutative-monoids funext +open import group-theory.abelian-groups +open import group-theory.cores-monoids +open import group-theory.groups +open import group-theory.submonoids-commutative-monoids -open import ring-theory.groups-of-units-rings funext -open import ring-theory.invertible-elements-rings funext -open import ring-theory.trivial-rings funext +open import ring-theory.groups-of-units-rings +open import ring-theory.invertible-elements-rings +open import ring-theory.trivial-rings ```
diff --git a/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md b/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md index 9fb781b8ec..8f8e78a309 100644 --- a/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md +++ b/src/elementary-number-theory/multiplicative-inverses-positive-integer-fractions.lagda.md @@ -1,27 +1,22 @@ # Multiplicative inverses of positive integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplicative-inverses-positive-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.multiplicative-inverses-positive-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.greatest-common-divisor-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.greatest-common-divisor-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions funext -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.positive-integer-fractions funext -open import elementary-number-theory.reduced-integer-fractions funext +open import elementary-number-theory.multiplication-integer-fractions +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.positive-integer-fractions +open import elementary-number-theory.reduced-integer-fractions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.transport-along-identifications ``` diff --git a/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md b/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md index 3c2c649a3d..691a9935fd 100644 --- a/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-monoid-of-natural-numbers.lagda.md @@ -1,25 +1,20 @@ # The multiplicative monoid of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplicative-monoid-of-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.multiplicative-monoid-of-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md b/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md index 91159ebfe1..781ac3df4c 100644 --- a/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/multiplicative-monoid-of-rational-numbers.lagda.md @@ -3,27 +3,22 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.multiplicative-monoid-of-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.multiplicative-monoid-of-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.multiplication-rational-numbers funext -open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.multiplication-rational-numbers +open import elementary-number-theory.rational-numbers open import foundation.dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.commutative-monoids +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/elementary-number-theory/negative-integers.lagda.md b/src/elementary-number-theory/negative-integers.lagda.md index 212fc9a23d..86dd90ed11 100644 --- a/src/elementary-number-theory/negative-integers.lagda.md +++ b/src/elementary-number-theory/negative-integers.lagda.md @@ -1,36 +1,31 @@ # The negative integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.negative-integers - (funext : function-extensionality) - where +module elementary-number-theory.negative-integers where ```
Imports ```agda -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.nonzero-integers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/nonnegative-integers.lagda.md b/src/elementary-number-theory/nonnegative-integers.lagda.md index 85d7c32dc1..d9c2b50561 100644 --- a/src/elementary-number-theory/nonnegative-integers.lagda.md +++ b/src/elementary-number-theory/nonnegative-integers.lagda.md @@ -1,35 +1,30 @@ # The nonnegative integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.nonnegative-integers - (funext : function-extensionality) - where +module elementary-number-theory.nonnegative-integers where ```
Imports ```agda -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/nonpositive-integers.lagda.md b/src/elementary-number-theory/nonpositive-integers.lagda.md index 21055aa06b..e5a31ad753 100644 --- a/src/elementary-number-theory/nonpositive-integers.lagda.md +++ b/src/elementary-number-theory/nonpositive-integers.lagda.md @@ -1,35 +1,30 @@ # The nonpositive integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.nonpositive-integers - (funext : function-extensionality) - where +module elementary-number-theory.nonpositive-integers where ```
Imports ```agda -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/nonzero-integers.lagda.md b/src/elementary-number-theory/nonzero-integers.lagda.md index 354a8bfd41..2d7dd2e4a9 100644 --- a/src/elementary-number-theory/nonzero-integers.lagda.md +++ b/src/elementary-number-theory/nonzero-integers.lagda.md @@ -1,12 +1,7 @@ # Nonzero integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.nonzero-integers - (funext : function-extensionality) - where +module elementary-number-theory.nonzero-integers where ```
Imports @@ -15,12 +10,12 @@ module open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/nonzero-natural-numbers.lagda.md b/src/elementary-number-theory/nonzero-natural-numbers.lagda.md index 45af8dfd26..4661f74095 100644 --- a/src/elementary-number-theory/nonzero-natural-numbers.lagda.md +++ b/src/elementary-number-theory/nonzero-natural-numbers.lagda.md @@ -1,28 +1,23 @@ # Nonzero natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.nonzero-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.nonzero-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/nonzero-rational-numbers.lagda.md b/src/elementary-number-theory/nonzero-rational-numbers.lagda.md index 3c3635b449..29defc2276 100644 --- a/src/elementary-number-theory/nonzero-rational-numbers.lagda.md +++ b/src/elementary-number-theory/nonzero-rational-numbers.lagda.md @@ -3,39 +3,34 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.nonzero-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.nonzero-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-rational-numbers funext -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext -open import elementary-number-theory.nonzero-integers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.reduced-integer-fractions funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-rational-numbers +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers +open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.reduced-integer-fractions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.submonoids funext +open import group-theory.submonoids ```
diff --git a/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md b/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md index ad8cf3ad71..80761f26c3 100644 --- a/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/ordinal-induction-natural-numbers.lagda.md @@ -1,21 +1,16 @@ # The ordinal induction principle for the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.ordinal-induction-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.ordinal-induction-natural-numbers where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers -open import foundation.empty-types funext +open import foundation.empty-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/parity-natural-numbers.lagda.md b/src/elementary-number-theory/parity-natural-numbers.lagda.md index cd59ccb495..78da36cfb4 100644 --- a/src/elementary-number-theory/parity-natural-numbers.lagda.md +++ b/src/elementary-number-theory/parity-natural-numbers.lagda.md @@ -1,30 +1,25 @@ # Parity of the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.parity-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.parity-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.negation funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.negation open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/peano-arithmetic.lagda.md b/src/elementary-number-theory/peano-arithmetic.lagda.md index 5e16b29e79..97139b2a63 100644 --- a/src/elementary-number-theory/peano-arithmetic.lagda.md +++ b/src/elementary-number-theory/peano-arithmetic.lagda.md @@ -1,12 +1,7 @@ # Peano arithmetic ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.peano-arithmetic - (funext : function-extensionality) - where +module elementary-number-theory.peano-arithmetic where ```
Imports @@ -15,11 +10,11 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negated-equality funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negated-equality +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/pisano-periods.lagda.md b/src/elementary-number-theory/pisano-periods.lagda.md index 085b071d38..f765a59fb3 100644 --- a/src/elementary-number-theory/pisano-periods.lagda.md +++ b/src/elementary-number-theory/pisano-periods.lagda.md @@ -1,42 +1,37 @@ # Pisano periods ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.pisano-periods - (funext : function-extensionality) - where +module elementary-number-theory.pisano-periods where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.fibonacci-sequence funext -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.lower-bounds-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.fibonacci-sequence +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.lower-bounds-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.well-ordering-principle-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.well-ordering-principle-natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.repetitions-sequences funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.repetitions-sequences +open import foundation.sets open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.sequences-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.sequences-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md b/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md index b131a7258a..4977a5e18b 100644 --- a/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md +++ b/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md @@ -9,21 +9,21 @@ module
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/elementary-number-theory/positive-and-negative-integers.lagda.md b/src/elementary-number-theory/positive-and-negative-integers.lagda.md index dceafdf324..844b95a8b8 100644 --- a/src/elementary-number-theory/positive-and-negative-integers.lagda.md +++ b/src/elementary-number-theory/positive-and-negative-integers.lagda.md @@ -1,12 +1,7 @@ # The positive, negative, nonnegative and nonpositive integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.positive-and-negative-integers - (funext : function-extensionality) - where +module elementary-number-theory.positive-and-negative-integers where ```
Imports @@ -14,20 +9,20 @@ module ```agda open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers funext -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.nonpositive-integers funext -open import elementary-number-theory.nonzero-integers funext -open import elementary-number-theory.positive-integers funext - -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import elementary-number-theory.negative-integers +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonpositive-integers +open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.positive-integers + +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation open import foundation.unit-type ``` diff --git a/src/elementary-number-theory/positive-conatural-numbers.lagda.md b/src/elementary-number-theory/positive-conatural-numbers.lagda.md index 6f20822ef4..4d2dd9340a 100644 --- a/src/elementary-number-theory/positive-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/positive-conatural-numbers.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.positive-conatural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.positive-conatural-numbers where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers funext -open import elementary-number-theory.zero-conatural-numbers funext +open import elementary-number-theory.conatural-numbers +open import elementary-number-theory.zero-conatural-numbers -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.negation funext +open import foundation.negation open import foundation.universe-levels open import foundation-core.empty-types diff --git a/src/elementary-number-theory/positive-integer-fractions.lagda.md b/src/elementary-number-theory/positive-integer-fractions.lagda.md index 3137adcbdb..7e92ff3e65 100644 --- a/src/elementary-number-theory/positive-integer-fractions.lagda.md +++ b/src/elementary-number-theory/positive-integer-fractions.lagda.md @@ -1,28 +1,23 @@ # Positive integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.positive-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.positive-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions funext -open import elementary-number-theory.addition-positive-and-negative-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-integer-fractions +open import elementary-number-theory.addition-positive-and-negative-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.reduced-integer-fractions funext +open import elementary-number-theory.multiplication-integer-fractions +open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.reduced-integer-fractions -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/positive-integers.lagda.md b/src/elementary-number-theory/positive-integers.lagda.md index eb52cf9a29..9070e78e0c 100644 --- a/src/elementary-number-theory/positive-integers.lagda.md +++ b/src/elementary-number-theory/positive-integers.lagda.md @@ -1,42 +1,37 @@ # The positive integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.positive-integers - (funext : function-extensionality) - where +module elementary-number-theory.positive-integers where ```
Imports ```agda -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers funext -open import elementary-number-theory.nonzero-natural-numbers funext +open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.nonzero-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import set-theory.countable-sets funext +open import set-theory.countable-sets ```
diff --git a/src/elementary-number-theory/positive-rational-numbers.lagda.md b/src/elementary-number-theory/positive-rational-numbers.lagda.md index c6d938475a..439940ac49 100644 --- a/src/elementary-number-theory/positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/positive-rational-numbers.lagda.md @@ -3,66 +3,61 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.positive-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.positive-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.additive-group-of-rational-numbers funext -open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext -open import elementary-number-theory.difference-rational-numbers funext -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.additive-group-of-rational-numbers +open import elementary-number-theory.cross-multiplication-difference-integer-fractions +open import elementary-number-theory.difference-rational-numbers +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integer-fractions funext -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext -open import elementary-number-theory.multiplication-rational-numbers funext -open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions funext -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext -open import elementary-number-theory.negative-integers funext -open import elementary-number-theory.nonzero-natural-numbers funext -open import elementary-number-theory.nonzero-rational-numbers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integer-fractions funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-integers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.multiplication-integer-fractions +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.multiplication-rational-numbers +open import elementary-number-theory.multiplicative-inverses-positive-integer-fractions +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers +open import elementary-number-theory.negative-integers +open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.nonzero-rational-numbers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integer-fractions +open import elementary-number-theory.positive-integers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.invertible-elements-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext -open import group-theory.submonoids funext -open import group-theory.submonoids funext-commutative-monoids -open import group-theory.subsemigroups funext +open import group-theory.commutative-monoids +open import group-theory.invertible-elements-monoids +open import group-theory.monoids +open import group-theory.semigroups +open import group-theory.submonoids +open import group-theory.submonoids-commutative-monoids +open import group-theory.subsemigroups ```
diff --git a/src/elementary-number-theory/powers-integers.lagda.md b/src/elementary-number-theory/powers-integers.lagda.md index 42ad59684a..05ec3f9e69 100644 --- a/src/elementary-number-theory/powers-integers.lagda.md +++ b/src/elementary-number-theory/powers-integers.lagda.md @@ -1,25 +1,20 @@ # Powers of integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.powers-integers - (funext : function-extensionality) - where +module elementary-number-theory.powers-integers where ```
Imports ```agda -open import commutative-algebra.powers-of-elements-commutative-rings funext +open import commutative-algebra.powers-of-elements-commutative-rings open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.ring-of-integers funext +open import elementary-number-theory.ring-of-integers -open import foundation.identity-types funext +open import foundation.identity-types ```
diff --git a/src/elementary-number-theory/powers-of-two.lagda.md b/src/elementary-number-theory/powers-of-two.lagda.md index 4e4237b21d..d856d60206 100644 --- a/src/elementary-number-theory/powers-of-two.lagda.md +++ b/src/elementary-number-theory/powers-of-two.lagda.md @@ -1,30 +1,25 @@ # Powers of two ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.powers-of-two - (funext : function-extensionality) - where +module elementary-number-theory.powers-of-two where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.exponentiation-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers funext -open import elementary-number-theory.strong-induction-natural-numbers funext +open import elementary-number-theory.parity-natural-numbers +open import elementary-number-theory.strong-induction-natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-types funext +open import foundation.function-types open import foundation.split-surjective-maps open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/elementary-number-theory/prime-numbers.lagda.md b/src/elementary-number-theory/prime-numbers.lagda.md index f94a341849..930d240933 100644 --- a/src/elementary-number-theory/prime-numbers.lagda.md +++ b/src/elementary-number-theory/prime-numbers.lagda.md @@ -1,39 +1,34 @@ # Prime numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.prime-numbers - (funext : function-extensionality) - where +module elementary-number-theory.prime-numbers where ```
Imports ```agda -open import elementary-number-theory.decidable-types funext -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.decidable-types +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.proper-divisors-natural-numbers funext -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.proper-divisors-natural-numbers +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext +open import foundation.empty-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negated-equality funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negated-equality +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/products-of-natural-numbers.lagda.md b/src/elementary-number-theory/products-of-natural-numbers.lagda.md index c4009c3964..bf853f365e 100644 --- a/src/elementary-number-theory/products-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/products-of-natural-numbers.lagda.md @@ -1,12 +1,7 @@ # Products of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.products-of-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.products-of-natural-numbers where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers -open import foundation.coproduct-types funext -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.coproduct-types +open import foundation.function-types +open import foundation.identity-types open import foundation.unit-type open import lists.lists -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md b/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md index 7caf0fd235..0f35339378 100644 --- a/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md +++ b/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md @@ -1,34 +1,29 @@ # Proper divisors of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.proper-divisors-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.proper-divisors-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions +open import foundation.type-arithmetic-empty-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/pythagorean-triples.lagda.md b/src/elementary-number-theory/pythagorean-triples.lagda.md index 6509312d59..bc76529522 100644 --- a/src/elementary-number-theory/pythagorean-triples.lagda.md +++ b/src/elementary-number-theory/pythagorean-triples.lagda.md @@ -1,12 +1,7 @@ # Pythagorean triples ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.pythagorean-triples - (funext : function-extensionality) - where +module elementary-number-theory.pythagorean-triples where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers funext +open import elementary-number-theory.squares-natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/rational-numbers.lagda.md b/src/elementary-number-theory/rational-numbers.lagda.md index c8290ccd3e..732f9bb66f 100644 --- a/src/elementary-number-theory/rational-numbers.lagda.md +++ b/src/elementary-number-theory/rational-numbers.lagda.md @@ -1,40 +1,35 @@ # The rational numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.rational-numbers where ```
Imports ```agda -open import elementary-number-theory.divisibility-integers funext -open import elementary-number-theory.greatest-common-divisor-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.divisibility-integers +open import elementary-number-theory.greatest-common-divisor-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.mediant-integer-fractions funext -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.reduced-integer-fractions funext +open import elementary-number-theory.mediant-integer-fractions +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.reduced-integer-fractions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.retracts-of-types funext -open import foundation.sections funext -open import foundation.sets funext +open import foundation.equality-dependent-pair-types +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions +open import foundation.reflecting-maps-equivalence-relations +open import foundation.retracts-of-types +open import foundation.sections +open import foundation.sets open import foundation.universe-levels -open import set-theory.countable-sets funext +open import set-theory.countable-sets ```
diff --git a/src/elementary-number-theory/reduced-integer-fractions.lagda.md b/src/elementary-number-theory/reduced-integer-fractions.lagda.md index 7fb038bbd6..b74d316dd3 100644 --- a/src/elementary-number-theory/reduced-integer-fractions.lagda.md +++ b/src/elementary-number-theory/reduced-integer-fractions.lagda.md @@ -1,40 +1,35 @@ # Reduced integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.reduced-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.reduced-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.bezouts-lemma-integers funext -open import elementary-number-theory.divisibility-integers funext -open import elementary-number-theory.equality-integers funext -open import elementary-number-theory.greatest-common-divisor-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.bezouts-lemma-integers +open import elementary-number-theory.divisibility-integers +open import elementary-number-theory.equality-integers +open import elementary-number-theory.greatest-common-divisor-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.relatively-prime-integers funext +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.relatively-prime-integers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext +open import foundation.empty-types open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.equality-dependent-pair-types +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/relatively-prime-integers.lagda.md b/src/elementary-number-theory/relatively-prime-integers.lagda.md index 485b1c1a78..a3719203ab 100644 --- a/src/elementary-number-theory/relatively-prime-integers.lagda.md +++ b/src/elementary-number-theory/relatively-prime-integers.lagda.md @@ -1,25 +1,20 @@ # Relatively prime integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.relatively-prime-integers - (funext : function-extensionality) - where +module elementary-number-theory.relatively-prime-integers where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers funext -open import elementary-number-theory.equality-integers funext -open import elementary-number-theory.greatest-common-divisor-integers funext +open import elementary-number-theory.absolute-value-integers +open import elementary-number-theory.equality-integers +open import elementary-number-theory.greatest-common-divisor-integers open import elementary-number-theory.integers -open import elementary-number-theory.relatively-prime-natural-numbers funext +open import elementary-number-theory.relatively-prime-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md b/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md index 6f2f38b833..01f59c2f4b 100644 --- a/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md +++ b/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md @@ -1,30 +1,25 @@ # Relatively prime natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.relatively-prime-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.relatively-prime-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.greatest-common-divisor-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.greatest-common-divisor-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers funext +open import elementary-number-theory.prime-numbers -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md b/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md index a59209b752..d8a354ec93 100644 --- a/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md +++ b/src/elementary-number-theory/repeating-element-standard-finite-type.lagda.md @@ -1,12 +1,7 @@ # Repeating an element in a standard finite type ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.repeating-element-standard-finite-type - (funext : function-extensionality) - where +module elementary-number-theory.repeating-element-standard-finite-type where ```
Imports @@ -15,14 +10,14 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext +open import foundation.coproduct-types +open import foundation.empty-types +open import foundation.identity-types +open import foundation.negated-equality open import foundation.unit-type -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md b/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md index ffa1a33e98..f6fc313258 100644 --- a/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/retracts-of-natural-numbers.lagda.md @@ -1,22 +1,17 @@ # Retracts of the type of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.retracts-of-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.retracts-of-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.decidable-maps funext -open import foundation.retractions funext +open import foundation.decidable-maps +open import foundation.retractions open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/ring-of-integers.lagda.md b/src/elementary-number-theory/ring-of-integers.lagda.md index 4cc1f3d020..1ef3b8fff6 100644 --- a/src/elementary-number-theory/ring-of-integers.lagda.md +++ b/src/elementary-number-theory/ring-of-integers.lagda.md @@ -1,40 +1,35 @@ # The ring of integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.ring-of-integers - (funext : function-extensionality) - where +module elementary-number-theory.ring-of-integers where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.group-of-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.nonzero-integers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator funext -open import group-theory.homomorphisms-groups funext +open import group-theory.free-groups-with-one-generator +open import group-theory.homomorphisms-groups -open import ring-theory.homomorphisms-rings funext -open import ring-theory.initial-rings funext -open import ring-theory.integer-multiples-of-elements-rings funext -open import ring-theory.rings funext -open import ring-theory.trivial-rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.initial-rings +open import ring-theory.integer-multiples-of-elements-rings +open import ring-theory.rings +open import ring-theory.trivial-rings ```
diff --git a/src/elementary-number-theory/ring-of-rational-numbers.lagda.md b/src/elementary-number-theory/ring-of-rational-numbers.lagda.md index f806c74ec4..d0e4e6f220 100644 --- a/src/elementary-number-theory/ring-of-rational-numbers.lagda.md +++ b/src/elementary-number-theory/ring-of-rational-numbers.lagda.md @@ -3,31 +3,26 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.ring-of-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.ring-of-rational-numbers where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings -open import elementary-number-theory.additive-group-of-rational-numbers funext -open import elementary-number-theory.multiplication-rational-numbers funext -open import elementary-number-theory.multiplicative-monoid-of-rational-numbers funext +open import elementary-number-theory.additive-group-of-rational-numbers +open import elementary-number-theory.multiplication-rational-numbers +open import elementary-number-theory.multiplicative-monoid-of-rational-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md b/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md index 9319b26661..1727176161 100644 --- a/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md +++ b/src/elementary-number-theory/sieve-of-eratosthenes.lagda.md @@ -1,34 +1,29 @@ # The sieve of Eratosthenes ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.sieve-of-eratosthenes - (funext : function-extensionality) - where +module elementary-number-theory.sieve-of-eratosthenes where ```
Imports ```agda -open import elementary-number-theory.decidable-types funext -open import elementary-number-theory.divisibility-natural-numbers funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.factorials funext -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.decidable-types +open import elementary-number-theory.divisibility-natural-numbers +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.factorials +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/square-free-natural-numbers.lagda.md b/src/elementary-number-theory/square-free-natural-numbers.lagda.md index 5c8145c7eb..c168fab9ea 100644 --- a/src/elementary-number-theory/square-free-natural-numbers.lagda.md +++ b/src/elementary-number-theory/square-free-natural-numbers.lagda.md @@ -1,20 +1,15 @@ # Square-free natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.square-free-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.square-free-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers funext +open import elementary-number-theory.squares-natural-numbers open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/squares-integers.lagda.md b/src/elementary-number-theory/squares-integers.lagda.md index a2e5d0a22b..2497b17b33 100644 --- a/src/elementary-number-theory/squares-integers.lagda.md +++ b/src/elementary-number-theory/squares-integers.lagda.md @@ -1,34 +1,29 @@ # Squares in the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.squares-integers - (funext : function-extensionality) - where +module elementary-number-theory.squares-integers where ```
Imports ```agda -open import elementary-number-theory.absolute-value-integers funext +open import elementary-number-theory.absolute-value-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.squares-natural-numbers funext +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.squares-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/elementary-number-theory/squares-modular-arithmetic.lagda.md b/src/elementary-number-theory/squares-modular-arithmetic.lagda.md index 5048114191..7d77108c0c 100644 --- a/src/elementary-number-theory/squares-modular-arithmetic.lagda.md +++ b/src/elementary-number-theory/squares-modular-arithmetic.lagda.md @@ -1,27 +1,22 @@ # Squares in ℤₚ ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.squares-modular-arithmetic - (funext : function-extensionality) - where +module elementary-number-theory.squares-modular-arithmetic where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.modular-arithmetic open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-integers funext +open import elementary-number-theory.squares-integers -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.fibers-of-maps funext +open import univalent-combinatorics.fibers-of-maps ```
diff --git a/src/elementary-number-theory/squares-natural-numbers.lagda.md b/src/elementary-number-theory/squares-natural-numbers.lagda.md index 380da85a51..f8afd7063e 100644 --- a/src/elementary-number-theory/squares-natural-numbers.lagda.md +++ b/src/elementary-number-theory/squares-natural-numbers.lagda.md @@ -1,29 +1,24 @@ # Squares in the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.squares-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.squares-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.decidable-types funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.decidable-types +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.negation funext +open import foundation.identity-types +open import foundation.negation open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/standard-cyclic-groups.lagda.md b/src/elementary-number-theory/standard-cyclic-groups.lagda.md index dc733a625f..dc65ddde36 100644 --- a/src/elementary-number-theory/standard-cyclic-groups.lagda.md +++ b/src/elementary-number-theory/standard-cyclic-groups.lagda.md @@ -1,26 +1,21 @@ # The standard cyclic groups ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.standard-cyclic-groups - (funext : function-extensionality) - where +module elementary-number-theory.standard-cyclic-groups where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.modular-arithmetic open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.semigroups ```
diff --git a/src/elementary-number-theory/standard-cyclic-rings.lagda.md b/src/elementary-number-theory/standard-cyclic-rings.lagda.md index 4acaf2d692..60ffeb3ce6 100644 --- a/src/elementary-number-theory/standard-cyclic-rings.lagda.md +++ b/src/elementary-number-theory/standard-cyclic-rings.lagda.md @@ -1,42 +1,37 @@ # The standard cyclic rings ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.standard-cyclic-rings - (funext : function-extensionality) - where +module elementary-number-theory.standard-cyclic-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic funext -open import elementary-number-theory.modular-arithmetic funext-standard-finite-types +open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.ring-of-integers funext -open import elementary-number-theory.standard-cyclic-groups funext +open import elementary-number-theory.ring-of-integers +open import elementary-number-theory.standard-cyclic-groups open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.surjective-maps funext +open import foundation.existential-quantification +open import foundation.homotopies +open import foundation.identity-types +open import foundation.surjective-maps open import foundation.universe-levels -open import group-theory.cyclic-groups funext -open import group-theory.generating-elements-groups funext +open import group-theory.cyclic-groups +open import group-theory.generating-elements-groups -open import ring-theory.cyclic-rings funext -open import ring-theory.integer-multiples-of-elements-rings funext -open import ring-theory.rings funext +open import ring-theory.cyclic-rings +open import ring-theory.integer-multiples-of-elements-rings +open import ring-theory.rings ```
diff --git a/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md b/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md index 3f653608c4..d58fbf1f4c 100644 --- a/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md +++ b/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md @@ -1,50 +1,45 @@ # Strict inequality on the integer fractions ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.strict-inequality-integer-fractions - (funext : function-extensionality) - where +module elementary-number-theory.strict-inequality-integer-fractions where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions funext -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.addition-positive-and-negative-integers funext -open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.inequality-integer-fractions funext -open import elementary-number-theory.inequality-integers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-integer-fractions +open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-positive-and-negative-integers +open import elementary-number-theory.cross-multiplication-difference-integer-fractions +open import elementary-number-theory.difference-integers +open import elementary-number-theory.inequality-integer-fractions +open import elementary-number-theory.inequality-integers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.mediant-integer-fractions funext -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-positive-and-negative-integers funext -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.nonpositive-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.strict-inequality-integers funext +open import elementary-number-theory.mediant-integer-fractions +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-positive-and-negative-integers +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonpositive-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.strict-inequality-integers open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.cartesian-product-types +open import foundation.conjunction +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.disjunction +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/strict-inequality-integers.lagda.md b/src/elementary-number-theory/strict-inequality-integers.lagda.md index a734e29b5b..107592ee5c 100644 --- a/src/elementary-number-theory/strict-inequality-integers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-integers.lagda.md @@ -1,49 +1,44 @@ # Strict inequality on the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.strict-inequality-integers - (funext : function-extensionality) - where +module elementary-number-theory.strict-inequality-integers where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.addition-positive-and-negative-integers funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.inequality-integers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.addition-positive-and-negative-integers +open import elementary-number-theory.difference-integers +open import elementary-number-theory.inequality-integers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.negative-integers funext -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.nonpositive-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.negative-integers +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonpositive-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md b/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md index 3a3a3a2668..623bc26c65 100644 --- a/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md @@ -1,36 +1,31 @@ # Strict inequality on the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.strict-inequality-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.strict-inequality-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels diff --git a/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md b/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md index dfeed4a537..99d4619055 100644 --- a/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md @@ -1,54 +1,49 @@ # Strict inequality on the rational numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.strict-inequality-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.strict-inequality-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.addition-integer-fractions funext -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.cross-multiplication-difference-integer-fractions funext -open import elementary-number-theory.difference-integers funext -open import elementary-number-theory.difference-rational-numbers funext -open import elementary-number-theory.inequality-integer-fractions funext -open import elementary-number-theory.inequality-integers funext -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.integer-fractions funext +open import elementary-number-theory.addition-integer-fractions +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.cross-multiplication-difference-integer-fractions +open import elementary-number-theory.difference-integers +open import elementary-number-theory.difference-rational-numbers +open import elementary-number-theory.inequality-integer-fractions +open import elementary-number-theory.inequality-integers +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.integer-fractions open import elementary-number-theory.integers -open import elementary-number-theory.mediant-integer-fractions funext -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.nonnegative-integers funext -open import elementary-number-theory.nonpositive-integers funext -open import elementary-number-theory.positive-and-negative-integers funext -open import elementary-number-theory.positive-integers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.reduced-integer-fractions funext -open import elementary-number-theory.strict-inequality-integer-fractions funext -open import elementary-number-theory.strict-inequality-integers funext +open import elementary-number-theory.mediant-integer-fractions +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.nonnegative-integers +open import elementary-number-theory.nonpositive-integers +open import elementary-number-theory.positive-and-negative-integers +open import elementary-number-theory.positive-integers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.reduced-integer-fractions +open import elementary-number-theory.strict-inequality-integer-fractions +open import elementary-number-theory.strict-inequality-integers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.binary-relations +open import foundation.cartesian-product-types +open import foundation.conjunction +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.disjunction +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md b/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md index 386ffb069a..5083034a1f 100644 --- a/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md @@ -1,31 +1,26 @@ # Strict inequality on the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.strict-inequality-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.strict-inequality-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.coproduct-types +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md b/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md index 4b4a3a7a42..faab496e28 100644 --- a/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strictly-ordered-pairs-of-natural-numbers.lagda.md @@ -1,28 +1,23 @@ # Strictly ordered pairs of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.strictly-ordered-pairs-of-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.strictly-ordered-pairs-of-natural-numbers where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.pairs-of-distinct-elements funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.pairs-of-distinct-elements open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md b/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md index 8fe08da086..6a0bf777c5 100644 --- a/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md @@ -1,31 +1,25 @@ # The strong induction principle for the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.strong-induction-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.strong-induction-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/sums-of-natural-numbers.lagda.md b/src/elementary-number-theory/sums-of-natural-numbers.lagda.md index a67b8c7c50..a026d32a7c 100644 --- a/src/elementary-number-theory/sums-of-natural-numbers.lagda.md +++ b/src/elementary-number-theory/sums-of-natural-numbers.lagda.md @@ -1,12 +1,7 @@ # Sums of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.sums-of-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.sums-of-natural-numbers where ```
Imports @@ -15,24 +10,24 @@ module open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.constant-maps funext -open import foundation.coproduct-types funext +open import foundation.constant-maps +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import lists.lists -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/sylvesters-sequence.lagda.md b/src/elementary-number-theory/sylvesters-sequence.lagda.md index 4dab1c75b2..5b7094c31d 100644 --- a/src/elementary-number-theory/sylvesters-sequence.lagda.md +++ b/src/elementary-number-theory/sylvesters-sequence.lagda.md @@ -1,22 +1,17 @@ # Sylvester's sequence ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.sylvesters-sequence - (funext : function-extensionality) - where +module elementary-number-theory.sylvesters-sequence where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.ordinal-induction-natural-numbers funext -open import elementary-number-theory.products-of-natural-numbers funext +open import elementary-number-theory.ordinal-induction-natural-numbers +open import elementary-number-theory.products-of-natural-numbers -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/taxicab-numbers.lagda.md b/src/elementary-number-theory/taxicab-numbers.lagda.md index 3f4a986b63..6c89d1db21 100644 --- a/src/elementary-number-theory/taxicab-numbers.lagda.md +++ b/src/elementary-number-theory/taxicab-numbers.lagda.md @@ -1,30 +1,25 @@ # Taxicab numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.taxicab-numbers - (funext : function-extensionality) - where +module elementary-number-theory.taxicab-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.cubes-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.cubes-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.nonzero-natural-numbers funext +open import elementary-number-theory.nonzero-natural-numbers -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/twin-prime-conjecture.lagda.md b/src/elementary-number-theory/twin-prime-conjecture.lagda.md index 3af15730ba..a3c6993cca 100644 --- a/src/elementary-number-theory/twin-prime-conjecture.lagda.md +++ b/src/elementary-number-theory/twin-prime-conjecture.lagda.md @@ -1,22 +1,17 @@ # The Twin Prime conjecture ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.twin-prime-conjecture - (funext : function-extensionality) - where +module elementary-number-theory.twin-prime-conjecture where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.prime-numbers funext +open import elementary-number-theory.prime-numbers -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md b/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md index 4870b16e9d..9d3fa6833f 100644 --- a/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md +++ b/src/elementary-number-theory/type-arithmetic-natural-numbers.lagda.md @@ -1,34 +1,29 @@ # Type arithmetic with natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.type-arithmetic-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.type-arithmetic-natural-numbers where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.divisibility-natural-numbers funext +open import elementary-number-theory.divisibility-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers funext -open import elementary-number-theory.powers-of-two funext +open import elementary-number-theory.parity-natural-numbers +open import elementary-number-theory.powers-of-two open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.iterating-functions funext +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.iterating-functions open import foundation.split-surjective-maps -open import foundation.type-arithmetic-coproduct-types funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-empty-type open import foundation.type-arithmetic-unit-type open import foundation.unit-type @@ -41,7 +36,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.negation -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md b/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md index 50027169cd..4b6f36cc3b 100644 --- a/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/unit-elements-standard-finite-types.lagda.md @@ -1,31 +1,26 @@ # Unit elements in the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.unit-elements-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.unit-elements-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.divisibility-standard-finite-types funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.divisibility-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.squares-natural-numbers funext +open import elementary-number-theory.squares-natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md b/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md index 8b18c2c036..6740932fae 100644 --- a/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md +++ b/src/elementary-number-theory/unit-fractions-rational-numbers.lagda.md @@ -3,36 +3,31 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.unit-fractions-rational-numbers - (funext : function-extensionality) - where +module elementary-number-theory.unit-fractions-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.archimedean-property-positive-rational-numbers funext -open import elementary-number-theory.inequality-integers funext -open import elementary-number-theory.inequality-rational-numbers funext +open import elementary-number-theory.archimedean-property-positive-rational-numbers +open import elementary-number-theory.inequality-integers +open import elementary-number-theory.inequality-rational-numbers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.multiplication-rational-numbers funext -open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers funext -open import elementary-number-theory.nonzero-natural-numbers funext -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-integers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.multiplication-rational-numbers +open import elementary-number-theory.multiplicative-group-of-positive-rational-numbers +open import elementary-number-theory.nonzero-natural-numbers +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-integers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types -open import group-theory.groups funext +open import group-theory.groups ```
diff --git a/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md b/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md index 0d12f7c2c0..3830ea8381 100644 --- a/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/unit-similarity-standard-finite-types.lagda.md @@ -1,30 +1,25 @@ # Unit similarity on the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.unit-similarity-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.unit-similarity-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.unit-elements-standard-finite-types funext +open import elementary-number-theory.unit-elements-standard-finite-types open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md index 241312ac95..54e612e108 100644 --- a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md @@ -1,20 +1,15 @@ # The universal property of the conatural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.universal-property-conatural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.universal-property-conatural-numbers where ```
Imports ```agda -open import foundation.coalgebras-maybe funext -open import foundation.contractible-types funext -open import foundation.morphisms-coalgebras-maybe funext +open import foundation.coalgebras-maybe +open import foundation.contractible-types +open import foundation.morphisms-coalgebras-maybe open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/universal-property-integers.lagda.md b/src/elementary-number-theory/universal-property-integers.lagda.md index 01b3fe13b1..2d36403b4e 100644 --- a/src/elementary-number-theory/universal-property-integers.lagda.md +++ b/src/elementary-number-theory/universal-property-integers.lagda.md @@ -1,12 +1,7 @@ # The universal property of the integers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.universal-property-integers - (funext : function-extensionality) - where +module elementary-number-theory.universal-property-integers where ```
Imports @@ -15,20 +10,20 @@ module open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositions open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/universal-property-natural-numbers.lagda.md b/src/elementary-number-theory/universal-property-natural-numbers.lagda.md index 1de318743b..69460d3015 100644 --- a/src/elementary-number-theory/universal-property-natural-numbers.lagda.md +++ b/src/elementary-number-theory/universal-property-natural-numbers.lagda.md @@ -1,12 +1,7 @@ # The universal property of the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.universal-property-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.universal-property-natural-numbers where ```
Imports @@ -15,19 +10,19 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation ```
diff --git a/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md b/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md index c667e4cbb4..2a0529164b 100644 --- a/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md +++ b/src/elementary-number-theory/upper-bounds-natural-numbers.lagda.md @@ -1,20 +1,15 @@ # Upper bounds for type families over the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.upper-bounds-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.upper-bounds-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md b/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md index 8155f22fee..a72905645f 100644 --- a/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md +++ b/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md @@ -1,33 +1,28 @@ # The well-ordering principle of the natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.well-ordering-principle-natural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.well-ordering-principle-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.lower-bounds-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.lower-bounds-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.hilberts-epsilon-operators funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.functoriality-dependent-pair-types +open import foundation.hilberts-epsilon-operators +open import foundation.identity-types +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md index 68a7cf59ae..a422c722f0 100644 --- a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md @@ -1,51 +1,46 @@ # The well-ordering principle of the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.well-ordering-principle-standard-finite-types - (funext : function-extensionality) - where +module elementary-number-theory.well-ordering-principle-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-natural-numbers funext +open import elementary-number-theory.well-ordering-principle-natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.hilberts-epsilon-operators funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-propositional-truncation +open import foundation.hilberts-epsilon-operators +open import foundation.identity-types +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-empty-type open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.decidable-dependent-pair-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.decidable-dependent-pair-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/elementary-number-theory/zero-conatural-numbers.lagda.md b/src/elementary-number-theory/zero-conatural-numbers.lagda.md index 0dda5718df..0daa319c80 100644 --- a/src/elementary-number-theory/zero-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/zero-conatural-numbers.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - elementary-number-theory.zero-conatural-numbers - (funext : function-extensionality) - where +module elementary-number-theory.zero-conatural-numbers where ```
Imports ```agda -open import elementary-number-theory.conatural-numbers funext +open import elementary-number-theory.conatural-numbers -open import foundation.coproduct-types funext -open import foundation.decidable-types funext -open import foundation.function-types funext -open import foundation.negation funext +open import foundation.coproduct-types +open import foundation.decidable-types +open import foundation.function-types +open import foundation.negation open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/finite-algebra.lagda.md b/src/finite-algebra.lagda.md index 87674a38f5..3e2d66d204 100644 --- a/src/finite-algebra.lagda.md +++ b/src/finite-algebra.lagda.md @@ -3,21 +3,16 @@ ## Modules in the finite algebra namespace ```agda -open import foundation.function-extensionality-axiom +module finite-algebra where -module - finite-algebra - (funext : function-extensionality) - where - -open import finite-algebra.commutative-finite-rings funext public -open import finite-algebra.dependent-products-commutative-finite-rings funext public -open import finite-algebra.dependent-products-finite-rings funext public -open import finite-algebra.finite-fields funext public -open import finite-algebra.finite-rings funext public -open import finite-algebra.homomorphisms-commutative-finite-rings funext public -open import finite-algebra.homomorphisms-finite-rings funext public -open import finite-algebra.products-commutative-finite-rings funext public -open import finite-algebra.products-finite-rings funext public -open import finite-algebra.semisimple-commutative-finite-rings funext public +open import finite-algebra.commutative-finite-rings public +open import finite-algebra.dependent-products-commutative-finite-rings public +open import finite-algebra.dependent-products-finite-rings public +open import finite-algebra.finite-fields public +open import finite-algebra.finite-rings public +open import finite-algebra.homomorphisms-commutative-finite-rings public +open import finite-algebra.homomorphisms-finite-rings public +open import finite-algebra.products-commutative-finite-rings public +open import finite-algebra.products-finite-rings public +open import finite-algebra.semisimple-commutative-finite-rings public ``` diff --git a/src/finite-algebra/commutative-finite-rings.lagda.md b/src/finite-algebra/commutative-finite-rings.lagda.md index 05cece41f0..035aeea3e7 100644 --- a/src/finite-algebra/commutative-finite-rings.lagda.md +++ b/src/finite-algebra/commutative-finite-rings.lagda.md @@ -1,56 +1,51 @@ # Commutative finite rings ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.commutative-finite-rings - (funext : function-extensionality) - where +module finite-algebra.commutative-finite-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-semirings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-algebra.finite-rings funext +open import finite-algebra.finite-rings open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps open import foundation.interchange-law -open import foundation.involutions funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.involutions +open import foundation.propositions +open import foundation.sets open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import ring-theory.rings funext -open import ring-theory.semirings funext +open import ring-theory.rings +open import ring-theory.semirings -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md b/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md index 0806911183..82cdf56aa9 100644 --- a/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/dependent-products-commutative-finite-rings.lagda.md @@ -1,37 +1,32 @@ # Dependent products of commutative finit rings ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.dependent-products-commutative-finite-rings - (funext : function-extensionality) - where +module finite-algebra.dependent-products-commutative-finite-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.dependent-products-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.dependent-products-commutative-rings -open import finite-algebra.commutative-finite-rings funext -open import finite-algebra.dependent-products-finite-rings funext -open import finite-algebra.finite-rings funext +open import finite-algebra.commutative-finite-rings +open import finite-algebra.dependent-products-finite-rings +open import finite-algebra.finite-rings open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids -open import ring-theory.dependent-products-rings funext -open import ring-theory.rings funext +open import ring-theory.dependent-products-rings +open import ring-theory.rings -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-algebra/dependent-products-finite-rings.lagda.md b/src/finite-algebra/dependent-products-finite-rings.lagda.md index 493d1bccdf..a1c2f98a52 100644 --- a/src/finite-algebra/dependent-products-finite-rings.lagda.md +++ b/src/finite-algebra/dependent-products-finite-rings.lagda.md @@ -1,36 +1,31 @@ # Dependent products of finite rings ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.dependent-products-finite-rings - (funext : function-extensionality) - where +module finite-algebra.dependent-products-finite-rings where ```
Imports ```agda -open import finite-algebra.finite-rings funext +open import finite-algebra.finite-rings open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import ring-theory.dependent-products-rings funext -open import ring-theory.rings funext -open import ring-theory.semirings funext +open import ring-theory.dependent-products-rings +open import ring-theory.rings +open import ring-theory.semirings -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-algebra/finite-fields.lagda.md b/src/finite-algebra/finite-fields.lagda.md index 56c2465cdd..27425b25c9 100644 --- a/src/finite-algebra/finite-fields.lagda.md +++ b/src/finite-algebra/finite-fields.lagda.md @@ -1,52 +1,47 @@ # Finite fields ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.finite-fields - (funext : function-extensionality) - where +module finite-algebra.finite-fields where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.commutative-semirings open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-algebra.commutative-finite-rings funext -open import finite-algebra.finite-rings funext +open import finite-algebra.commutative-finite-rings +open import finite-algebra.finite-rings open import foundation.action-on-identifications-binary-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.involutions funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.involutions +open import foundation.propositions +open import foundation.sets open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import ring-theory.division-rings funext -open import ring-theory.rings funext -open import ring-theory.semirings funext +open import ring-theory.division-rings +open import ring-theory.rings +open import ring-theory.semirings ```
diff --git a/src/finite-algebra/finite-rings.lagda.md b/src/finite-algebra/finite-rings.lagda.md index 199d1dbc48..e78ca56b4d 100644 --- a/src/finite-algebra/finite-rings.lagda.md +++ b/src/finite-algebra/finite-rings.lagda.md @@ -1,12 +1,7 @@ # Finite rings ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.finite-rings - (funext : function-extensionality) - where +module finite-algebra.finite-rings where ```
Imports @@ -15,39 +10,39 @@ module open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-abelian-groups funext -open import finite-group-theory.finite-groups funext -open import finite-group-theory.finite-monoids funext +open import finite-group-theory.finite-abelian-groups +open import finite-group-theory.finite-groups +open import finite-group-theory.finite-monoids -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.involutions funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.involutions +open import foundation.propositions +open import foundation.sets open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import ring-theory.rings funext -open import ring-theory.semirings funext +open import ring-theory.rings +open import ring-theory.semirings -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md b/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md index d0f57b14d8..21ac9504c6 100644 --- a/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md @@ -1,33 +1,28 @@ # Homomorphisms of commutative finite rings ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.homomorphisms-commutative-finite-rings - (funext : function-extensionality) - where +module finite-algebra.homomorphisms-commutative-finite-rings where ```
Imports ```agda -open import commutative-algebra.homomorphisms-commutative-rings funext -open import commutative-algebra.homomorphisms-commutative-semirings funext +open import commutative-algebra.homomorphisms-commutative-rings +open import commutative-algebra.homomorphisms-commutative-semirings -open import finite-algebra.commutative-finite-rings funext +open import finite-algebra.commutative-finite-rings -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.homomorphisms-monoids funext +open import group-theory.homomorphisms-abelian-groups +open import group-theory.homomorphisms-monoids -open import ring-theory.homomorphisms-rings funext +open import ring-theory.homomorphisms-rings ```
diff --git a/src/finite-algebra/homomorphisms-finite-rings.lagda.md b/src/finite-algebra/homomorphisms-finite-rings.lagda.md index e7b4be06cc..9cc03a1249 100644 --- a/src/finite-algebra/homomorphisms-finite-rings.lagda.md +++ b/src/finite-algebra/homomorphisms-finite-rings.lagda.md @@ -1,30 +1,25 @@ # Homomorphisms of finite rings ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.homomorphisms-finite-rings - (funext : function-extensionality) - where +module finite-algebra.homomorphisms-finite-rings where ```
Imports ```agda -open import finite-algebra.finite-rings funext +open import finite-algebra.finite-rings -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.homomorphisms-monoids funext +open import group-theory.homomorphisms-abelian-groups +open import group-theory.homomorphisms-monoids -open import ring-theory.homomorphisms-rings funext +open import ring-theory.homomorphisms-rings ```
diff --git a/src/finite-algebra/products-commutative-finite-rings.lagda.md b/src/finite-algebra/products-commutative-finite-rings.lagda.md index c0c5f3654a..46ad564c75 100644 --- a/src/finite-algebra/products-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/products-commutative-finite-rings.lagda.md @@ -1,33 +1,28 @@ # Products of commutative finite rings ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.products-commutative-finite-rings - (funext : function-extensionality) - where +module finite-algebra.products-commutative-finite-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext -open import commutative-algebra.products-commutative-rings funext +open import commutative-algebra.commutative-rings +open import commutative-algebra.products-commutative-rings -open import finite-algebra.commutative-finite-rings funext -open import finite-algebra.products-finite-rings funext +open import finite-algebra.commutative-finite-rings +open import finite-algebra.products-finite-rings open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.semigroups -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-algebra/products-finite-rings.lagda.md b/src/finite-algebra/products-finite-rings.lagda.md index c97d3d8d74..4555ad4b74 100644 --- a/src/finite-algebra/products-finite-rings.lagda.md +++ b/src/finite-algebra/products-finite-rings.lagda.md @@ -1,33 +1,28 @@ # Products of finite rings ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.products-finite-rings - (funext : function-extensionality) - where +module finite-algebra.products-finite-rings where ```
Imports ```agda -open import finite-algebra.finite-rings funext +open import finite-algebra.finite-rings open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.semigroups -open import ring-theory.products-rings funext -open import ring-theory.rings funext +open import ring-theory.products-rings +open import ring-theory.rings -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md b/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md index 2e3029af1b..7c72cb1712 100644 --- a/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/semisimple-commutative-finite-rings.lagda.md @@ -1,12 +1,7 @@ # Semisimple commutative finite rings ```agda -open import foundation.function-extensionality-axiom - -module - finite-algebra.semisimple-commutative-finite-rings - (funext : function-extensionality) - where +module finite-algebra.semisimple-commutative-finite-rings where ```
Imports @@ -14,20 +9,20 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-algebra.commutative-finite-rings funext -open import finite-algebra.dependent-products-commutative-finite-rings funext -open import finite-algebra.finite-fields funext -open import finite-algebra.homomorphisms-commutative-finite-rings funext +open import finite-algebra.commutative-finite-rings +open import finite-algebra.dependent-products-commutative-finite-rings +open import finite-algebra.finite-fields +open import finite-algebra.homomorphisms-commutative-finite-rings open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.propositional-truncations open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory.lagda.md b/src/finite-group-theory.lagda.md index 82cd1a7004..8c555ee159 100644 --- a/src/finite-group-theory.lagda.md +++ b/src/finite-group-theory.lagda.md @@ -3,33 +3,28 @@ ## Modules in the finite group theory namespace ```agda -open import foundation.function-extensionality-axiom +module finite-group-theory where -module - finite-group-theory - (funext : function-extensionality) - where - -open import finite-group-theory.abstract-quaternion-group funext public -open import finite-group-theory.alternating-concrete-groups funext public -open import finite-group-theory.alternating-groups funext public -open import finite-group-theory.cartier-delooping-sign-homomorphism funext public -open import finite-group-theory.concrete-quaternion-group funext public -open import finite-group-theory.delooping-sign-homomorphism funext public -open import finite-group-theory.finite-abelian-groups funext public -open import finite-group-theory.finite-commutative-monoids funext public -open import finite-group-theory.finite-groups funext public -open import finite-group-theory.finite-monoids funext public -open import finite-group-theory.finite-semigroups funext public -open import finite-group-theory.finite-type-groups funext public -open import finite-group-theory.groups-of-order-2 funext public -open import finite-group-theory.orbits-permutations funext public -open import finite-group-theory.permutations funext public -open import finite-group-theory.permutations-standard-finite-types funext public -open import finite-group-theory.sign-homomorphism funext public -open import finite-group-theory.simpson-delooping-sign-homomorphism funext public -open import finite-group-theory.subgroups-finite-groups funext public -open import finite-group-theory.tetrahedra-in-3-space funext public -open import finite-group-theory.transpositions funext public -open import finite-group-theory.transpositions-standard-finite-types funext public +open import finite-group-theory.abstract-quaternion-group public +open import finite-group-theory.alternating-concrete-groups public +open import finite-group-theory.alternating-groups public +open import finite-group-theory.cartier-delooping-sign-homomorphism public +open import finite-group-theory.concrete-quaternion-group public +open import finite-group-theory.delooping-sign-homomorphism public +open import finite-group-theory.finite-abelian-groups public +open import finite-group-theory.finite-commutative-monoids public +open import finite-group-theory.finite-groups public +open import finite-group-theory.finite-monoids public +open import finite-group-theory.finite-semigroups public +open import finite-group-theory.finite-type-groups public +open import finite-group-theory.groups-of-order-2 public +open import finite-group-theory.orbits-permutations public +open import finite-group-theory.permutations public +open import finite-group-theory.permutations-standard-finite-types public +open import finite-group-theory.sign-homomorphism public +open import finite-group-theory.simpson-delooping-sign-homomorphism public +open import finite-group-theory.subgroups-finite-groups public +open import finite-group-theory.tetrahedra-in-3-space public +open import finite-group-theory.transpositions public +open import finite-group-theory.transpositions-standard-finite-types public ``` diff --git a/src/finite-group-theory/abstract-quaternion-group.lagda.md b/src/finite-group-theory/abstract-quaternion-group.lagda.md index 2b947f4143..c8a8199ee7 100644 --- a/src/finite-group-theory/abstract-quaternion-group.lagda.md +++ b/src/finite-group-theory/abstract-quaternion-group.lagda.md @@ -1,38 +1,33 @@ # The abstract quaternion group of order `8` ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.abstract-quaternion-group - (funext : function-extensionality) - where +module finite-group-theory.abstract-quaternion-group where ```
Imports ```agda -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.groups +open import group-theory.semigroups -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/alternating-concrete-groups.lagda.md b/src/finite-group-theory/alternating-concrete-groups.lagda.md index 3a2447efff..388be53b80 100644 --- a/src/finite-group-theory/alternating-concrete-groups.lagda.md +++ b/src/finite-group-theory/alternating-concrete-groups.lagda.md @@ -1,12 +1,7 @@ # Alternating concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.alternating-concrete-groups - (funext : function-extensionality) - where +module finite-group-theory.alternating-concrete-groups where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.cartier-delooping-sign-homomorphism funext -open import finite-group-theory.finite-type-groups funext +open import finite-group-theory.cartier-delooping-sign-homomorphism +open import finite-group-theory.finite-type-groups open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.kernels-homomorphisms-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.kernels-homomorphisms-concrete-groups ```
diff --git a/src/finite-group-theory/alternating-groups.lagda.md b/src/finite-group-theory/alternating-groups.lagda.md index 02a37d0493..975c699ac4 100644 --- a/src/finite-group-theory/alternating-groups.lagda.md +++ b/src/finite-group-theory/alternating-groups.lagda.md @@ -1,12 +1,7 @@ # Alternating groups ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.alternating-groups - (funext : function-extensionality) - where +module finite-group-theory.alternating-groups where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.sign-homomorphism funext +open import finite-group-theory.sign-homomorphism -open import group-theory.groups funext -open import group-theory.kernels-homomorphisms-groups funext -open import group-theory.symmetric-groups funext +open import group-theory.groups +open import group-theory.kernels-homomorphisms-groups +open import group-theory.symmetric-groups -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md index d89db866d8..bf4f606cc2 100644 --- a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - finite-group-theory.cartier-delooping-sign-homomorphism - (funext : function-extensionality) - where +module finite-group-theory.cartier-delooping-sign-homomorphism where ```
Imports @@ -17,36 +12,36 @@ module open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.delooping-sign-homomorphism funext -open import finite-group-theory.finite-type-groups funext -open import finite-group-theory.sign-homomorphism funext -open import finite-group-theory.transpositions funext +open import finite-group-theory.delooping-sign-homomorphism +open import finite-group-theory.finite-type-groups +open import finite-group-theory.sign-homomorphism +open import finite-group-theory.transpositions -open import foundation.action-on-equivalences-type-families-over-subuniverses funext +open import foundation.action-on-equivalences-type-families-over-subuniverses open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.mere-equivalences funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.raising-universe-levels funext +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.identity-types +open import foundation.mere-equivalences +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.raising-universe-levels open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type open import foundation.universe-levels -open import group-theory.homomorphisms-concrete-groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.loop-groups-sets funext -open import group-theory.symmetric-groups funext +open import group-theory.homomorphisms-concrete-groups +open import group-theory.homomorphisms-groups +open import group-theory.isomorphisms-groups +open import group-theory.loop-groups-sets +open import group-theory.symmetric-groups -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.orientations-complete-undirected-graph funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.orientations-complete-undirected-graph +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/concrete-quaternion-group.lagda.md b/src/finite-group-theory/concrete-quaternion-group.lagda.md index aa95200325..d424d3600b 100644 --- a/src/finite-group-theory/concrete-quaternion-group.lagda.md +++ b/src/finite-group-theory/concrete-quaternion-group.lagda.md @@ -1,12 +1,7 @@ # The concrete quaternion group ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.concrete-quaternion-group - (funext : function-extensionality) - where +module finite-group-theory.concrete-quaternion-group where ```
Imports @@ -15,16 +10,16 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.isolated-elements funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.isolated-elements open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.complements-isolated-elements funext -open import univalent-combinatorics.cubes funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.equivalences-cubes funext +open import univalent-combinatorics.complements-isolated-elements +open import univalent-combinatorics.cubes +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.equivalences-cubes ```
diff --git a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md index 230155c4a4..4cc333bf45 100644 --- a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md @@ -3,86 +3,80 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - finite-group-theory.delooping-sign-homomorphism - (funext : function-extensionality) - where +module finite-group-theory.delooping-sign-homomorphism where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-type-groups funext -open import finite-group-theory.permutations funext -open import finite-group-theory.sign-homomorphism funext -open import finite-group-theory.transpositions funext +open import finite-group-theory.finite-type-groups +open import finite-group-theory.permutations +open import finite-group-theory.sign-homomorphism +open import finite-group-theory.transpositions -open import foundation.action-on-equivalences-type-families-over-subuniverses funext +open import foundation.action-on-equivalences-type-families-over-subuniverses open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalence-classes funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalence-induction funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.functoriality-set-quotients funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.involutions funext -open import foundation.logical-equivalences funext -open import foundation.mere-equivalences funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalence-classes +open import foundation.equivalence-extensionality +open import foundation.equivalence-induction +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-propositional-truncation +open import foundation.functoriality-set-quotients +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.involutions +open import foundation.logical-equivalences +open import foundation.mere-equivalences +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.reflecting-maps-equivalence-relations +open import foundation.sets open import foundation.transport-along-identifications -open import foundation.truncated-types funext -open import foundation.uniqueness-set-quotients funext +open import foundation.truncated-types +open import foundation.uniqueness-set-quotients open import foundation.unit-type -open import foundation.univalence funext -open import foundation.universal-property-set-quotients funext +open import foundation.univalence +open import foundation.universal-property-set-quotients open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import group-theory.generating-sets-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-concrete-groups funext -open import group-theory.homomorphisms-generated-subgroups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-semigroups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.loop-groups-sets funext -open import group-theory.symmetric-groups funext +open import group-theory.generating-sets-groups +open import group-theory.groups +open import group-theory.homomorphisms-concrete-groups +open import group-theory.homomorphisms-generated-subgroups +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-semigroups +open import group-theory.isomorphisms-groups +open import group-theory.loop-groups-sets +open import group-theory.symmetric-groups -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.set-quotients-of-index-two funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.set-quotients-of-index-two +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/finite-abelian-groups.lagda.md b/src/finite-group-theory/finite-abelian-groups.lagda.md index f4fb6e2263..51bc616d82 100644 --- a/src/finite-group-theory/finite-abelian-groups.lagda.md +++ b/src/finite-group-theory/finite-abelian-groups.lagda.md @@ -1,36 +1,31 @@ # Abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.finite-abelian-groups - (funext : function-extensionality) - where +module finite-group-theory.finite-abelian-groups where ```
Imports ```agda -open import finite-group-theory.finite-groups funext +open import finite-group-theory.finite-groups -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.interchange-law -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-group-theory/finite-commutative-monoids.lagda.md b/src/finite-group-theory/finite-commutative-monoids.lagda.md index 8003e1c6bb..d66dd10353 100644 --- a/src/finite-group-theory/finite-commutative-monoids.lagda.md +++ b/src/finite-group-theory/finite-commutative-monoids.lagda.md @@ -1,32 +1,27 @@ # Finite Commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.finite-commutative-monoids - (funext : function-extensionality) - where +module finite-group-theory.finite-commutative-monoids where ```
Imports ```agda -open import finite-group-theory.finite-monoids funext +open import finite-group-theory.finite-monoids -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.commutative-monoids +open import group-theory.monoids +open import group-theory.semigroups -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-group-theory/finite-groups.lagda.md b/src/finite-group-theory/finite-groups.lagda.md index faf3070352..b52469f559 100644 --- a/src/finite-group-theory/finite-groups.lagda.md +++ b/src/finite-group-theory/finite-groups.lagda.md @@ -1,12 +1,7 @@ # Finite groups ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.finite-groups - (funext : function-extensionality) - where +module finite-group-theory.finite-groups where ```
Imports @@ -14,51 +9,51 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-monoids funext -open import finite-group-theory.finite-semigroups funext +open import finite-group-theory.finite-monoids +open import finite-group-theory.finite-semigroups -open import foundation.1-types funext -open import foundation.binary-embeddings funext +open import foundation.1-types +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.decidable-equality funext -open import foundation.decidable-types funext -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.decidable-equality +open import foundation.decidable-types +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.mere-equivalences +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.set-truncations +open import foundation.sets open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.category-of-groups funext -open import group-theory.commuting-elements-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.category-of-groups +open import group-theory.commuting-elements-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups open import structured-types.pointed-types -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-dependent-pair-types -open import univalent-combinatorics.decidable-dependent-function-types funext -open import univalent-combinatorics.decidable-dependent-pair-types funext -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.finitely-many-connected-components funext -open import univalent-combinatorics.function-types funext -open import univalent-combinatorics.pi-finite-types funext -open import univalent-combinatorics.standard-finite-types funext -open import univalent-combinatorics.untruncated-pi-finite-types funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-dependent-pair-types +open import univalent-combinatorics.decidable-dependent-function-types +open import univalent-combinatorics.decidable-dependent-pair-types +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finitely-many-connected-components +open import univalent-combinatorics.function-types +open import univalent-combinatorics.pi-finite-types +open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.untruncated-pi-finite-types ```
diff --git a/src/finite-group-theory/finite-monoids.lagda.md b/src/finite-group-theory/finite-monoids.lagda.md index 4215719fa4..36b3f1e29b 100644 --- a/src/finite-group-theory/finite-monoids.lagda.md +++ b/src/finite-group-theory/finite-monoids.lagda.md @@ -1,12 +1,7 @@ # Finite monoids ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.finite-monoids - (funext : function-extensionality) - where +module finite-group-theory.finite-monoids where ```
Imports @@ -14,38 +9,38 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.finite-semigroups funext +open import finite-group-theory.finite-semigroups -open import foundation.1-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.1-types +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.mere-equivalences +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.set-truncations +open import foundation.sets open import foundation.type-arithmetic-dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.monoids funext -open import group-theory.semigroups funext - -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.decidable-dependent-function-types funext -open import univalent-combinatorics.decidable-dependent-pair-types funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.finitely-many-connected-components funext -open import univalent-combinatorics.pi-finite-types funext -open import univalent-combinatorics.standard-finite-types funext -open import univalent-combinatorics.untruncated-pi-finite-types funext +open import group-theory.monoids +open import group-theory.semigroups + +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.decidable-dependent-function-types +open import univalent-combinatorics.decidable-dependent-pair-types +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finitely-many-connected-components +open import univalent-combinatorics.pi-finite-types +open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.untruncated-pi-finite-types ```
diff --git a/src/finite-group-theory/finite-semigroups.lagda.md b/src/finite-group-theory/finite-semigroups.lagda.md index 18769ff110..40f90172d9 100644 --- a/src/finite-group-theory/finite-semigroups.lagda.md +++ b/src/finite-group-theory/finite-semigroups.lagda.md @@ -1,12 +1,7 @@ # Finite semigroups ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.finite-semigroups - (funext : function-extensionality) - where +module finite-group-theory.finite-semigroups where ```
Imports @@ -14,31 +9,31 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types funext -open import foundation.decidable-propositions funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.mere-equivalences funext -open import foundation.propositions funext -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.1-types +open import foundation.decidable-propositions +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.mere-equivalences +open import foundation.propositions +open import foundation.set-truncations +open import foundation.sets open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.category-of-semigroups funext -open import group-theory.semigroups funext - -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.finitely-many-connected-components funext -open import univalent-combinatorics.function-types funext -open import univalent-combinatorics.pi-finite-types funext -open import univalent-combinatorics.standard-finite-types funext -open import univalent-combinatorics.untruncated-pi-finite-types funext +open import group-theory.category-of-semigroups +open import group-theory.semigroups + +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finitely-many-connected-components +open import univalent-combinatorics.function-types +open import univalent-combinatorics.pi-finite-types +open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.untruncated-pi-finite-types ```
diff --git a/src/finite-group-theory/finite-type-groups.lagda.md b/src/finite-group-theory/finite-type-groups.lagda.md index 32862afa87..4b7783f027 100644 --- a/src/finite-group-theory/finite-type-groups.lagda.md +++ b/src/finite-group-theory/finite-type-groups.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - finite-group-theory.finite-type-groups - (funext : function-extensionality) - where +module finite-group-theory.finite-type-groups where ```
Imports @@ -16,36 +11,35 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.sets funext -open import foundation.truncated-types funext +open import foundation.equality-dependent-pair-types +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.sets +open import foundation.truncated-types open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-semigroups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.loop-groups-sets funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.concrete-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-semigroups +open import group-theory.isomorphisms-groups +open import group-theory.loop-groups-sets +open import group-theory.monoids +open import group-theory.semigroups -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/groups-of-order-2.lagda.md b/src/finite-group-theory/groups-of-order-2.lagda.md index 623f3cc98e..05de139f31 100644 --- a/src/finite-group-theory/groups-of-order-2.lagda.md +++ b/src/finite-group-theory/groups-of-order-2.lagda.md @@ -3,39 +3,34 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - finite-group-theory.groups-of-order-2 - (funext : function-extensionality) - where +module finite-group-theory.groups-of-order-2 where ```
Imports ```agda -open import elementary-number-theory.standard-cyclic-groups funext +open import elementary-number-theory.standard-cyclic-groups -open import finite-group-theory.finite-groups funext +open import finite-group-theory.finite-groups open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.mere-equivalences +open import foundation.propositional-truncations +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.symmetric-groups funext +open import group-theory.groups +open import group-theory.isomorphisms-groups +open import group-theory.symmetric-groups -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/orbits-permutations.lagda.md b/src/finite-group-theory/orbits-permutations.lagda.md index 743761041a..06919a3b39 100644 --- a/src/finite-group-theory/orbits-permutations.lagda.md +++ b/src/finite-group-theory/orbits-permutations.lagda.md @@ -3,71 +3,66 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - finite-group-theory.orbits-permutations - (funext : function-extensionality) - where +module finite-group-theory.orbits-permutations where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.decidable-types funext -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.euclidean-division-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.lower-bounds-natural-numbers funext +open import elementary-number-theory.decidable-types +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.euclidean-division-natural-numbers +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.lower-bounds-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.well-ordering-principle-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.well-ordering-principle-natural-numbers -open import finite-group-theory.transpositions funext +open import finite-group-theory.transpositions open import foundation.action-on-identifications-functions -open import foundation.automorphisms funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-equivalence-relations funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.automorphisms +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-equivalence-relations +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalence-classes funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.iterating-functions funext -open import foundation.logical-equivalences funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.repetitions-of-values funext -open import foundation.sets funext +open import foundation.double-negation +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalence-classes +open import foundation.equivalence-extensionality +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.iterating-functions +open import foundation.logical-equivalences +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.repetitions-of-values +open import foundation.sets open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.image-of-maps funext -open import univalent-combinatorics.pigeonhole-principle funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.image-of-maps +open import univalent-combinatorics.pigeonhole-principle +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/permutations-standard-finite-types.lagda.md b/src/finite-group-theory/permutations-standard-finite-types.lagda.md index 7c89ca92cc..0be0d3314d 100644 --- a/src/finite-group-theory/permutations-standard-finite-types.lagda.md +++ b/src/finite-group-theory/permutations-standard-finite-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - finite-group-theory.permutations-standard-finite-types - (funext : function-extensionality) - where +module finite-group-theory.permutations-standard-finite-types where ```
Imports @@ -16,37 +11,37 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.transpositions funext +open import finite-group-theory.transpositions open import foundation.action-on-identifications-functions -open import foundation.automorphisms funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.automorphisms +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.equivalences funext-maybe -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.equivalences-maybe +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.propositions +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import lists.functoriality-lists funext +open import lists.functoriality-lists open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/permutations.lagda.md b/src/finite-group-theory/permutations.lagda.md index 65e2f75e14..02097ffebf 100644 --- a/src/finite-group-theory/permutations.lagda.md +++ b/src/finite-group-theory/permutations.lagda.md @@ -3,58 +3,53 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - finite-group-theory.permutations - (funext : function-extensionality) - where +module finite-group-theory.permutations where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import finite-group-theory.orbits-permutations funext -open import finite-group-theory.permutations-standard-finite-types funext -open import finite-group-theory.transpositions funext +open import finite-group-theory.orbits-permutations +open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.transpositions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.iterating-functions funext -open import foundation.iterating-involutions funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.truncated-types funext +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.iterating-functions +open import foundation.iterating-involutions +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.generating-sets-groups funext -open import group-theory.subgroups-generated-by-subsets-groups funext -open import group-theory.symmetric-groups funext +open import group-theory.generating-sets-groups +open import group-theory.subgroups-generated-by-subsets-groups +open import group-theory.symmetric-groups -open import lists.functoriality-lists funext +open import lists.functoriality-lists open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/sign-homomorphism.lagda.md b/src/finite-group-theory/sign-homomorphism.lagda.md index 152ac57b17..877705c2d4 100644 --- a/src/finite-group-theory/sign-homomorphism.lagda.md +++ b/src/finite-group-theory/sign-homomorphism.lagda.md @@ -1,50 +1,45 @@ # The sign homomorphism ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.sign-homomorphism - (funext : function-extensionality) - where +module finite-group-theory.sign-homomorphism where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations funext -open import finite-group-theory.transpositions funext +open import finite-group-theory.permutations +open import finite-group-theory.transpositions open import foundation.action-on-identifications-functions -open import foundation.automorphisms funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.automorphisms +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-semigroups funext -open import group-theory.symmetric-groups funext +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-semigroups +open import group-theory.symmetric-groups -open import lists.concatenation-lists funext -open import lists.functoriality-lists funext +open import lists.concatenation-lists +open import lists.functoriality-lists open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md index 197facd71d..b416cd96b6 100644 --- a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md @@ -3,70 +3,65 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - finite-group-theory.simpson-delooping-sign-homomorphism - (funext : function-extensionality) - where +module finite-group-theory.simpson-delooping-sign-homomorphism where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import finite-group-theory.delooping-sign-homomorphism funext -open import finite-group-theory.finite-type-groups funext -open import finite-group-theory.permutations funext -open import finite-group-theory.sign-homomorphism funext -open import finite-group-theory.transpositions funext +open import finite-group-theory.delooping-sign-homomorphism +open import finite-group-theory.finite-type-groups +open import finite-group-theory.permutations +open import finite-group-theory.sign-homomorphism +open import finite-group-theory.transpositions -open import foundation.action-on-equivalences-type-families-over-subuniverses funext +open import foundation.action-on-equivalences-type-families-over-subuniverses open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-equivalence-relations funext -open import foundation.decidable-types funext +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-equivalence-relations +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalence-classes funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.involutions funext -open import foundation.logical-equivalences funext -open import foundation.mere-equivalences funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.raising-universe-levels funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equivalence-classes +open import foundation.equivalence-extensionality +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.involutions +open import foundation.logical-equivalences +open import foundation.mere-equivalences +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.raising-universe-levels +open import foundation.sets open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-concrete-groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.loop-groups-sets funext -open import group-theory.symmetric-groups funext +open import group-theory.groups +open import group-theory.homomorphisms-concrete-groups +open import group-theory.homomorphisms-groups +open import group-theory.isomorphisms-groups +open import group-theory.loop-groups-sets +open import group-theory.symmetric-groups open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.counting +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/subgroups-finite-groups.lagda.md b/src/finite-group-theory/subgroups-finite-groups.lagda.md index 613bc2c382..e693dcaa67 100644 --- a/src/finite-group-theory/subgroups-finite-groups.lagda.md +++ b/src/finite-group-theory/subgroups-finite-groups.lagda.md @@ -1,39 +1,34 @@ # Subgroups of finite groups ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.subgroups-finite-groups - (funext : function-extensionality) - where +module finite-group-theory.subgroups-finite-groups where ```
Imports ```agda -open import finite-group-theory.finite-groups funext -open import finite-group-theory.finite-semigroups funext +open import finite-group-theory.finite-groups +open import finite-group-theory.finite-semigroups -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.decidable-subgroups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.semigroups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.decidable-subgroups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.semigroups +open import group-theory.subgroups +open import group-theory.subsets-groups -open import univalent-combinatorics.decidable-subtypes funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.decidable-subtypes +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-group-theory/tetrahedra-in-3-space.lagda.md b/src/finite-group-theory/tetrahedra-in-3-space.lagda.md index c3b5fc5b66..6fac18a6da 100644 --- a/src/finite-group-theory/tetrahedra-in-3-space.lagda.md +++ b/src/finite-group-theory/tetrahedra-in-3-space.lagda.md @@ -1,24 +1,19 @@ # Tetrahedra in `3`-dimensional space ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.tetrahedra-in-3-space - (funext : function-extensionality) - where +module finite-group-theory.tetrahedra-in-3-space where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types funext +open import foundation.empty-types open import foundation.universe-levels -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.cyclic-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.cyclic-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/finite-group-theory/transpositions-standard-finite-types.lagda.md b/src/finite-group-theory/transpositions-standard-finite-types.lagda.md index fc8a76b666..bd345f2692 100644 --- a/src/finite-group-theory/transpositions-standard-finite-types.lagda.md +++ b/src/finite-group-theory/transpositions-standard-finite-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - finite-group-theory.transpositions-standard-finite-types - (funext : function-extensionality) - where +module finite-group-theory.transpositions-standard-finite-types where ```
Imports @@ -16,31 +11,31 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext -open import finite-group-theory.transpositions funext +open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.transpositions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import lists.functoriality-lists funext +open import lists.functoriality-lists open import lists.lists -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/finite-group-theory/transpositions.lagda.md b/src/finite-group-theory/transpositions.lagda.md index 8a6de1d4bb..ad26d6e6af 100644 --- a/src/finite-group-theory/transpositions.lagda.md +++ b/src/finite-group-theory/transpositions.lagda.md @@ -1,67 +1,62 @@ # Transpositions ```agda -open import foundation.function-extensionality-axiom - -module - finite-group-theory.transpositions - (funext : function-extensionality) - where +module finite-group-theory.transpositions where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types funext +open import elementary-number-theory.well-ordering-principle-standard-finite-types open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.automorphisms funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-propositions funext -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.automorphisms +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-propositions +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.equivalences funext-maybe -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.involutions funext -open import foundation.logical-equivalences funext -open import foundation.negated-equality funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.equivalences-maybe +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.involutions +open import foundation.logical-equivalences +open import foundation.negated-equality +open import foundation.propositional-extensionality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.sets open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import lists.concatenation-lists funext -open import lists.functoriality-lists funext +open import lists.concatenation-lists +open import lists.functoriality-lists open import lists.lists -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation-core.lagda.md b/src/foundation-core.lagda.md index 071efcb72f..17d58ece65 100644 --- a/src/foundation-core.lagda.md +++ b/src/foundation-core.lagda.md @@ -3,41 +3,36 @@ ## Modules in the foundation-core namespace ```agda -open import foundation.function-extensionality-axiom +module foundation-core where -module - foundation-core - (funext : function-extensionality) - where - -open import foundation-core.1-types funext public +open import foundation-core.1-types public open import foundation-core.booleans public open import foundation-core.cartesian-product-types public open import foundation-core.coherently-invertible-maps public -open import foundation-core.commuting-prisms-of-maps funext public +open import foundation-core.commuting-prisms-of-maps public open import foundation-core.commuting-squares-of-homotopies public open import foundation-core.commuting-squares-of-identifications public -open import foundation-core.commuting-squares-of-maps funext public +open import foundation-core.commuting-squares-of-maps public open import foundation-core.commuting-triangles-of-maps public open import foundation-core.constant-maps public open import foundation-core.contractible-maps public open import foundation-core.contractible-types public open import foundation-core.coproduct-types public -open import foundation-core.decidable-propositions funext public +open import foundation-core.decidable-propositions public open import foundation-core.dependent-identifications public open import foundation-core.diagonal-maps-cartesian-products-of-types public open import foundation-core.diagonal-maps-of-types public -open import foundation-core.discrete-types funext public +open import foundation-core.discrete-types public open import foundation-core.embeddings public open import foundation-core.empty-types public -open import foundation-core.endomorphisms funext public +open import foundation-core.endomorphisms public open import foundation-core.equality-dependent-pair-types public -open import foundation-core.equivalence-relations funext public +open import foundation-core.equivalence-relations public open import foundation-core.equivalences public open import foundation-core.families-of-equivalences public open import foundation-core.fibers-of-maps public open import foundation-core.function-types public -open import foundation-core.functoriality-dependent-function-types funext public +open import foundation-core.functoriality-dependent-function-types public open import foundation-core.functoriality-dependent-pair-types public open import foundation-core.homotopies public open import foundation-core.identity-types public @@ -46,8 +41,8 @@ open import foundation-core.invertible-maps public open import foundation-core.logical-equivalences public open import foundation-core.maybe public open import foundation-core.negation public -open import foundation-core.operations-span-diagrams funext public -open import foundation-core.operations-spans funext public +open import foundation-core.operations-span-diagrams public +open import foundation-core.operations-spans public open import foundation-core.path-split-maps public open import foundation-core.postcomposition-dependent-functions public open import foundation-core.postcomposition-functions public @@ -55,22 +50,22 @@ open import foundation-core.precomposition-dependent-functions public open import foundation-core.precomposition-functions public open import foundation-core.propositional-maps public open import foundation-core.propositions public -open import foundation-core.pullbacks funext public +open import foundation-core.pullbacks public open import foundation-core.retractions public open import foundation-core.retracts-of-types public open import foundation-core.sections public open import foundation-core.sets public -open import foundation-core.small-types funext public -open import foundation-core.subtypes funext public +open import foundation-core.small-types public +open import foundation-core.subtypes public open import foundation-core.torsorial-type-families public open import foundation-core.transport-along-identifications public -open import foundation-core.truncated-maps funext public +open import foundation-core.truncated-maps public open import foundation-core.truncated-types public open import foundation-core.truncation-levels public open import foundation-core.type-theoretic-principle-of-choice public open import foundation-core.univalence public -open import foundation-core.universal-property-pullbacks funext public -open import foundation-core.universal-property-truncation funext public +open import foundation-core.universal-property-pullbacks public +open import foundation-core.universal-property-truncation public open import foundation-core.whiskering-homotopies-concatenation public open import foundation-core.whiskering-identifications-concatenation public ``` diff --git a/src/foundation-core/1-types.lagda.md b/src/foundation-core/1-types.lagda.md index 6f313c023b..79ac7bd491 100644 --- a/src/foundation-core/1-types.lagda.md +++ b/src/foundation-core/1-types.lagda.md @@ -1,20 +1,15 @@ # `1`-Types ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.1-types - (funext : function-extensionality) - where +module foundation-core.1-types where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation-core/commuting-prisms-of-maps.lagda.md b/src/foundation-core/commuting-prisms-of-maps.lagda.md index 811b534295..40f37dea92 100644 --- a/src/foundation-core/commuting-prisms-of-maps.lagda.md +++ b/src/foundation-core/commuting-prisms-of-maps.lagda.md @@ -1,12 +1,7 @@ # Commuting prisms of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.commuting-prisms-of-maps - (funext : function-extensionality) - where +module foundation-core.commuting-prisms-of-maps where ```
Imports @@ -17,7 +12,7 @@ open import foundation.commuting-pentagons-of-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.commuting-triangles-of-maps open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation-core/commuting-squares-of-maps.lagda.md b/src/foundation-core/commuting-squares-of-maps.lagda.md index 5112dbca55..6cce4fb386 100644 --- a/src/foundation-core/commuting-squares-of-maps.lagda.md +++ b/src/foundation-core/commuting-squares-of-maps.lagda.md @@ -1,19 +1,14 @@ # Commuting squares of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.commuting-squares-of-maps - (funext : function-extensionality) - where +module foundation-core.commuting-squares-of-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.transposition-identifications-along-equivalences open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation-core/decidable-propositions.lagda.md b/src/foundation-core/decidable-propositions.lagda.md index a50983318c..8337ddd8fa 100644 --- a/src/foundation-core/decidable-propositions.lagda.md +++ b/src/foundation-core/decidable-propositions.lagda.md @@ -1,24 +1,19 @@ # Decidable propositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.decidable-propositions - (funext : function-extensionality) - where +module foundation-core.decidable-propositions where ```
Imports ```agda -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.double-negation funext -open import foundation.negation funext -open import foundation.propositional-truncations funext +open import foundation.dependent-products-propositions +open import foundation.double-negation +open import foundation.negation +open import foundation.propositional-truncations open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels @@ -29,7 +24,7 @@ open import foundation-core.empty-types open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation-core/discrete-types.lagda.md b/src/foundation-core/discrete-types.lagda.md index 26de275f2f..6ace450fc3 100644 --- a/src/foundation-core/discrete-types.lagda.md +++ b/src/foundation-core/discrete-types.lagda.md @@ -1,18 +1,13 @@ # Discrete types ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.discrete-types - (funext : function-extensionality) - where +module foundation-core.discrete-types where ```
Imports ```agda -open import foundation.decidable-equality funext +open import foundation.decidable-equality open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation-core/endomorphisms.lagda.md b/src/foundation-core/endomorphisms.lagda.md index 531b90c65a..b374c58abd 100644 --- a/src/foundation-core/endomorphisms.lagda.md +++ b/src/foundation-core/endomorphisms.lagda.md @@ -1,20 +1,15 @@ # Endomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.endomorphisms - (funext : function-extensionality) - where +module foundation-core.endomorphisms where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.sets funext +open import foundation.dependent-products-truncated-types +open import foundation.sets open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation-core/equivalence-relations.lagda.md b/src/foundation-core/equivalence-relations.lagda.md index 09493249f2..cf970f3056 100644 --- a/src/foundation-core/equivalence-relations.lagda.md +++ b/src/foundation-core/equivalence-relations.lagda.md @@ -1,24 +1,19 @@ # Equivalence relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.equivalence-relations - (funext : function-extensionality) - where +module foundation-core.equivalence-relations where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-subtypes funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.inhabited-subtypes +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.raising-universe-levels-unit-type open import foundation.subtype-identity-principle open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation-core/functoriality-dependent-function-types.lagda.md b/src/foundation-core/functoriality-dependent-function-types.lagda.md index 181bd0643a..6c17228aec 100644 --- a/src/foundation-core/functoriality-dependent-function-types.lagda.md +++ b/src/foundation-core/functoriality-dependent-function-types.lagda.md @@ -1,21 +1,15 @@ # Functoriality of dependent function types ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.functoriality-dependent-function-types - (funext : function-extensionality) - where +module foundation-core.functoriality-dependent-function-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.function-extensionality funext - +open import foundation.dependent-products-contractible-types +open import foundation.function-extensionality open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation-core/operations-span-diagrams.lagda.md b/src/foundation-core/operations-span-diagrams.lagda.md index b6900df2c2..78b68e8722 100644 --- a/src/foundation-core/operations-span-diagrams.lagda.md +++ b/src/foundation-core/operations-span-diagrams.lagda.md @@ -1,21 +1,16 @@ # Operations on span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.operations-span-diagrams - (funext : function-extensionality) - where +module foundation-core.operations-span-diagrams where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows funext -open import foundation.operations-spans funext -open import foundation.span-diagrams funext +open import foundation.morphisms-arrows +open import foundation.operations-spans +open import foundation.span-diagrams open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation-core/operations-spans.lagda.md b/src/foundation-core/operations-spans.lagda.md index 7b4b9095c7..47e60de4d7 100644 --- a/src/foundation-core/operations-spans.lagda.md +++ b/src/foundation-core/operations-spans.lagda.md @@ -1,19 +1,14 @@ # Operations on spans ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.operations-spans - (funext : function-extensionality) - where +module foundation-core.operations-spans where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows funext +open import foundation.morphisms-arrows open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation-core/pullbacks.lagda.md b/src/foundation-core/pullbacks.lagda.md index 8d22d3eff4..332e6e96e2 100644 --- a/src/foundation-core/pullbacks.lagda.md +++ b/src/foundation-core/pullbacks.lagda.md @@ -1,26 +1,21 @@ # Pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.pullbacks - (funext : function-extensionality) - where +module foundation-core.pullbacks where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-fibers-of-maps funext -open import foundation.identity-types funext -open import foundation.morphisms-arrows funext -open import foundation.standard-pullbacks funext -open import foundation.type-arithmetic-standard-pullbacks funext +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-fibers-of-maps +open import foundation.identity-types +open import foundation.morphisms-arrows +open import foundation.standard-pullbacks +open import foundation.type-arithmetic-standard-pullbacks open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -32,7 +27,7 @@ open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation-core/small-types.lagda.md b/src/foundation-core/small-types.lagda.md index 13e556ba81..adb78b9475 100644 --- a/src/foundation-core/small-types.lagda.md +++ b/src/foundation-core/small-types.lagda.md @@ -1,30 +1,25 @@ # Small types ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.small-types - (funext : function-extensionality) - where +module foundation-core.small-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.logical-equivalences funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type +open import foundation.equivalences +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-function-types +open import foundation.logical-equivalences +open import foundation.mere-equivalences +open import foundation.propositional-truncations +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation-core/subtypes.lagda.md b/src/foundation-core/subtypes.lagda.md index 4926f69e19..c6a4afc4c4 100644 --- a/src/foundation-core/subtypes.lagda.md +++ b/src/foundation-core/subtypes.lagda.md @@ -1,12 +1,7 @@ # Subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.subtypes - (funext : function-extensionality) - where +module foundation-core.subtypes where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.logical-equivalences funext +open import foundation.dependent-products-propositions +open import foundation.logical-equivalences open import foundation.subtype-identity-principle open import foundation.universe-levels @@ -29,7 +24,7 @@ open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets open import foundation-core.transport-along-identifications -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation-core/truncated-maps.lagda.md b/src/foundation-core/truncated-maps.lagda.md index c5d3c59d6f..6c68755acc 100644 --- a/src/foundation-core/truncated-maps.lagda.md +++ b/src/foundation-core/truncated-maps.lagda.md @@ -1,12 +1,7 @@ # Truncated maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.truncated-maps - (funext : function-extensionality) - where +module foundation-core.truncated-maps where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-fibers-of-maps funext +open import foundation.equality-fibers-of-maps open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation-core/universal-property-pullbacks.lagda.md b/src/foundation-core/universal-property-pullbacks.lagda.md index 83f6e54f11..8ec97f1f27 100644 --- a/src/foundation-core/universal-property-pullbacks.lagda.md +++ b/src/foundation-core/universal-property-pullbacks.lagda.md @@ -1,21 +1,16 @@ # The universal property of pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.universal-property-pullbacks - (funext : function-extensionality) - where +module foundation-core.universal-property-pullbacks where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.postcomposition-functions funext +open import foundation.postcomposition-functions open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation-core/universal-property-truncation.lagda.md b/src/foundation-core/universal-property-truncation.lagda.md index fa87fddef3..875fd1d2ba 100644 --- a/src/foundation-core/universal-property-truncation.lagda.md +++ b/src/foundation-core/universal-property-truncation.lagda.md @@ -1,22 +1,16 @@ # The universal property of truncations ```agda -open import foundation.function-extensionality-axiom - -module - foundation-core.universal-property-truncation - (funext : function-extensionality) - where +module foundation-core.universal-property-truncation where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.function-extensionality funext - -open import foundation.universal-property-equivalences funext +open import foundation.dependent-products-truncated-types +open import foundation.function-extensionality +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation.lagda.md b/src/foundation.lagda.md index 5a67c7c2ae..ebab239526 100644 --- a/src/foundation.lagda.md +++ b/src/foundation.lagda.md @@ -7,514 +7,508 @@ ## Modules in the foundation namespace ```agda -open import foundation.function-extensionality-axiom +module foundation where -module - foundation - (funext : function-extensionality) - where - -open import foundation.0-connected-types funext public -open import foundation.0-images-of-maps funext public -open import foundation.0-maps funext public -open import foundation.1-types funext public +open import foundation.0-connected-types public +open import foundation.0-images-of-maps public +open import foundation.0-maps public +open import foundation.1-types public open import foundation.2-types public -open import foundation.action-on-equivalences-functions funext public -open import foundation.action-on-equivalences-functions-out-of-subuniverses funext public -open import foundation.action-on-equivalences-type-families funext public -open import foundation.action-on-equivalences-type-families-over-subuniverses funext public -open import foundation.action-on-higher-identifications-functions funext public -open import foundation.action-on-homotopies-functions funext public +open import foundation.action-on-equivalences-functions public +open import foundation.action-on-equivalences-functions-out-of-subuniverses public +open import foundation.action-on-equivalences-type-families public +open import foundation.action-on-equivalences-type-families-over-subuniverses public +open import foundation.action-on-higher-identifications-functions public +open import foundation.action-on-homotopies-functions public open import foundation.action-on-identifications-binary-dependent-functions public open import foundation.action-on-identifications-binary-functions public open import foundation.action-on-identifications-dependent-functions public open import foundation.action-on-identifications-functions public -open import foundation.apartness-relations funext public -open import foundation.arithmetic-law-coproduct-and-sigma-decompositions funext public -open import foundation.arithmetic-law-product-and-pi-decompositions funext public -open import foundation.automorphisms funext public -open import foundation.axiom-of-choice funext public -open import foundation.bands funext public -open import foundation.base-changes-span-diagrams funext public -open import foundation.bicomposition-functions funext public +open import foundation.apartness-relations public +open import foundation.arithmetic-law-coproduct-and-sigma-decompositions public +open import foundation.arithmetic-law-product-and-pi-decompositions public +open import foundation.automorphisms public +open import foundation.axiom-of-choice public +open import foundation.bands public +open import foundation.base-changes-span-diagrams public +open import foundation.bicomposition-functions public open import foundation.binary-dependent-identifications public -open import foundation.binary-embeddings funext public +open import foundation.binary-embeddings public open import foundation.binary-equivalences public -open import foundation.binary-equivalences-unordered-pairs-of-types funext public -open import foundation.binary-functoriality-set-quotients funext public -open import foundation.binary-homotopies funext public -open import foundation.binary-operations-unordered-pairs-of-types funext public -open import foundation.binary-reflecting-maps-equivalence-relations funext public -open import foundation.binary-relations funext public -open import foundation.binary-relations-with-extensions funext public -open import foundation.binary-relations-with-lifts funext public +open import foundation.binary-equivalences-unordered-pairs-of-types public +open import foundation.binary-functoriality-set-quotients public +open import foundation.binary-homotopies public +open import foundation.binary-operations-unordered-pairs-of-types public +open import foundation.binary-reflecting-maps-equivalence-relations public +open import foundation.binary-relations public +open import foundation.binary-relations-with-extensions public +open import foundation.binary-relations-with-lifts public open import foundation.binary-transport public -open import foundation.binary-type-duality funext public -open import foundation.booleans funext public -open import foundation.cantor-schroder-bernstein-escardo funext public -open import foundation.cantors-theorem funext public -open import foundation.cartesian-morphisms-arrows funext public -open import foundation.cartesian-morphisms-span-diagrams funext public -open import foundation.cartesian-product-types funext public -open import foundation.cartesian-products-set-quotients funext public -open import foundation.category-of-families-of-sets funext public -open import foundation.category-of-sets funext public -open import foundation.choice-of-representatives-equivalence-relation funext public -open import foundation.coalgebras-maybe funext public +open import foundation.binary-type-duality public +open import foundation.booleans public +open import foundation.cantor-schroder-bernstein-escardo public +open import foundation.cantors-theorem public +open import foundation.cartesian-morphisms-arrows public +open import foundation.cartesian-morphisms-span-diagrams public +open import foundation.cartesian-product-types public +open import foundation.cartesian-products-set-quotients public +open import foundation.category-of-families-of-sets public +open import foundation.category-of-sets public +open import foundation.choice-of-representatives-equivalence-relation public +open import foundation.coalgebras-maybe public open import foundation.codiagonal-maps-of-types public -open import foundation.coherently-idempotent-maps funext public -open import foundation.coherently-invertible-maps funext public -open import foundation.coinhabited-pairs-of-types funext public -open import foundation.commuting-cubes-of-maps funext public +open import foundation.coherently-idempotent-maps public +open import foundation.coherently-invertible-maps public +open import foundation.coinhabited-pairs-of-types public +open import foundation.commuting-cubes-of-maps public open import foundation.commuting-hexagons-of-identifications public open import foundation.commuting-pentagons-of-identifications public -open import foundation.commuting-prisms-of-maps funext public -open import foundation.commuting-squares-of-homotopies funext public -open import foundation.commuting-squares-of-identifications funext public -open import foundation.commuting-squares-of-maps funext public -open import foundation.commuting-tetrahedra-of-homotopies funext public +open import foundation.commuting-prisms-of-maps public +open import foundation.commuting-squares-of-homotopies public +open import foundation.commuting-squares-of-identifications public +open import foundation.commuting-squares-of-maps public +open import foundation.commuting-tetrahedra-of-homotopies public open import foundation.commuting-tetrahedra-of-maps public -open import foundation.commuting-triangles-of-homotopies funext public -open import foundation.commuting-triangles-of-identifications funext public -open import foundation.commuting-triangles-of-maps funext public -open import foundation.commuting-triangles-of-morphisms-arrows funext public +open import foundation.commuting-triangles-of-homotopies public +open import foundation.commuting-triangles-of-identifications public +open import foundation.commuting-triangles-of-maps public +open import foundation.commuting-triangles-of-morphisms-arrows public open import foundation.complements public -open import foundation.complements-subtypes funext public -open import foundation.composite-maps-in-inverse-sequential-diagrams funext public -open import foundation.composition-algebra funext public -open import foundation.composition-spans funext public -open import foundation.computational-identity-types funext public -open import foundation.cones-over-cospan-diagrams funext public -open import foundation.cones-over-inverse-sequential-diagrams funext public -open import foundation.conjunction funext public -open import foundation.connected-components funext public -open import foundation.connected-components-universes funext public -open import foundation.connected-maps funext public -open import foundation.connected-types funext public -open import foundation.constant-maps funext public -open import foundation.constant-span-diagrams funext public -open import foundation.constant-type-families funext public -open import foundation.continuations funext public -open import foundation.contractible-maps funext public -open import foundation.contractible-types funext public -open import foundation.copartial-elements funext public -open import foundation.copartial-functions funext public -open import foundation.coproduct-decompositions funext public -open import foundation.coproduct-decompositions-subuniverse funext public -open import foundation.coproduct-types funext public -open import foundation.coproducts-pullbacks funext public -open import foundation.coslice funext public +open import foundation.complements-subtypes public +open import foundation.composite-maps-in-inverse-sequential-diagrams public +open import foundation.composition-algebra public +open import foundation.composition-spans public +open import foundation.computational-identity-types public +open import foundation.cones-over-cospan-diagrams public +open import foundation.cones-over-inverse-sequential-diagrams public +open import foundation.conjunction public +open import foundation.connected-components public +open import foundation.connected-components-universes public +open import foundation.connected-maps public +open import foundation.connected-types public +open import foundation.constant-maps public +open import foundation.constant-span-diagrams public +open import foundation.constant-type-families public +open import foundation.continuations public +open import foundation.contractible-maps public +open import foundation.contractible-types public +open import foundation.copartial-elements public +open import foundation.copartial-functions public +open import foundation.coproduct-decompositions public +open import foundation.coproduct-decompositions-subuniverse public +open import foundation.coproduct-types public +open import foundation.coproducts-pullbacks public +open import foundation.coslice public open import foundation.cospan-diagrams public open import foundation.cospans public -open import foundation.decidable-dependent-function-types funext public -open import foundation.decidable-dependent-pair-types funext public -open import foundation.decidable-embeddings funext public -open import foundation.decidable-equality funext public -open import foundation.decidable-equivalence-relations funext public -open import foundation.decidable-maps funext public -open import foundation.decidable-propositions funext public -open import foundation.decidable-relations funext public -open import foundation.decidable-subtypes funext public -open import foundation.decidable-types funext public -open import foundation.dependent-binary-homotopies funext public -open import foundation.dependent-binomial-theorem funext public -open import foundation.dependent-epimorphisms funext public -open import foundation.dependent-epimorphisms-with-respect-to-truncated-types funext public -open import foundation.dependent-function-types funext public +open import foundation.decidable-dependent-function-types public +open import foundation.decidable-dependent-pair-types public +open import foundation.decidable-embeddings public +open import foundation.decidable-equality public +open import foundation.decidable-equivalence-relations public +open import foundation.decidable-maps public +open import foundation.decidable-propositions public +open import foundation.decidable-relations public +open import foundation.decidable-subtypes public +open import foundation.decidable-types public +open import foundation.dependent-binary-homotopies public +open import foundation.dependent-binomial-theorem public +open import foundation.dependent-epimorphisms public +open import foundation.dependent-epimorphisms-with-respect-to-truncated-types public +open import foundation.dependent-function-types public open import foundation.dependent-homotopies public -open import foundation.dependent-identifications funext public -open import foundation.dependent-inverse-sequential-diagrams funext public +open import foundation.dependent-identifications public +open import foundation.dependent-inverse-sequential-diagrams public open import foundation.dependent-pair-types public -open import foundation.dependent-products-contractible-types funext public -open import foundation.dependent-products-propositions funext public -open import foundation.dependent-products-pullbacks funext public -open import foundation.dependent-products-truncated-types funext public +open import foundation.dependent-products-contractible-types public +open import foundation.dependent-products-propositions public +open import foundation.dependent-products-pullbacks public +open import foundation.dependent-products-truncated-types public open import foundation.dependent-sequences public -open import foundation.dependent-sums-pullbacks funext public +open import foundation.dependent-sums-pullbacks public open import foundation.dependent-telescopes public -open import foundation.dependent-universal-property-equivalences funext public -open import foundation.descent-coproduct-types funext public -open import foundation.descent-dependent-pair-types funext public -open import foundation.descent-empty-types funext public -open import foundation.descent-equivalences funext public -open import foundation.diaconescus-theorem funext public -open import foundation.diagonal-maps-cartesian-products-of-types funext public -open import foundation.diagonal-maps-of-types funext public -open import foundation.diagonal-span-diagrams funext public -open import foundation.diagonals-of-maps funext public +open import foundation.dependent-universal-property-equivalences public +open import foundation.descent-coproduct-types public +open import foundation.descent-dependent-pair-types public +open import foundation.descent-empty-types public +open import foundation.descent-equivalences public +open import foundation.diaconescus-theorem public +open import foundation.diagonal-maps-cartesian-products-of-types public +open import foundation.diagonal-maps-of-types public +open import foundation.diagonal-span-diagrams public +open import foundation.diagonals-of-maps public open import foundation.diagonals-of-morphisms-arrows public -open import foundation.discrete-binary-relations funext public -open import foundation.discrete-reflexive-relations funext public -open import foundation.discrete-relaxed-sigma-decompositions funext public -open import foundation.discrete-sigma-decompositions funext public -open import foundation.discrete-types funext public -open import foundation.disjoint-subtypes funext public -open import foundation.disjunction funext public +open import foundation.discrete-binary-relations public +open import foundation.discrete-reflexive-relations public +open import foundation.discrete-relaxed-sigma-decompositions public +open import foundation.discrete-sigma-decompositions public +open import foundation.discrete-types public +open import foundation.disjoint-subtypes public +open import foundation.disjunction public open import foundation.double-arrows public -open import foundation.double-negation funext public -open import foundation.double-negation-modality funext public -open import foundation.double-negation-stable-equality funext public -open import foundation.double-negation-stable-propositions funext public -open import foundation.double-powersets funext public -open import foundation.dubuc-penon-compact-types funext public -open import foundation.effective-maps-equivalence-relations funext public -open import foundation.embeddings funext public -open import foundation.empty-types funext public -open import foundation.endomorphisms funext public -open import foundation.epimorphisms funext public -open import foundation.epimorphisms-with-respect-to-sets funext public -open import foundation.epimorphisms-with-respect-to-truncated-types funext public +open import foundation.double-negation public +open import foundation.double-negation-modality public +open import foundation.double-negation-stable-equality public +open import foundation.double-negation-stable-propositions public +open import foundation.double-powersets public +open import foundation.dubuc-penon-compact-types public +open import foundation.effective-maps-equivalence-relations public +open import foundation.embeddings public +open import foundation.empty-types public +open import foundation.endomorphisms public +open import foundation.epimorphisms public +open import foundation.epimorphisms-with-respect-to-sets public +open import foundation.epimorphisms-with-respect-to-truncated-types public open import foundation.equality-cartesian-product-types public -open import foundation.equality-coproduct-types funext public -open import foundation.equality-dependent-function-types funext public -open import foundation.equality-dependent-pair-types funext public -open import foundation.equality-fibers-of-maps funext public -open import foundation.equivalence-classes funext public -open import foundation.equivalence-extensionality funext public -open import foundation.equivalence-induction funext public -open import foundation.equivalence-injective-type-families funext public -open import foundation.equivalence-relations funext public -open import foundation.equivalences funext public -open import foundation.equivalences-arrows funext public -open import foundation.equivalences-cospans funext public -open import foundation.equivalences-double-arrows funext public -open import foundation.equivalences-inverse-sequential-diagrams funext public -open import foundation.equivalences-maybe funext public -open import foundation.equivalences-span-diagrams funext public -open import foundation.equivalences-span-diagrams-families-of-types funext public -open import foundation.equivalences-spans funext public -open import foundation.equivalences-spans-families-of-types funext public +open import foundation.equality-coproduct-types public +open import foundation.equality-dependent-function-types public +open import foundation.equality-dependent-pair-types public +open import foundation.equality-fibers-of-maps public +open import foundation.equivalence-classes public +open import foundation.equivalence-extensionality public +open import foundation.equivalence-induction public +open import foundation.equivalence-injective-type-families public +open import foundation.equivalence-relations public +open import foundation.equivalences public +open import foundation.equivalences-arrows public +open import foundation.equivalences-cospans public +open import foundation.equivalences-double-arrows public +open import foundation.equivalences-inverse-sequential-diagrams public +open import foundation.equivalences-maybe public +open import foundation.equivalences-span-diagrams public +open import foundation.equivalences-span-diagrams-families-of-types public +open import foundation.equivalences-spans public +open import foundation.equivalences-spans-families-of-types public open import foundation.evaluation-functions public -open import foundation.exclusive-disjunction funext public -open import foundation.exclusive-sum funext public -open import foundation.existential-quantification funext public -open import foundation.exponents-set-quotients funext public -open import foundation.extensions-types funext public -open import foundation.extensions-types-global-subuniverses funext public -open import foundation.extensions-types-subuniverses funext public -open import foundation.faithful-maps funext public -open import foundation.families-of-equivalences funext public -open import foundation.families-of-maps funext public -open import foundation.families-over-telescopes funext public -open import foundation.fiber-inclusions funext public -open import foundation.fibered-equivalences funext public -open import foundation.fibered-involutions funext public -open import foundation.fibered-maps funext public -open import foundation.fibers-of-maps funext public -open import foundation.finitely-coherent-equivalences funext public -open import foundation.finitely-coherently-invertible-maps funext public +open import foundation.exclusive-disjunction public +open import foundation.exclusive-sum public +open import foundation.existential-quantification public +open import foundation.exponents-set-quotients public +open import foundation.extensions-types public +open import foundation.extensions-types-global-subuniverses public +open import foundation.extensions-types-subuniverses public +open import foundation.faithful-maps public +open import foundation.families-of-equivalences public +open import foundation.families-of-maps public +open import foundation.families-over-telescopes public +open import foundation.fiber-inclusions public +open import foundation.fibered-equivalences public +open import foundation.fibered-involutions public +open import foundation.fibered-maps public +open import foundation.fibers-of-maps public +open import foundation.finitely-coherent-equivalences public +open import foundation.finitely-coherently-invertible-maps public open import foundation.fixed-points-endofunctions public -open import foundation.full-subtypes funext public -open import foundation.function-extensionality funext - public +open import foundation.full-subtypes public +open import foundation.function-extensionality public open import foundation.function-extensionality-axiom public -open import foundation.function-types funext public -open import foundation.functional-correspondences funext public -open import foundation.functoriality-action-on-identifications-functions funext public -open import foundation.functoriality-cartesian-product-types funext public -open import foundation.functoriality-coproduct-types funext public -open import foundation.functoriality-dependent-function-types funext public -open import foundation.functoriality-dependent-pair-types funext public -open import foundation.functoriality-fibers-of-maps funext public -open import foundation.functoriality-function-types funext public -open import foundation.functoriality-morphisms-arrows funext public -open import foundation.functoriality-propositional-truncation funext public -open import foundation.functoriality-pullbacks funext public -open import foundation.functoriality-sequential-limits funext public -open import foundation.functoriality-set-quotients funext public -open import foundation.functoriality-set-truncation funext public -open import foundation.functoriality-truncation funext public -open import foundation.fundamental-theorem-of-equivalence-relations funext public +open import foundation.function-types public +open import foundation.functional-correspondences public +open import foundation.functoriality-action-on-identifications-functions public +open import foundation.functoriality-cartesian-product-types public +open import foundation.functoriality-coproduct-types public +open import foundation.functoriality-dependent-function-types public +open import foundation.functoriality-dependent-pair-types public +open import foundation.functoriality-fibers-of-maps public +open import foundation.functoriality-function-types public +open import foundation.functoriality-morphisms-arrows public +open import foundation.functoriality-propositional-truncation public +open import foundation.functoriality-pullbacks public +open import foundation.functoriality-sequential-limits public +open import foundation.functoriality-set-quotients public +open import foundation.functoriality-set-truncation public +open import foundation.functoriality-truncation public +open import foundation.fundamental-theorem-of-equivalence-relations public open import foundation.fundamental-theorem-of-identity-types public -open import foundation.global-choice funext public -open import foundation.global-subuniverses funext public -open import foundation.globular-type-of-dependent-functions funext public -open import foundation.globular-type-of-functions funext public -open import foundation.higher-homotopies-morphisms-arrows funext public -open import foundation.hilberts-epsilon-operators funext public -open import foundation.homotopies funext public -open import foundation.homotopies-morphisms-arrows funext public -open import foundation.homotopies-morphisms-cospan-diagrams funext public +open import foundation.global-choice public +open import foundation.global-subuniverses public +open import foundation.globular-type-of-dependent-functions public +open import foundation.globular-type-of-functions public +open import foundation.higher-homotopies-morphisms-arrows public +open import foundation.hilberts-epsilon-operators public +open import foundation.homotopies public +open import foundation.homotopies-morphisms-arrows public +open import foundation.homotopies-morphisms-cospan-diagrams public open import foundation.homotopy-algebra public -open import foundation.homotopy-induction funext public -open import foundation.homotopy-preorder-of-types funext public -open import foundation.horizontal-composition-spans-of-spans funext public -open import foundation.idempotent-maps funext public +open import foundation.homotopy-induction public +open import foundation.homotopy-preorder-of-types public +open import foundation.horizontal-composition-spans-of-spans public +open import foundation.idempotent-maps public open import foundation.identity-systems public -open import foundation.identity-truncated-types funext public -open import foundation.identity-types funext public -open import foundation.images funext public -open import foundation.images-subtypes funext public +open import foundation.identity-truncated-types public +open import foundation.identity-types public +open import foundation.images public +open import foundation.images-subtypes public open import foundation.implicit-function-types public -open import foundation.impredicative-encodings funext public -open import foundation.impredicative-universes funext public +open import foundation.impredicative-encodings public +open import foundation.impredicative-universes public open import foundation.induction-principle-propositional-truncation public -open import foundation.infinitely-coherent-equivalences funext public -open import foundation.inhabited-subtypes funext public -open import foundation.inhabited-types funext public -open import foundation.injective-maps funext public +open import foundation.infinitely-coherent-equivalences public +open import foundation.inhabited-subtypes public +open import foundation.inhabited-types public +open import foundation.injective-maps public open import foundation.interchange-law public -open import foundation.intersections-subtypes funext public -open import foundation.inverse-sequential-diagrams funext public -open import foundation.invertible-maps funext public -open import foundation.involutions funext public -open import foundation.irrefutable-propositions funext public -open import foundation.isolated-elements funext public -open import foundation.isomorphisms-of-sets funext public -open import foundation.iterated-cartesian-product-types funext public +open import foundation.intersections-subtypes public +open import foundation.inverse-sequential-diagrams public +open import foundation.invertible-maps public +open import foundation.involutions public +open import foundation.irrefutable-propositions public +open import foundation.isolated-elements public +open import foundation.isomorphisms-of-sets public +open import foundation.iterated-cartesian-product-types public open import foundation.iterated-dependent-pair-types public -open import foundation.iterated-dependent-product-types funext public -open import foundation.iterating-automorphisms funext public -open import foundation.iterating-families-of-maps funext public -open import foundation.iterating-functions funext public -open import foundation.iterating-involutions funext public -open import foundation.kernel-span-diagrams-of-maps funext public -open import foundation.large-apartness-relations funext public -open import foundation.large-binary-relations funext public +open import foundation.iterated-dependent-product-types public +open import foundation.iterating-automorphisms public +open import foundation.iterating-families-of-maps public +open import foundation.iterating-functions public +open import foundation.iterating-involutions public +open import foundation.kernel-span-diagrams-of-maps public +open import foundation.large-apartness-relations public +open import foundation.large-binary-relations public open import foundation.large-dependent-pair-types public open import foundation.large-homotopies public open import foundation.large-identity-types public -open import foundation.large-locale-of-propositions funext public -open import foundation.large-locale-of-subtypes funext public -open import foundation.law-of-excluded-middle funext public -open import foundation.lawveres-fixed-point-theorem funext public -open import foundation.lesser-limited-principle-of-omniscience funext public +open import foundation.large-locale-of-propositions public +open import foundation.large-locale-of-subtypes public +open import foundation.law-of-excluded-middle public +open import foundation.lawveres-fixed-point-theorem public +open import foundation.lesser-limited-principle-of-omniscience public open import foundation.lifts-types public -open import foundation.limited-principle-of-omniscience funext public -open import foundation.locale-of-propositions funext public -open import foundation.locally-small-types funext public -open import foundation.logical-equivalences funext public -open import foundation.maps-in-global-subuniverses funext public -open import foundation.maps-in-subuniverses funext public -open import foundation.maybe funext public -open import foundation.mere-embeddings funext public -open import foundation.mere-equality funext public -open import foundation.mere-equivalences funext public -open import foundation.mere-functions funext public -open import foundation.mere-logical-equivalences funext public -open import foundation.mere-path-cosplit-maps funext public -open import foundation.monomorphisms funext public -open import foundation.morphisms-arrows funext public -open import foundation.morphisms-binary-relations funext public -open import foundation.morphisms-coalgebras-maybe funext public +open import foundation.limited-principle-of-omniscience public +open import foundation.locale-of-propositions public +open import foundation.locally-small-types public +open import foundation.logical-equivalences public +open import foundation.maps-in-global-subuniverses public +open import foundation.maps-in-subuniverses public +open import foundation.maybe public +open import foundation.mere-embeddings public +open import foundation.mere-equality public +open import foundation.mere-equivalences public +open import foundation.mere-functions public +open import foundation.mere-logical-equivalences public +open import foundation.mere-path-cosplit-maps public +open import foundation.monomorphisms public +open import foundation.morphisms-arrows public +open import foundation.morphisms-binary-relations public +open import foundation.morphisms-coalgebras-maybe public open import foundation.morphisms-cospan-diagrams public open import foundation.morphisms-cospans public -open import foundation.morphisms-double-arrows funext public -open import foundation.morphisms-inverse-sequential-diagrams funext public -open import foundation.morphisms-span-diagrams funext public +open import foundation.morphisms-double-arrows public +open import foundation.morphisms-inverse-sequential-diagrams public +open import foundation.morphisms-span-diagrams public open import foundation.morphisms-spans public -open import foundation.morphisms-spans-families-of-types funext public +open import foundation.morphisms-spans-families-of-types public open import foundation.morphisms-twisted-arrows public -open import foundation.multisubsets funext public -open import foundation.multivariable-correspondences funext public -open import foundation.multivariable-decidable-relations funext public -open import foundation.multivariable-functoriality-set-quotients funext public -open import foundation.multivariable-homotopies funext public -open import foundation.multivariable-operations funext public -open import foundation.multivariable-relations funext public -open import foundation.multivariable-sections funext public -open import foundation.negated-equality funext public -open import foundation.negation funext public -open import foundation.noncontractible-types funext public -open import foundation.null-homotopic-maps funext public -open import foundation.operations-span-diagrams funext public -open import foundation.operations-spans funext public +open import foundation.multisubsets public +open import foundation.multivariable-correspondences public +open import foundation.multivariable-decidable-relations public +open import foundation.multivariable-functoriality-set-quotients public +open import foundation.multivariable-homotopies public +open import foundation.multivariable-operations public +open import foundation.multivariable-relations public +open import foundation.multivariable-sections public +open import foundation.negated-equality public +open import foundation.negation public +open import foundation.noncontractible-types public +open import foundation.null-homotopic-maps public +open import foundation.operations-span-diagrams public +open import foundation.operations-spans public open import foundation.operations-spans-families-of-types public open import foundation.opposite-spans public -open import foundation.pairs-of-distinct-elements funext public +open import foundation.pairs-of-distinct-elements public open import foundation.partial-elements public open import foundation.partial-functions public open import foundation.partial-sequences public -open import foundation.partitions funext public -open import foundation.path-algebra funext public -open import foundation.path-cosplit-maps funext public -open import foundation.path-split-maps funext public -open import foundation.path-split-type-families funext public -open import foundation.perfect-images funext public +open import foundation.partitions public +open import foundation.path-algebra public +open import foundation.path-cosplit-maps public +open import foundation.path-split-maps public +open import foundation.path-split-type-families public +open import foundation.perfect-images public open import foundation.permutations-spans-families-of-types public -open import foundation.pi-decompositions funext public -open import foundation.pi-decompositions-subuniverse funext public -open import foundation.pointed-torsorial-type-families funext public -open import foundation.postcomposition-dependent-functions funext public -open import foundation.postcomposition-functions funext public -open import foundation.postcomposition-pullbacks funext public -open import foundation.powersets funext public -open import foundation.precomposition-dependent-functions funext public -open import foundation.precomposition-functions funext public -open import foundation.precomposition-functions-into-subuniverses funext public -open import foundation.precomposition-type-families funext public -open import foundation.preunivalence funext public -open import foundation.preunivalent-type-families funext public -open import foundation.principle-of-omniscience funext public +open import foundation.pi-decompositions public +open import foundation.pi-decompositions-subuniverse public +open import foundation.pointed-torsorial-type-families public +open import foundation.postcomposition-dependent-functions public +open import foundation.postcomposition-functions public +open import foundation.postcomposition-pullbacks public +open import foundation.powersets public +open import foundation.precomposition-dependent-functions public +open import foundation.precomposition-functions public +open import foundation.precomposition-functions-into-subuniverses public +open import foundation.precomposition-type-families public +open import foundation.preunivalence public +open import foundation.preunivalent-type-families public +open import foundation.principle-of-omniscience public open import foundation.product-decompositions public -open import foundation.product-decompositions-subuniverse funext public -open import foundation.products-binary-relations funext public -open import foundation.products-equivalence-relations funext public -open import foundation.products-of-tuples-of-types funext public -open import foundation.products-pullbacks funext public -open import foundation.products-unordered-pairs-of-types funext public -open import foundation.products-unordered-tuples-of-types funext public -open import foundation.projective-types funext public -open import foundation.proper-subtypes funext public -open import foundation.propositional-extensionality funext public -open import foundation.propositional-maps funext public -open import foundation.propositional-resizing funext public -open import foundation.propositional-truncations funext public -open import foundation.propositions funext public -open import foundation.pullback-cones funext public -open import foundation.pullbacks funext public -open import foundation.pullbacks-subtypes funext public -open import foundation.quasicoherently-idempotent-maps funext public -open import foundation.raising-universe-levels funext public -open import foundation.raising-universe-levels-booleans funext public -open import foundation.raising-universe-levels-unit-type funext public -open import foundation.reflecting-maps-equivalence-relations funext public -open import foundation.reflexive-relations funext public -open import foundation.regensburg-extension-fundamental-theorem-of-identity-types funext public -open import foundation.relaxed-sigma-decompositions funext public -open import foundation.repetitions-of-values funext public -open import foundation.repetitions-sequences funext public -open import foundation.replacement funext public -open import foundation.retractions funext public -open import foundation.retracts-of-maps funext public -open import foundation.retracts-of-types funext public -open import foundation.sections funext public -open import foundation.separated-types-subuniverses funext public +open import foundation.product-decompositions-subuniverse public +open import foundation.products-binary-relations public +open import foundation.products-equivalence-relations public +open import foundation.products-of-tuples-of-types public +open import foundation.products-pullbacks public +open import foundation.products-unordered-pairs-of-types public +open import foundation.products-unordered-tuples-of-types public +open import foundation.projective-types public +open import foundation.proper-subtypes public +open import foundation.propositional-extensionality public +open import foundation.propositional-maps public +open import foundation.propositional-resizing public +open import foundation.propositional-truncations public +open import foundation.propositions public +open import foundation.pullback-cones public +open import foundation.pullbacks public +open import foundation.pullbacks-subtypes public +open import foundation.quasicoherently-idempotent-maps public +open import foundation.raising-universe-levels public +open import foundation.raising-universe-levels-booleans public +open import foundation.raising-universe-levels-unit-type public +open import foundation.reflecting-maps-equivalence-relations public +open import foundation.reflexive-relations public +open import foundation.regensburg-extension-fundamental-theorem-of-identity-types public +open import foundation.relaxed-sigma-decompositions public +open import foundation.repetitions-of-values public +open import foundation.repetitions-sequences public +open import foundation.replacement public +open import foundation.retractions public +open import foundation.retracts-of-maps public +open import foundation.retracts-of-types public +open import foundation.sections public +open import foundation.separated-types-subuniverses public open import foundation.sequences public -open import foundation.sequential-limits funext public -open import foundation.set-presented-types funext public -open import foundation.set-quotients funext public -open import foundation.set-truncations funext public -open import foundation.sets funext public +open import foundation.sequential-limits public +open import foundation.set-presented-types public +open import foundation.set-quotients public +open import foundation.set-truncations public +open import foundation.sets public open import foundation.shifting-sequences public -open import foundation.sigma-closed-subuniverses funext public -open import foundation.sigma-decomposition-subuniverse funext public -open import foundation.sigma-decompositions funext public +open import foundation.sigma-closed-subuniverses public +open import foundation.sigma-decomposition-subuniverse public +open import foundation.sigma-decompositions public open import foundation.singleton-induction public -open import foundation.singleton-subtypes funext public -open import foundation.slice funext public -open import foundation.small-maps funext public -open import foundation.small-types funext public -open import foundation.small-universes funext public +open import foundation.singleton-subtypes public +open import foundation.slice public +open import foundation.small-maps public +open import foundation.small-types public +open import foundation.small-universes public open import foundation.sorial-type-families public -open import foundation.span-diagrams funext public +open import foundation.span-diagrams public open import foundation.span-diagrams-families-of-types public open import foundation.spans public open import foundation.spans-families-of-types public -open import foundation.spans-of-spans funext public -open import foundation.split-idempotent-maps funext public +open import foundation.spans-of-spans public +open import foundation.split-idempotent-maps public open import foundation.split-surjective-maps public -open import foundation.standard-apartness-relations funext public -open import foundation.standard-pullbacks funext public -open import foundation.standard-ternary-pullbacks funext public -open import foundation.strict-symmetrization-binary-relations funext public -open import foundation.strictly-involutive-identity-types funext public +open import foundation.standard-apartness-relations public +open import foundation.standard-pullbacks public +open import foundation.standard-ternary-pullbacks public +open import foundation.strict-symmetrization-binary-relations public +open import foundation.strictly-involutive-identity-types public open import foundation.strictly-right-unital-concatenation-identifications public -open import foundation.strong-preunivalence funext public -open import foundation.strongly-extensional-maps funext public -open import foundation.structure funext public +open import foundation.strong-preunivalence public +open import foundation.strongly-extensional-maps public +open import foundation.structure public open import foundation.structure-identity-principle public -open import foundation.structured-equality-duality funext public -open import foundation.structured-type-duality funext public +open import foundation.structured-equality-duality public +open import foundation.structured-type-duality public open import foundation.subsingleton-induction public open import foundation.subterminal-types public -open import foundation.subtype-duality funext public +open import foundation.subtype-duality public open import foundation.subtype-identity-principle public -open import foundation.subtypes funext public -open import foundation.subuniverses funext public -open import foundation.surjective-maps funext public -open import foundation.symmetric-binary-relations funext public -open import foundation.symmetric-cores-binary-relations funext public -open import foundation.symmetric-difference funext public -open import foundation.symmetric-identity-types funext public -open import foundation.symmetric-operations funext public +open import foundation.subtypes public +open import foundation.subuniverses public +open import foundation.surjective-maps public +open import foundation.symmetric-binary-relations public +open import foundation.symmetric-cores-binary-relations public +open import foundation.symmetric-difference public +open import foundation.symmetric-identity-types public +open import foundation.symmetric-operations public open import foundation.telescopes public -open import foundation.terminal-spans-families-of-types funext public -open import foundation.tight-apartness-relations funext public -open import foundation.torsorial-type-families funext public +open import foundation.terminal-spans-families-of-types public +open import foundation.tight-apartness-relations public +open import foundation.torsorial-type-families public open import foundation.total-partial-elements public -open import foundation.total-partial-functions funext public -open import foundation.transfinite-cocomposition-of-maps funext public -open import foundation.transport-along-equivalences funext public -open import foundation.transport-along-higher-identifications funext public -open import foundation.transport-along-homotopies funext public +open import foundation.total-partial-functions public +open import foundation.transfinite-cocomposition-of-maps public +open import foundation.transport-along-equivalences public +open import foundation.transport-along-higher-identifications public +open import foundation.transport-along-homotopies public open import foundation.transport-along-identifications public -open import foundation.transport-split-type-families funext public -open import foundation.transposition-identifications-along-equivalences funext public -open import foundation.transposition-identifications-along-retractions funext public -open import foundation.transposition-identifications-along-sections funext public -open import foundation.transposition-span-diagrams funext public -open import foundation.trivial-relaxed-sigma-decompositions funext public -open import foundation.trivial-sigma-decompositions funext public -open import foundation.truncated-equality funext public -open import foundation.truncated-maps funext public -open import foundation.truncated-types funext public -open import foundation.truncation-equivalences funext public -open import foundation.truncation-images-of-maps funext public +open import foundation.transport-split-type-families public +open import foundation.transposition-identifications-along-equivalences public +open import foundation.transposition-identifications-along-retractions public +open import foundation.transposition-identifications-along-sections public +open import foundation.transposition-span-diagrams public +open import foundation.trivial-relaxed-sigma-decompositions public +open import foundation.trivial-sigma-decompositions public +open import foundation.truncated-equality public +open import foundation.truncated-maps public +open import foundation.truncated-types public +open import foundation.truncation-equivalences public +open import foundation.truncation-images-of-maps public open import foundation.truncation-levels public -open import foundation.truncation-modalities funext public -open import foundation.truncations funext public -open import foundation.tuples-of-types funext public +open import foundation.truncation-modalities public +open import foundation.truncations public +open import foundation.tuples-of-types public open import foundation.type-arithmetic-booleans public open import foundation.type-arithmetic-cartesian-product-types public -open import foundation.type-arithmetic-coproduct-types funext public -open import foundation.type-arithmetic-dependent-function-types funext public +open import foundation.type-arithmetic-coproduct-types public +open import foundation.type-arithmetic-dependent-function-types public open import foundation.type-arithmetic-dependent-pair-types public -open import foundation.type-arithmetic-empty-type funext public -open import foundation.type-arithmetic-standard-pullbacks funext public +open import foundation.type-arithmetic-empty-type public +open import foundation.type-arithmetic-standard-pullbacks public open import foundation.type-arithmetic-unit-type public -open import foundation.type-duality funext public -open import foundation.type-theoretic-principle-of-choice funext public -open import foundation.uniformly-decidable-type-families funext public -open import foundation.unions-subtypes funext public -open import foundation.uniqueness-image funext public -open import foundation.uniqueness-quantification funext public -open import foundation.uniqueness-set-quotients funext public -open import foundation.uniqueness-set-truncations funext public -open import foundation.uniqueness-truncation funext public +open import foundation.type-duality public +open import foundation.type-theoretic-principle-of-choice public +open import foundation.uniformly-decidable-type-families public +open import foundation.unions-subtypes public +open import foundation.uniqueness-image public +open import foundation.uniqueness-quantification public +open import foundation.uniqueness-set-quotients public +open import foundation.uniqueness-set-truncations public +open import foundation.uniqueness-truncation public open import foundation.unit-type public open import foundation.unital-binary-operations public -open import foundation.univalence funext public -open import foundation.univalence-implies-function-extensionality funext public -open import foundation.univalent-type-families funext public -open import foundation.universal-property-booleans funext public -open import foundation.universal-property-cartesian-product-types funext public -open import foundation.universal-property-contractible-types funext public -open import foundation.universal-property-coproduct-types funext public -open import foundation.universal-property-dependent-function-types funext public -open import foundation.universal-property-dependent-pair-types funext public -open import foundation.universal-property-empty-type funext public -open import foundation.universal-property-equivalences funext public -open import foundation.universal-property-family-of-fibers-of-maps funext public -open import foundation.universal-property-fiber-products funext public -open import foundation.universal-property-identity-systems funext public -open import foundation.universal-property-identity-types funext public -open import foundation.universal-property-image funext public -open import foundation.universal-property-maybe funext public -open import foundation.universal-property-propositional-truncation funext public -open import foundation.universal-property-propositional-truncation-into-sets funext public -open import foundation.universal-property-pullbacks funext public -open import foundation.universal-property-sequential-limits funext public -open import foundation.universal-property-set-quotients funext public -open import foundation.universal-property-set-truncation funext public -open import foundation.universal-property-truncation funext public -open import foundation.universal-property-unit-type funext public -open import foundation.universal-quantification funext public +open import foundation.univalence public +open import foundation.univalence-implies-function-extensionality public +open import foundation.univalent-type-families public +open import foundation.universal-property-booleans public +open import foundation.universal-property-cartesian-product-types public +open import foundation.universal-property-contractible-types public +open import foundation.universal-property-coproduct-types public +open import foundation.universal-property-dependent-function-types public +open import foundation.universal-property-dependent-pair-types public +open import foundation.universal-property-empty-type public +open import foundation.universal-property-equivalences public +open import foundation.universal-property-family-of-fibers-of-maps public +open import foundation.universal-property-fiber-products public +open import foundation.universal-property-identity-systems public +open import foundation.universal-property-identity-types public +open import foundation.universal-property-image public +open import foundation.universal-property-maybe public +open import foundation.universal-property-propositional-truncation public +open import foundation.universal-property-propositional-truncation-into-sets public +open import foundation.universal-property-pullbacks public +open import foundation.universal-property-sequential-limits public +open import foundation.universal-property-set-quotients public +open import foundation.universal-property-set-truncation public +open import foundation.universal-property-truncation public +open import foundation.universal-property-unit-type public +open import foundation.universal-quantification public open import foundation.universe-levels public -open import foundation.unordered-pairs funext public -open import foundation.unordered-pairs-of-types funext public -open import foundation.unordered-tuples funext public -open import foundation.unordered-tuples-of-types funext public -open import foundation.vectors-set-quotients funext public -open import foundation.vertical-composition-spans-of-spans funext public -open import foundation.weak-function-extensionality funext public -open import foundation.weak-limited-principle-of-omniscience funext public -open import foundation.weakly-constant-maps funext public +open import foundation.unordered-pairs public +open import foundation.unordered-pairs-of-types public +open import foundation.unordered-tuples public +open import foundation.unordered-tuples-of-types public +open import foundation.vectors-set-quotients public +open import foundation.vertical-composition-spans-of-spans public +open import foundation.weak-function-extensionality public +open import foundation.weak-limited-principle-of-omniscience public +open import foundation.weakly-constant-maps public open import foundation.whiskering-higher-homotopies-composition public open import foundation.whiskering-homotopies-composition public -open import foundation.whiskering-homotopies-concatenation funext public -open import foundation.whiskering-identifications-concatenation funext public +open import foundation.whiskering-homotopies-concatenation public +open import foundation.whiskering-identifications-concatenation public open import foundation.whiskering-operations public -open import foundation.wild-category-of-types funext public -open import foundation.yoneda-identity-types funext public +open import foundation.wild-category-of-types public +open import foundation.yoneda-identity-types public ``` diff --git a/src/foundation/0-connected-types.lagda.md b/src/foundation/0-connected-types.lagda.md index 5e19217f13..d2bdc9203d 100644 --- a/src/foundation/0-connected-types.lagda.md +++ b/src/foundation/0-connected-types.lagda.md @@ -1,33 +1,28 @@ # `0`-Connected types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.0-connected-types - (funext : function-extensionality) - where +module foundation.0-connected-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.constant-maps funext -open import foundation.contractible-types funext +open import foundation.constant-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.fiber-inclusions funext -open import foundation.functoriality-set-truncation funext -open import foundation.images funext -open import foundation.inhabited-types funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.set-truncations funext -open import foundation.sets funext -open import foundation.surjective-maps funext +open import foundation.fiber-inclusions +open import foundation.functoriality-set-truncation +open import foundation.images +open import foundation.inhabited-types +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.set-truncations +open import foundation.sets +open import foundation.surjective-maps open import foundation.unit-type -open import foundation.universal-property-contractible-types funext -open import foundation.universal-property-unit-type funext +open import foundation.universal-property-contractible-types +open import foundation.universal-property-unit-type open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -37,7 +32,7 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.precomposition-functions open import foundation-core.propositions -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/0-images-of-maps.lagda.md b/src/foundation/0-images-of-maps.lagda.md index 839add5b7c..26121635f8 100644 --- a/src/foundation/0-images-of-maps.lagda.md +++ b/src/foundation/0-images-of-maps.lagda.md @@ -1,18 +1,13 @@ # `0`-Images of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.0-images-of-maps - (funext : function-extensionality) - where +module foundation.0-images-of-maps where ```
Imports ```agda -open import foundation.truncation-images-of-maps funext +open import foundation.truncation-images-of-maps open import foundation.universe-levels open import foundation-core.truncation-levels diff --git a/src/foundation/0-maps.lagda.md b/src/foundation/0-maps.lagda.md index 8b214200f4..365e87053d 100644 --- a/src/foundation/0-maps.lagda.md +++ b/src/foundation/0-maps.lagda.md @@ -1,26 +1,21 @@ # `0`-Maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.0-maps - (funext : function-extensionality) - where +module foundation.0-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.sets -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncation-levels ``` diff --git a/src/foundation/1-types.lagda.md b/src/foundation/1-types.lagda.md index c4517552a1..9a4b7da289 100644 --- a/src/foundation/1-types.lagda.md +++ b/src/foundation/1-types.lagda.md @@ -1,30 +1,25 @@ # `1`-Types ```agda -open import foundation.function-extensionality-axiom +module foundation.1-types where -module - foundation.1-types - (funext : function-extensionality) - where - -open import foundation-core.1-types funext public +open import foundation-core.1-types public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.subuniverses funext -open import foundation.truncated-types funext +open import foundation.dependent-products-truncated-types +open import foundation.subuniverses +open import foundation.truncated-types open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families open import foundation-core.truncation-levels ``` diff --git a/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md b/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md index 90ef1a273a..77d4813bf5 100644 --- a/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md +++ b/src/foundation/action-on-equivalences-functions-out-of-subuniverses.lagda.md @@ -1,22 +1,17 @@ # The action on equivalences of functions out of subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - foundation.action-on-equivalences-functions-out-of-subuniverses - (funext : function-extensionality) - where +module foundation.action-on-equivalences-functions-out-of-subuniverses where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-induction funext -open import foundation.subuniverses funext +open import foundation.equivalence-induction +open import foundation.subuniverses open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/action-on-equivalences-functions.lagda.md b/src/foundation/action-on-equivalences-functions.lagda.md index 3caf907230..497a160778 100644 --- a/src/foundation/action-on-equivalences-functions.lagda.md +++ b/src/foundation/action-on-equivalences-functions.lagda.md @@ -1,22 +1,17 @@ # Action on equivalences of functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.action-on-equivalences-functions - (funext : function-extensionality) - where +module foundation.action-on-equivalences-functions where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-induction funext -open import foundation.univalence funext +open import foundation.equivalence-induction +open import foundation.univalence open import foundation.universe-levels open import foundation-core.constant-maps diff --git a/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md b/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md index 383e2cd014..9285de702a 100644 --- a/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md +++ b/src/foundation/action-on-equivalences-type-families-over-subuniverses.lagda.md @@ -1,12 +1,7 @@ # Action on equivalences in type families over subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - foundation.action-on-equivalences-type-families-over-subuniverses - (funext : function-extensionality) - where +module foundation.action-on-equivalences-type-families-over-subuniverses where ```
Imports @@ -14,11 +9,11 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-induction funext -open import foundation.subuniverses funext +open import foundation.equivalence-induction +open import foundation.subuniverses open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation/action-on-equivalences-type-families.lagda.md b/src/foundation/action-on-equivalences-type-families.lagda.md index 39601ce297..909f4c4011 100644 --- a/src/foundation/action-on-equivalences-type-families.lagda.md +++ b/src/foundation/action-on-equivalences-type-families.lagda.md @@ -1,25 +1,20 @@ # Action on equivalences of type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.action-on-equivalences-type-families - (funext : function-extensionality) - where +module foundation.action-on-equivalences-type-families where ```
Imports ```agda -open import foundation.action-on-equivalences-functions funext +open import foundation.action-on-equivalences-functions open import foundation.action-on-identifications-functions -open import foundation.equivalence-induction funext -open import foundation.univalence funext +open import foundation.equivalence-induction +open import foundation.univalence open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.constant-maps open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/action-on-higher-identifications-functions.lagda.md b/src/foundation/action-on-higher-identifications-functions.lagda.md index 784280cc66..ad3c91bea7 100644 --- a/src/foundation/action-on-higher-identifications-functions.lagda.md +++ b/src/foundation/action-on-higher-identifications-functions.lagda.md @@ -1,19 +1,14 @@ # The action of functions on higher identifications ```agda -open import foundation.function-extensionality-axiom - -module - foundation.action-on-higher-identifications-functions - (funext : function-extensionality) - where +module foundation.action-on-higher-identifications-functions where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.path-algebra funext +open import foundation.path-algebra open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications diff --git a/src/foundation/action-on-homotopies-functions.lagda.md b/src/foundation/action-on-homotopies-functions.lagda.md index a19c63291c..e8dbeeaaba 100644 --- a/src/foundation/action-on-homotopies-functions.lagda.md +++ b/src/foundation/action-on-homotopies-functions.lagda.md @@ -1,23 +1,17 @@ # The action on homotopies of functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.action-on-homotopies-functions - (funext : function-extensionality) - where +module foundation.action-on-homotopies-functions where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.homotopy-induction funext +open import foundation.function-extensionality +open import foundation.homotopy-induction open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/apartness-relations.lagda.md b/src/foundation/apartness-relations.lagda.md index a8cf30a73c..605d8b5b43 100644 --- a/src/foundation/apartness-relations.lagda.md +++ b/src/foundation/apartness-relations.lagda.md @@ -1,24 +1,19 @@ # Apartness relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.apartness-relations - (funext : function-extensionality) - where +module foundation.apartness-relations where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.disjunction funext -open import foundation.existential-quantification funext -open import foundation.propositional-truncations funext -open import foundation.universal-quantification funext +open import foundation.dependent-products-propositions +open import foundation.disjunction +open import foundation.existential-quantification +open import foundation.propositional-truncations +open import foundation.universal-quantification open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md b/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md index c6654596ca..c29be5ba4a 100644 --- a/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md +++ b/src/foundation/arithmetic-law-coproduct-and-sigma-decompositions.lagda.md @@ -1,26 +1,21 @@ # Arithmetic law for coproduct decomposition and Σ-decomposition ```agda -open import foundation.function-extensionality-axiom - -module - foundation.arithmetic-law-coproduct-and-sigma-decompositions - (funext : function-extensionality) - where +module foundation.arithmetic-law-coproduct-and-sigma-decompositions where ```
Imports ```agda -open import foundation.coproduct-decompositions funext +open import foundation.coproduct-decompositions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-coproduct-types funext -open import foundation.relaxed-sigma-decompositions funext -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.equivalences +open import foundation.functoriality-coproduct-types +open import foundation.relaxed-sigma-decompositions +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext -open import foundation.universal-property-coproduct-types funext +open import foundation.univalence +open import foundation.universal-property-coproduct-types open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md b/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md index b965cbe4f0..2f70b0a358 100644 --- a/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md +++ b/src/foundation/arithmetic-law-product-and-pi-decompositions.lagda.md @@ -1,26 +1,21 @@ # Arithmetic law for product decomposition and Π-decomposition ```agda -open import foundation.function-extensionality-axiom - -module - foundation.arithmetic-law-product-and-pi-decompositions - (funext : function-extensionality) - where +module foundation.arithmetic-law-product-and-pi-decompositions where ```
Imports ```agda -open import foundation.coproduct-decompositions funext +open import foundation.coproduct-decompositions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.pi-decompositions funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.pi-decompositions open import foundation.product-decompositions open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext -open import foundation.universal-property-coproduct-types funext +open import foundation.univalence +open import foundation.universal-property-coproduct-types open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/automorphisms.lagda.md b/src/foundation/automorphisms.lagda.md index 8170916f8c..bc5d12d351 100644 --- a/src/foundation/automorphisms.lagda.md +++ b/src/foundation/automorphisms.lagda.md @@ -1,19 +1,14 @@ # Automorphisms ```agda -open import foundation.function-extensionality-axiom - -module - foundation.automorphisms - (funext : function-extensionality) - where +module foundation.automorphisms where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.sets funext +open import foundation.sets open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/axiom-of-choice.lagda.md b/src/foundation/axiom-of-choice.lagda.md index 70ca2d3a27..aa6b055a68 100644 --- a/src/foundation/axiom-of-choice.lagda.md +++ b/src/foundation/axiom-of-choice.lagda.md @@ -1,25 +1,21 @@ # The axiom of choice ```agda -open import foundation.function-extensionality-axiom - -module - foundation.axiom-of-choice - (funext : function-extensionality) - where +module foundation.axiom-of-choice where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation funext -open import foundation.inhabited-types funext -open import foundation.postcomposition-functions funext -open import foundation.projective-types funext -open import foundation.sections funext +open import foundation.function-extensionality-axiom +open import foundation.functoriality-propositional-truncation +open import foundation.inhabited-types +open import foundation.postcomposition-functions +open import foundation.projective-types +open import foundation.sections open import foundation.split-surjective-maps -open import foundation.surjective-maps funext +open import foundation.surjective-maps open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/bands.lagda.md b/src/foundation/bands.lagda.md index 07ac2553b7..9b846f6934 100644 --- a/src/foundation/bands.lagda.md +++ b/src/foundation/bands.lagda.md @@ -1,18 +1,13 @@ # Bands ```agda -open import foundation.function-extensionality-axiom - -module - foundation.bands - (funext : function-extensionality) - where +module foundation.bands where ```
Imports ```agda -open import foundation.set-truncations funext +open import foundation.set-truncations open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/base-changes-span-diagrams.lagda.md b/src/foundation/base-changes-span-diagrams.lagda.md index caf7f650b7..10882ba5e2 100644 --- a/src/foundation/base-changes-span-diagrams.lagda.md +++ b/src/foundation/base-changes-span-diagrams.lagda.md @@ -1,24 +1,19 @@ # Base changes of span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.base-changes-span-diagrams - (funext : function-extensionality) - where +module foundation.base-changes-span-diagrams where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows funext -open import foundation.cartesian-morphisms-span-diagrams funext -open import foundation.commuting-squares-of-maps funext +open import foundation.cartesian-morphisms-arrows +open import foundation.cartesian-morphisms-span-diagrams +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.morphisms-arrows funext -open import foundation.morphisms-span-diagrams funext -open import foundation.span-diagrams funext +open import foundation.morphisms-arrows +open import foundation.morphisms-span-diagrams +open import foundation.span-diagrams open import foundation.universe-levels ``` diff --git a/src/foundation/bicomposition-functions.lagda.md b/src/foundation/bicomposition-functions.lagda.md index 824dd875ee..fceca92642 100644 --- a/src/foundation/bicomposition-functions.lagda.md +++ b/src/foundation/bicomposition-functions.lagda.md @@ -1,12 +1,7 @@ # Bicomposition of functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.bicomposition-functions - (funext : function-extensionality) - where +module foundation.bicomposition-functions where ```
Imports @@ -14,20 +9,19 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.postcomposition-dependent-functions funext +open import foundation.function-extensionality +open import foundation.postcomposition-dependent-functions open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/binary-embeddings.lagda.md b/src/foundation/binary-embeddings.lagda.md index 64e6d3adb3..fb822a3918 100644 --- a/src/foundation/binary-embeddings.lagda.md +++ b/src/foundation/binary-embeddings.lagda.md @@ -1,12 +1,7 @@ # Binary embeddings ```agda -open import foundation.function-extensionality-axiom - -module - foundation.binary-embeddings - (funext : function-extensionality) - where +module foundation.binary-embeddings where ```
Imports @@ -16,7 +11,7 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md b/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md index d7802914d4..8f52b2aee3 100644 --- a/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md +++ b/src/foundation/binary-equivalences-unordered-pairs-of-types.lagda.md @@ -1,21 +1,16 @@ # Binary equivalences on unordered pairs of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.binary-equivalences-unordered-pairs-of-types - (funext : function-extensionality) - where +module foundation.binary-equivalences-unordered-pairs-of-types where ```
Imports ```agda -open import foundation.binary-operations-unordered-pairs-of-types funext -open import foundation.products-unordered-pairs-of-types funext +open import foundation.binary-operations-unordered-pairs-of-types +open import foundation.products-unordered-pairs-of-types open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/binary-functoriality-set-quotients.lagda.md b/src/foundation/binary-functoriality-set-quotients.lagda.md index b683cde907..767805918d 100644 --- a/src/foundation/binary-functoriality-set-quotients.lagda.md +++ b/src/foundation/binary-functoriality-set-quotients.lagda.md @@ -3,43 +3,38 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.binary-functoriality-set-quotients - (funext : function-extensionality) - where +module foundation.binary-functoriality-set-quotients where ```
Imports ```agda -open import foundation.binary-homotopies funext +open import foundation.binary-homotopies open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.exponents-set-quotients funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-set-quotients funext +open import foundation.dependent-products-propositions +open import foundation.exponents-set-quotients +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.functoriality-set-quotients open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.set-quotients funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.reflecting-maps-equivalence-relations +open import foundation.set-quotients +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.surjective-maps funext -open import foundation.universal-property-set-quotients funext +open import foundation.surjective-maps +open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation-core.contractible-types -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/binary-homotopies.lagda.md b/src/foundation/binary-homotopies.lagda.md index 117d5781dd..bbfde019b4 100644 --- a/src/foundation/binary-homotopies.lagda.md +++ b/src/foundation/binary-homotopies.lagda.md @@ -1,23 +1,17 @@ # Homotopies of binary operations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.binary-homotopies - (funext : function-extensionality) - where +module foundation.binary-homotopies where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.function-extensionality funext - +open import foundation.equality-dependent-function-types +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext +open import foundation.homotopy-induction open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md b/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md index ed8a02e9c9..2f5a31ac3c 100644 --- a/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md +++ b/src/foundation/binary-operations-unordered-pairs-of-types.lagda.md @@ -1,20 +1,15 @@ # Binary operations on unordered pairs of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.binary-operations-unordered-pairs-of-types - (funext : function-extensionality) - where +module foundation.binary-operations-unordered-pairs-of-types where ```
Imports ```agda -open import foundation.products-unordered-pairs-of-types funext +open import foundation.products-unordered-pairs-of-types open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs ```
diff --git a/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md b/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md index feac4c0b4e..954e06617b 100644 --- a/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md +++ b/src/foundation/binary-reflecting-maps-equivalence-relations.lagda.md @@ -1,26 +1,21 @@ # Binary reflecting maps of equivalence relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.binary-reflecting-maps-equivalence-relations - (funext : function-extensionality) - where +module foundation.binary-reflecting-maps-equivalence-relations where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equality-dependent-function-types funext +open import foundation.dependent-products-propositions +open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext +open import foundation.homotopy-induction open import foundation.subtype-identity-principle open import foundation.universe-levels -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/binary-relations-with-extensions.lagda.md b/src/foundation/binary-relations-with-extensions.lagda.md index 25ff3c4acf..50543f32af 100644 --- a/src/foundation/binary-relations-with-extensions.lagda.md +++ b/src/foundation/binary-relations-with-extensions.lagda.md @@ -1,20 +1,15 @@ # Binary relations with extensions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.binary-relations-with-extensions - (funext : function-extensionality) - where +module foundation.binary-relations-with-extensions where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types funext +open import foundation.iterated-dependent-product-types open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/binary-relations-with-lifts.lagda.md b/src/foundation/binary-relations-with-lifts.lagda.md index dd81c2f64f..f6ef244510 100644 --- a/src/foundation/binary-relations-with-lifts.lagda.md +++ b/src/foundation/binary-relations-with-lifts.lagda.md @@ -1,20 +1,15 @@ # Binary relations with lifts ```agda -open import foundation.function-extensionality-axiom - -module - foundation.binary-relations-with-lifts - (funext : function-extensionality) - where +module foundation.binary-relations-with-lifts where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types funext +open import foundation.iterated-dependent-product-types open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/binary-relations.lagda.md b/src/foundation/binary-relations.lagda.md index 862847ca22..d564eebeb0 100644 --- a/src/foundation/binary-relations.lagda.md +++ b/src/foundation/binary-relations.lagda.md @@ -1,25 +1,20 @@ # Binary relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.binary-relations - (funext : function-extensionality) - where +module foundation.binary-relations where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equality-dependent-function-types funext +open import foundation.dependent-products-propositions +open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.iterated-dependent-product-types funext -open import foundation.subtypes funext +open import foundation.iterated-dependent-product-types +open import foundation.subtypes open import foundation.telescopes -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/binary-type-duality.lagda.md b/src/foundation/binary-type-duality.lagda.md index 0011b7a204..5a4cfa15a6 100644 --- a/src/foundation/binary-type-duality.lagda.md +++ b/src/foundation/binary-type-duality.lagda.md @@ -1,27 +1,22 @@ # Binary type duality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.binary-type-duality - (funext : function-extensionality) - where +module foundation.binary-type-duality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-spans -open import foundation.function-types funext -open import foundation.multivariable-homotopies funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.equivalences-spans +open import foundation.function-types +open import foundation.multivariable-homotopies +open import foundation.retractions +open import foundation.sections open import foundation.spans open import foundation.telescopes -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/booleans.lagda.md b/src/foundation/booleans.lagda.md index 52841cd831..3ac9ef298c 100644 --- a/src/foundation/booleans.lagda.md +++ b/src/foundation/booleans.lagda.md @@ -1,12 +1,7 @@ # The booleans ```agda -open import foundation.function-extensionality-axiom - -module - foundation.booleans - (funext : function-extensionality) - where +module foundation.booleans where open import foundation-core.booleans public ``` @@ -14,11 +9,11 @@ open import foundation-core.booleans public
Imports ```agda -open import foundation.decidable-equality funext +open import foundation.decidable-equality open import foundation.dependent-pair-types -open import foundation.discrete-types funext -open import foundation.involutions funext -open import foundation.negated-equality funext +open import foundation.discrete-types +open import foundation.involutions +open import foundation.negated-equality open import foundation.unit-type open import foundation.universe-levels @@ -34,8 +29,8 @@ open import foundation-core.propositions open import foundation-core.sections open import foundation-core.sets -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/cantor-schroder-bernstein-escardo.lagda.md b/src/foundation/cantor-schroder-bernstein-escardo.lagda.md index bc12428176..c48597b785 100644 --- a/src/foundation/cantor-schroder-bernstein-escardo.lagda.md +++ b/src/foundation/cantor-schroder-bernstein-escardo.lagda.md @@ -1,23 +1,18 @@ # The Cantor–Schröder–Bernstein–Escardó theorem ```agda -open import foundation.function-extensionality-axiom - -module - foundation.cantor-schroder-bernstein-escardo - (funext : function-extensionality) - where +module foundation.cantor-schroder-bernstein-escardo where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.injective-maps funext -open import foundation.law-of-excluded-middle funext -open import foundation.perfect-images funext +open import foundation.injective-maps +open import foundation.law-of-excluded-middle +open import foundation.perfect-images open import foundation.split-surjective-maps open import foundation.universe-levels diff --git a/src/foundation/cantors-theorem.lagda.md b/src/foundation/cantors-theorem.lagda.md index 6b5a0e6fbd..f44e28067a 100644 --- a/src/foundation/cantors-theorem.lagda.md +++ b/src/foundation/cantors-theorem.lagda.md @@ -1,35 +1,31 @@ # Cantor's theorem ```agda -open import foundation.function-extensionality-axiom - -module - foundation.cantors-theorem - (funext : function-extensionality) - where +module foundation.cantors-theorem where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.decidable-propositions funext -open import foundation.decidable-subtypes funext +open import foundation.decidable-propositions +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.surjective-maps funext +open import foundation.double-negation-stable-propositions +open import foundation.function-extensionality-axiom +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.surjective-maps open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.fibers-of-maps -open import logic.de-morgan-propositions funext -open import logic.de-morgan-subtypes funext -open import logic.double-negation-stable-subtypes funext +open import logic.de-morgan-propositions +open import logic.de-morgan-subtypes +open import logic.double-negation-stable-subtypes ```
diff --git a/src/foundation/cartesian-morphisms-arrows.lagda.md b/src/foundation/cartesian-morphisms-arrows.lagda.md index dd0c0fe1d1..58ea9ebfbb 100644 --- a/src/foundation/cartesian-morphisms-arrows.lagda.md +++ b/src/foundation/cartesian-morphisms-arrows.lagda.md @@ -1,49 +1,44 @@ # Cartesian morphisms of arrows ```agda -open import foundation.function-extensionality-axiom - -module - foundation.cartesian-morphisms-arrows - (funext : function-extensionality) - where +module foundation.cartesian-morphisms-arrows where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps funext -open import foundation.commuting-triangles-of-morphisms-arrows funext -open import foundation.cones-over-cospan-diagrams funext -open import foundation.coproducts-pullbacks funext +open import foundation.commuting-triangles-of-maps +open import foundation.commuting-triangles-of-morphisms-arrows +open import foundation.cones-over-cospan-diagrams +open import foundation.coproducts-pullbacks open import foundation.dependent-pair-types -open import foundation.dependent-products-pullbacks funext -open import foundation.dependent-sums-pullbacks funext -open import foundation.diagonal-maps-cartesian-products-of-types funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-fibers-of-maps funext -open import foundation.homotopies-morphisms-arrows funext -open import foundation.identity-types funext -open import foundation.morphisms-arrows funext -open import foundation.postcomposition-functions funext -open import foundation.postcomposition-pullbacks funext -open import foundation.products-pullbacks funext -open import foundation.pullbacks funext -open import foundation.standard-pullbacks funext +open import foundation.dependent-products-pullbacks +open import foundation.dependent-sums-pullbacks +open import foundation.diagonal-maps-cartesian-products-of-types +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-fibers-of-maps +open import foundation.homotopies-morphisms-arrows +open import foundation.identity-types +open import foundation.morphisms-arrows +open import foundation.postcomposition-functions +open import foundation.postcomposition-pullbacks +open import foundation.products-pullbacks +open import foundation.pullbacks +open import foundation.standard-pullbacks open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.homotopies open import foundation-core.propositions -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/cartesian-morphisms-span-diagrams.lagda.md b/src/foundation/cartesian-morphisms-span-diagrams.lagda.md index d338a43fa6..0441d162f7 100644 --- a/src/foundation/cartesian-morphisms-span-diagrams.lagda.md +++ b/src/foundation/cartesian-morphisms-span-diagrams.lagda.md @@ -1,24 +1,19 @@ # Cartesian morphisms of span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.cartesian-morphisms-span-diagrams - (funext : function-extensionality) - where +module foundation.cartesian-morphisms-span-diagrams where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows funext -open import foundation.cartesian-product-types funext -open import foundation.commuting-squares-of-maps funext +open import foundation.cartesian-morphisms-arrows +open import foundation.cartesian-product-types +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.morphisms-arrows funext -open import foundation.morphisms-span-diagrams funext -open import foundation.span-diagrams funext +open import foundation.morphisms-arrows +open import foundation.morphisms-span-diagrams +open import foundation.span-diagrams open import foundation.universe-levels ``` diff --git a/src/foundation/cartesian-product-types.lagda.md b/src/foundation/cartesian-product-types.lagda.md index 5a117cd369..08740b0e83 100644 --- a/src/foundation/cartesian-product-types.lagda.md +++ b/src/foundation/cartesian-product-types.lagda.md @@ -1,12 +1,7 @@ # Cartesian product types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.cartesian-product-types - (funext : function-extensionality) - where +module foundation.cartesian-product-types where open import foundation-core.cartesian-product-types public ``` @@ -15,7 +10,7 @@ open import foundation-core.cartesian-product-types public ```agda open import foundation.dependent-pair-types -open import foundation.subuniverses funext +open import foundation.subuniverses open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/cartesian-products-set-quotients.lagda.md b/src/foundation/cartesian-products-set-quotients.lagda.md index a11402b82f..f016d8c0f7 100644 --- a/src/foundation/cartesian-products-set-quotients.lagda.md +++ b/src/foundation/cartesian-products-set-quotients.lagda.md @@ -1,12 +1,7 @@ # Cartesian products of set quotients ```agda -open import foundation.function-extensionality-axiom - -module - foundation.cartesian-products-set-quotients - (funext : function-extensionality) - where +module foundation.cartesian-products-set-quotients where ```
Imports @@ -15,19 +10,19 @@ module open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality funext - -open import foundation.products-equivalence-relations funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.set-quotients funext -open import foundation.sets funext -open import foundation.uniqueness-set-quotients funext -open import foundation.universal-property-set-quotients funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.products-equivalence-relations +open import foundation.reflecting-maps-equivalence-relations +open import foundation.set-quotients +open import foundation.sets +open import foundation.uniqueness-set-quotients +open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.equality-dependent-pair-types -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies diff --git a/src/foundation/category-of-families-of-sets.lagda.md b/src/foundation/category-of-families-of-sets.lagda.md index ccf7350d8a..a5d7dff0ff 100644 --- a/src/foundation/category-of-families-of-sets.lagda.md +++ b/src/foundation/category-of-families-of-sets.lagda.md @@ -1,25 +1,20 @@ # The category of families of sets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.category-of-families-of-sets - (funext : function-extensionality) - where +module foundation.category-of-families-of-sets where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.large-categories funext -open import category-theory.large-function-categories funext -open import category-theory.large-function-precategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext - -open import foundation.category-of-sets funext +open import category-theory.categories +open import category-theory.large-categories +open import category-theory.large-function-categories +open import category-theory.large-function-precategories +open import category-theory.large-precategories +open import category-theory.precategories + +open import foundation.category-of-sets open import foundation.universe-levels ``` diff --git a/src/foundation/category-of-sets.lagda.md b/src/foundation/category-of-sets.lagda.md index cbe5e451ba..23f7b9be68 100644 --- a/src/foundation/category-of-sets.lagda.md +++ b/src/foundation/category-of-sets.lagda.md @@ -1,43 +1,38 @@ # The category of sets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.category-of-sets - (funext : function-extensionality) - where +module foundation.category-of-sets where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.complete-precategories funext -open import category-theory.cones-precategories funext -open import category-theory.constant-functors funext -open import category-theory.functors-precategories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.limits-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.complete-precategories +open import category-theory.cones-precategories +open import category-theory.constant-functors +open import category-theory.functors-precategories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.limits-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.isomorphisms-of-sets funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.isomorphisms-of-sets +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type +open import foundation.retractions +open import foundation.sections +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/choice-of-representatives-equivalence-relation.lagda.md b/src/foundation/choice-of-representatives-equivalence-relation.lagda.md index 3f9fa8f6cc..6ba3e69b75 100644 --- a/src/foundation/choice-of-representatives-equivalence-relation.lagda.md +++ b/src/foundation/choice-of-representatives-equivalence-relation.lagda.md @@ -1,12 +1,7 @@ # Choice of representatives for an equivalence relation ```agda -open import foundation.function-extensionality-axiom - -module - foundation.choice-of-representatives-equivalence-relation - (funext : function-extensionality) - where +module foundation.choice-of-representatives-equivalence-relation where ```
Imports @@ -14,18 +9,18 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-classes funext +open import foundation.equivalence-classes open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.surjective-maps funext +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.surjective-maps open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.contractible-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.functoriality-dependent-pair-types diff --git a/src/foundation/coalgebras-maybe.lagda.md b/src/foundation/coalgebras-maybe.lagda.md index 45627df61e..afca8c6ef1 100644 --- a/src/foundation/coalgebras-maybe.lagda.md +++ b/src/foundation/coalgebras-maybe.lagda.md @@ -1,12 +1,7 @@ # Coalgebras of the maybe monad ```agda -open import foundation.function-extensionality-axiom - -module - foundation.coalgebras-maybe - (funext : function-extensionality) - where +module foundation.coalgebras-maybe where ```
Imports @@ -17,7 +12,7 @@ open import foundation.universe-levels open import foundation-core.maybe -open import trees.polynomial-endofunctors funext +open import trees.polynomial-endofunctors ```
diff --git a/src/foundation/coherently-idempotent-maps.lagda.md b/src/foundation/coherently-idempotent-maps.lagda.md index 3e9b54d0b6..d746a1ec6a 100644 --- a/src/foundation/coherently-idempotent-maps.lagda.md +++ b/src/foundation/coherently-idempotent-maps.lagda.md @@ -1,12 +1,7 @@ # Coherently idempotent maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.coherently-idempotent-maps - (funext : function-extensionality) - where +module foundation.coherently-idempotent-maps where ```
Imports @@ -16,8 +11,8 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.homotopy-algebra -open import foundation.quasicoherently-idempotent-maps funext -open import foundation.split-idempotent-maps funext +open import foundation.quasicoherently-idempotent-maps +open import foundation.split-idempotent-maps open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/coherently-invertible-maps.lagda.md b/src/foundation/coherently-invertible-maps.lagda.md index 62415c3ea1..d811bbad78 100644 --- a/src/foundation/coherently-invertible-maps.lagda.md +++ b/src/foundation/coherently-invertible-maps.lagda.md @@ -1,12 +1,7 @@ # Coherently invertible maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.coherently-invertible-maps - (funext : function-extensionality) - where +module foundation.coherently-invertible-maps where open import foundation-core.coherently-invertible-maps public ``` @@ -15,10 +10,10 @@ open import foundation-core.coherently-invertible-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.dependent-products-contractible-types funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext +open import foundation.dependent-products-contractible-types +open import foundation.equivalences +open import foundation.identity-types +open import foundation.logical-equivalences open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/coinhabited-pairs-of-types.lagda.md b/src/foundation/coinhabited-pairs-of-types.lagda.md index 7a578be166..bb9be37fb9 100644 --- a/src/foundation/coinhabited-pairs-of-types.lagda.md +++ b/src/foundation/coinhabited-pairs-of-types.lagda.md @@ -1,20 +1,15 @@ # Coinhabited pairs of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.coinhabited-pairs-of-types - (funext : function-extensionality) - where +module foundation.coinhabited-pairs-of-types where ```
Imports ```agda -open import foundation.inhabited-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.inhabited-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/commuting-cubes-of-maps.lagda.md b/src/foundation/commuting-cubes-of-maps.lagda.md index 8420b590d7..0309bafe4b 100644 --- a/src/foundation/commuting-cubes-of-maps.lagda.md +++ b/src/foundation/commuting-cubes-of-maps.lagda.md @@ -1,12 +1,7 @@ # Commuting cubes of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.commuting-cubes-of-maps - (funext : function-extensionality) - where +module foundation.commuting-cubes-of-maps where ```
Imports @@ -14,16 +9,15 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.commuting-hexagons-of-identifications -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-maps funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-maps +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.homotopies funext +open import foundation.function-extensionality +open import foundation.homotopies open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation funext +open import foundation.whiskering-homotopies-concatenation open import foundation-core.function-types open import foundation-core.identity-types diff --git a/src/foundation/commuting-prisms-of-maps.lagda.md b/src/foundation/commuting-prisms-of-maps.lagda.md index d08afb582c..1abe1edc03 100644 --- a/src/foundation/commuting-prisms-of-maps.lagda.md +++ b/src/foundation/commuting-prisms-of-maps.lagda.md @@ -1,35 +1,29 @@ # Commuting prisms of maps ```agda -open import foundation.function-extensionality-axiom +module foundation.commuting-prisms-of-maps where -module - foundation.commuting-prisms-of-maps - (funext : function-extensionality) - where - -open import foundation-core.commuting-prisms-of-maps funext public +open import foundation-core.commuting-prisms-of-maps public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.composition-algebra funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-functions funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps +open import foundation.composition-algebra +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.postcomposition-functions +open import foundation.precomposition-functions open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.homotopies ``` diff --git a/src/foundation/commuting-squares-of-homotopies.lagda.md b/src/foundation/commuting-squares-of-homotopies.lagda.md index bbbc0d1673..102c3cee57 100644 --- a/src/foundation/commuting-squares-of-homotopies.lagda.md +++ b/src/foundation/commuting-squares-of-homotopies.lagda.md @@ -1,12 +1,7 @@ # Commuting squares of homotopies ```agda -open import foundation.function-extensionality-axiom - -module - foundation.commuting-squares-of-homotopies - (funext : function-extensionality) - where +module foundation.commuting-squares-of-homotopies where open import foundation-core.commuting-squares-of-homotopies public ``` @@ -14,13 +9,13 @@ open import foundation-core.commuting-squares-of-homotopies public
Imports ```agda -open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-identifications open import foundation.dependent-pair-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.universe-levels open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types ```
diff --git a/src/foundation/commuting-squares-of-identifications.lagda.md b/src/foundation/commuting-squares-of-identifications.lagda.md index a755bd1fce..d0b7caf8b4 100644 --- a/src/foundation/commuting-squares-of-identifications.lagda.md +++ b/src/foundation/commuting-squares-of-identifications.lagda.md @@ -1,12 +1,7 @@ # Commuting squares of identifications ```agda -open import foundation.function-extensionality-axiom - -module - foundation.commuting-squares-of-identifications - (funext : function-extensionality) - where +module foundation.commuting-squares-of-identifications where open import foundation-core.commuting-squares-of-identifications public ``` @@ -15,7 +10,7 @@ open import foundation-core.commuting-squares-of-identifications public ```agda open import foundation.dependent-pair-types -open import foundation.path-algebra funext +open import foundation.path-algebra open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/commuting-squares-of-maps.lagda.md b/src/foundation/commuting-squares-of-maps.lagda.md index 2bd0ff7863..347bb16120 100644 --- a/src/foundation/commuting-squares-of-maps.lagda.md +++ b/src/foundation/commuting-squares-of-maps.lagda.md @@ -1,14 +1,9 @@ # Commuting squares of maps ```agda -open import foundation.function-extensionality-axiom +module foundation.commuting-squares-of-maps where -module - foundation.commuting-squares-of-maps - (funext : function-extensionality) - where - -open import foundation-core.commuting-squares-of-maps funext public +open import foundation-core.commuting-squares-of-maps public ```
Imports @@ -16,19 +11,18 @@ open import foundation-core.commuting-squares-of-maps funext public ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-homotopies funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.function-extensionality funext - +open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-maps +open import foundation.function-extensionality open import foundation.homotopy-algebra -open import foundation.postcomposition-functions funext -open import foundation.precomposition-functions funext -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.postcomposition-functions +open import foundation.precomposition-functions +open import foundation.transposition-identifications-along-equivalences open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-prisms-of-maps funext +open import foundation-core.commuting-prisms-of-maps open import foundation-core.commuting-squares-of-homotopies open import foundation-core.commuting-squares-of-identifications open import foundation-core.equivalences diff --git a/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md b/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md index 6c2e191aae..2aa6902f83 100644 --- a/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md +++ b/src/foundation/commuting-tetrahedra-of-homotopies.lagda.md @@ -1,18 +1,13 @@ # Commuting tetrahedra of homotopies ```agda -open import foundation.function-extensionality-axiom - -module - foundation.commuting-tetrahedra-of-homotopies - (funext : function-extensionality) - where +module foundation.commuting-tetrahedra-of-homotopies where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-homotopies open import foundation.universe-levels open import foundation-core.homotopies diff --git a/src/foundation/commuting-triangles-of-homotopies.lagda.md b/src/foundation/commuting-triangles-of-homotopies.lagda.md index 6342b7ebc0..a9a57c0d7e 100644 --- a/src/foundation/commuting-triangles-of-homotopies.lagda.md +++ b/src/foundation/commuting-triangles-of-homotopies.lagda.md @@ -1,18 +1,13 @@ # Commuting triangles of homotopies ```agda -open import foundation.function-extensionality-axiom - -module - foundation.commuting-triangles-of-homotopies - (funext : function-extensionality) - where +module foundation.commuting-triangles-of-homotopies where ```
Imports ```agda -open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-triangles-of-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/commuting-triangles-of-identifications.lagda.md b/src/foundation/commuting-triangles-of-identifications.lagda.md index b3476511f3..ab6e12a82d 100644 --- a/src/foundation/commuting-triangles-of-identifications.lagda.md +++ b/src/foundation/commuting-triangles-of-identifications.lagda.md @@ -1,12 +1,7 @@ # Commuting triangles of identifications ```agda -open import foundation.function-extensionality-axiom - -module - foundation.commuting-triangles-of-identifications - (funext : function-extensionality) - where +module foundation.commuting-triangles-of-identifications where ```
Imports @@ -15,9 +10,9 @@ module open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation open import foundation-core.commuting-squares-of-identifications open import foundation-core.equivalences diff --git a/src/foundation/commuting-triangles-of-maps.lagda.md b/src/foundation/commuting-triangles-of-maps.lagda.md index 9e90b435ba..ef0e081b0a 100644 --- a/src/foundation/commuting-triangles-of-maps.lagda.md +++ b/src/foundation/commuting-triangles-of-maps.lagda.md @@ -1,12 +1,7 @@ # Commuting triangles of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.commuting-triangles-of-maps - (funext : function-extensionality) - where +module foundation.commuting-triangles-of-maps where open import foundation-core.commuting-triangles-of-maps public ``` @@ -15,16 +10,16 @@ open import foundation-core.commuting-triangles-of-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.functoriality-dependent-function-types funext -open import foundation.homotopies funext +open import foundation.functoriality-dependent-function-types +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-functions funext +open import foundation.identity-types +open import foundation.postcomposition-functions +open import foundation.precomposition-functions open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.whiskering-identifications-concatenation diff --git a/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md b/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md index 1b958b4538..2e375cefa7 100644 --- a/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md +++ b/src/foundation/commuting-triangles-of-morphisms-arrows.lagda.md @@ -1,19 +1,14 @@ # Commuting triangles of morphisms of arrows ```agda -open import foundation.function-extensionality-axiom - -module - foundation.commuting-triangles-of-morphisms-arrows - (funext : function-extensionality) - where +module foundation.commuting-triangles-of-morphisms-arrows where ```
Imports ```agda -open import foundation.homotopies-morphisms-arrows funext -open import foundation.morphisms-arrows funext +open import foundation.homotopies-morphisms-arrows +open import foundation.morphisms-arrows open import foundation.universe-levels ``` diff --git a/src/foundation/complements-subtypes.lagda.md b/src/foundation/complements-subtypes.lagda.md index 73cc09728b..3331a3455c 100644 --- a/src/foundation/complements-subtypes.lagda.md +++ b/src/foundation/complements-subtypes.lagda.md @@ -1,40 +1,35 @@ # Complements of subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.complements-subtypes - (funext : function-extensionality) - where +module foundation.complements-subtypes where ```
Imports ```agda -open import foundation.decidable-propositions funext -open import foundation.decidable-subtypes funext -open import foundation.double-negation-stable-propositions funext -open import foundation.full-subtypes funext -open import foundation.negation funext -open import foundation.postcomposition-functions funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.unions-subtypes funext +open import foundation.decidable-propositions +open import foundation.decidable-subtypes +open import foundation.double-negation-stable-propositions +open import foundation.full-subtypes +open import foundation.negation +open import foundation.postcomposition-functions +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.unions-subtypes open import foundation.universe-levels open import foundation-core.function-types -open import foundation-core.subtypes funext +open import foundation-core.subtypes -open import logic.double-negation-stable-subtypes funext +open import logic.double-negation-stable-subtypes -open import order-theory.large-posets funext -open import order-theory.opposite-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.order-preserving-maps-preorders funext -open import order-theory.posets funext +open import order-theory.large-posets +open import order-theory.opposite-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.order-preserving-maps-posets +open import order-theory.order-preserving-maps-preorders +open import order-theory.posets ```
diff --git a/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md b/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md index dde0f03941..78c23727e3 100644 --- a/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/composite-maps-in-inverse-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Composite maps in inverse sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.composite-maps-in-inverse-sequential-diagrams - (funext : function-extensionality) - where +module foundation.composite-maps-in-inverse-sequential-diagrams where ```
Imports @@ -15,8 +10,8 @@ module open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.dependent-inverse-sequential-diagrams funext -open import foundation.inverse-sequential-diagrams funext +open import foundation.dependent-inverse-sequential-diagrams +open import foundation.inverse-sequential-diagrams open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/composition-algebra.lagda.md b/src/foundation/composition-algebra.lagda.md index 6ab2802918..d78d99cfee 100644 --- a/src/foundation/composition-algebra.lagda.md +++ b/src/foundation/composition-algebra.lagda.md @@ -1,23 +1,17 @@ # Composition algebra ```agda -open import foundation.function-extensionality-axiom - -module - foundation.composition-algebra - (funext : function-extensionality) - where +module foundation.composition-algebra where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-extensionality funext - -open import foundation.homotopy-induction funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-functions funext +open import foundation.function-extensionality +open import foundation.homotopy-induction +open import foundation.postcomposition-functions +open import foundation.precomposition-functions open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/composition-spans.lagda.md b/src/foundation/composition-spans.lagda.md index 2ffff15d37..2611cdf5b1 100644 --- a/src/foundation/composition-spans.lagda.md +++ b/src/foundation/composition-spans.lagda.md @@ -1,30 +1,25 @@ # Composition of spans ```agda -open import foundation.function-extensionality-axiom - -module - foundation.composition-spans - (funext : function-extensionality) - where +module foundation.composition-spans where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.equivalences-spans funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.morphisms-arrows funext +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.equivalences-spans +open import foundation.homotopies +open import foundation.identity-types +open import foundation.morphisms-arrows open import foundation.morphisms-spans -open import foundation.pullbacks funext +open import foundation.pullbacks open import foundation.spans -open import foundation.standard-pullbacks funext -open import foundation.type-arithmetic-standard-pullbacks funext +open import foundation.standard-pullbacks +open import foundation.type-arithmetic-standard-pullbacks open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/computational-identity-types.lagda.md b/src/foundation/computational-identity-types.lagda.md index 1d64404a7e..5c40b6da91 100644 --- a/src/foundation/computational-identity-types.lagda.md +++ b/src/foundation/computational-identity-types.lagda.md @@ -1,12 +1,7 @@ # Computational identity types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.computational-identity-types - (funext : function-extensionality) - where +module foundation.computational-identity-types where ```
Imports @@ -16,14 +11,14 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.strictly-right-unital-concatenation-identifications open import foundation.transport-along-identifications -open import foundation.univalence funext -open import foundation.universal-property-identity-systems funext +open import foundation.univalence +open import foundation.universal-property-identity-systems open import foundation.universe-levels -open import foundation.yoneda-identity-types funext +open import foundation.yoneda-identity-types open import foundation-core.cartesian-product-types open import foundation-core.contractible-types diff --git a/src/foundation/cones-over-cospan-diagrams.lagda.md b/src/foundation/cones-over-cospan-diagrams.lagda.md index 072599a672..8bc7769426 100644 --- a/src/foundation/cones-over-cospan-diagrams.lagda.md +++ b/src/foundation/cones-over-cospan-diagrams.lagda.md @@ -1,12 +1,7 @@ # Cones over cospan diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.cones-over-cospan-diagrams - (funext : function-extensionality) - where +module foundation.cones-over-cospan-diagrams where ```
Imports @@ -14,20 +9,19 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.function-extensionality funext - +open import foundation.dependent-universal-property-equivalences +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.multivariable-homotopies funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.multivariable-homotopies open import foundation.structure-identity-principle open import foundation.telescopes open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md b/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md index 9ede8855b1..a062c7b9d4 100644 --- a/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/cones-over-inverse-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Cones over inverse sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.cones-over-inverse-sequential-diagrams - (funext : function-extensionality) - where +module foundation.cones-over-inverse-sequential-diagrams where ```
Imports @@ -14,14 +9,13 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies funext +open import foundation.binary-homotopies open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.function-extensionality funext - +open import foundation.equality-dependent-function-types +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.inverse-sequential-diagrams funext +open import foundation.homotopy-induction +open import foundation.inverse-sequential-diagrams open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/conjunction.lagda.md b/src/foundation/conjunction.lagda.md index 5305e5f67d..0ba08d98b8 100644 --- a/src/foundation/conjunction.lagda.md +++ b/src/foundation/conjunction.lagda.md @@ -1,27 +1,22 @@ # Conjunction ```agda -open import foundation.function-extensionality-axiom - -module - foundation.conjunction - (funext : function-extensionality) - where +module foundation.conjunction where ```
Imports ```agda -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.universal-property-cartesian-product-types funext +open import foundation.dependent-products-propositions +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.universal-property-cartesian-product-types open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.propositions diff --git a/src/foundation/connected-components-universes.lagda.md b/src/foundation/connected-components-universes.lagda.md index 0aaeb111cd..6e4a87e413 100644 --- a/src/foundation/connected-components-universes.lagda.md +++ b/src/foundation/connected-components-universes.lagda.md @@ -1,34 +1,29 @@ # Connected components of universes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.connected-components-universes - (funext : function-extensionality) - where +module foundation.connected-components-universes where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.functoriality-propositional-truncation funext +open import foundation.empty-types +open import foundation.functoriality-propositional-truncation open import foundation.fundamental-theorem-of-identity-types -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.raising-universe-levels funext +open import foundation.mere-equivalences +open import foundation.propositional-truncations +open import foundation.raising-universe-levels open import foundation.subtype-identity-principle -open import foundation.subuniverses funext -open import foundation.univalence funext +open import foundation.subuniverses +open import foundation.univalence open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.identity-types -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/connected-components.lagda.md b/src/foundation/connected-components.lagda.md index 757f7433f6..9de3f80bbc 100644 --- a/src/foundation/connected-components.lagda.md +++ b/src/foundation/connected-components.lagda.md @@ -1,32 +1,27 @@ # Connected components of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.connected-components - (funext : function-extensionality) - where +module foundation.connected-components where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.dependent-pair-types -open import foundation.logical-equivalences funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.logical-equivalences +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.universe-levels open import foundation-core.equality-dependent-pair-types open import foundation-core.identity-types -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types ``` diff --git a/src/foundation/connected-maps.lagda.md b/src/foundation/connected-maps.lagda.md index a0fb4af1b7..74bc45c267 100644 --- a/src/foundation/connected-maps.lagda.md +++ b/src/foundation/connected-maps.lagda.md @@ -1,30 +1,26 @@ # Connected maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.connected-maps - (funext : function-extensionality) - where +module foundation.connected-maps where ```
Imports ```agda -open import foundation.connected-types funext +open import foundation.connected-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-propositions +open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.precomposition-dependent-functions funext +open import foundation.homotopy-induction +open import foundation.precomposition-dependent-functions open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels -open import foundation.truncations funext -open import foundation.univalence funext -open import foundation.universal-property-family-of-fibers-of-maps funext +open import foundation.truncations +open import foundation.univalence +open import foundation.universal-property-family-of-fibers-of-maps open import foundation.universe-levels open import foundation-core.contractible-maps @@ -36,9 +32,9 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps ```
diff --git a/src/foundation/connected-types.lagda.md b/src/foundation/connected-types.lagda.md index b2e349ae7c..433b38821f 100644 --- a/src/foundation/connected-types.lagda.md +++ b/src/foundation/connected-types.lagda.md @@ -1,24 +1,20 @@ # Connected types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.connected-types - (funext : function-extensionality) - where +module foundation.connected-types where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.functoriality-truncation funext -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.truncations funext +open import foundation.function-extensionality-axiom +open import foundation.functoriality-truncation +open import foundation.inhabited-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/constant-maps.lagda.md b/src/foundation/constant-maps.lagda.md index 2b418dd759..ec686e7417 100644 --- a/src/foundation/constant-maps.lagda.md +++ b/src/foundation/constant-maps.lagda.md @@ -1,12 +1,7 @@ # Constant maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.constant-maps - (funext : function-extensionality) - where +module foundation.constant-maps where open import foundation-core.constant-maps public ``` @@ -14,29 +9,28 @@ open import foundation-core.constant-maps public
Imports ```agda -open import foundation.0-maps funext -open import foundation.action-on-homotopies-functions funext +open import foundation.0-maps +open import foundation.action-on-homotopies-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.faithful-maps funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-dependent-pair-types funext -open import foundation.images funext -open import foundation.morphisms-arrows funext -open import foundation.postcomposition-functions funext -open import foundation.propositional-truncations funext -open import foundation.retracts-of-maps funext -open import foundation.retracts-of-types funext -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.faithful-maps +open import foundation.function-extensionality +open import foundation.functoriality-dependent-pair-types +open import foundation.images +open import foundation.morphisms-arrows +open import foundation.postcomposition-functions +open import foundation.propositional-truncations +open import foundation.retracts-of-maps +open import foundation.retracts-of-types +open import foundation.transposition-identifications-along-equivalences open import foundation.type-arithmetic-unit-type -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.1-types funext -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.1-types +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.embeddings @@ -49,7 +43,7 @@ open import foundation-core.injective-maps open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/constant-span-diagrams.lagda.md b/src/foundation/constant-span-diagrams.lagda.md index 8a9a36d8e2..eb2e81061d 100644 --- a/src/foundation/constant-span-diagrams.lagda.md +++ b/src/foundation/constant-span-diagrams.lagda.md @@ -1,20 +1,15 @@ # Constant span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.constant-span-diagrams - (funext : function-extensionality) - where +module foundation.constant-span-diagrams where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.span-diagrams funext +open import foundation.span-diagrams open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/constant-type-families.lagda.md b/src/foundation/constant-type-families.lagda.md index 318489eb31..80e1f984df 100644 --- a/src/foundation/constant-type-families.lagda.md +++ b/src/foundation/constant-type-families.lagda.md @@ -1,12 +1,7 @@ # Constant type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.constant-type-families - (funext : function-extensionality) - where +module foundation.constant-type-families where ```
Imports @@ -15,7 +10,7 @@ module open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications diff --git a/src/foundation/continuations.lagda.md b/src/foundation/continuations.lagda.md index b580a5993e..8792570be4 100644 --- a/src/foundation/continuations.lagda.md +++ b/src/foundation/continuations.lagda.md @@ -1,26 +1,21 @@ # The continuation monad ```agda -open import foundation.function-extensionality-axiom - -module - foundation.continuations - (funext : function-extensionality) - where +module foundation.continuations where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.empty-types funext +open import foundation.dependent-products-propositions +open import foundation.empty-types open import foundation.evaluation-functions -open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.type-arithmetic-dependent-function-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-empty-type funext -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-empty-type +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.equivalences @@ -28,7 +23,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.propositions -open import orthogonal-factorization-systems.extensions-maps funext +open import orthogonal-factorization-systems.extensions-maps ```
diff --git a/src/foundation/contractible-maps.lagda.md b/src/foundation/contractible-maps.lagda.md index 9a195dd4df..15c5bb6786 100644 --- a/src/foundation/contractible-maps.lagda.md +++ b/src/foundation/contractible-maps.lagda.md @@ -1,12 +1,7 @@ # Contractible maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.contractible-maps - (funext : function-extensionality) - where +module foundation.contractible-maps where open import foundation-core.contractible-maps public ``` @@ -15,9 +10,9 @@ open import foundation-core.contractible-maps public ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.logical-equivalences funext -open import foundation.truncated-maps funext +open import foundation.equivalences +open import foundation.logical-equivalences +open import foundation.truncated-maps open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/contractible-types.lagda.md b/src/foundation/contractible-types.lagda.md index e4c85c22fe..0a1a3f297f 100644 --- a/src/foundation/contractible-types.lagda.md +++ b/src/foundation/contractible-types.lagda.md @@ -1,15 +1,10 @@ # Contractible types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.contractible-types - (funext : function-extensionality) - where +module foundation.contractible-types where open import foundation-core.contractible-types public -open import foundation.dependent-products-contractible-types funext public +open import foundation.dependent-products-contractible-types public ```
Imports @@ -17,11 +12,11 @@ open import foundation.dependent-products-contractible-types funext public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.logical-equivalences funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.subuniverses funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.logical-equivalences +open import foundation.raising-universe-levels-unit-type +open import foundation.subuniverses open import foundation.unit-type open import foundation.universe-levels @@ -32,7 +27,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/copartial-elements.lagda.md b/src/foundation/copartial-elements.lagda.md index fa271b8e5b..857e423d5b 100644 --- a/src/foundation/copartial-elements.lagda.md +++ b/src/foundation/copartial-elements.lagda.md @@ -1,28 +1,23 @@ # Copartial elements ```agda -open import foundation.function-extensionality-axiom - -module - foundation.copartial-elements - (funext : function-extensionality) - where +module foundation.copartial-elements where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.negation funext +open import foundation.empty-types +open import foundation.negation open import foundation.partial-elements open import foundation.universe-levels open import foundation-core.propositions -open import orthogonal-factorization-systems.closed-modalities funext +open import orthogonal-factorization-systems.closed-modalities -open import synthetic-homotopy-theory.joins-of-types funext +open import synthetic-homotopy-theory.joins-of-types ```
diff --git a/src/foundation/copartial-functions.lagda.md b/src/foundation/copartial-functions.lagda.md index 02b2a87745..6b5c611c47 100644 --- a/src/foundation/copartial-functions.lagda.md +++ b/src/foundation/copartial-functions.lagda.md @@ -1,20 +1,15 @@ # Copartial functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.copartial-functions - (funext : function-extensionality) - where +module foundation.copartial-functions where ```
Imports ```agda -open import foundation.copartial-elements funext +open import foundation.copartial-elements open import foundation.partial-functions -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/foundation/coproduct-decompositions-subuniverse.lagda.md b/src/foundation/coproduct-decompositions-subuniverse.lagda.md index 4ab34bf7f3..3d8495b9a1 100644 --- a/src/foundation/coproduct-decompositions-subuniverse.lagda.md +++ b/src/foundation/coproduct-decompositions-subuniverse.lagda.md @@ -1,31 +1,26 @@ # Coproduct decompositions in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - foundation.coproduct-decompositions-subuniverse - (funext : function-extensionality) - where +module foundation.coproduct-decompositions-subuniverse where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.functoriality-coproduct-types funext +open import foundation.empty-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.functoriality-coproduct-types open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.subuniverses funext +open import foundation.subuniverses open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext -open import foundation.univalence funext +open import foundation.type-arithmetic-empty-type +open import foundation.univalence open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/coproduct-decompositions.lagda.md b/src/foundation/coproduct-decompositions.lagda.md index bde65ad63b..4f8dfd14be 100644 --- a/src/foundation/coproduct-decompositions.lagda.md +++ b/src/foundation/coproduct-decompositions.lagda.md @@ -1,32 +1,26 @@ # Coproduct decompositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.coproduct-decompositions - (funext : function-extensionality) - where +module foundation.coproduct-decompositions where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-decompositions-subuniverse funext +open import foundation.coproduct-decompositions-subuniverse open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-coproduct-types funext +open import foundation.equivalence-extensionality +open import foundation.function-extensionality +open import foundation.functoriality-coproduct-types open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.transposition-identifications-along-equivalences funext -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.transposition-identifications-along-equivalences +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -43,8 +37,8 @@ open import foundation-core.propositions open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/coproduct-types.lagda.md b/src/foundation/coproduct-types.lagda.md index 3288cf7c32..aaadc73d63 100644 --- a/src/foundation/coproduct-types.lagda.md +++ b/src/foundation/coproduct-types.lagda.md @@ -1,12 +1,7 @@ # Coproduct types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.coproduct-types - (funext : function-extensionality) - where +module foundation.coproduct-types where open import foundation-core.coproduct-types public ``` @@ -16,9 +11,9 @@ open import foundation-core.coproduct-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.negated-equality funext -open import foundation.noncontractible-types funext -open import foundation.subuniverses funext +open import foundation.negated-equality +open import foundation.noncontractible-types +open import foundation.subuniverses open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/coproducts-pullbacks.lagda.md b/src/foundation/coproducts-pullbacks.lagda.md index a778c23153..780fecc445 100644 --- a/src/foundation/coproducts-pullbacks.lagda.md +++ b/src/foundation/coproducts-pullbacks.lagda.md @@ -1,25 +1,20 @@ # Coproducts of pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.coproducts-pullbacks - (funext : function-extensionality) - where +module foundation.coproducts-pullbacks where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext -open import foundation.coproduct-types funext +open import foundation.cones-over-cospan-diagrams +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.standard-pullbacks funext +open import foundation.equality-coproduct-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.standard-pullbacks open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -27,10 +22,10 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/coslice.lagda.md b/src/foundation/coslice.lagda.md index ee7a4cb6f8..20e4829866 100644 --- a/src/foundation/coslice.lagda.md +++ b/src/foundation/coslice.lagda.md @@ -1,21 +1,15 @@ # Morphisms in the coslice category of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.coslice - (funext : function-extensionality) - where +module foundation.coslice where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-homotopies open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/decidable-dependent-function-types.lagda.md b/src/foundation/decidable-dependent-function-types.lagda.md index aaa68b26f1..efc5cf4919 100644 --- a/src/foundation/decidable-dependent-function-types.lagda.md +++ b/src/foundation/decidable-dependent-function-types.lagda.md @@ -1,22 +1,17 @@ # Decidability of dependent function types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.decidable-dependent-function-types - (funext : function-extensionality) - where +module foundation.decidable-dependent-function-types where ```
Imports ```agda -open import foundation.decidable-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.uniformly-decidable-type-families funext -open import foundation.universal-property-coproduct-types funext -open import foundation.universal-property-maybe funext +open import foundation.decidable-types +open import foundation.functoriality-dependent-function-types +open import foundation.uniformly-decidable-type-families +open import foundation.universal-property-coproduct-types +open import foundation.universal-property-maybe open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/decidable-dependent-pair-types.lagda.md b/src/foundation/decidable-dependent-pair-types.lagda.md index 3d278073e9..eb012329f7 100644 --- a/src/foundation/decidable-dependent-pair-types.lagda.md +++ b/src/foundation/decidable-dependent-pair-types.lagda.md @@ -1,22 +1,17 @@ # Decidability of dependent pair types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.decidable-dependent-pair-types - (funext : function-extensionality) - where +module foundation.decidable-dependent-pair-types where ```
Imports ```agda -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-unit-type -open import foundation.uniformly-decidable-type-families funext +open import foundation.uniformly-decidable-type-families open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/decidable-embeddings.lagda.md b/src/foundation/decidable-embeddings.lagda.md index b7391dfb6b..3b869167e1 100644 --- a/src/foundation/decidable-embeddings.lagda.md +++ b/src/foundation/decidable-embeddings.lagda.md @@ -1,39 +1,34 @@ # Decidable embeddings ```agda -open import foundation.function-extensionality-axiom - -module - foundation.decidable-embeddings - (funext : function-extensionality) - where +module foundation.decidable-embeddings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows funext -open import foundation.decidable-maps funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.cartesian-morphisms-arrows +open import foundation.decidable-maps +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext -open import foundation.fibers-of-maps funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext +open import foundation.dependent-products-propositions +open import foundation.embeddings +open import foundation.fibers-of-maps +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-maps funext -open import foundation.propositions funext -open import foundation.retracts-of-maps funext +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositional-maps +open import foundation.propositions +open import foundation.retracts-of-maps open import foundation.subtype-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/decidable-equality.lagda.md b/src/foundation/decidable-equality.lagda.md index 8b149f00c1..dbd26b93ec 100644 --- a/src/foundation/decidable-equality.lagda.md +++ b/src/foundation/decidable-equality.lagda.md @@ -1,27 +1,22 @@ # Decidable equality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.decidable-equality - (funext : function-extensionality) - where +module foundation.decidable-equality where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.double-negation funext -open import foundation.injective-maps funext -open import foundation.negation funext -open import foundation.sections funext -open import foundation.sets funext +open import foundation.dependent-products-propositions +open import foundation.double-negation +open import foundation.injective-maps +open import foundation.negation +open import foundation.sections +open import foundation.sets open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/decidable-equivalence-relations.lagda.md b/src/foundation/decidable-equivalence-relations.lagda.md index 3d21272b0a..935c973f50 100644 --- a/src/foundation/decidable-equivalence-relations.lagda.md +++ b/src/foundation/decidable-equivalence-relations.lagda.md @@ -1,43 +1,37 @@ # Decidable equivalence relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.decidable-equivalence-relations - (funext : function-extensionality) - where +module foundation.decidable-equivalence-relations where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.decidable-equality funext -open import foundation.decidable-propositions funext -open import foundation.decidable-relations funext -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.decidable-equality +open import foundation.decidable-propositions +open import foundation.decidable-relations +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.effective-maps-equivalence-relations funext -open import foundation.equivalence-classes funext -open import foundation.equivalence-relations funext -open import foundation.existential-quantification funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-cartesian-product-types funext +open import foundation.dependent-products-propositions +open import foundation.effective-maps-equivalence-relations +open import foundation.equivalence-classes +open import foundation.equivalence-relations +open import foundation.existential-quantification +open import foundation.function-extensionality +open import foundation.functoriality-cartesian-product-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.images funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.sets funext -open import foundation.slice funext -open import foundation.surjective-maps funext +open import foundation.images +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.reflecting-maps-equivalence-relations +open import foundation.sets +open import foundation.slice +open import foundation.surjective-maps open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-image funext +open import foundation.universal-property-image open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -50,7 +44,7 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/decidable-maps.lagda.md b/src/foundation/decidable-maps.lagda.md index a82e5f1e8d..926253c0dc 100644 --- a/src/foundation/decidable-maps.lagda.md +++ b/src/foundation/decidable-maps.lagda.md @@ -1,27 +1,22 @@ # Decidable maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.decidable-maps - (funext : function-extensionality) - where +module foundation.decidable-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows funext -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.cartesian-morphisms-arrows +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.retracts-of-maps funext +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.retracts-of-maps open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/decidable-propositions.lagda.md b/src/foundation/decidable-propositions.lagda.md index 00508f519d..5a6cc27816 100644 --- a/src/foundation/decidable-propositions.lagda.md +++ b/src/foundation/decidable-propositions.lagda.md @@ -1,34 +1,29 @@ # Decidable propositions ```agda -open import foundation.function-extensionality-axiom +module foundation.decidable-propositions where -module - foundation.decidable-propositions - (funext : function-extensionality) - where - -open import foundation-core.decidable-propositions funext public +open import foundation-core.decidable-propositions public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.booleans funext -open import foundation.decidable-types funext +open import foundation.booleans +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equivalences +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-extensionality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -40,12 +35,12 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.retracts-of-types open import foundation-core.sets -open import foundation-core.small-types funext -open import foundation-core.subtypes funext +open import foundation-core.small-types +open import foundation-core.subtypes open import foundation-core.transport-along-identifications -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.finite-types ```
diff --git a/src/foundation/decidable-relations.lagda.md b/src/foundation/decidable-relations.lagda.md index c2f9a06686..770d4b5f81 100644 --- a/src/foundation/decidable-relations.lagda.md +++ b/src/foundation/decidable-relations.lagda.md @@ -1,23 +1,18 @@ # Decidable relations on types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.decidable-relations - (funext : function-extensionality) - where +module foundation.decidable-relations where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.propositions diff --git a/src/foundation/decidable-subtypes.lagda.md b/src/foundation/decidable-subtypes.lagda.md index 052fd88784..208d8f6862 100644 --- a/src/foundation/decidable-subtypes.lagda.md +++ b/src/foundation/decidable-subtypes.lagda.md @@ -1,35 +1,30 @@ # Decidable subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.decidable-subtypes - (funext : function-extensionality) - where +module foundation.decidable-subtypes where ```
Imports ```agda -open import foundation.1-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-embeddings funext -open import foundation.decidable-maps funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.1-types +open import foundation.coproduct-types +open import foundation.decidable-embeddings +open import foundation.decidable-maps +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equality-dependent-function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-maps funext -open import foundation.sets funext -open import foundation.structured-type-duality funext -open import foundation.subtypes funext -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.dependent-products-propositions +open import foundation.equality-dependent-function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.logical-equivalences +open import foundation.propositional-maps +open import foundation.sets +open import foundation.structured-type-duality +open import foundation.subtypes +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels open import foundation-core.embeddings @@ -43,7 +38,7 @@ open import foundation-core.transport-along-identifications open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import logic.double-negation-stable-subtypes funext +open import logic.double-negation-stable-subtypes ```
diff --git a/src/foundation/decidable-types.lagda.md b/src/foundation/decidable-types.lagda.md index 271bc9a714..93bdd1707e 100644 --- a/src/foundation/decidable-types.lagda.md +++ b/src/foundation/decidable-types.lagda.md @@ -1,30 +1,25 @@ # Decidable types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.decidable-types - (funext : function-extensionality) - where +module foundation.decidable-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.hilberts-epsilon-operators funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.raising-universe-levels funext -open import foundation.retracts-of-types funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.double-negation +open import foundation.empty-types +open import foundation.equivalences +open import foundation.hilberts-epsilon-operators +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.raising-universe-levels +open import foundation.retracts-of-types +open import foundation.type-arithmetic-empty-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/dependent-binary-homotopies.lagda.md b/src/foundation/dependent-binary-homotopies.lagda.md index 3ef4030306..affccfbaf5 100644 --- a/src/foundation/dependent-binary-homotopies.lagda.md +++ b/src/foundation/dependent-binary-homotopies.lagda.md @@ -1,18 +1,13 @@ # Dependent binary homotopies ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-binary-homotopies - (funext : function-extensionality) - where +module foundation.dependent-binary-homotopies where ```
Imports ```agda -open import foundation.binary-homotopies funext +open import foundation.binary-homotopies open import foundation.universe-levels open import foundation-core.dependent-identifications diff --git a/src/foundation/dependent-binomial-theorem.lagda.md b/src/foundation/dependent-binomial-theorem.lagda.md index 23566c7ab9..d86a4ac378 100644 --- a/src/foundation/dependent-binomial-theorem.lagda.md +++ b/src/foundation/dependent-binomial-theorem.lagda.md @@ -1,28 +1,23 @@ # The dependent binomial theorem for types (distributivity of dependent function types over coproduct types) ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-binomial-theorem - (funext : function-extensionality) - where +module foundation.dependent-binomial-theorem where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-decompositions funext +open import foundation.contractible-types +open import foundation.coproduct-decompositions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.raising-universe-levels funext +open import foundation.equality-dependent-pair-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.raising-universe-levels open import foundation.transport-along-identifications -open import foundation.universal-property-coproduct-types funext -open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-coproduct-types +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -34,8 +29,8 @@ open import foundation-core.homotopies open import foundation-core.type-theoretic-principle-of-choice open import foundation-core.univalence -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md b/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md index e2a1ac1b8a..7e107654bd 100644 --- a/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md +++ b/src/foundation/dependent-epimorphisms-with-respect-to-truncated-types.lagda.md @@ -1,18 +1,13 @@ # Dependent epimorphisms with respect to truncated types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-epimorphisms-with-respect-to-truncated-types - (funext : function-extensionality) - where +module foundation.dependent-epimorphisms-with-respect-to-truncated-types where ```
Imports ```agda -open import foundation.epimorphisms-with-respect-to-truncated-types funext +open import foundation.epimorphisms-with-respect-to-truncated-types open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/dependent-epimorphisms.lagda.md b/src/foundation/dependent-epimorphisms.lagda.md index 5a16b30287..d4da0dd5e6 100644 --- a/src/foundation/dependent-epimorphisms.lagda.md +++ b/src/foundation/dependent-epimorphisms.lagda.md @@ -1,18 +1,13 @@ # Dependent epimorphisms ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-epimorphisms - (funext : function-extensionality) - where +module foundation.dependent-epimorphisms where ```
Imports ```agda -open import foundation.epimorphisms funext +open import foundation.epimorphisms open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/dependent-function-types.lagda.md b/src/foundation/dependent-function-types.lagda.md index 9d352331cb..9ac456c7c7 100644 --- a/src/foundation/dependent-function-types.lagda.md +++ b/src/foundation/dependent-function-types.lagda.md @@ -1,12 +1,7 @@ # Dependent function types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-function-types - (funext : function-extensionality) - where +module foundation.dependent-function-types where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.dependent-pair-types open import foundation.spans-families-of-types -open import foundation.terminal-spans-families-of-types funext -open import foundation.type-arithmetic-dependent-function-types funext -open import foundation.universal-property-dependent-function-types funext +open import foundation.terminal-spans-families-of-types +open import foundation.type-arithmetic-dependent-function-types +open import foundation.universal-property-dependent-function-types open import foundation.universe-levels ``` diff --git a/src/foundation/dependent-identifications.lagda.md b/src/foundation/dependent-identifications.lagda.md index b63e3a3dec..4a1da7c967 100644 --- a/src/foundation/dependent-identifications.lagda.md +++ b/src/foundation/dependent-identifications.lagda.md @@ -1,12 +1,7 @@ # Dependent identifications ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-identifications - (funext : function-extensionality) - where +module foundation.dependent-identifications where open import foundation-core.dependent-identifications public ``` @@ -18,7 +13,7 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.strictly-right-unital-concatenation-identifications -open import foundation.transport-along-higher-identifications funext +open import foundation.transport-along-higher-identifications open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/dependent-inverse-sequential-diagrams.lagda.md b/src/foundation/dependent-inverse-sequential-diagrams.lagda.md index 8d25d5d93f..7fa699aa8e 100644 --- a/src/foundation/dependent-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/dependent-inverse-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Dependent inverse sequential diagrams of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-inverse-sequential-diagrams - (funext : function-extensionality) - where +module foundation.dependent-inverse-sequential-diagrams where ```
Imports @@ -15,9 +10,9 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.inverse-sequential-diagrams funext -open import foundation.iterating-families-of-maps funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.inverse-sequential-diagrams +open import foundation.iterating-families-of-maps +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/dependent-products-contractible-types.lagda.md b/src/foundation/dependent-products-contractible-types.lagda.md index c9ff67b98d..0cf967700c 100644 --- a/src/foundation/dependent-products-contractible-types.lagda.md +++ b/src/foundation/dependent-products-contractible-types.lagda.md @@ -1,20 +1,14 @@ # Dependent products of contractible types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-products-contractible-types - (funext : function-extensionality) - where +module foundation.dependent-products-contractible-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation/dependent-products-propositions.lagda.md b/src/foundation/dependent-products-propositions.lagda.md index 2dd021fc2c..029f396e8a 100644 --- a/src/foundation/dependent-products-propositions.lagda.md +++ b/src/foundation/dependent-products-propositions.lagda.md @@ -1,19 +1,14 @@ # Dependent products of propositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-products-propositions - (funext : function-extensionality) - where +module foundation.dependent-products-propositions where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-contractible-types open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/dependent-products-pullbacks.lagda.md b/src/foundation/dependent-products-pullbacks.lagda.md index 2f3f39caf4..63b84f2dce 100644 --- a/src/foundation/dependent-products-pullbacks.lagda.md +++ b/src/foundation/dependent-products-pullbacks.lagda.md @@ -1,33 +1,28 @@ # Dependent products of pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-products-pullbacks - (funext : function-extensionality) - where +module foundation.dependent-products-pullbacks where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.functoriality-dependent-function-types funext -open import foundation.identity-types funext -open import foundation.standard-pullbacks funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.functoriality-dependent-function-types +open import foundation.identity-types +open import foundation.standard-pullbacks open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/dependent-products-truncated-types.lagda.md b/src/foundation/dependent-products-truncated-types.lagda.md index f9218ed622..52960698b7 100644 --- a/src/foundation/dependent-products-truncated-types.lagda.md +++ b/src/foundation/dependent-products-truncated-types.lagda.md @@ -1,12 +1,7 @@ # Dependent products truncated types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-products-truncated-types - (funext : function-extensionality) - where +module foundation.dependent-products-truncated-types where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-contractible-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/dependent-sums-pullbacks.lagda.md b/src/foundation/dependent-sums-pullbacks.lagda.md index 2ff36f966d..c1f09588ee 100644 --- a/src/foundation/dependent-sums-pullbacks.lagda.md +++ b/src/foundation/dependent-sums-pullbacks.lagda.md @@ -1,22 +1,17 @@ # Dependent sums of pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-sums-pullbacks - (funext : function-extensionality) - where +module foundation.dependent-sums-pullbacks where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.standard-pullbacks funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.standard-pullbacks open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -26,10 +21,10 @@ open import foundation-core.families-of-equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/dependent-universal-property-equivalences.lagda.md b/src/foundation/dependent-universal-property-equivalences.lagda.md index 83c2c5d4b8..e02bb797f2 100644 --- a/src/foundation/dependent-universal-property-equivalences.lagda.md +++ b/src/foundation/dependent-universal-property-equivalences.lagda.md @@ -1,12 +1,7 @@ # The dependent universal property of equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dependent-universal-property-equivalences - (funext : function-extensionality) - where +module foundation.dependent-universal-property-equivalences where ```
Imports @@ -15,8 +10,8 @@ module open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation-core.coherently-invertible-maps diff --git a/src/foundation/descent-coproduct-types.lagda.md b/src/foundation/descent-coproduct-types.lagda.md index 22d2325ad3..03c1a582ba 100644 --- a/src/foundation/descent-coproduct-types.lagda.md +++ b/src/foundation/descent-coproduct-types.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.descent-coproduct-types - (funext : function-extensionality) - where +module foundation.descent-coproduct-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-fibers-of-maps funext +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-fibers-of-maps open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation open import foundation-core.coproduct-types open import foundation-core.equality-dependent-pair-types @@ -29,7 +24,7 @@ open import foundation-core.families-of-equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks ```
diff --git a/src/foundation/descent-dependent-pair-types.lagda.md b/src/foundation/descent-dependent-pair-types.lagda.md index b58c862f09..9f3cdfc133 100644 --- a/src/foundation/descent-dependent-pair-types.lagda.md +++ b/src/foundation/descent-dependent-pair-types.lagda.md @@ -1,20 +1,15 @@ # Descent for dependent pair types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.descent-dependent-pair-types - (funext : function-extensionality) - where +module foundation.descent-dependent-pair-types where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.functoriality-fibers-of-maps funext +open import foundation.functoriality-fibers-of-maps open import foundation.universe-levels open import foundation-core.equivalences @@ -22,7 +17,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks ```
diff --git a/src/foundation/descent-empty-types.lagda.md b/src/foundation/descent-empty-types.lagda.md index 7a064fe359..ca408517a6 100644 --- a/src/foundation/descent-empty-types.lagda.md +++ b/src/foundation/descent-empty-types.lagda.md @@ -1,23 +1,18 @@ # Descent for the empty type ```agda -open import foundation.function-extensionality-axiom - -module - foundation.descent-empty-types - (funext : function-extensionality) - where +module foundation.descent-empty-types where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation-core.empty-types -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks ```
diff --git a/src/foundation/descent-equivalences.lagda.md b/src/foundation/descent-equivalences.lagda.md index f9c13cd4cf..2a2da46991 100644 --- a/src/foundation/descent-equivalences.lagda.md +++ b/src/foundation/descent-equivalences.lagda.md @@ -1,25 +1,20 @@ # Descent for equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.descent-equivalences - (funext : function-extensionality) - where +module foundation.descent-equivalences where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext -open import foundation.dependent-universal-property-equivalences funext -open import foundation.equivalences funext -open import foundation.functoriality-fibers-of-maps funext +open import foundation.cones-over-cospan-diagrams +open import foundation.dependent-universal-property-equivalences +open import foundation.equivalences +open import foundation.functoriality-fibers-of-maps open import foundation.universe-levels open import foundation-core.function-types -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks ```
diff --git a/src/foundation/diaconescus-theorem.lagda.md b/src/foundation/diaconescus-theorem.lagda.md index fb523d4f53..246899fdd2 100644 --- a/src/foundation/diaconescus-theorem.lagda.md +++ b/src/foundation/diaconescus-theorem.lagda.md @@ -1,35 +1,30 @@ # Diaconescu's theorem ```agda -open import foundation.function-extensionality-axiom - -module - foundation.diaconescus-theorem - (funext : function-extensionality) - where +module foundation.diaconescus-theorem where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.axiom-of-choice funext -open import foundation.booleans funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.axiom-of-choice +open import foundation.booleans +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.law-of-excluded-middle funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.law-of-excluded-middle +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.identity-types -open import synthetic-homotopy-theory.suspensions-of-propositions funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.suspensions-of-propositions +open import synthetic-homotopy-theory.suspensions-of-types ```
diff --git a/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md b/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md index 11a321cc37..06fe26c051 100644 --- a/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md +++ b/src/foundation/diagonal-maps-cartesian-products-of-types.lagda.md @@ -1,12 +1,7 @@ # Diagonal maps into cartesian products of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.diagonal-maps-cartesian-products-of-types - (funext : function-extensionality) - where +module foundation.diagonal-maps-cartesian-products-of-types where open import foundation-core.diagonal-maps-cartesian-products-of-types public ``` @@ -14,12 +9,12 @@ open import foundation-core.diagonal-maps-cartesian-products-of-types public
Imports ```agda -open import foundation.0-maps funext +open import foundation.0-maps open import foundation.dependent-pair-types -open import foundation.faithful-maps funext +open import foundation.faithful-maps open import foundation.universe-levels -open import foundation-core.1-types funext +open import foundation-core.1-types open import foundation-core.cartesian-product-types open import foundation-core.contractible-maps open import foundation-core.embeddings @@ -28,7 +23,7 @@ open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/diagonal-maps-of-types.lagda.md b/src/foundation/diagonal-maps-of-types.lagda.md index 23f9628404..ed122f9939 100644 --- a/src/foundation/diagonal-maps-of-types.lagda.md +++ b/src/foundation/diagonal-maps-of-types.lagda.md @@ -1,12 +1,7 @@ # Diagonal maps of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.diagonal-maps-of-types - (funext : function-extensionality) - where +module foundation.diagonal-maps-of-types where open import foundation-core.diagonal-maps-of-types public ``` @@ -16,9 +11,9 @@ open import foundation-core.diagonal-maps-of-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.transposition-identifications-along-equivalences open import foundation.universe-levels open import foundation-core.constant-maps diff --git a/src/foundation/diagonal-span-diagrams.lagda.md b/src/foundation/diagonal-span-diagrams.lagda.md index 03a3c1798a..bde07d12e9 100644 --- a/src/foundation/diagonal-span-diagrams.lagda.md +++ b/src/foundation/diagonal-span-diagrams.lagda.md @@ -1,18 +1,13 @@ # Diagonal span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.diagonal-span-diagrams - (funext : function-extensionality) - where +module foundation.diagonal-span-diagrams where ```
Imports ```agda -open import foundation.span-diagrams funext +open import foundation.span-diagrams open import foundation.universe-levels ``` diff --git a/src/foundation/diagonals-of-maps.lagda.md b/src/foundation/diagonals-of-maps.lagda.md index cb5e519927..a965e62bc4 100644 --- a/src/foundation/diagonals-of-maps.lagda.md +++ b/src/foundation/diagonals-of-maps.lagda.md @@ -1,12 +1,7 @@ # Diagonals of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.diagonals-of-maps - (funext : function-extensionality) - where +module foundation.diagonals-of-maps where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-fibers-of-maps funext -open import foundation.standard-pullbacks funext +open import foundation.equality-fibers-of-maps +open import foundation.standard-pullbacks open import foundation.universe-levels open import foundation-core.contractible-maps @@ -28,7 +23,7 @@ open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/discrete-binary-relations.lagda.md b/src/foundation/discrete-binary-relations.lagda.md index 3a98bf2009..ef556b6912 100644 --- a/src/foundation/discrete-binary-relations.lagda.md +++ b/src/foundation/discrete-binary-relations.lagda.md @@ -1,21 +1,16 @@ # Discrete binary relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.discrete-binary-relations - (funext : function-extensionality) - where +module foundation.discrete-binary-relations where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.dependent-products-propositions funext -open import foundation.empty-types funext -open import foundation.propositions funext +open import foundation.binary-relations +open import foundation.dependent-products-propositions +open import foundation.empty-types +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/foundation/discrete-reflexive-relations.lagda.md b/src/foundation/discrete-reflexive-relations.lagda.md index 8ee69b4d05..2bb6edc906 100644 --- a/src/foundation/discrete-reflexive-relations.lagda.md +++ b/src/foundation/discrete-reflexive-relations.lagda.md @@ -1,23 +1,18 @@ # Discrete reflexive relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.discrete-reflexive-relations - (funext : function-extensionality) - where +module foundation.discrete-reflexive-relations where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.contractible-types funext +open import foundation.binary-relations +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.reflexive-relations funext -open import foundation.torsorial-type-families funext +open import foundation.dependent-products-propositions +open import foundation.reflexive-relations +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md index 0e50275ccc..5c88106f31 100644 --- a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md @@ -1,24 +1,19 @@ # Discrete relaxed Σ-decompositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.discrete-relaxed-sigma-decompositions - (funext : function-extensionality) - where +module foundation.discrete-relaxed-sigma-decompositions where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalences funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.relaxed-sigma-decompositions funext +open import foundation.dependent-products-propositions +open import foundation.equivalences +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -27,7 +22,7 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/discrete-sigma-decompositions.lagda.md b/src/foundation/discrete-sigma-decompositions.lagda.md index cc16457309..4f46918e5b 100644 --- a/src/foundation/discrete-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-sigma-decompositions.lagda.md @@ -1,25 +1,20 @@ # Discrete Σ-decompositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.discrete-sigma-decompositions - (funext : function-extensionality) - where +module foundation.discrete-sigma-decompositions where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalences funext -open import foundation.propositional-truncations funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sigma-decompositions funext +open import foundation.dependent-products-propositions +open import foundation.equivalences +open import foundation.propositional-truncations +open import foundation.raising-universe-levels-unit-type +open import foundation.sigma-decompositions open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -28,7 +23,7 @@ open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/discrete-types.lagda.md b/src/foundation/discrete-types.lagda.md index 8a13297a89..9f52a992b4 100644 --- a/src/foundation/discrete-types.lagda.md +++ b/src/foundation/discrete-types.lagda.md @@ -1,26 +1,21 @@ # Discrete types ```agda -open import foundation.function-extensionality-axiom +module foundation.discrete-types where -module - foundation.discrete-types - (funext : function-extensionality) - where - -open import foundation-core.discrete-types funext public +open import foundation-core.discrete-types public ```
Imports ```agda -open import foundation.apartness-relations funext -open import foundation.binary-relations funext -open import foundation.decidable-types funext +open import foundation.apartness-relations +open import foundation.binary-relations +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.tight-apartness-relations funext +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.tight-apartness-relations open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/disjoint-subtypes.lagda.md b/src/foundation/disjoint-subtypes.lagda.md index 55a3e036f0..f336231418 100644 --- a/src/foundation/disjoint-subtypes.lagda.md +++ b/src/foundation/disjoint-subtypes.lagda.md @@ -1,23 +1,18 @@ # Disjoint subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.disjoint-subtypes - (funext : function-extensionality) - where +module foundation.disjoint-subtypes where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.empty-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.dependent-products-propositions +open import foundation.empty-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/foundation/disjunction.lagda.md b/src/foundation/disjunction.lagda.md index 20f80a14c9..21a764be49 100644 --- a/src/foundation/disjunction.lagda.md +++ b/src/foundation/disjunction.lagda.md @@ -1,28 +1,23 @@ # Disjunction ```agda -open import foundation.function-extensionality-axiom - -module - foundation.disjunction - (funext : function-extensionality) - where +module foundation.disjunction where ```
Imports ```agda -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.functoriality-coproduct-types funext -open import foundation.inhabited-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.functoriality-coproduct-types +open import foundation.inhabited-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.coproduct-types -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/double-negation-modality.lagda.md b/src/foundation/double-negation-modality.lagda.md index c999691859..89f91c3ee0 100644 --- a/src/foundation/double-negation-modality.lagda.md +++ b/src/foundation/double-negation-modality.lagda.md @@ -1,37 +1,32 @@ # The double negation modality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.double-negation-modality - (funext : function-extensionality) - where +module foundation.double-negation-modality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.empty-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.double-negation +open import foundation.empty-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.transport-along-identifications -open import logic.double-negation-elimination funext +open import logic.double-negation-elimination -open import orthogonal-factorization-systems.continuation-modalities funext -open import orthogonal-factorization-systems.large-lawvere-tierney-topologies funext -open import orthogonal-factorization-systems.lawvere-tierney-topologies funext -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.types-local-at-maps funext -open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext +open import orthogonal-factorization-systems.continuation-modalities +open import orthogonal-factorization-systems.large-lawvere-tierney-topologies +open import orthogonal-factorization-systems.lawvere-tierney-topologies +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.uniquely-eliminating-modalities ```
diff --git a/src/foundation/double-negation-stable-equality.lagda.md b/src/foundation/double-negation-stable-equality.lagda.md index bc68e52780..9dced91af2 100644 --- a/src/foundation/double-negation-stable-equality.lagda.md +++ b/src/foundation/double-negation-stable-equality.lagda.md @@ -1,12 +1,7 @@ # Double negation stable equality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.double-negation-stable-equality - (funext : function-extensionality) - where +module foundation.double-negation-stable-equality where ```
Imports @@ -14,17 +9,17 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.double-negation funext +open import foundation.dependent-products-propositions +open import foundation.double-negation open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.sets funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation +open import foundation.sets open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels @@ -36,7 +31,7 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.retracts-of-types -open import logic.double-negation-elimination funext +open import logic.double-negation-elimination ```
diff --git a/src/foundation/double-negation-stable-propositions.lagda.md b/src/foundation/double-negation-stable-propositions.lagda.md index 0ddb34a9ec..8fb70bf27b 100644 --- a/src/foundation/double-negation-stable-propositions.lagda.md +++ b/src/foundation/double-negation-stable-propositions.lagda.md @@ -1,40 +1,35 @@ # Double negation stable propositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.double-negation-stable-propositions - (funext : function-extensionality) - where +module foundation.double-negation-stable-propositions where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.conjunction +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.disjunction funext -open import foundation.double-negation funext -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-extensionality funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.dependent-products-propositions +open import foundation.disjunction +open import foundation.double-negation +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-extensionality +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-quantification funext +open import foundation.universal-quantification open import foundation.universe-levels open import foundation-core.contractible-types @@ -42,7 +37,7 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.retracts-of-types -open import logic.double-negation-elimination funext +open import logic.double-negation-elimination ```
diff --git a/src/foundation/double-negation.lagda.md b/src/foundation/double-negation.lagda.md index 0ce9fb6b50..ee813f6384 100644 --- a/src/foundation/double-negation.lagda.md +++ b/src/foundation/double-negation.lagda.md @@ -1,19 +1,14 @@ # Double negation ```agda -open import foundation.function-extensionality-axiom - -module - foundation.double-negation - (funext : function-extensionality) - where +module foundation.double-negation where ```
Imports ```agda -open import foundation.negation funext -open import foundation.propositional-truncations funext +open import foundation.negation +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/double-powersets.lagda.md b/src/foundation/double-powersets.lagda.md index 22cb3bb998..19aabecf18 100644 --- a/src/foundation/double-powersets.lagda.md +++ b/src/foundation/double-powersets.lagda.md @@ -1,29 +1,24 @@ # Double powersets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.double-powersets - (funext : function-extensionality) - where +module foundation.double-powersets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.existential-quantification funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext +open import foundation.dependent-products-propositions +open import foundation.existential-quantification +open import foundation.powersets +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes -open import order-theory.large-posets funext -open import order-theory.posets funext +open import order-theory.large-posets +open import order-theory.posets ```
diff --git a/src/foundation/dubuc-penon-compact-types.lagda.md b/src/foundation/dubuc-penon-compact-types.lagda.md index 6a275891fe..6f726c9481 100644 --- a/src/foundation/dubuc-penon-compact-types.lagda.md +++ b/src/foundation/dubuc-penon-compact-types.lagda.md @@ -1,24 +1,19 @@ # Dubuc-Penon compact types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.dubuc-penon-compact-types - (funext : function-extensionality) - where +module foundation.dubuc-penon-compact-types where ```
Imports ```agda -open import foundation.dependent-products-propositions funext -open import foundation.disjunction funext -open import foundation.universal-quantification funext +open import foundation.dependent-products-propositions +open import foundation.disjunction +open import foundation.universal-quantification open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/effective-maps-equivalence-relations.lagda.md b/src/foundation/effective-maps-equivalence-relations.lagda.md index 1009cb4aec..2e7cb51d1b 100644 --- a/src/foundation/effective-maps-equivalence-relations.lagda.md +++ b/src/foundation/effective-maps-equivalence-relations.lagda.md @@ -1,22 +1,17 @@ # Effective maps for equivalence relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.effective-maps-equivalence-relations - (funext : function-extensionality) - where +module foundation.effective-maps-equivalence-relations where ```
Imports ```agda -open import foundation.surjective-maps funext +open import foundation.surjective-maps open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.identity-types ``` diff --git a/src/foundation/embeddings.lagda.md b/src/foundation/embeddings.lagda.md index 3f922fce8c..16bc0c8d80 100644 --- a/src/foundation/embeddings.lagda.md +++ b/src/foundation/embeddings.lagda.md @@ -1,12 +1,7 @@ # Embeddings ```agda -open import foundation.function-extensionality-axiom - -module - foundation.embeddings - (funext : function-extensionality) - where +module foundation.embeddings where open import foundation-core.embeddings public ``` @@ -15,20 +10,20 @@ open import foundation-core.embeddings public ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.dependent-products-propositions +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.transport-along-identifications -open import foundation.truncated-maps funext +open import foundation.truncated-maps open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-types open import foundation-core.fibers-of-maps @@ -36,7 +31,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks open import foundation-core.retractions open import foundation-core.sections open import foundation-core.torsorial-type-families diff --git a/src/foundation/empty-types.lagda.md b/src/foundation/empty-types.lagda.md index 912e1f9dc5..28925f767f 100644 --- a/src/foundation/empty-types.lagda.md +++ b/src/foundation/empty-types.lagda.md @@ -1,12 +1,7 @@ # Empty types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.empty-types - (funext : function-extensionality) - where +module foundation.empty-types where open import foundation-core.empty-types public ``` @@ -15,13 +10,13 @@ open import foundation-core.empty-types public ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.propositional-truncations funext -open import foundation.raising-universe-levels funext -open import foundation.subuniverses funext -open import foundation.univalence funext +open import foundation.dependent-products-propositions +open import foundation.embeddings +open import foundation.equivalences +open import foundation.propositional-truncations +open import foundation.raising-universe-levels +open import foundation.subuniverses +open import foundation.univalence open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/endomorphisms.lagda.md b/src/foundation/endomorphisms.lagda.md index 3d0fd48c5d..178d2f3786 100644 --- a/src/foundation/endomorphisms.lagda.md +++ b/src/foundation/endomorphisms.lagda.md @@ -1,14 +1,9 @@ # Endomorphisms ```agda -open import foundation.function-extensionality-axiom +module foundation.endomorphisms where -module - foundation.endomorphisms - (funext : function-extensionality) - where - -open import foundation-core.endomorphisms funext public +open import foundation-core.endomorphisms public ```
Imports @@ -22,10 +17,10 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.sets -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.monoids +open import group-theory.semigroups -open import structured-types.wild-monoids funext +open import structured-types.wild-monoids ```
diff --git a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md index a4fcda03d6..63bd907d28 100644 --- a/src/foundation/epimorphisms-with-respect-to-sets.lagda.md +++ b/src/foundation/epimorphisms-with-respect-to-sets.lagda.md @@ -1,12 +1,7 @@ # Epimorphisms with respect to maps into sets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.epimorphisms-with-respect-to-sets - (funext : function-extensionality) - where +module foundation.epimorphisms-with-respect-to-sets where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sets funext -open import foundation.surjective-maps funext +open import foundation.existential-quantification +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.propositional-extensionality +open import foundation.propositional-truncations +open import foundation.raising-universe-levels-unit-type +open import foundation.sets +open import foundation.surjective-maps open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md b/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md index 7cce27197b..3a0d69c835 100644 --- a/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md +++ b/src/foundation/epimorphisms-with-respect-to-truncated-types.lagda.md @@ -1,30 +1,24 @@ # Epimorphisms with respect to truncated types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.epimorphisms-with-respect-to-truncated-types - (funext : function-extensionality) - where +module foundation.epimorphisms-with-respect-to-truncated-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.connected-maps funext +open import foundation.commuting-squares-of-maps +open import foundation.connected-maps open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-truncation funext -open import foundation.precomposition-functions funext -open import foundation.sections funext -open import foundation.truncation-equivalences funext -open import foundation.truncations funext +open import foundation.dependent-products-propositions +open import foundation.embeddings +open import foundation.function-extensionality +open import foundation.functoriality-truncation +open import foundation.precomposition-functions +open import foundation.sections +open import foundation.truncation-equivalences +open import foundation.truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -38,9 +32,9 @@ open import foundation-core.propositions open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.codiagonals-of-maps funext -open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.codiagonals-of-maps +open import synthetic-homotopy-theory.pushouts ```
diff --git a/src/foundation/epimorphisms.lagda.md b/src/foundation/epimorphisms.lagda.md index 99e108b528..b7c5bb9ab4 100644 --- a/src/foundation/epimorphisms.lagda.md +++ b/src/foundation/epimorphisms.lagda.md @@ -1,24 +1,19 @@ # Epimorphisms ```agda -open import foundation.function-extensionality-axiom - -module - foundation.epimorphisms - (funext : function-extensionality) - where +module foundation.epimorphisms where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.precomposition-functions funext -open import foundation.sections funext +open import foundation.embeddings +open import foundation.precomposition-functions +open import foundation.sections open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types @@ -26,10 +21,10 @@ open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.propositions -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.codiagonals-of-maps funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.codiagonals-of-maps +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/foundation/equality-coproduct-types.lagda.md b/src/foundation/equality-coproduct-types.lagda.md index e84197717d..83776f0ce3 100644 --- a/src/foundation/equality-coproduct-types.lagda.md +++ b/src/foundation/equality-coproduct-types.lagda.md @@ -1,22 +1,17 @@ # Equality of coproduct types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equality-coproduct-types - (funext : function-extensionality) - where +module foundation.equality-coproduct-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.negated-equality funext +open import foundation.negated-equality open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/equality-dependent-function-types.lagda.md b/src/foundation/equality-dependent-function-types.lagda.md index b15ea08237..2512259ea6 100644 --- a/src/foundation/equality-dependent-function-types.lagda.md +++ b/src/foundation/equality-dependent-function-types.lagda.md @@ -1,19 +1,14 @@ # Equality on dependent function types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equality-dependent-function-types - (funext : function-extensionality) - where +module foundation.equality-dependent-function-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext +open import foundation.dependent-products-contractible-types open import foundation.fundamental-theorem-of-identity-types open import foundation.implicit-function-types open import foundation.universe-levels diff --git a/src/foundation/equality-dependent-pair-types.lagda.md b/src/foundation/equality-dependent-pair-types.lagda.md index b406c87294..6ab7a7bbb3 100644 --- a/src/foundation/equality-dependent-pair-types.lagda.md +++ b/src/foundation/equality-dependent-pair-types.lagda.md @@ -1,12 +1,7 @@ # Equality of dependent pair types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equality-dependent-pair-types - (funext : function-extensionality) - where +module foundation.equality-dependent-pair-types where open import foundation-core.equality-dependent-pair-types public ``` @@ -16,7 +11,7 @@ open import foundation-core.equality-dependent-pair-types public ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.dependent-identifications funext +open import foundation.dependent-identifications open import foundation.dependent-pair-types open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types diff --git a/src/foundation/equality-fibers-of-maps.lagda.md b/src/foundation/equality-fibers-of-maps.lagda.md index 2e37f3cce3..e5fa8e6684 100644 --- a/src/foundation/equality-fibers-of-maps.lagda.md +++ b/src/foundation/equality-fibers-of-maps.lagda.md @@ -1,12 +1,7 @@ # Equality in the fibers of a map ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equality-fibers-of-maps - (funext : function-extensionality) - where +module foundation.equality-fibers-of-maps where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/equivalence-classes.lagda.md b/src/foundation/equivalence-classes.lagda.md index 433573a5fb..71954bae57 100644 --- a/src/foundation/equivalence-classes.lagda.md +++ b/src/foundation/equivalence-classes.lagda.md @@ -1,39 +1,34 @@ # Equivalence classes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalence-classes - (funext : function-extensionality) - where +module foundation.equivalence-classes where ```
Imports ```agda -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations funext -open import foundation.existential-quantification funext -open import foundation.functoriality-propositional-truncation funext +open import foundation.effective-maps-equivalence-relations +open import foundation.existential-quantification +open import foundation.functoriality-propositional-truncation open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-subtypes funext -open import foundation.locally-small-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.slice funext -open import foundation.small-types funext +open import foundation.inhabited-subtypes +open import foundation.locally-small-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.reflecting-maps-equivalence-relations +open import foundation.slice +open import foundation.small-types open import foundation.subtype-identity-principle -open import foundation.subtypes funext -open import foundation.surjective-maps funext -open import foundation.universal-property-image funext +open import foundation.subtypes +open import foundation.surjective-maps +open import foundation.universal-property-image open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types diff --git a/src/foundation/equivalence-extensionality.lagda.md b/src/foundation/equivalence-extensionality.lagda.md index 20d32a6cd6..6facfb0297 100644 --- a/src/foundation/equivalence-extensionality.lagda.md +++ b/src/foundation/equivalence-extensionality.lagda.md @@ -1,22 +1,17 @@ # Equivalence extensionality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalence-extensionality - (funext : function-extensionality) - where +module foundation.equivalence-extensionality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.dependent-universal-property-equivalences funext -open import foundation.function-extensionality funext - +open import foundation.dependent-products-contractible-types +open import foundation.dependent-universal-property-equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-systems open import foundation.subtype-identity-principle diff --git a/src/foundation/equivalence-induction.lagda.md b/src/foundation/equivalence-induction.lagda.md index 86e320e314..a4b437a51f 100644 --- a/src/foundation/equivalence-induction.lagda.md +++ b/src/foundation/equivalence-induction.lagda.md @@ -1,12 +1,7 @@ # Equivalence induction ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalence-induction - (funext : function-extensionality) - where +module foundation.equivalence-induction where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.dependent-pair-types open import foundation.identity-systems -open import foundation.subuniverses funext -open import foundation.univalence funext -open import foundation.universal-property-identity-systems funext +open import foundation.subuniverses +open import foundation.univalence +open import foundation.universal-property-identity-systems open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/equivalence-injective-type-families.lagda.md b/src/foundation/equivalence-injective-type-families.lagda.md index e912a64a09..f204fe7573 100644 --- a/src/foundation/equivalence-injective-type-families.lagda.md +++ b/src/foundation/equivalence-injective-type-families.lagda.md @@ -1,24 +1,19 @@ # Equivalence injective type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalence-injective-type-families - (funext : function-extensionality) - where +module foundation.equivalence-injective-type-families where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.iterated-dependent-product-types funext +open import foundation.dependent-products-propositions +open import foundation.functoriality-dependent-function-types +open import foundation.iterated-dependent-product-types open import foundation.telescopes -open import foundation.univalence funext -open import foundation.universal-property-equivalences funext +open import foundation.univalence +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/equivalence-relations.lagda.md b/src/foundation/equivalence-relations.lagda.md index 5c00940f7a..931f0e8264 100644 --- a/src/foundation/equivalence-relations.lagda.md +++ b/src/foundation/equivalence-relations.lagda.md @@ -1,32 +1,27 @@ # Equivalence relations ```agda -open import foundation.function-extensionality-axiom +module foundation.equivalence-relations where -module - foundation.equivalence-relations - (funext : function-extensionality) - where - -open import foundation-core.equivalence-relations funext public +open import foundation-core.equivalence-relations public ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations funext -open import foundation.fundamental-theorem-of-equivalence-relations funext -open import foundation.logical-equivalences funext -open import foundation.partitions funext -open import foundation.propositional-truncations funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.set-quotients funext -open import foundation.sigma-decompositions funext -open import foundation.surjective-maps funext -open import foundation.uniqueness-set-quotients funext -open import foundation.universal-property-set-quotients funext +open import foundation.effective-maps-equivalence-relations +open import foundation.fundamental-theorem-of-equivalence-relations +open import foundation.logical-equivalences +open import foundation.partitions +open import foundation.propositional-truncations +open import foundation.reflecting-maps-equivalence-relations +open import foundation.set-quotients +open import foundation.sigma-decompositions +open import foundation.surjective-maps +open import foundation.uniqueness-set-quotients +open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/equivalences-arrows.lagda.md b/src/foundation/equivalences-arrows.lagda.md index 361657f6f4..23e82b5948 100644 --- a/src/foundation/equivalences-arrows.lagda.md +++ b/src/foundation/equivalences-arrows.lagda.md @@ -1,27 +1,22 @@ # Equivalences of arrows ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences-arrows - (funext : function-extensionality) - where +module foundation.equivalences-arrows where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows funext -open import foundation.commuting-squares-of-maps funext +open import foundation.cartesian-morphisms-arrows +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.morphisms-arrows funext -open import foundation.retractions funext -open import foundation.retracts-of-maps funext -open import foundation.sections funext -open import foundation.span-diagrams funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.morphisms-arrows +open import foundation.retractions +open import foundation.retracts-of-maps +open import foundation.sections +open import foundation.span-diagrams open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/equivalences-cospans.lagda.md b/src/foundation/equivalences-cospans.lagda.md index f610c32814..a44b7e3b11 100644 --- a/src/foundation/equivalences-cospans.lagda.md +++ b/src/foundation/equivalences-cospans.lagda.md @@ -1,12 +1,7 @@ # Equivalences of cospans ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences-cospans - (funext : function-extensionality) - where +module foundation.equivalences-cospans where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.cospans open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext +open import foundation.homotopy-induction open import foundation.morphisms-cospans open import foundation.structure-identity-principle -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/equivalences-double-arrows.lagda.md b/src/foundation/equivalences-double-arrows.lagda.md index d7c92dc09a..54c7f508e0 100644 --- a/src/foundation/equivalences-double-arrows.lagda.md +++ b/src/foundation/equivalences-double-arrows.lagda.md @@ -1,25 +1,20 @@ # Equivalences of double arrows ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences-double-arrows - (funext : function-extensionality) - where +module foundation.equivalences-double-arrows where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.commuting-squares-of-maps funext +open import foundation.cartesian-product-types +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.homotopies funext -open import foundation.morphisms-double-arrows funext +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.homotopies +open import foundation.morphisms-double-arrows open import foundation.universe-levels ``` diff --git a/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md b/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md index 98c403b9fa..3653847a20 100644 --- a/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/equivalences-inverse-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Equivalences of inverse sequential diagrams of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences-inverse-sequential-diagrams - (funext : function-extensionality) - where +module foundation.equivalences-inverse-sequential-diagrams where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies funext +open import foundation.binary-homotopies open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext +open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.inverse-sequential-diagrams funext -open import foundation.morphisms-inverse-sequential-diagrams funext +open import foundation.homotopy-induction +open import foundation.inverse-sequential-diagrams +open import foundation.morphisms-inverse-sequential-diagrams open import foundation.structure-identity-principle -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/equivalences-maybe.lagda.md b/src/foundation/equivalences-maybe.lagda.md index 1fc49d9bf1..c656a2d528 100644 --- a/src/foundation/equivalences-maybe.lagda.md +++ b/src/foundation/equivalences-maybe.lagda.md @@ -1,12 +1,7 @@ # Equivalences on `Maybe` ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences-maybe - (funext : function-extensionality) - where +module foundation.equivalences-maybe where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.functoriality-coproduct-types funext -open import foundation.maybe funext +open import foundation.equality-coproduct-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.functoriality-coproduct-types +open import foundation.maybe open import foundation.unit-type -open import foundation.universal-property-maybe funext +open import foundation.universal-property-maybe open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md b/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md index deb5820177..05c24bbdad 100644 --- a/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md +++ b/src/foundation/equivalences-span-diagrams-families-of-types.lagda.md @@ -1,22 +1,17 @@ # Equivalences of span diagrams on families of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences-span-diagrams-families-of-types - (funext : function-extensionality) - where +module foundation.equivalences-span-diagrams-families-of-types where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-spans-families-of-types -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.equivalences-spans-families-of-types +open import foundation.homotopies open import foundation.operations-spans-families-of-types open import foundation.span-diagrams-families-of-types open import foundation.universe-levels diff --git a/src/foundation/equivalences-span-diagrams.lagda.md b/src/foundation/equivalences-span-diagrams.lagda.md index 2065e280a5..92238d6cff 100644 --- a/src/foundation/equivalences-span-diagrams.lagda.md +++ b/src/foundation/equivalences-span-diagrams.lagda.md @@ -1,34 +1,29 @@ # Equivalences of span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences-span-diagrams - (funext : function-extensionality) - where +module foundation.equivalences-span-diagrams where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.equivalences-spans funext +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.equivalences-spans open import foundation.fundamental-theorem-of-identity-types -open import foundation.morphisms-span-diagrams funext +open import foundation.morphisms-span-diagrams open import foundation.morphisms-spans -open import foundation.operations-spans funext -open import foundation.propositions funext -open import foundation.span-diagrams funext +open import foundation.operations-spans +open import foundation.propositions +open import foundation.span-diagrams open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.torsorial-type-families diff --git a/src/foundation/equivalences-spans-families-of-types.lagda.md b/src/foundation/equivalences-spans-families-of-types.lagda.md index 3be364137a..f76bbf5f10 100644 --- a/src/foundation/equivalences-spans-families-of-types.lagda.md +++ b/src/foundation/equivalences-spans-families-of-types.lagda.md @@ -1,27 +1,22 @@ # Equivalences of spans of families of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences-spans-families-of-types - (funext : function-extensionality) - where +module foundation.equivalences-spans-families-of-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext +open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.morphisms-spans-families-of-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.morphisms-spans-families-of-types open import foundation.spans-families-of-types open import foundation.structure-identity-principle -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/equivalences-spans.lagda.md b/src/foundation/equivalences-spans.lagda.md index f438a7fc5d..4e804c318a 100644 --- a/src/foundation/equivalences-spans.lagda.md +++ b/src/foundation/equivalences-spans.lagda.md @@ -1,28 +1,23 @@ # Equivalences of spans ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences-spans - (funext : function-extensionality) - where +module foundation.equivalences-spans where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.commuting-squares-of-maps funext +open import foundation.cartesian-product-types +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext +open import foundation.homotopy-induction open import foundation.morphisms-spans open import foundation.spans open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -30,7 +25,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.operations-spans funext +open import foundation-core.operations-spans open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/equivalences.lagda.md b/src/foundation/equivalences.lagda.md index b83a093f11..c7c26fb5c4 100644 --- a/src/foundation/equivalences.lagda.md +++ b/src/foundation/equivalences.lagda.md @@ -1,12 +1,7 @@ # Equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.equivalences - (funext : function-extensionality) - where +module foundation.equivalences where open import foundation-core.equivalences public ``` @@ -15,18 +10,17 @@ open import foundation-core.equivalences public ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.equivalence-extensionality funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-fibers-of-maps funext -open import foundation.logical-equivalences funext +open import foundation.dependent-products-contractible-types +open import foundation.equivalence-extensionality +open import foundation.function-extensionality +open import foundation.functoriality-fibers-of-maps +open import foundation.logical-equivalences open import foundation.transport-along-identifications -open import foundation.transposition-identifications-along-equivalences funext -open import foundation.truncated-maps funext -open import foundation.universal-property-equivalences funext +open import foundation.transposition-identifications-along-equivalences +open import foundation.truncated-maps +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps @@ -40,11 +34,11 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositions -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks open import foundation-core.retractions open import foundation-core.retracts-of-types open import foundation-core.sections -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.truncation-levels open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/exclusive-disjunction.lagda.md b/src/foundation/exclusive-disjunction.lagda.md index 4cfd139d2c..5d95f4c232 100644 --- a/src/foundation/exclusive-disjunction.lagda.md +++ b/src/foundation/exclusive-disjunction.lagda.md @@ -1,33 +1,28 @@ # Exclusive disjunctions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.exclusive-disjunction - (funext : function-extensionality) - where +module foundation.exclusive-disjunction where ```
Imports ```agda -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.equality-coproduct-types funext -open import foundation.exclusive-sum funext -open import foundation.functoriality-coproduct-types funext -open import foundation.propositional-truncations funext +open import foundation.dependent-products-contractible-types +open import foundation.equality-coproduct-types +open import foundation.exclusive-sum +open import foundation.functoriality-coproduct-types +open import foundation.propositional-truncations open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types funext -open import foundation.universal-property-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types +open import foundation.universal-property-coproduct-types open import foundation.universe-levels open import foundation-core.embeddings open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions diff --git a/src/foundation/exclusive-sum.lagda.md b/src/foundation/exclusive-sum.lagda.md index 8afa84bfe8..d18bfe341a 100644 --- a/src/foundation/exclusive-sum.lagda.md +++ b/src/foundation/exclusive-sum.lagda.md @@ -1,40 +1,35 @@ # Exclusive sums ```agda -open import foundation.function-extensionality-axiom - -module - foundation.exclusive-sum - (funext : function-extensionality) - where +module foundation.exclusive-sum where ```
Imports ```agda -open import foundation.conjunction funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.conjunction +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.negation funext -open import foundation.propositional-extensionality funext -open import foundation.symmetric-operations funext +open import foundation.dependent-products-propositions +open import foundation.negation +open import foundation.propositional-extensionality +open import foundation.symmetric-operations open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs open import foundation-core.cartesian-product-types -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.empty-types open import foundation-core.equality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.transport-along-identifications -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/existential-quantification.lagda.md b/src/foundation/existential-quantification.lagda.md index e071eb51f5..1cb3523d44 100644 --- a/src/foundation/existential-quantification.lagda.md +++ b/src/foundation/existential-quantification.lagda.md @@ -1,23 +1,18 @@ # Existential quantification ```agda -open import foundation.function-extensionality-axiom - -module - foundation.existential-quantification - (funext : function-extensionality) - where +module foundation.existential-quantification where ```
Imports ```agda -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.logical-equivalences funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext +open import foundation.dependent-products-propositions +open import foundation.logical-equivalences +open import foundation.propositional-extensionality +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/exponents-set-quotients.lagda.md b/src/foundation/exponents-set-quotients.lagda.md index 82555ca69d..7002792799 100644 --- a/src/foundation/exponents-set-quotients.lagda.md +++ b/src/foundation/exponents-set-quotients.lagda.md @@ -3,34 +3,29 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.exponents-set-quotients - (funext : function-extensionality) - where +module foundation.exponents-set-quotients where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-set-quotients funext -open import foundation.postcomposition-functions funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.set-quotients funext -open import foundation.sets funext -open import foundation.universal-property-set-quotients funext +open import foundation.dependent-products-propositions +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.functoriality-set-quotients +open import foundation.postcomposition-functions +open import foundation.reflecting-maps-equivalence-relations +open import foundation.set-quotients +open import foundation.sets +open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.contractible-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/extensions-types-global-subuniverses.lagda.md b/src/foundation/extensions-types-global-subuniverses.lagda.md index 1b38266da0..a75184e2aa 100644 --- a/src/foundation/extensions-types-global-subuniverses.lagda.md +++ b/src/foundation/extensions-types-global-subuniverses.lagda.md @@ -1,37 +1,32 @@ # Extensions of types in a global subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - foundation.extensions-types-global-subuniverses - (funext : function-extensionality) - where +module foundation.extensions-types-global-subuniverses where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.extensions-types funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.extensions-types +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositional-maps funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositional-maps +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels ``` diff --git a/src/foundation/extensions-types-subuniverses.lagda.md b/src/foundation/extensions-types-subuniverses.lagda.md index 95f0b01400..b76a1afee1 100644 --- a/src/foundation/extensions-types-subuniverses.lagda.md +++ b/src/foundation/extensions-types-subuniverses.lagda.md @@ -1,39 +1,34 @@ # Extensions of types in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - foundation.extensions-types-subuniverses - (funext : function-extensionality) - where +module foundation.extensions-types-subuniverses where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.extensions-types funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.extensions-types +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositional-maps funext -open import foundation.propositions funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositional-maps +open import foundation.propositions open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.subuniverses funext -open import foundation.torsorial-type-families funext +open import foundation.subuniverses +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels ``` diff --git a/src/foundation/extensions-types.lagda.md b/src/foundation/extensions-types.lagda.md index c3d388f6f7..7d78a32bdd 100644 --- a/src/foundation/extensions-types.lagda.md +++ b/src/foundation/extensions-types.lagda.md @@ -1,27 +1,22 @@ # Extensions of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.extensions-types - (funext : function-extensionality) - where +module foundation.extensions-types where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels ``` diff --git a/src/foundation/faithful-maps.lagda.md b/src/foundation/faithful-maps.lagda.md index fccd1c7f7b..0e523f08b3 100644 --- a/src/foundation/faithful-maps.lagda.md +++ b/src/foundation/faithful-maps.lagda.md @@ -1,18 +1,13 @@ # Faithful maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.faithful-maps - (funext : function-extensionality) - where +module foundation.faithful-maps where ```
Imports ```agda -open import foundation.0-maps funext +open import foundation.0-maps open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.universe-levels @@ -25,7 +20,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.sets -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncation-levels ``` diff --git a/src/foundation/families-of-equivalences.lagda.md b/src/foundation/families-of-equivalences.lagda.md index fc844cbec0..172bf565b9 100644 --- a/src/foundation/families-of-equivalences.lagda.md +++ b/src/foundation/families-of-equivalences.lagda.md @@ -1,12 +1,7 @@ # Families of equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.families-of-equivalences - (funext : function-extensionality) - where +module foundation.families-of-equivalences where open import foundation-core.families-of-equivalences public ``` @@ -14,8 +9,8 @@ open import foundation-core.families-of-equivalences public
Imports ```agda -open import foundation.dependent-products-propositions funext -open import foundation.equivalences funext +open import foundation.dependent-products-propositions +open import foundation.equivalences open import foundation.universe-levels open import foundation-core.propositions diff --git a/src/foundation/families-of-maps.lagda.md b/src/foundation/families-of-maps.lagda.md index bbde2001ba..ffcfb2087d 100644 --- a/src/foundation/families-of-maps.lagda.md +++ b/src/foundation/families-of-maps.lagda.md @@ -1,33 +1,28 @@ # Families of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.families-of-maps - (funext : function-extensionality) - where +module foundation.families-of-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalences funext +open import foundation.dependent-products-propositions +open import foundation.equivalences open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.families-of-equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/families-over-telescopes.lagda.md b/src/foundation/families-over-telescopes.lagda.md index 9d9bc64b5d..a6a2844f56 100644 --- a/src/foundation/families-over-telescopes.lagda.md +++ b/src/foundation/families-over-telescopes.lagda.md @@ -1,12 +1,7 @@ # Families of types over telescopes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.families-over-telescopes - (funext : function-extensionality) - where +module foundation.families-over-telescopes where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels open import foundation.telescopes open import foundation.universe-levels ``` diff --git a/src/foundation/fiber-inclusions.lagda.md b/src/foundation/fiber-inclusions.lagda.md index c74d7e0935..ca0e8f0ac8 100644 --- a/src/foundation/fiber-inclusions.lagda.md +++ b/src/foundation/fiber-inclusions.lagda.md @@ -1,30 +1,25 @@ # Fiber inclusions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.fiber-inclusions - (funext : function-extensionality) - where +module foundation.fiber-inclusions where ```
Imports ```agda -open import foundation.0-maps funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.0-maps +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.faithful-maps funext -open import foundation.fibers-of-maps funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.standard-pullbacks funext +open import foundation.faithful-maps +open import foundation.fibers-of-maps +open import foundation.raising-universe-levels-unit-type +open import foundation.standard-pullbacks open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.1-types funext +open import foundation-core.1-types open import foundation-core.contractible-maps open import foundation-core.embeddings open import foundation-core.equality-dependent-pair-types @@ -34,9 +29,9 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks open import foundation-core.sets -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/fibered-equivalences.lagda.md b/src/foundation/fibered-equivalences.lagda.md index f9ef0504c4..3d899df149 100644 --- a/src/foundation/fibered-equivalences.lagda.md +++ b/src/foundation/fibered-equivalences.lagda.md @@ -1,24 +1,19 @@ # Fibered equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.fibered-equivalences - (funext : function-extensionality) - where +module foundation.fibered-equivalences where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.fibered-maps funext -open import foundation.logical-equivalences funext -open import foundation.pullbacks funext -open import foundation.slice funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.fibered-maps +open import foundation.logical-equivalences +open import foundation.pullbacks +open import foundation.slice open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -28,7 +23,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/fibered-involutions.lagda.md b/src/foundation/fibered-involutions.lagda.md index 64e0d7a945..e00fab4ca6 100644 --- a/src/foundation/fibered-involutions.lagda.md +++ b/src/foundation/fibered-involutions.lagda.md @@ -1,20 +1,15 @@ # Fibered involutions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.fibered-involutions - (funext : function-extensionality) - where +module foundation.fibered-involutions where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibered-maps funext -open import foundation.involutions funext +open import foundation.fibered-maps +open import foundation.involutions open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/fibered-maps.lagda.md b/src/foundation/fibered-maps.lagda.md index 39ca646d98..1ba4249488 100644 --- a/src/foundation/fibered-maps.lagda.md +++ b/src/foundation/fibered-maps.lagda.md @@ -1,34 +1,28 @@ # Maps fibered over a map ```agda -open import foundation.function-extensionality-axiom - -module - foundation.fibered-maps - (funext : function-extensionality) - where +module foundation.fibered-maps where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.dependent-products-truncated-types funext -open import foundation.function-extensionality funext - +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-truncated-types +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.slice funext +open import foundation.homotopy-induction +open import foundation.slice open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-empty-type funext +open import foundation.universal-property-empty-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-types open import foundation-core.empty-types open import foundation-core.equality-dependent-pair-types @@ -37,7 +31,7 @@ open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.small-types funext +open import foundation-core.small-types open import foundation-core.torsorial-type-families open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/fibers-of-maps.lagda.md b/src/foundation/fibers-of-maps.lagda.md index 6e323a2ee8..01e4a3f77b 100644 --- a/src/foundation/fibers-of-maps.lagda.md +++ b/src/foundation/fibers-of-maps.lagda.md @@ -1,12 +1,7 @@ # Fibers of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.fibers-of-maps - (funext : function-extensionality) - where +module foundation.fibers-of-maps where open import foundation-core.fibers-of-maps public ``` @@ -15,9 +10,9 @@ open import foundation-core.fibers-of-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.postcomposition-functions funext +open import foundation.postcomposition-functions open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type @@ -26,13 +21,13 @@ open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks open import foundation-core.transport-along-identifications -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/finitely-coherent-equivalences.lagda.md b/src/foundation/finitely-coherent-equivalences.lagda.md index 46db3d5430..ad8dcd5167 100644 --- a/src/foundation/finitely-coherent-equivalences.lagda.md +++ b/src/foundation/finitely-coherent-equivalences.lagda.md @@ -1,12 +1,7 @@ # Finitely coherent equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.finitely-coherent-equivalences - (funext : function-extensionality) - where +module foundation.finitely-coherent-equivalences where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/finitely-coherently-invertible-maps.lagda.md b/src/foundation/finitely-coherently-invertible-maps.lagda.md index 20c7e997e2..a48d827c1e 100644 --- a/src/foundation/finitely-coherently-invertible-maps.lagda.md +++ b/src/foundation/finitely-coherently-invertible-maps.lagda.md @@ -1,12 +1,7 @@ # Finitely coherently invertible maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.finitely-coherently-invertible-maps - (funext : function-extensionality) - where +module foundation.finitely-coherently-invertible-maps where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/full-subtypes.lagda.md b/src/foundation/full-subtypes.lagda.md index c94db60b15..c2cb38a34f 100644 --- a/src/foundation/full-subtypes.lagda.md +++ b/src/foundation/full-subtypes.lagda.md @@ -1,28 +1,23 @@ # Full subtypes of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.full-subtypes - (funext : function-extensionality) - where +module foundation.full-subtypes where ```
Imports ```agda -open import foundation.decidable-subtypes funext +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.dependent-products-propositions +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/function-extensionality.lagda.md b/src/foundation/function-extensionality.lagda.md index b6ca9801f6..d26c3c48c8 100644 --- a/src/foundation/function-extensionality.lagda.md +++ b/src/foundation/function-extensionality.lagda.md @@ -3,10 +3,7 @@ ```agda open import foundation.function-extensionality-axiom -module - foundation.function-extensionality - (funext : function-extensionality) - where +module foundation.function-extensionality where ```
Imports @@ -15,7 +12,6 @@ module open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.evaluation-functions open import foundation.implicit-function-types open import foundation.universe-levels @@ -82,23 +78,23 @@ module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} where - eq-htpy : f ~ g → f ＝ g - eq-htpy = map-inv-is-equiv (funext f g) + postulate + eq-htpy : f ~ g → f ＝ g - opaque is-section-eq-htpy : is-section htpy-eq eq-htpy - is-section-eq-htpy = is-section-map-inv-is-equiv (funext f g) - is-retraction-eq-htpy : is-retraction htpy-eq eq-htpy - is-retraction-eq-htpy = is-retraction-map-inv-is-equiv (funext f g) + is-retraction-eq-htpy' : is-retraction htpy-eq eq-htpy - coh-eq-htpy : + coh-eq-htpy' : coherence-is-coherently-invertible ( htpy-eq) ( eq-htpy) ( is-section-eq-htpy) - ( is-retraction-eq-htpy) - coh-eq-htpy = coherence-map-inv-is-equiv (funext f g) + ( is-retraction-eq-htpy') + +funext : function-extensionality +funext f g = + is-equiv-is-invertible eq-htpy is-section-eq-htpy is-retraction-eq-htpy' module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} @@ -111,7 +107,12 @@ module _ is-equiv-eq-htpy : (f g : (x : A) → B x) → is-equiv (eq-htpy {f = f} {g}) is-equiv-eq-htpy f g = - is-equiv-is-invertible htpy-eq is-retraction-eq-htpy is-section-eq-htpy + is-equiv-is-invertible htpy-eq is-retraction-eq-htpy' is-section-eq-htpy + + abstract + is-retraction-eq-htpy : + {f g : (x : A) → B x} → is-retraction (htpy-eq {f = f} {g}) eq-htpy + is-retraction-eq-htpy {f} {g} = is-retraction-map-inv-is-equiv (funext f g) eq-htpy-refl-htpy : (f : (x : A) → B x) → eq-htpy (refl-htpy {f = f}) ＝ refl diff --git a/src/foundation/function-types.lagda.md b/src/foundation/function-types.lagda.md index 09d8ad6fb7..d6fb4ed16f 100644 --- a/src/foundation/function-types.lagda.md +++ b/src/foundation/function-types.lagda.md @@ -1,12 +1,7 @@ # Function types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.function-types - (funext : function-extensionality) - where +module foundation.function-types where open import foundation-core.function-types public ``` @@ -18,9 +13,8 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.commuting-pentagons-of-identifications open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.homotopy-induction funext +open import foundation.function-extensionality +open import foundation.homotopy-induction open import foundation.universe-levels open import foundation-core.dependent-identifications diff --git a/src/foundation/functional-correspondences.lagda.md b/src/foundation/functional-correspondences.lagda.md index 2da6d47e8b..d2a98ae2fe 100644 --- a/src/foundation/functional-correspondences.lagda.md +++ b/src/foundation/functional-correspondences.lagda.md @@ -1,34 +1,28 @@ # Functional correspondences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functional-correspondences - (funext : function-extensionality) - where +module foundation.functional-correspondences where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equality-dependent-function-types funext -open import foundation.function-extensionality funext - +open import foundation.dependent-products-propositions +open import foundation.equality-dependent-function-types +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/functoriality-action-on-identifications-functions.lagda.md b/src/foundation/functoriality-action-on-identifications-functions.lagda.md index 202eea9a8c..987e964955 100644 --- a/src/foundation/functoriality-action-on-identifications-functions.lagda.md +++ b/src/foundation/functoriality-action-on-identifications-functions.lagda.md @@ -1,31 +1,26 @@ # Functoriality of the action on identifications of functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-action-on-identifications-functions - (funext : function-extensionality) - where +module foundation.functoriality-action-on-identifications-functions where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-morphisms-arrows funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.commuting-triangles-of-morphisms-arrows +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.homotopies-morphisms-arrows funext -open import foundation.morphisms-arrows funext -open import foundation.path-algebra funext +open import foundation.homotopies-morphisms-arrows +open import foundation.morphisms-arrows +open import foundation.path-algebra open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.equality-dependent-pair-types open import foundation-core.fibers-of-maps open import foundation-core.function-types diff --git a/src/foundation/functoriality-cartesian-product-types.lagda.md b/src/foundation/functoriality-cartesian-product-types.lagda.md index 393e2fd3c2..08be06910b 100644 --- a/src/foundation/functoriality-cartesian-product-types.lagda.md +++ b/src/foundation/functoriality-cartesian-product-types.lagda.md @@ -1,12 +1,7 @@ # Functoriality of cartesian product types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-cartesian-product-types - (funext : function-extensionality) - where +module foundation.functoriality-cartesian-product-types where ```
Imports @@ -15,11 +10,11 @@ module open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.morphisms-arrows funext +open import foundation.morphisms-arrows open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/functoriality-coproduct-types.lagda.md b/src/foundation/functoriality-coproduct-types.lagda.md index 3724122c76..1c629f6117 100644 --- a/src/foundation/functoriality-coproduct-types.lagda.md +++ b/src/foundation/functoriality-coproduct-types.lagda.md @@ -1,36 +1,30 @@ # Functoriality of coproduct types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-coproduct-types - (funext : function-extensionality) - where +module foundation.functoriality-coproduct-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equality-coproduct-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-cartesian-product-types funext -open import foundation.homotopy-induction funext -open import foundation.morphisms-arrows funext -open import foundation.negated-equality funext -open import foundation.propositional-truncations funext -open import foundation.retractions funext +open import foundation.equality-coproduct-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.functoriality-cartesian-product-types +open import foundation.homotopy-induction +open import foundation.morphisms-arrows +open import foundation.negated-equality +open import foundation.propositional-truncations +open import foundation.retractions open import foundation.structure-identity-principle -open import foundation.surjective-maps funext +open import foundation.surjective-maps open import foundation.unit-type -open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-coproduct-types open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -39,7 +33,7 @@ open import foundation-core.embeddings open import foundation-core.empty-types open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/functoriality-dependent-function-types.lagda.md b/src/foundation/functoriality-dependent-function-types.lagda.md index cf3245fc9c..290c471228 100644 --- a/src/foundation/functoriality-dependent-function-types.lagda.md +++ b/src/foundation/functoriality-dependent-function-types.lagda.md @@ -1,14 +1,9 @@ # Functoriality of dependent function types ```agda -open import foundation.function-extensionality-axiom +module foundation.functoriality-dependent-function-types where -module - foundation.functoriality-dependent-function-types - (funext : function-extensionality) - where - -open import foundation-core.functoriality-dependent-function-types funext public +open import foundation-core.functoriality-dependent-function-types public ```
Imports @@ -16,15 +11,14 @@ open import foundation-core.functoriality-dependent-function-types funext public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.dependent-universal-property-equivalences funext -open import foundation.equivalence-extensionality funext -open import foundation.function-extensionality funext - -open import foundation.retracts-of-types funext +open import foundation.dependent-products-truncated-types +open import foundation.dependent-universal-property-equivalences +open import foundation.equivalence-extensionality +open import foundation.function-extensionality +open import foundation.retracts-of-types open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-unit-type funext +open import foundation.universal-property-unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -38,7 +32,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.precomposition-dependent-functions open import foundation-core.propositional-maps -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/functoriality-dependent-pair-types.lagda.md b/src/foundation/functoriality-dependent-pair-types.lagda.md index c8c75ea374..beffdd38f2 100644 --- a/src/foundation/functoriality-dependent-pair-types.lagda.md +++ b/src/foundation/functoriality-dependent-pair-types.lagda.md @@ -1,12 +1,7 @@ # Functoriality of dependent pair types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-dependent-pair-types - (funext : function-extensionality) - where +module foundation.functoriality-dependent-pair-types where open import foundation-core.functoriality-dependent-pair-types public ``` @@ -17,10 +12,10 @@ open import foundation-core.functoriality-dependent-pair-types public open import foundation.action-on-identifications-functions open import foundation.dependent-homotopies open import foundation.dependent-pair-types -open import foundation.morphisms-arrows funext +open import foundation.morphisms-arrows open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.dependent-identifications @@ -33,7 +28,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositional-maps open import foundation-core.transport-along-identifications -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/functoriality-fibers-of-maps.lagda.md b/src/foundation/functoriality-fibers-of-maps.lagda.md index 2f01630494..5beb6de9e9 100644 --- a/src/foundation/functoriality-fibers-of-maps.lagda.md +++ b/src/foundation/functoriality-fibers-of-maps.lagda.md @@ -1,28 +1,23 @@ # Functoriality of fibers of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-fibers-of-maps - (funext : function-extensionality) - where +module foundation.functoriality-fibers-of-maps where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.homotopies-morphisms-arrows funext -open import foundation.morphisms-arrows funext +open import foundation.homotopies-morphisms-arrows +open import foundation.morphisms-arrows open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.equality-dependent-pair-types open import foundation-core.fibers-of-maps open import foundation-core.function-types diff --git a/src/foundation/functoriality-function-types.lagda.md b/src/foundation/functoriality-function-types.lagda.md index 937763a8f4..a86808a6d2 100644 --- a/src/foundation/functoriality-function-types.lagda.md +++ b/src/foundation/functoriality-function-types.lagda.md @@ -1,12 +1,7 @@ # Functoriality of function types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-function-types - (funext : function-extensionality) - where +module foundation.functoriality-function-types where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types funext -open import foundation.postcomposition-functions funext +open import foundation.functoriality-dependent-function-types +open import foundation.postcomposition-functions open import foundation.unit-type -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.embeddings @@ -26,7 +21,7 @@ open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.precomposition-functions open import foundation-core.propositional-maps -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncation-levels ``` diff --git a/src/foundation/functoriality-morphisms-arrows.lagda.md b/src/foundation/functoriality-morphisms-arrows.lagda.md index 8571919b54..8ad3592690 100644 --- a/src/foundation/functoriality-morphisms-arrows.lagda.md +++ b/src/foundation/functoriality-morphisms-arrows.lagda.md @@ -1,12 +1,7 @@ # Functoriality of morphisms of arrows ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-morphisms-arrows - (funext : function-extensionality) - where +module foundation.functoriality-morphisms-arrows where ```
Imports @@ -14,32 +9,32 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.bicomposition-functions funext -open import foundation.commuting-squares-of-maps funext -open import foundation.composition-algebra funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.bicomposition-functions +open import foundation.commuting-squares-of-maps +open import foundation.composition-algebra +open import foundation.cones-over-cospan-diagrams open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-pullbacks funext -open import foundation.homotopies funext -open import foundation.homotopies funext-morphisms-arrows -open import foundation.homotopies-morphisms-cospan-diagrams funext -open import foundation.identity-types funext -open import foundation.morphisms-arrows funext +open import foundation.dependent-products-propositions +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-pullbacks +open import foundation.homotopies +open import foundation.homotopies-morphisms-arrows +open import foundation.homotopies-morphisms-cospan-diagrams +open import foundation.identity-types +open import foundation.morphisms-arrows open import foundation.morphisms-cospan-diagrams -open import foundation.postcomposition-functions funext -open import foundation.precomposition-functions funext -open import foundation.pullback-cones funext -open import foundation.pullbacks funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.standard-pullbacks funext +open import foundation.postcomposition-functions +open import foundation.precomposition-functions +open import foundation.pullback-cones +open import foundation.pullbacks +open import foundation.retractions +open import foundation.sections +open import foundation.standard-pullbacks open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/functoriality-propositional-truncation.lagda.md b/src/foundation/functoriality-propositional-truncation.lagda.md index 65b2c63ee5..32fdfc1b87 100644 --- a/src/foundation/functoriality-propositional-truncation.lagda.md +++ b/src/foundation/functoriality-propositional-truncation.lagda.md @@ -1,12 +1,7 @@ # Functoriality of propositional truncations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-propositional-truncation - (funext : function-extensionality) - where +module foundation.functoriality-propositional-truncation where ```
Imports @@ -14,9 +9,10 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.dependent-products-propositions +open import foundation.function-extensionality-axiom +open import foundation.logical-equivalences +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/functoriality-pullbacks.lagda.md b/src/foundation/functoriality-pullbacks.lagda.md index 2a19574328..60e01bf16e 100644 --- a/src/foundation/functoriality-pullbacks.lagda.md +++ b/src/foundation/functoriality-pullbacks.lagda.md @@ -1,34 +1,29 @@ # Functorialty of pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-pullbacks - (funext : function-extensionality) - where +module foundation.functoriality-pullbacks where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.homotopies funext-morphisms-cospan-diagrams +open import foundation.equality-dependent-pair-types +open import foundation.function-types +open import foundation.homotopies +open import foundation.homotopies-morphisms-cospan-diagrams open import foundation.morphisms-cospan-diagrams -open import foundation.pullback-cones funext -open import foundation.standard-pullbacks funext +open import foundation.pullback-cones +open import foundation.standard-pullbacks open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.equivalences open import foundation-core.identity-types -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks ```
diff --git a/src/foundation/functoriality-sequential-limits.lagda.md b/src/foundation/functoriality-sequential-limits.lagda.md index d6b49fe4d2..32979a1d7b 100644 --- a/src/foundation/functoriality-sequential-limits.lagda.md +++ b/src/foundation/functoriality-sequential-limits.lagda.md @@ -1,12 +1,7 @@ # Functoriality of sequential limits ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-sequential-limits - (funext : function-extensionality) - where +module foundation.functoriality-sequential-limits where ```
Imports @@ -15,11 +10,11 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cones-over-inverse-sequential-diagrams funext +open import foundation.cones-over-inverse-sequential-diagrams open import foundation.dependent-pair-types -open import foundation.inverse-sequential-diagrams funext -open import foundation.morphisms-inverse-sequential-diagrams funext -open import foundation.sequential-limits funext +open import foundation.inverse-sequential-diagrams +open import foundation.morphisms-inverse-sequential-diagrams +open import foundation.sequential-limits open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/functoriality-set-quotients.lagda.md b/src/foundation/functoriality-set-quotients.lagda.md index b71732a282..31b756d2f8 100644 --- a/src/foundation/functoriality-set-quotients.lagda.md +++ b/src/foundation/functoriality-set-quotients.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-set-quotients - (funext : function-extensionality) - where +module foundation.functoriality-set-quotients where ```
Imports @@ -16,29 +11,29 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalence-extensionality funext +open import foundation.dependent-products-propositions +open import foundation.equivalence-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.logical-equivalences funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.set-quotients funext +open import foundation.homotopy-induction +open import foundation.logical-equivalences +open import foundation.reflecting-maps-equivalence-relations +open import foundation.set-quotients open import foundation.subtype-identity-principle -open import foundation.surjective-maps funext -open import foundation.uniqueness-set-quotients funext -open import foundation.universal-property-set-quotients funext +open import foundation.surjective-maps +open import foundation.uniqueness-set-quotients +open import foundation.universal-property-set-quotients open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-types -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/functoriality-set-truncation.lagda.md b/src/foundation/functoriality-set-truncation.lagda.md index bbaec842be..e10e05a582 100644 --- a/src/foundation/functoriality-set-truncation.lagda.md +++ b/src/foundation/functoriality-set-truncation.lagda.md @@ -1,12 +1,7 @@ # Functoriality of set truncation ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-set-truncation - (funext : function-extensionality) - where +module foundation.functoriality-set-truncation where ```
Imports @@ -14,20 +9,20 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.functoriality-truncation funext -open import foundation.images funext -open import foundation.injective-maps funext -open import foundation.propositional-truncations funext -open import foundation.retracts-of-types funext -open import foundation.set-truncations funext -open import foundation.sets funext -open import foundation.slice funext -open import foundation.surjective-maps funext -open import foundation.uniqueness-image funext -open import foundation.uniqueness-set-truncations funext -open import foundation.universal-property-image funext -open import foundation.universal-property-set-truncation funext +open import foundation.dependent-products-propositions +open import foundation.functoriality-truncation +open import foundation.images +open import foundation.injective-maps +open import foundation.propositional-truncations +open import foundation.retracts-of-types +open import foundation.set-truncations +open import foundation.sets +open import foundation.slice +open import foundation.surjective-maps +open import foundation.uniqueness-image +open import foundation.uniqueness-set-truncations +open import foundation.universal-property-image +open import foundation.universal-property-set-truncation open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/functoriality-truncation.lagda.md b/src/foundation/functoriality-truncation.lagda.md index 11f1dd3010..86a3aaecad 100644 --- a/src/foundation/functoriality-truncation.lagda.md +++ b/src/foundation/functoriality-truncation.lagda.md @@ -1,12 +1,7 @@ # Functoriality of truncations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.functoriality-truncation - (funext : function-extensionality) - where +module foundation.functoriality-truncation where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.truncations funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.truncations open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md b/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md index 69ddb915e5..8bd7600e74 100644 --- a/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md +++ b/src/foundation/fundamental-theorem-of-equivalence-relations.lagda.md @@ -1,33 +1,28 @@ # Fundamental theorem of equivalence relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.fundamental-theorem-of-equivalence-relations - (funext : function-extensionality) - where +module foundation.fundamental-theorem-of-equivalence-relations where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-classes funext -open import foundation.full-subtypes funext -open import foundation.inhabited-subtypes funext -open import foundation.logical-equivalences funext -open import foundation.partitions funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext +open import foundation.equivalence-classes +open import foundation.full-subtypes +open import foundation.inhabited-subtypes +open import foundation.logical-equivalences +open import foundation.partitions +open import foundation.propositional-truncations +open import foundation.subtypes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.contractible-types -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types diff --git a/src/foundation/global-choice.lagda.md b/src/foundation/global-choice.lagda.md index 581f9a4186..dde44fdbc8 100644 --- a/src/foundation/global-choice.lagda.md +++ b/src/foundation/global-choice.lagda.md @@ -1,27 +1,22 @@ # Global choice ```agda -open import foundation.function-extensionality-axiom - -module - foundation.global-choice - (funext : function-extensionality) - where +module foundation.global-choice where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation funext -open import foundation.hilberts-epsilon-operators funext +open import foundation.functoriality-propositional-truncation +open import foundation.hilberts-epsilon-operators open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.negation -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/global-subuniverses.lagda.md b/src/foundation/global-subuniverses.lagda.md index b061ab2cb3..375ab98286 100644 --- a/src/foundation/global-subuniverses.lagda.md +++ b/src/foundation/global-subuniverses.lagda.md @@ -1,20 +1,15 @@ # Global subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - foundation.global-subuniverses - (funext : function-extensionality) - where +module foundation.global-subuniverses where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types funext -open import foundation.subuniverses funext +open import foundation.iterated-dependent-product-types +open import foundation.subuniverses open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/globular-type-of-dependent-functions.lagda.md b/src/foundation/globular-type-of-dependent-functions.lagda.md index beb076102e..c620d17ec1 100644 --- a/src/foundation/globular-type-of-dependent-functions.lagda.md +++ b/src/foundation/globular-type-of-dependent-functions.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - foundation.globular-type-of-dependent-functions - (funext : function-extensionality) - where +module foundation.globular-type-of-dependent-functions where ```
Imports @@ -19,8 +14,8 @@ open import foundation.universe-levels open import foundation-core.homotopies open import globular-types.globular-types -open import globular-types.reflexive-globular-types funext -open import globular-types.transitive-globular-types funext +open import globular-types.reflexive-globular-types +open import globular-types.transitive-globular-types ```
diff --git a/src/foundation/globular-type-of-functions.lagda.md b/src/foundation/globular-type-of-functions.lagda.md index ceab9d078e..41533c9aee 100644 --- a/src/foundation/globular-type-of-functions.lagda.md +++ b/src/foundation/globular-type-of-functions.lagda.md @@ -3,25 +3,20 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - foundation.globular-type-of-functions - (funext : function-extensionality) - where +module foundation.globular-type-of-functions where ```
Imports ```agda -open import foundation.globular-type-of-dependent-functions funext +open import foundation.globular-type-of-dependent-functions open import foundation.universe-levels open import foundation-core.homotopies open import globular-types.globular-types -open import globular-types.reflexive-globular-types funext -open import globular-types.transitive-globular-types funext +open import globular-types.reflexive-globular-types +open import globular-types.transitive-globular-types ```
diff --git a/src/foundation/higher-homotopies-morphisms-arrows.lagda.md b/src/foundation/higher-homotopies-morphisms-arrows.lagda.md index 830a4eda4c..842b83be66 100644 --- a/src/foundation/higher-homotopies-morphisms-arrows.lagda.md +++ b/src/foundation/higher-homotopies-morphisms-arrows.lagda.md @@ -1,32 +1,27 @@ # Higher homotopies of morphisms of arrows ```agda -open import foundation.function-extensionality-axiom - -module - foundation.higher-homotopies-morphisms-arrows - (funext : function-extensionality) - where +module foundation.higher-homotopies-morphisms-arrows where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-identifications open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies-morphisms-arrows funext -open import foundation.homotopy-induction funext -open import foundation.morphisms-arrows funext -open import foundation.path-algebra funext +open import foundation.homotopies-morphisms-arrows +open import foundation.homotopy-induction +open import foundation.morphisms-arrows +open import foundation.path-algebra open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import foundation.whiskering-homotopies-concatenation funext -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-homotopies-concatenation +open import foundation.whiskering-identifications-concatenation open import foundation-core.equivalences open import foundation-core.homotopies diff --git a/src/foundation/hilberts-epsilon-operators.lagda.md b/src/foundation/hilberts-epsilon-operators.lagda.md index 0d7dfd78ae..1c23904a8b 100644 --- a/src/foundation/hilberts-epsilon-operators.lagda.md +++ b/src/foundation/hilberts-epsilon-operators.lagda.md @@ -1,19 +1,14 @@ # Hilbert's `ε`-operators ```agda -open import foundation.function-extensionality-axiom - -module - foundation.hilberts-epsilon-operators - (funext : function-extensionality) - where +module foundation.hilberts-epsilon-operators where ```
Imports ```agda -open import foundation.functoriality-propositional-truncation funext -open import foundation.propositional-truncations funext +open import foundation.functoriality-propositional-truncation +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/homotopies-morphisms-arrows.lagda.md b/src/foundation/homotopies-morphisms-arrows.lagda.md index 8f314a55fb..4eb4eeead5 100644 --- a/src/foundation/homotopies-morphisms-arrows.lagda.md +++ b/src/foundation/homotopies-morphisms-arrows.lagda.md @@ -1,35 +1,29 @@ # Homotopies of morphisms of arrows ```agda -open import foundation.function-extensionality-axiom - -module - foundation.homotopies-morphisms-arrows - (funext : function-extensionality) - where +module foundation.homotopies-morphisms-arrows where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.commuting-triangles-of-identifications funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.commuting-squares-of-identifications +open import foundation.commuting-triangles-of-identifications +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.morphisms-arrows funext -open import foundation.postcomposition-functions funext +open import foundation.homotopy-induction +open import foundation.morphisms-arrows +open import foundation.postcomposition-functions open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation open import foundation-core.commuting-squares-of-homotopies -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies diff --git a/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md b/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md index 15afd1e562..0b4e7d6bb5 100644 --- a/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md +++ b/src/foundation/homotopies-morphisms-cospan-diagrams.lagda.md @@ -1,28 +1,22 @@ # Homotopies of morphisms of cospan diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.homotopies-morphisms-cospan-diagrams - (funext : function-extensionality) - where +module foundation.homotopies-morphisms-cospan-diagrams where ```
Imports ```agda -open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-homotopies open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.morphisms-cospan-diagrams open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/homotopies.lagda.md b/src/foundation/homotopies.lagda.md index c40d62e172..54f138533e 100644 --- a/src/foundation/homotopies.lagda.md +++ b/src/foundation/homotopies.lagda.md @@ -1,12 +1,7 @@ # Homotopies ```agda -open import foundation.function-extensionality-axiom - -module - foundation.homotopies - (funext : function-extensionality) - where +module foundation.homotopies where open import foundation-core.homotopies public ``` @@ -14,23 +9,22 @@ open import foundation-core.homotopies public
Imports ```agda -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.path-algebra funext +open import foundation.function-extensionality +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.path-algebra open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications open import foundation-core.dependent-identifications open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.transport-along-identifications open import foundation-core.whiskering-homotopies-concatenation ``` diff --git a/src/foundation/homotopy-induction.lagda.md b/src/foundation/homotopy-induction.lagda.md index d91803b6e5..0e79b789dd 100644 --- a/src/foundation/homotopy-induction.lagda.md +++ b/src/foundation/homotopy-induction.lagda.md @@ -1,22 +1,17 @@ # Homotopy induction ```agda -open import foundation.function-extensionality-axiom - -module - foundation.homotopy-induction - (funext : function-extensionality) - where +module foundation.homotopy-induction where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.identity-systems -open import foundation.universal-property-identity-systems funext +open import foundation.universal-property-identity-systems open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/homotopy-preorder-of-types.lagda.md b/src/foundation/homotopy-preorder-of-types.lagda.md index 3b9801d90c..c6c1e1902e 100644 --- a/src/foundation/homotopy-preorder-of-types.lagda.md +++ b/src/foundation/homotopy-preorder-of-types.lagda.md @@ -10,17 +10,17 @@ module ```agda open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.mere-functions funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.mere-functions +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.large-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.large-preorders +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/foundation/horizontal-composition-spans-of-spans.lagda.md b/src/foundation/horizontal-composition-spans-of-spans.lagda.md index 7555b03022..eed1567115 100644 --- a/src/foundation/horizontal-composition-spans-of-spans.lagda.md +++ b/src/foundation/horizontal-composition-spans-of-spans.lagda.md @@ -1,33 +1,28 @@ # Horizontal composition of spans of spans ```agda -open import foundation.function-extensionality-axiom - -module - foundation.horizontal-composition-spans-of-spans - (funext : function-extensionality) - where +module foundation.horizontal-composition-spans-of-spans where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps funext -open import foundation.composition-spans funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.commuting-triangles-of-maps +open import foundation.composition-spans +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.equivalences-spans funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.morphisms-arrows funext +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.equivalences-spans +open import foundation.homotopies +open import foundation.identity-types +open import foundation.morphisms-arrows open import foundation.morphisms-spans -open import foundation.pullbacks funext +open import foundation.pullbacks open import foundation.spans -open import foundation.spans-of-spans funext -open import foundation.standard-pullbacks funext -open import foundation.type-arithmetic-standard-pullbacks funext +open import foundation.spans-of-spans +open import foundation.standard-pullbacks +open import foundation.type-arithmetic-standard-pullbacks open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/idempotent-maps.lagda.md b/src/foundation/idempotent-maps.lagda.md index ea94170419..3e0e0adf77 100644 --- a/src/foundation/idempotent-maps.lagda.md +++ b/src/foundation/idempotent-maps.lagda.md @@ -1,19 +1,14 @@ # Idempotent maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.idempotent-maps - (funext : function-extensionality) - where +module foundation.idempotent-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-propositions open import foundation.homotopy-algebra open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/identity-truncated-types.lagda.md b/src/foundation/identity-truncated-types.lagda.md index 7d5577f475..0201dea2e3 100644 --- a/src/foundation/identity-truncated-types.lagda.md +++ b/src/foundation/identity-truncated-types.lagda.md @@ -1,19 +1,14 @@ # Identity types of truncated types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.identity-truncated-types - (funext : function-extensionality) - where +module foundation.identity-truncated-types where ```
Imports ```agda -open import foundation.dependent-products-truncated-types funext -open import foundation.univalence funext +open import foundation.dependent-products-truncated-types +open import foundation.univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/identity-types.lagda.md b/src/foundation/identity-types.lagda.md index fd892bfdee..2f517ddffe 100644 --- a/src/foundation/identity-types.lagda.md +++ b/src/foundation/identity-types.lagda.md @@ -1,12 +1,7 @@ # Identity types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.identity-types - (funext : function-extensionality) - where +module foundation.identity-types where open import foundation-core.identity-types public ``` @@ -18,9 +13,8 @@ open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.commuting-pentagons-of-identifications open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.function-extensionality funext - +open import foundation.equivalence-extensionality +open import foundation.function-extensionality open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/images-subtypes.lagda.md b/src/foundation/images-subtypes.lagda.md index 350f19968e..f2959311bd 100644 --- a/src/foundation/images-subtypes.lagda.md +++ b/src/foundation/images-subtypes.lagda.md @@ -1,26 +1,21 @@ # Images of subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.images-subtypes - (funext : function-extensionality) - where +module foundation.images-subtypes where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.full-subtypes funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.images funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.pullbacks-subtypes funext -open import foundation.subtypes funext +open import foundation.full-subtypes +open import foundation.functoriality-propositional-truncation +open import foundation.images +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.pullbacks-subtypes +open import foundation.subtypes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -30,10 +25,10 @@ open import foundation-core.fibers-of-maps open import foundation-core.function-types open import foundation-core.identity-types -open import order-theory.galois-connections-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.similarity-of-order-preserving-maps-large-posets funext +open import order-theory.galois-connections-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.similarity-of-order-preserving-maps-large-posets ```
diff --git a/src/foundation/images.lagda.md b/src/foundation/images.lagda.md index 39dbd81d29..4ffd596c45 100644 --- a/src/foundation/images.lagda.md +++ b/src/foundation/images.lagda.md @@ -1,12 +1,7 @@ # The image of a map ```agda -open import foundation.function-extensionality-axiom - -module - foundation.images - (funext : function-extensionality) - where +module foundation.images where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.propositional-truncations funext -open import foundation.slice funext +open import foundation.propositional-truncations +open import foundation.slice open import foundation.subtype-identity-principle -open import foundation.surjective-maps funext +open import foundation.surjective-maps open import foundation.universe-levels -open import foundation-core.1-types funext +open import foundation-core.1-types open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-types open import foundation-core.embeddings @@ -31,7 +26,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/impredicative-encodings.lagda.md b/src/foundation/impredicative-encodings.lagda.md index 604f2594c1..fadc6aea05 100644 --- a/src/foundation/impredicative-encodings.lagda.md +++ b/src/foundation/impredicative-encodings.lagda.md @@ -1,28 +1,23 @@ # Impredicative encodings of the logical operations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.impredicative-encodings - (funext : function-extensionality) - where +module foundation.impredicative-encodings where ```
Imports ```agda -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.disjunction funext -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.homotopies funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.universal-quantification funext +open import foundation.dependent-products-propositions +open import foundation.disjunction +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.homotopies +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.universal-quantification open import foundation.universe-levels open import foundation-core.coproduct-types diff --git a/src/foundation/impredicative-universes.lagda.md b/src/foundation/impredicative-universes.lagda.md index 3145b640c0..c1f2ed3f59 100644 --- a/src/foundation/impredicative-universes.lagda.md +++ b/src/foundation/impredicative-universes.lagda.md @@ -1,12 +1,7 @@ # Impredicative universes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.impredicative-universes - (funext : function-extensionality) - where +module foundation.impredicative-universes where ```
Imports @@ -15,7 +10,7 @@ module open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.small-types funext +open import foundation-core.small-types ```
diff --git a/src/foundation/infinitely-coherent-equivalences.lagda.md b/src/foundation/infinitely-coherent-equivalences.lagda.md index 35edb30326..a650beffa9 100644 --- a/src/foundation/infinitely-coherent-equivalences.lagda.md +++ b/src/foundation/infinitely-coherent-equivalences.lagda.md @@ -3,27 +3,22 @@ ```agda {-# OPTIONS --guardedness --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.infinitely-coherent-equivalences - (funext : function-extensionality) - where +module foundation.infinitely-coherent-equivalences where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.transposition-identifications-along-equivalences open import foundation.universe-levels ``` diff --git a/src/foundation/inhabited-subtypes.lagda.md b/src/foundation/inhabited-subtypes.lagda.md index 4d64e0ae5e..5a4a67c0b3 100644 --- a/src/foundation/inhabited-subtypes.lagda.md +++ b/src/foundation/inhabited-subtypes.lagda.md @@ -1,22 +1,17 @@ # Inhabited subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.inhabited-subtypes - (funext : function-extensionality) - where +module foundation.inhabited-subtypes where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext +open import foundation.inhabited-types +open import foundation.propositional-truncations open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/inhabited-types.lagda.md b/src/foundation/inhabited-types.lagda.md index caaad0d4b2..ff290bc467 100644 --- a/src/foundation/inhabited-types.lagda.md +++ b/src/foundation/inhabited-types.lagda.md @@ -1,25 +1,20 @@ # Inhabited types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.inhabited-types - (funext : function-extensionality) - where +module foundation.inhabited-types where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.functoriality-propositional-truncation funext +open import foundation.equality-dependent-function-types +open import foundation.functoriality-propositional-truncation open import foundation.fundamental-theorem-of-identity-types -open import foundation.propositional-truncations funext +open import foundation.propositional-truncations open import foundation.subtype-identity-principle -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/injective-maps.lagda.md b/src/foundation/injective-maps.lagda.md index e5a4ebed7b..09640c54b1 100644 --- a/src/foundation/injective-maps.lagda.md +++ b/src/foundation/injective-maps.lagda.md @@ -1,12 +1,7 @@ # Injective maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.injective-maps - (funext : function-extensionality) - where +module foundation.injective-maps where open import foundation-core.injective-maps public ``` @@ -16,10 +11,10 @@ open import foundation-core.injective-maps public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.function-extensionality funext - -open import foundation.logical-equivalences funext +open import foundation.dependent-products-propositions +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.logical-equivalences open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/intersections-subtypes.lagda.md b/src/foundation/intersections-subtypes.lagda.md index 7d254d6825..776056c8e1 100644 --- a/src/foundation/intersections-subtypes.lagda.md +++ b/src/foundation/intersections-subtypes.lagda.md @@ -1,30 +1,25 @@ # Intersections of subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.intersections-subtypes - (funext : function-extensionality) - where +module foundation.intersections-subtypes where ```
Imports ```agda -open import foundation.conjunction funext -open import foundation.decidable-subtypes funext +open import foundation.conjunction +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.large-locale-of-subtypes funext -open import foundation.powersets funext +open import foundation.dependent-products-propositions +open import foundation.large-locale-of-subtypes +open import foundation.powersets open import foundation.universe-levels -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes -open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets ```
diff --git a/src/foundation/inverse-sequential-diagrams.lagda.md b/src/foundation/inverse-sequential-diagrams.lagda.md index 1007dca5ea..553548e870 100644 --- a/src/foundation/inverse-sequential-diagrams.lagda.md +++ b/src/foundation/inverse-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Inverse sequential diagrams of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.inverse-sequential-diagrams - (funext : function-extensionality) - where +module foundation.inverse-sequential-diagrams where ```
Imports @@ -15,8 +10,8 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.iterating-functions funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.iterating-functions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/foundation/invertible-maps.lagda.md b/src/foundation/invertible-maps.lagda.md index d5f0f8a3eb..3edb105808 100644 --- a/src/foundation/invertible-maps.lagda.md +++ b/src/foundation/invertible-maps.lagda.md @@ -1,12 +1,7 @@ # Invertible maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.invertible-maps - (funext : function-extensionality) - where +module foundation.invertible-maps where open import foundation-core.invertible-maps public ``` @@ -15,23 +10,22 @@ open import foundation-core.invertible-maps public ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-homotopies open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext +open import foundation.dependent-products-truncated-types open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.full-subtypes funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-cartesian-product-types funext +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.full-subtypes +open import foundation.function-extensionality +open import foundation.functoriality-cartesian-product-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.homotopy-induction funext -open import foundation.postcomposition-functions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.homotopy-induction +open import foundation.postcomposition-functions +open import foundation.retractions +open import foundation.sections open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -47,7 +41,7 @@ open import foundation-core.torsorial-type-families open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.free-loops ```
diff --git a/src/foundation/involutions.lagda.md b/src/foundation/involutions.lagda.md index 699b315c0a..8f2ad4d544 100644 --- a/src/foundation/involutions.lagda.md +++ b/src/foundation/involutions.lagda.md @@ -1,27 +1,21 @@ # Involutions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.involutions - (funext : function-extensionality) - where +module foundation.involutions where ```
Imports ```agda -open import foundation.automorphisms funext +open import foundation.automorphisms open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - +open import foundation.dependent-products-truncated-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-algebra -open import foundation.homotopy-induction funext +open import foundation.homotopy-induction open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/irrefutable-propositions.lagda.md b/src/foundation/irrefutable-propositions.lagda.md index 1d6ea36e6a..d89ec3fd7b 100644 --- a/src/foundation/irrefutable-propositions.lagda.md +++ b/src/foundation/irrefutable-propositions.lagda.md @@ -1,34 +1,29 @@ # Irrefutable propositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.irrefutable-propositions - (funext : function-extensionality) - where +module foundation.irrefutable-propositions where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.double-negation funext -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.subuniverses funext +open import foundation.dependent-products-propositions +open import foundation.double-negation +open import foundation.empty-types +open import foundation.function-types +open import foundation.negation +open import foundation.propositions +open import foundation.subuniverses open import foundation.unit-type open import foundation.universe-levels -open import logic.double-negation-elimination funext +open import logic.double-negation-elimination ```
diff --git a/src/foundation/isolated-elements.lagda.md b/src/foundation/isolated-elements.lagda.md index 1a022d4a0e..994d1a5448 100644 --- a/src/foundation/isolated-elements.lagda.md +++ b/src/foundation/isolated-elements.lagda.md @@ -1,39 +1,34 @@ # Isolated elements ```agda -open import foundation.function-extensionality-axiom - -module - foundation.isolated-elements - (funext : function-extensionality) - where +module foundation.isolated-elements where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.constant-maps funext -open import foundation.decidable-embeddings funext -open import foundation.decidable-equality funext -open import foundation.decidable-maps funext -open import foundation.decidable-types funext +open import foundation.constant-maps +open import foundation.decidable-embeddings +open import foundation.decidable-equality +open import foundation.decidable-maps +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext +open import foundation.dependent-products-propositions +open import foundation.embeddings open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation +open import foundation.sets open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.coproduct-types -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types @@ -41,7 +36,7 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.maybe open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/isomorphisms-of-sets.lagda.md b/src/foundation/isomorphisms-of-sets.lagda.md index 4692b5f04a..c5f46ffa11 100644 --- a/src/foundation/isomorphisms-of-sets.lagda.md +++ b/src/foundation/isomorphisms-of-sets.lagda.md @@ -1,12 +1,7 @@ # Isomorphisms of sets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.isomorphisms-of-sets - (funext : function-extensionality) - where +module foundation.isomorphisms-of-sets where ```
Imports @@ -14,17 +9,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.sets open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/iterated-cartesian-product-types.lagda.md b/src/foundation/iterated-cartesian-product-types.lagda.md index d944078297..8a20d00913 100644 --- a/src/foundation/iterated-cartesian-product-types.lagda.md +++ b/src/foundation/iterated-cartesian-product-types.lagda.md @@ -1,12 +1,7 @@ # Iterated cartesian product types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.iterated-cartesian-product-types - (funext : function-extensionality) - where +module foundation.iterated-cartesian-product-types where ```
Imports @@ -14,19 +9,19 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.type-arithmetic-dependent-function-types open import foundation.unit-type -open import foundation.univalence funext -open import foundation.universal-property-coproduct-types funext -open import foundation.universal-property-empty-type funext +open import foundation.univalence +open import foundation.universal-property-coproduct-types +open import foundation.universal-property-empty-type open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -36,12 +31,12 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types -open import lists.arrays funext -open import lists.concatenation-lists funext +open import lists.arrays +open import lists.concatenation-lists open import lists.lists -open import lists.permutation-lists funext +open import lists.permutation-lists -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/iterated-dependent-product-types.lagda.md b/src/foundation/iterated-dependent-product-types.lagda.md index 404f3c5041..a5cada2333 100644 --- a/src/foundation/iterated-dependent-product-types.lagda.md +++ b/src/foundation/iterated-dependent-product-types.lagda.md @@ -1,12 +1,7 @@ # Iterated dependent product types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.iterated-dependent-product-types - (funext : function-extensionality) - where +module foundation.iterated-dependent-product-types where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.dependent-products-contractible-types funext -open import foundation.dependent-products-propositions funext -open import foundation.dependent-products-truncated-types funext +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.implicit-function-types open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.propositions open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/iterating-automorphisms.lagda.md b/src/foundation/iterating-automorphisms.lagda.md index aef82113e6..dfae65d2f3 100644 --- a/src/foundation/iterating-automorphisms.lagda.md +++ b/src/foundation/iterating-automorphisms.lagda.md @@ -1,24 +1,19 @@ # Iterating automorphisms ```agda -open import foundation.function-extensionality-axiom - -module - foundation.iterating-automorphisms - (funext : function-extensionality) - where +module foundation.iterating-automorphisms where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.automorphisms funext -open import foundation.equivalence-extensionality funext -open import foundation.iterating-functions funext +open import foundation.automorphisms +open import foundation.equivalence-extensionality +open import foundation.iterating-functions open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/iterating-families-of-maps.lagda.md b/src/foundation/iterating-families-of-maps.lagda.md index a94b3ed4c2..968976eaf1 100644 --- a/src/foundation/iterating-families-of-maps.lagda.md +++ b/src/foundation/iterating-families-of-maps.lagda.md @@ -1,12 +1,7 @@ # Iterating families of maps over a map ```agda -open import foundation.function-extensionality-axiom - -module - foundation.iterating-families-of-maps - (funext : function-extensionality) - where +module foundation.iterating-families-of-maps where ```
Imports @@ -15,8 +10,8 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.dependent-identifications funext -open import foundation.iterating-functions funext +open import foundation.dependent-identifications +open import foundation.iterating-functions open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/iterating-functions.lagda.md b/src/foundation/iterating-functions.lagda.md index dad12c698e..7c6c17cdaf 100644 --- a/src/foundation/iterating-functions.lagda.md +++ b/src/foundation/iterating-functions.lagda.md @@ -1,37 +1,32 @@ # Iterating functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.iterating-functions - (funext : function-extensionality) - where +module foundation.iterating-functions where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.exponentiation-natural-numbers funext +open import elementary-number-theory.exponentiation-natural-numbers open import elementary-number-theory.multiplication-natural-numbers -open import elementary-number-theory.multiplicative-monoid-of-natural-numbers funext +open import elementary-number-theory.multiplicative-monoid-of-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext -open import foundation-core.endomorphisms funext +open import foundation-core.commuting-squares-of-maps +open import foundation-core.endomorphisms open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.sets -open import group-theory.monoid-actions funext +open import group-theory.monoid-actions ```
diff --git a/src/foundation/iterating-involutions.lagda.md b/src/foundation/iterating-involutions.lagda.md index 361affaa35..06170f10fe 100644 --- a/src/foundation/iterating-involutions.lagda.md +++ b/src/foundation/iterating-involutions.lagda.md @@ -1,29 +1,24 @@ # Iterating involutions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.iterating-involutions - (funext : function-extensionality) - where +module foundation.iterating-involutions where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.involutions funext -open import foundation.iterating-functions funext +open import foundation.involutions +open import foundation.iterating-functions open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.identity-types -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/kernel-span-diagrams-of-maps.lagda.md b/src/foundation/kernel-span-diagrams-of-maps.lagda.md index 7eac0660fd..37d56efd8d 100644 --- a/src/foundation/kernel-span-diagrams-of-maps.lagda.md +++ b/src/foundation/kernel-span-diagrams-of-maps.lagda.md @@ -1,19 +1,14 @@ # Kernel span diagrams of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.kernel-span-diagrams-of-maps - (funext : function-extensionality) - where +module foundation.kernel-span-diagrams-of-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.span-diagrams funext +open import foundation.span-diagrams open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/large-apartness-relations.lagda.md b/src/foundation/large-apartness-relations.lagda.md index 9e0e14ae12..b87c9a5b09 100644 --- a/src/foundation/large-apartness-relations.lagda.md +++ b/src/foundation/large-apartness-relations.lagda.md @@ -1,22 +1,17 @@ # Large apartness relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.large-apartness-relations - (funext : function-extensionality) - where +module foundation.large-apartness-relations where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/foundation/large-binary-relations.lagda.md b/src/foundation/large-binary-relations.lagda.md index 769f60bad2..2a4b155124 100644 --- a/src/foundation/large-binary-relations.lagda.md +++ b/src/foundation/large-binary-relations.lagda.md @@ -1,20 +1,15 @@ # Large binary relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.large-binary-relations - (funext : function-extensionality) - where +module foundation.large-binary-relations where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.disjunction funext +open import foundation.disjunction open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/large-locale-of-propositions.lagda.md b/src/foundation/large-locale-of-propositions.lagda.md index 47a40e65e0..671ef5ad4b 100644 --- a/src/foundation/large-locale-of-propositions.lagda.md +++ b/src/foundation/large-locale-of-propositions.lagda.md @@ -1,39 +1,34 @@ # The large locale of propositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.large-locale-of-propositions - (funext : function-extensionality) - where +module foundation.large-locale-of-propositions where ```
Imports ```agda -open import foundation.conjunction funext -open import foundation.dependent-products-propositions funext -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.logical-equivalences funext -open import foundation.propositional-extensionality funext +open import foundation.conjunction +open import foundation.dependent-products-propositions +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.logical-equivalences +open import foundation.propositional-extensionality open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-cartesian-product-types open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.propositions -open import order-theory.bottom-elements-large-posets funext -open import order-theory.large-frames funext -open import order-theory.large-locales funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.top-elements-large-posets funext +open import order-theory.bottom-elements-large-posets +open import order-theory.large-frames +open import order-theory.large-locales +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.top-elements-large-posets ```
diff --git a/src/foundation/large-locale-of-subtypes.lagda.md b/src/foundation/large-locale-of-subtypes.lagda.md index bf32155c73..2661d3c83d 100644 --- a/src/foundation/large-locale-of-subtypes.lagda.md +++ b/src/foundation/large-locale-of-subtypes.lagda.md @@ -1,34 +1,29 @@ # The large locale of subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.large-locale-of-subtypes - (funext : function-extensionality) - where +module foundation.large-locale-of-subtypes where ```
Imports ```agda -open import foundation.large-binary-relations funext -open import foundation.large-locale-of-propositions funext +open import foundation.large-binary-relations +open import foundation.large-locale-of-propositions open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.sets -open import order-theory.bottom-elements-large-posets funext -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-locales funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.powers-of-large-locales funext -open import order-theory.top-elements-large-posets funext +open import order-theory.bottom-elements-large-posets +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-locales +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.powers-of-large-locales +open import order-theory.top-elements-large-posets ```
diff --git a/src/foundation/law-of-excluded-middle.lagda.md b/src/foundation/law-of-excluded-middle.lagda.md index f9b832cb1a..2a3935ebdc 100644 --- a/src/foundation/law-of-excluded-middle.lagda.md +++ b/src/foundation/law-of-excluded-middle.lagda.md @@ -1,27 +1,22 @@ # The law of excluded middle ```agda -open import foundation.function-extensionality-axiom - -module - foundation.law-of-excluded-middle - (funext : function-extensionality) - where +module foundation.law-of-excluded-middle where ```
Imports ```agda -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-propositions open import foundation.universe-levels -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.negation open import foundation-core.propositions -open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.2-element-types ```
diff --git a/src/foundation/lawveres-fixed-point-theorem.lagda.md b/src/foundation/lawveres-fixed-point-theorem.lagda.md index b4733c3d77..603c14897d 100644 --- a/src/foundation/lawveres-fixed-point-theorem.lagda.md +++ b/src/foundation/lawveres-fixed-point-theorem.lagda.md @@ -1,21 +1,17 @@ # Lawvere's fixed point theorem ```agda -open import foundation.function-extensionality-axiom - -module - foundation.lawveres-fixed-point-theorem - (funext : function-extensionality) - where +module foundation.lawveres-fixed-point-theorem where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.propositional-truncations funext -open import foundation.surjective-maps funext +open import foundation.existential-quantification +open import foundation.function-extensionality-axiom +open import foundation.propositional-truncations +open import foundation.surjective-maps open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md index 9abc4e611e..5c9d5e9e71 100644 --- a/src/foundation/lesser-limited-principle-of-omniscience.lagda.md +++ b/src/foundation/lesser-limited-principle-of-omniscience.lagda.md @@ -1,24 +1,19 @@ # The lesser limited principle of omniscience ```agda -open import foundation.function-extensionality-axiom - -module - foundation.lesser-limited-principle-of-omniscience - (funext : function-extensionality) - where +module foundation.lesser-limited-principle-of-omniscience where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers funext +open import elementary-number-theory.parity-natural-numbers open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.disjunction funext -open import foundation.universal-quantification funext +open import foundation.dependent-products-propositions +open import foundation.disjunction +open import foundation.universal-quantification open import foundation.universe-levels open import foundation-core.booleans diff --git a/src/foundation/limited-principle-of-omniscience.lagda.md b/src/foundation/limited-principle-of-omniscience.lagda.md index 3d6dd83878..58bfd6a8d7 100644 --- a/src/foundation/limited-principle-of-omniscience.lagda.md +++ b/src/foundation/limited-principle-of-omniscience.lagda.md @@ -1,12 +1,7 @@ # The limited principle of omniscience ```agda -open import foundation.function-extensionality-axiom - -module - foundation.limited-principle-of-omniscience - (funext : function-extensionality) - where +module foundation.limited-principle-of-omniscience where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.disjunction funext -open import foundation.existential-quantification funext -open import foundation.negation funext -open import foundation.universal-quantification funext +open import foundation.dependent-products-propositions +open import foundation.disjunction +open import foundation.existential-quantification +open import foundation.negation +open import foundation.universal-quantification open import foundation.universe-levels open import foundation-core.booleans @@ -28,7 +23,7 @@ open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/locale-of-propositions.lagda.md b/src/foundation/locale-of-propositions.lagda.md index 9a2de3f6ca..dd65321505 100644 --- a/src/foundation/locale-of-propositions.lagda.md +++ b/src/foundation/locale-of-propositions.lagda.md @@ -1,38 +1,33 @@ # The locale of propositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.locale-of-propositions - (funext : function-extensionality) - where +module foundation.locale-of-propositions where ```
Imports ```agda -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.large-locale-of-propositions funext -open import foundation.logical-equivalences funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.existential-quantification +open import foundation.large-locale-of-propositions +open import foundation.logical-equivalences +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels open import foundation-core.function-types -open import order-theory.frames funext -open import order-theory.greatest-lower-bounds-posets funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.meet-semilattices funext -open import order-theory.meet-suplattices funext -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.suplattices funext -open import order-theory.top-elements-posets funext +open import order-theory.frames +open import order-theory.greatest-lower-bounds-posets +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.meet-semilattices +open import order-theory.meet-suplattices +open import order-theory.posets +open import order-theory.preorders +open import order-theory.suplattices +open import order-theory.top-elements-posets ```
diff --git a/src/foundation/locally-small-types.lagda.md b/src/foundation/locally-small-types.lagda.md index f4e69c151b..2c54ced78e 100644 --- a/src/foundation/locally-small-types.lagda.md +++ b/src/foundation/locally-small-types.lagda.md @@ -1,26 +1,20 @@ # Locally small types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.locally-small-types - (funext : function-extensionality) - where +module foundation.locally-small-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.dependent-products-truncated-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.inhabited-subtypes funext -open import foundation.subuniverses funext -open import foundation.univalence funext +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.inhabited-subtypes +open import foundation.subuniverses +open import foundation.univalence open import foundation.universe-levels open import foundation-core.embeddings @@ -29,8 +23,8 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.small-types funext -open import foundation-core.subtypes funext +open import foundation-core.small-types +open import foundation-core.subtypes open import foundation-core.transport-along-identifications open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/logical-equivalences.lagda.md b/src/foundation/logical-equivalences.lagda.md index 929afb8780..f95d0aacb7 100644 --- a/src/foundation/logical-equivalences.lagda.md +++ b/src/foundation/logical-equivalences.lagda.md @@ -1,12 +1,7 @@ # Logical equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.logical-equivalences - (funext : function-extensionality) - where +module foundation.logical-equivalences where open import foundation-core.logical-equivalences public ``` @@ -15,12 +10,11 @@ open import foundation-core.logical-equivalences public ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-propositions open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-cartesian-product-types funext +open import foundation.equivalence-extensionality +open import foundation.function-extensionality +open import foundation.functoriality-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/maps-in-global-subuniverses.lagda.md b/src/foundation/maps-in-global-subuniverses.lagda.md index e92a945013..93a167a49c 100644 --- a/src/foundation/maps-in-global-subuniverses.lagda.md +++ b/src/foundation/maps-in-global-subuniverses.lagda.md @@ -1,23 +1,18 @@ # Maps in global subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - foundation.maps-in-global-subuniverses - (funext : function-extensionality) - where +module foundation.maps-in-global-subuniverses where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows funext +open import foundation.cartesian-morphisms-arrows open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.fibers-of-maps funext -open import foundation.functoriality-fibers-of-maps funext -open import foundation.global-subuniverses funext +open import foundation.dependent-products-propositions +open import foundation.fibers-of-maps +open import foundation.functoriality-fibers-of-maps +open import foundation.global-subuniverses open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/maps-in-subuniverses.lagda.md b/src/foundation/maps-in-subuniverses.lagda.md index 8cbf3758bd..52c43cb7cc 100644 --- a/src/foundation/maps-in-subuniverses.lagda.md +++ b/src/foundation/maps-in-subuniverses.lagda.md @@ -1,19 +1,14 @@ # Maps in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - foundation.maps-in-subuniverses - (funext : function-extensionality) - where +module foundation.maps-in-subuniverses where ```
Imports ```agda -open import foundation.homotopies funext -open import foundation.subuniverses funext +open import foundation.homotopies +open import foundation.subuniverses open import foundation.universe-levels open import foundation-core.fibers-of-maps diff --git a/src/foundation/maybe.lagda.md b/src/foundation/maybe.lagda.md index 149520a637..a7c8ed3e01 100644 --- a/src/foundation/maybe.lagda.md +++ b/src/foundation/maybe.lagda.md @@ -1,12 +1,7 @@ # The maybe monad ```agda -open import foundation.function-extensionality-axiom - -module - foundation.maybe - (funext : function-extensionality) - where +module foundation.maybe where open import foundation-core.maybe public ``` @@ -15,14 +10,14 @@ open import foundation-core.maybe public ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types funext -open import foundation.existential-quantification funext -open import foundation.propositional-truncations funext -open import foundation.surjective-maps funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.equality-coproduct-types +open import foundation.existential-quantification +open import foundation.propositional-truncations +open import foundation.surjective-maps +open import foundation.type-arithmetic-empty-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/mere-embeddings.lagda.md b/src/foundation/mere-embeddings.lagda.md index 0215657878..4fbccc13d4 100644 --- a/src/foundation/mere-embeddings.lagda.md +++ b/src/foundation/mere-embeddings.lagda.md @@ -1,27 +1,22 @@ # Mere embeddings ```agda -open import foundation.function-extensionality-axiom - -module - foundation.mere-embeddings - (funext : function-extensionality) - where +module foundation.mere-embeddings where ```
Imports ```agda -open import foundation.cantor-schroder-bernstein-escardo funext -open import foundation.embeddings funext -open import foundation.law-of-excluded-middle funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.cantor-schroder-bernstein-escardo +open import foundation.embeddings +open import foundation.law-of-excluded-middle +open import foundation.mere-equivalences +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.propositions -open import order-theory.large-preorders funext +open import order-theory.large-preorders ```
diff --git a/src/foundation/mere-equality.lagda.md b/src/foundation/mere-equality.lagda.md index 77b75565f0..d5319cae0a 100644 --- a/src/foundation/mere-equality.lagda.md +++ b/src/foundation/mere-equality.lagda.md @@ -1,26 +1,21 @@ # Mere equality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.mere-equality - (funext : function-extensionality) - where +module foundation.mere-equality where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation funext -open import foundation.propositional-truncations funext -open import foundation.reflecting-maps-equivalence-relations funext +open import foundation.functoriality-propositional-truncation +open import foundation.propositional-truncations +open import foundation.reflecting-maps-equivalence-relations open import foundation.universe-levels -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets diff --git a/src/foundation/mere-equivalences.lagda.md b/src/foundation/mere-equivalences.lagda.md index b4e91b45a0..27fecbd0f1 100644 --- a/src/foundation/mere-equivalences.lagda.md +++ b/src/foundation/mere-equivalences.lagda.md @@ -1,24 +1,19 @@ # Mere equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.mere-equivalences - (funext : function-extensionality) - where +module foundation.mere-equivalences where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.decidable-equality funext -open import foundation.dependent-products-truncated-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.univalence funext +open import foundation.binary-relations +open import foundation.decidable-equality +open import foundation.dependent-products-truncated-types +open import foundation.functoriality-propositional-truncation +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/mere-functions.lagda.md b/src/foundation/mere-functions.lagda.md index 6a5c87b810..4597357ccd 100644 --- a/src/foundation/mere-functions.lagda.md +++ b/src/foundation/mere-functions.lagda.md @@ -1,18 +1,13 @@ # Mere functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.mere-functions - (funext : function-extensionality) - where +module foundation.mere-functions where ```
Imports ```agda -open import foundation.propositional-truncations funext +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/mere-logical-equivalences.lagda.md b/src/foundation/mere-logical-equivalences.lagda.md index 5490b4e7c2..5bf9ebe781 100644 --- a/src/foundation/mere-logical-equivalences.lagda.md +++ b/src/foundation/mere-logical-equivalences.lagda.md @@ -1,23 +1,18 @@ # Mere logical equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.mere-logical-equivalences - (funext : function-extensionality) - where +module foundation.mere-logical-equivalences where ```
Imports ```agda -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.inhabited-types funext -open import foundation.logical-equivalences funext -open import foundation.mere-functions funext -open import foundation.propositional-truncations funext +open import foundation.inhabited-types +open import foundation.logical-equivalences +open import foundation.mere-functions +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/mere-path-cosplit-maps.lagda.md b/src/foundation/mere-path-cosplit-maps.lagda.md index ac3addf472..5cd5644ffe 100644 --- a/src/foundation/mere-path-cosplit-maps.lagda.md +++ b/src/foundation/mere-path-cosplit-maps.lagda.md @@ -1,12 +1,7 @@ # Mere path-cosplit maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.mere-path-cosplit-maps - (funext : function-extensionality) - where +module foundation.mere-path-cosplit-maps where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalences-arrows funext -open import foundation.inhabited-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.truncated-maps funext +open import foundation.dependent-products-propositions +open import foundation.equivalences-arrows +open import foundation.inhabited-types +open import foundation.iterated-dependent-product-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.truncated-maps open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/foundation/monomorphisms.lagda.md b/src/foundation/monomorphisms.lagda.md index eb98657ed8..9fc0e6bd82 100644 --- a/src/foundation/monomorphisms.lagda.md +++ b/src/foundation/monomorphisms.lagda.md @@ -1,12 +1,7 @@ # Monomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - foundation.monomorphisms - (funext : function-extensionality) - where +module foundation.monomorphisms where ```
Imports @@ -14,12 +9,11 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-function-types funext -open import foundation.postcomposition-functions funext +open import foundation.dependent-products-propositions +open import foundation.embeddings +open import foundation.function-extensionality +open import foundation.functoriality-function-types +open import foundation.postcomposition-functions open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/morphisms-arrows.lagda.md b/src/foundation/morphisms-arrows.lagda.md index 04cbfd8dce..b80513a416 100644 --- a/src/foundation/morphisms-arrows.lagda.md +++ b/src/foundation/morphisms-arrows.lagda.md @@ -1,27 +1,21 @@ # Morphisms of arrows ```agda -open import foundation.function-extensionality-axiom - -module - foundation.morphisms-arrows - (funext : function-extensionality) - where +module foundation.morphisms-arrows where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/morphisms-binary-relations.lagda.md b/src/foundation/morphisms-binary-relations.lagda.md index 06b0427747..5e9c42e904 100644 --- a/src/foundation/morphisms-binary-relations.lagda.md +++ b/src/foundation/morphisms-binary-relations.lagda.md @@ -1,19 +1,14 @@ # Morphisms of binary relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.morphisms-binary-relations - (funext : function-extensionality) - where +module foundation.morphisms-binary-relations where ```
Imports ```agda -open import foundation.binary-homotopies funext -open import foundation.binary-relations funext +open import foundation.binary-homotopies +open import foundation.binary-relations open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/morphisms-coalgebras-maybe.lagda.md b/src/foundation/morphisms-coalgebras-maybe.lagda.md index 049b157edf..41c03ed586 100644 --- a/src/foundation/morphisms-coalgebras-maybe.lagda.md +++ b/src/foundation/morphisms-coalgebras-maybe.lagda.md @@ -1,25 +1,20 @@ # Morphisms of coalgebras of the maybe monad ```agda -open import foundation.function-extensionality-axiom - -module - foundation.morphisms-coalgebras-maybe - (funext : function-extensionality) - where +module foundation.morphisms-coalgebras-maybe where ```
Imports ```agda -open import foundation.coalgebras-maybe funext -open import foundation.commuting-squares-of-maps funext +open import foundation.coalgebras-maybe +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types open import foundation.universe-levels open import foundation-core.maybe -open import trees.polynomial-endofunctors funext +open import trees.polynomial-endofunctors ```
diff --git a/src/foundation/morphisms-double-arrows.lagda.md b/src/foundation/morphisms-double-arrows.lagda.md index 0e80732b07..33810a5de8 100644 --- a/src/foundation/morphisms-double-arrows.lagda.md +++ b/src/foundation/morphisms-double-arrows.lagda.md @@ -1,24 +1,19 @@ # Morphisms of double arrows ```agda -open import foundation.function-extensionality-axiom - -module - foundation.morphisms-double-arrows - (funext : function-extensionality) - where +module foundation.morphisms-double-arrows where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.commuting-squares-of-maps funext +open import foundation.cartesian-product-types +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.morphisms-arrows funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.morphisms-arrows open import foundation.universe-levels ``` diff --git a/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md b/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md index 255776a6b5..515f06b8ce 100644 --- a/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md +++ b/src/foundation/morphisms-inverse-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Morphisms of inverse sequential diagrams of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.morphisms-inverse-sequential-diagrams - (funext : function-extensionality) - where +module foundation.morphisms-inverse-sequential-diagrams where ```
Imports @@ -15,13 +10,13 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-homotopies funext -open import foundation.dependent-inverse-sequential-diagrams funext +open import foundation.binary-homotopies +open import foundation.dependent-inverse-sequential-diagrams open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext +open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.inverse-sequential-diagrams funext +open import foundation.homotopy-induction +open import foundation.inverse-sequential-diagrams open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/morphisms-span-diagrams.lagda.md b/src/foundation/morphisms-span-diagrams.lagda.md index 0f93f1d095..604d0c6d6e 100644 --- a/src/foundation/morphisms-span-diagrams.lagda.md +++ b/src/foundation/morphisms-span-diagrams.lagda.md @@ -1,25 +1,20 @@ # Morphisms of span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.morphisms-span-diagrams - (funext : function-extensionality) - where +module foundation.morphisms-span-diagrams where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows funext +open import foundation.morphisms-arrows open import foundation.morphisms-spans -open import foundation.operations-spans funext -open import foundation.span-diagrams funext +open import foundation.operations-spans +open import foundation.span-diagrams open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps ```
diff --git a/src/foundation/morphisms-spans-families-of-types.lagda.md b/src/foundation/morphisms-spans-families-of-types.lagda.md index 310d245cbc..8c372f1a61 100644 --- a/src/foundation/morphisms-spans-families-of-types.lagda.md +++ b/src/foundation/morphisms-spans-families-of-types.lagda.md @@ -1,22 +1,17 @@ # Morphisms of spans on families of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.morphisms-spans-families-of-types - (funext : function-extensionality) - where +module foundation.morphisms-spans-families-of-types where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-homotopies open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext +open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext +open import foundation.homotopy-induction open import foundation.spans-families-of-types open import foundation.structure-identity-principle open import foundation.universe-levels diff --git a/src/foundation/multisubsets.lagda.md b/src/foundation/multisubsets.lagda.md index f0a5cc7cc1..3819e8ba69 100644 --- a/src/foundation/multisubsets.lagda.md +++ b/src/foundation/multisubsets.lagda.md @@ -1,12 +1,7 @@ # Multisubsets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.multisubsets - (funext : function-extensionality) - where +module foundation.multisubsets where ```
Imports @@ -15,14 +10,14 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.images funext -open import foundation.negated-equality funext +open import foundation.images +open import foundation.negated-equality open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.sets -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/foundation/multivariable-correspondences.lagda.md b/src/foundation/multivariable-correspondences.lagda.md index 1148321a72..817901c593 100644 --- a/src/foundation/multivariable-correspondences.lagda.md +++ b/src/foundation/multivariable-correspondences.lagda.md @@ -1,12 +1,7 @@ # Multivariable correspondences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.multivariable-correspondences - (funext : function-extensionality) - where +module foundation.multivariable-correspondences where ```
Imports @@ -16,7 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/multivariable-decidable-relations.lagda.md b/src/foundation/multivariable-decidable-relations.lagda.md index 80cf44621b..9a5467028e 100644 --- a/src/foundation/multivariable-decidable-relations.lagda.md +++ b/src/foundation/multivariable-decidable-relations.lagda.md @@ -1,12 +1,7 @@ # Multivariable decidable relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.multivariable-decidable-relations - (funext : function-extensionality) - where +module foundation.multivariable-decidable-relations where ```
Imports @@ -14,12 +9,12 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-subtypes funext -open import foundation.multivariable-correspondences funext -open import foundation.multivariable-relations funext +open import foundation.decidable-subtypes +open import foundation.multivariable-correspondences +open import foundation.multivariable-relations open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/multivariable-functoriality-set-quotients.lagda.md b/src/foundation/multivariable-functoriality-set-quotients.lagda.md index aec02ce5ae..62cad9dc12 100644 --- a/src/foundation/multivariable-functoriality-set-quotients.lagda.md +++ b/src/foundation/multivariable-functoriality-set-quotients.lagda.md @@ -1,12 +1,7 @@ # Multivariable functoriality of set quotients ```agda -open import foundation.function-extensionality-axiom - -module - foundation.multivariable-functoriality-set-quotients - (funext : function-extensionality) - where +module foundation.multivariable-functoriality-set-quotients where ```
Imports @@ -14,18 +9,18 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.functoriality-set-quotients funext -open import foundation.set-quotients funext +open import foundation.functoriality-set-quotients +open import foundation.set-quotients open import foundation.universe-levels -open import foundation.vectors-set-quotients funext +open import foundation.vectors-set-quotients -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.function-types open import foundation-core.homotopies -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/multivariable-homotopies.lagda.md b/src/foundation/multivariable-homotopies.lagda.md index 83ec67d484..3d3588b02c 100644 --- a/src/foundation/multivariable-homotopies.lagda.md +++ b/src/foundation/multivariable-homotopies.lagda.md @@ -1,12 +1,7 @@ # Multivariable homotopies ```agda -open import foundation.function-extensionality-axiom - -module - foundation.multivariable-homotopies - (funext : function-extensionality) - where +module foundation.multivariable-homotopies where ```
Imports @@ -15,17 +10,17 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.function-extensionality funext - +open import foundation.equality-dependent-function-types +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.implicit-function-types -open import foundation.iterated-dependent-product-types funext +open import foundation.iterated-dependent-product-types open import foundation.telescopes open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.torsorial-type-families diff --git a/src/foundation/multivariable-operations.lagda.md b/src/foundation/multivariable-operations.lagda.md index 3dfa907628..fd82bdc4d4 100644 --- a/src/foundation/multivariable-operations.lagda.md +++ b/src/foundation/multivariable-operations.lagda.md @@ -1,12 +1,7 @@ # Multivariable operations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.multivariable-operations - (funext : function-extensionality) - where +module foundation.multivariable-operations where ```
Imports @@ -17,8 +12,8 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels @@ -29,7 +24,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import linear-algebra.vectors funext +open import linear-algebra.vectors ```
diff --git a/src/foundation/multivariable-relations.lagda.md b/src/foundation/multivariable-relations.lagda.md index 9b1d2bfbce..630c453e97 100644 --- a/src/foundation/multivariable-relations.lagda.md +++ b/src/foundation/multivariable-relations.lagda.md @@ -1,12 +1,7 @@ # Multivariable relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.multivariable-relations - (funext : function-extensionality) - where +module foundation.multivariable-relations where ```
Imports @@ -14,12 +9,12 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.multivariable-correspondences funext +open import foundation.multivariable-correspondences open import foundation.universe-levels -open import foundation-core.subtypes funext +open import foundation-core.subtypes -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/multivariable-sections.lagda.md b/src/foundation/multivariable-sections.lagda.md index 5c317627b2..f3fd8820d7 100644 --- a/src/foundation/multivariable-sections.lagda.md +++ b/src/foundation/multivariable-sections.lagda.md @@ -1,12 +1,7 @@ # Multivariable sections ```agda -open import foundation.function-extensionality-axiom - -module - foundation.multivariable-sections - (funext : function-extensionality) - where +module foundation.multivariable-sections where ```
Imports @@ -15,8 +10,8 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.iterated-dependent-product-types funext -open import foundation.multivariable-homotopies funext +open import foundation.iterated-dependent-product-types +open import foundation.multivariable-homotopies open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/negated-equality.lagda.md b/src/foundation/negated-equality.lagda.md index 3469298fcc..6978557244 100644 --- a/src/foundation/negated-equality.lagda.md +++ b/src/foundation/negated-equality.lagda.md @@ -1,21 +1,17 @@ # Negated equality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.negated-equality - (funext : function-extensionality) - where +module foundation.negated-equality where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.negation funext +open import foundation.function-extensionality-axiom +open import foundation.negation open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/negation.lagda.md b/src/foundation/negation.lagda.md index d3574d49fc..6e01b1d0a1 100644 --- a/src/foundation/negation.lagda.md +++ b/src/foundation/negation.lagda.md @@ -1,12 +1,7 @@ # Negation ```agda -open import foundation.function-extensionality-axiom - -module - foundation.negation - (funext : function-extensionality) - where +module foundation.negation where open import foundation-core.negation public ``` @@ -15,8 +10,8 @@ open import foundation-core.negation public ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.logical-equivalences funext +open import foundation.dependent-products-propositions +open import foundation.logical-equivalences open import foundation.universe-levels open import foundation-core.empty-types diff --git a/src/foundation/noncontractible-types.lagda.md b/src/foundation/noncontractible-types.lagda.md index 56e62a8088..98d2d49311 100644 --- a/src/foundation/noncontractible-types.lagda.md +++ b/src/foundation/noncontractible-types.lagda.md @@ -1,12 +1,7 @@ # Noncontractible types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.noncontractible-types - (funext : function-extensionality) - where +module foundation.noncontractible-types where ```
Imports @@ -15,8 +10,8 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.inhabited-types funext +open import foundation.empty-types +open import foundation.inhabited-types open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/null-homotopic-maps.lagda.md b/src/foundation/null-homotopic-maps.lagda.md index 7b73047a38..2500c019f4 100644 --- a/src/foundation/null-homotopic-maps.lagda.md +++ b/src/foundation/null-homotopic-maps.lagda.md @@ -1,38 +1,33 @@ # Null-homotopic maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.null-homotopic-maps - (funext : function-extensionality) - where +module foundation.null-homotopic-maps where ```
Imports ```agda -open import foundation.commuting-triangles-of-identifications funext -open import foundation.constant-maps funext +open import foundation.commuting-triangles-of-identifications +open import foundation.constant-maps open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.empty-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.inhabited-types funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.images +open import foundation.inhabited-types +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-empty-type funext +open import foundation.universal-property-empty-type open import foundation.universe-levels -open import foundation.weakly-constant-maps funext +open import foundation.weakly-constant-maps open import foundation-core.contractible-types open import foundation-core.equivalences diff --git a/src/foundation/operations-span-diagrams.lagda.md b/src/foundation/operations-span-diagrams.lagda.md index 6896795247..9337e9f12a 100644 --- a/src/foundation/operations-span-diagrams.lagda.md +++ b/src/foundation/operations-span-diagrams.lagda.md @@ -1,23 +1,18 @@ # Operations on span diagrams ```agda -open import foundation.function-extensionality-axiom +module foundation.operations-span-diagrams where -module - foundation.operations-span-diagrams - (funext : function-extensionality) - where - -open import foundation-core.operations-span-diagrams funext public +open import foundation-core.operations-span-diagrams public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences-arrows funext -open import foundation.operations-spans funext -open import foundation.span-diagrams funext +open import foundation.equivalences-arrows +open import foundation.operations-spans +open import foundation.span-diagrams open import foundation.spans open import foundation.universe-levels ``` diff --git a/src/foundation/operations-spans.lagda.md b/src/foundation/operations-spans.lagda.md index 9f589ec323..6562513941 100644 --- a/src/foundation/operations-spans.lagda.md +++ b/src/foundation/operations-spans.lagda.md @@ -1,22 +1,17 @@ # Operations on spans ```agda -open import foundation.function-extensionality-axiom +module foundation.operations-spans where -module - foundation.operations-spans - (funext : function-extensionality) - where - -open import foundation-core.operations-spans funext public +open import foundation-core.operations-spans public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences-arrows funext -open import foundation.morphisms-arrows funext +open import foundation.equivalences-arrows +open import foundation.morphisms-arrows open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/pairs-of-distinct-elements.lagda.md b/src/foundation/pairs-of-distinct-elements.lagda.md index 7d52cab993..8b152f6408 100644 --- a/src/foundation/pairs-of-distinct-elements.lagda.md +++ b/src/foundation/pairs-of-distinct-elements.lagda.md @@ -1,23 +1,18 @@ # Pairs of distinct elements ```agda -open import foundation.function-extensionality-axiom - -module - foundation.pairs-of-distinct-elements - (funext : function-extensionality) - where +module foundation.pairs-of-distinct-elements where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext +open import foundation.embeddings +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.negated-equality funext -open import foundation.negation funext +open import foundation.negated-equality +open import foundation.negation open import foundation.structure-identity-principle open import foundation.subtype-identity-principle open import foundation.universe-levels diff --git a/src/foundation/partitions.lagda.md b/src/foundation/partitions.lagda.md index 51af928f19..b46f3f5c10 100644 --- a/src/foundation/partitions.lagda.md +++ b/src/foundation/partitions.lagda.md @@ -1,37 +1,32 @@ # Partitions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.partitions - (funext : function-extensionality) - where +module foundation.partitions where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.conjunction funext -open import foundation.contractible-types funext +open import foundation.conjunction +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.fiber-inclusions funext +open import foundation.dependent-products-propositions +open import foundation.embeddings +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.fiber-inclusions open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-subtypes funext -open import foundation.inhabited-types funext -open import foundation.locally-small-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.sigma-decompositions funext -open import foundation.small-types funext +open import foundation.inhabited-subtypes +open import foundation.inhabited-types +open import foundation.locally-small-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.sigma-decompositions +open import foundation.small-types open import foundation.subtype-identity-principle -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -39,7 +34,7 @@ open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/path-algebra.lagda.md b/src/foundation/path-algebra.lagda.md index 1e09e92baa..471a4d85e1 100644 --- a/src/foundation/path-algebra.lagda.md +++ b/src/foundation/path-algebra.lagda.md @@ -1,12 +1,7 @@ # Path algebra ```agda -open import foundation.function-extensionality-axiom - -module - foundation.path-algebra - (funext : function-extensionality) - where +module foundation.path-algebra where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels open import foundation-core.commuting-squares-of-identifications diff --git a/src/foundation/path-cosplit-maps.lagda.md b/src/foundation/path-cosplit-maps.lagda.md index b46909a175..cf0e458b12 100644 --- a/src/foundation/path-cosplit-maps.lagda.md +++ b/src/foundation/path-cosplit-maps.lagda.md @@ -1,12 +1,7 @@ # Path-cosplit maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.path-cosplit-maps - (funext : function-extensionality) - where +module foundation.path-cosplit-maps where ```
Imports @@ -15,39 +10,38 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps funext -open import foundation.coproduct-types funext +open import foundation.commuting-triangles-of-maps +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.dependent-products-propositions funext -open import foundation.dependent-products-truncated-types funext -open import foundation.empty-types funext +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types +open import foundation.empty-types open import foundation.equality-cartesian-product-types -open import foundation.equality-coproduct-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences-arrows funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-action-on-identifications-functions funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.logical-equivalences funext -open import foundation.mere-path-cosplit-maps funext -open import foundation.morphisms-arrows funext -open import foundation.negated-equality funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-functions funext -open import foundation.propositional-truncations funext -open import foundation.retractions funext -open import foundation.retracts-of-maps funext -open import foundation.truncated-maps funext +open import foundation.equality-coproduct-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences-arrows +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-action-on-identifications-functions +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.iterated-dependent-product-types +open import foundation.logical-equivalences +open import foundation.mere-path-cosplit-maps +open import foundation.morphisms-arrows +open import foundation.negated-equality +open import foundation.postcomposition-functions +open import foundation.precomposition-functions +open import foundation.propositional-truncations +open import foundation.retractions +open import foundation.retracts-of-maps +open import foundation.truncated-maps open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/foundation/path-split-maps.lagda.md b/src/foundation/path-split-maps.lagda.md index 4a9e40a544..28223aec36 100644 --- a/src/foundation/path-split-maps.lagda.md +++ b/src/foundation/path-split-maps.lagda.md @@ -1,12 +1,7 @@ # Path-split maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.path-split-maps - (funext : function-extensionality) - where +module foundation.path-split-maps where open import foundation-core.path-split-maps public ``` @@ -15,9 +10,9 @@ open import foundation-core.path-split-maps public ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.iterated-dependent-product-types funext -open import foundation.logical-equivalences funext +open import foundation.equivalences +open import foundation.iterated-dependent-product-types +open import foundation.logical-equivalences open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/path-split-type-families.lagda.md b/src/foundation/path-split-type-families.lagda.md index 3c2d33fac1..0aad6110c8 100644 --- a/src/foundation/path-split-type-families.lagda.md +++ b/src/foundation/path-split-type-families.lagda.md @@ -1,12 +1,7 @@ # Path-split type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.path-split-type-families - (funext : function-extensionality) - where +module foundation.path-split-type-families where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.embeddings funext +open import foundation.dependent-products-contractible-types +open import foundation.embeddings open import foundation.transport-along-identifications open import foundation.universe-levels @@ -26,7 +21,7 @@ open import foundation-core.identity-types open import foundation-core.injective-maps open import foundation-core.propositions open import foundation-core.sections -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/perfect-images.lagda.md b/src/foundation/perfect-images.lagda.md index 9db1a591ef..2a0569e866 100644 --- a/src/foundation/perfect-images.lagda.md +++ b/src/foundation/perfect-images.lagda.md @@ -1,12 +1,7 @@ # Perfect images ```agda -open import foundation.function-extensionality-axiom - -module - foundation.perfect-images - (funext : function-extensionality) - where +module foundation.perfect-images where ```
Imports @@ -15,14 +10,14 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.iterated-dependent-product-types funext -open import foundation.iterating-functions funext -open import foundation.law-of-excluded-middle funext -open import foundation.negated-equality funext -open import foundation.negation funext +open import foundation.double-negation +open import foundation.iterated-dependent-product-types +open import foundation.iterating-functions +open import foundation.law-of-excluded-middle +open import foundation.negated-equality +open import foundation.negation open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/pi-decompositions-subuniverse.lagda.md b/src/foundation/pi-decompositions-subuniverse.lagda.md index b204251f70..940decfffb 100644 --- a/src/foundation/pi-decompositions-subuniverse.lagda.md +++ b/src/foundation/pi-decompositions-subuniverse.lagda.md @@ -1,20 +1,15 @@ # Π-decompositions of types into types in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - foundation.pi-decompositions-subuniverse - (funext : function-extensionality) - where +module foundation.pi-decompositions-subuniverse where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.pi-decompositions funext -open import foundation.subuniverses funext +open import foundation.pi-decompositions +open import foundation.subuniverses open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/pi-decompositions.lagda.md b/src/foundation/pi-decompositions.lagda.md index a47a21b6f6..dcbbb9f548 100644 --- a/src/foundation/pi-decompositions.lagda.md +++ b/src/foundation/pi-decompositions.lagda.md @@ -3,25 +3,20 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.pi-decompositions - (funext : function-extensionality) - where +module foundation.pi-decompositions where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-function-types funext +open import foundation.dependent-products-contractible-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.functoriality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/pointed-torsorial-type-families.lagda.md b/src/foundation/pointed-torsorial-type-families.lagda.md index a6e533b8d1..ac06797f4c 100644 --- a/src/foundation/pointed-torsorial-type-families.lagda.md +++ b/src/foundation/pointed-torsorial-type-families.lagda.md @@ -1,28 +1,23 @@ # Pointed torsorial type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.pointed-torsorial-type-families - (funext : function-extensionality) - where +module foundation.pointed-torsorial-type-families where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalences funext +open import foundation.dependent-products-propositions +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.locally-small-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.locally-small-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations open import foundation.sorial-type-families open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -30,7 +25,7 @@ open import foundation-core.contractible-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.small-types funext +open import foundation-core.small-types open import foundation-core.torsorial-type-families open import structured-types.pointed-types diff --git a/src/foundation/postcomposition-dependent-functions.lagda.md b/src/foundation/postcomposition-dependent-functions.lagda.md index a6f88b40db..f01cde3833 100644 --- a/src/foundation/postcomposition-dependent-functions.lagda.md +++ b/src/foundation/postcomposition-dependent-functions.lagda.md @@ -1,12 +1,7 @@ # Postcomposition of dependent functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.postcomposition-dependent-functions - (funext : function-extensionality) - where +module foundation.postcomposition-dependent-functions where open import foundation-core.postcomposition-dependent-functions public ``` @@ -15,12 +10,12 @@ open import foundation-core.postcomposition-dependent-functions public ```agda open import foundation.action-on-identifications-functions -open import foundation.function-extensionality funext - +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.identity-types ``` diff --git a/src/foundation/postcomposition-functions.lagda.md b/src/foundation/postcomposition-functions.lagda.md index 5fc3bc233f..247b3d1eb1 100644 --- a/src/foundation/postcomposition-functions.lagda.md +++ b/src/foundation/postcomposition-functions.lagda.md @@ -1,12 +1,7 @@ # Postcomposition of functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.postcomposition-functions - (funext : function-extensionality) - where +module foundation.postcomposition-functions where open import foundation-core.postcomposition-functions public ``` @@ -16,20 +11,20 @@ open import foundation-core.postcomposition-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.postcomposition-dependent-functions funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.postcomposition-dependent-functions open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/postcomposition-pullbacks.lagda.md b/src/foundation/postcomposition-pullbacks.lagda.md index bacad23184..7b3dc4fee2 100644 --- a/src/foundation/postcomposition-pullbacks.lagda.md +++ b/src/foundation/postcomposition-pullbacks.lagda.md @@ -1,23 +1,18 @@ # Postcomposition of pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.postcomposition-pullbacks - (funext : function-extensionality) - where +module foundation.postcomposition-pullbacks where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.standard-pullbacks funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.standard-pullbacks open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -27,8 +22,8 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.postcomposition-functions -open import foundation-core.pullbacks funext -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.pullbacks +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/powersets.lagda.md b/src/foundation/powersets.lagda.md index 18d5056158..e195cf37f9 100644 --- a/src/foundation/powersets.lagda.md +++ b/src/foundation/powersets.lagda.md @@ -1,46 +1,41 @@ # Powersets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.powersets - (funext : function-extensionality) - where +module foundation.powersets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.large-locale-of-propositions funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.large-locale-of-propositions +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels open import foundation-core.sets -open import order-theory.bottom-elements-large-posets funext -open import order-theory.bottom-elements-posets funext -open import order-theory.dependent-products-large-meet-semilattices funext -open import order-theory.dependent-products-large-posets funext -open import order-theory.dependent-products-large-preorders funext -open import order-theory.dependent-products-large-suplattices funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.large-suplattices funext -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.similarity-of-elements-large-posets funext -open import order-theory.suplattices funext -open import order-theory.top-elements-large-posets funext -open import order-theory.top-elements-posets funext +open import order-theory.bottom-elements-large-posets +open import order-theory.bottom-elements-posets +open import order-theory.dependent-products-large-meet-semilattices +open import order-theory.dependent-products-large-posets +open import order-theory.dependent-products-large-preorders +open import order-theory.dependent-products-large-suplattices +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.large-suplattices +open import order-theory.posets +open import order-theory.preorders +open import order-theory.similarity-of-elements-large-posets +open import order-theory.suplattices +open import order-theory.top-elements-large-posets +open import order-theory.top-elements-posets ```
diff --git a/src/foundation/precomposition-dependent-functions.lagda.md b/src/foundation/precomposition-dependent-functions.lagda.md index cb45239ca4..f7a092edc9 100644 --- a/src/foundation/precomposition-dependent-functions.lagda.md +++ b/src/foundation/precomposition-dependent-functions.lagda.md @@ -1,12 +1,7 @@ # Precomposition of dependent functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.precomposition-dependent-functions - (funext : function-extensionality) - where +module foundation.precomposition-dependent-functions where open import foundation-core.precomposition-dependent-functions public ``` @@ -16,18 +11,18 @@ open import foundation-core.precomposition-dependent-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.function-extensionality funext - +open import foundation.dependent-universal-property-equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncation-levels open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/precomposition-functions-into-subuniverses.lagda.md b/src/foundation/precomposition-functions-into-subuniverses.lagda.md index 75cf74b2bb..c6dcd9527c 100644 --- a/src/foundation/precomposition-functions-into-subuniverses.lagda.md +++ b/src/foundation/precomposition-functions-into-subuniverses.lagda.md @@ -1,12 +1,7 @@ # Precomposition of functions into subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - foundation.precomposition-functions-into-subuniverses - (funext : function-extensionality) - where +module foundation.precomposition-functions-into-subuniverses where ```
Imports @@ -14,7 +9,8 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.precomposition-functions funext +open import foundation.function-extensionality-axiom +open import foundation.precomposition-functions open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/precomposition-functions.lagda.md b/src/foundation/precomposition-functions.lagda.md index 4aac6bfe01..c8216b79b9 100644 --- a/src/foundation/precomposition-functions.lagda.md +++ b/src/foundation/precomposition-functions.lagda.md @@ -1,12 +1,7 @@ # Precomposition of functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.precomposition-functions - (funext : function-extensionality) - where +module foundation.precomposition-functions where open import foundation-core.precomposition-functions public ``` @@ -16,14 +11,14 @@ open import foundation-core.precomposition-functions public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.precomposition-dependent-functions funext -open import foundation.sections funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.precomposition-dependent-functions +open import foundation.sections open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.commuting-triangles-of-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation/precomposition-type-families.lagda.md b/src/foundation/precomposition-type-families.lagda.md index 52d180ac99..0d86dd8b97 100644 --- a/src/foundation/precomposition-type-families.lagda.md +++ b/src/foundation/precomposition-type-families.lagda.md @@ -1,19 +1,14 @@ # Precomposition of type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.precomposition-type-families - (funext : function-extensionality) - where +module foundation.precomposition-type-families where ```
Imports ```agda -open import foundation.homotopy-induction funext -open import foundation.transport-along-homotopies funext +open import foundation.homotopy-induction +open import foundation.transport-along-homotopies open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/preunivalence.lagda.md b/src/foundation/preunivalence.lagda.md index 6832bf367d..9fe3c4409c 100644 --- a/src/foundation/preunivalence.lagda.md +++ b/src/foundation/preunivalence.lagda.md @@ -1,26 +1,21 @@ # The preunivalence axiom ```agda -open import foundation.function-extensionality-axiom - -module - foundation.preunivalence - (funext : function-extensionality) - where +module foundation.preunivalence where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.sets funext -open import foundation.univalence funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.sets +open import foundation.univalence open import foundation.universe-levels open import foundation-core.identity-types -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/preunivalent-type-families.lagda.md b/src/foundation/preunivalent-type-families.lagda.md index 2efee40de9..933a182ad5 100644 --- a/src/foundation/preunivalent-type-families.lagda.md +++ b/src/foundation/preunivalent-type-families.lagda.md @@ -1,29 +1,24 @@ # Preunivalent type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.preunivalent-type-families - (funext : function-extensionality) - where +module foundation.preunivalent-type-families where ```
Imports ```agda -open import foundation.0-maps funext +open import foundation.0-maps open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalence-injective-type-families funext -open import foundation.faithful-maps funext -open import foundation.function-types funext -open import foundation.injective-maps funext -open import foundation.preunivalence funext -open import foundation.retractions funext -open import foundation.sets funext -open import foundation.subuniverses funext +open import foundation.embeddings +open import foundation.equivalence-injective-type-families +open import foundation.faithful-maps +open import foundation.function-types +open import foundation.injective-maps +open import foundation.preunivalence +open import foundation.retractions +open import foundation.sets +open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/foundation/principle-of-omniscience.lagda.md b/src/foundation/principle-of-omniscience.lagda.md index 0b7bc97076..6b5ce7a3d1 100644 --- a/src/foundation/principle-of-omniscience.lagda.md +++ b/src/foundation/principle-of-omniscience.lagda.md @@ -1,23 +1,18 @@ # The principle of omniscience ```agda -open import foundation.function-extensionality-axiom - -module - foundation.principle-of-omniscience - (funext : function-extensionality) - where +module foundation.principle-of-omniscience where ```
Imports ```agda -open import foundation.decidable-subtypes funext -open import foundation.dependent-products-propositions funext -open import foundation.propositional-truncations funext +open import foundation.decidable-subtypes +open import foundation.dependent-products-propositions +open import foundation.propositional-truncations open import foundation.universe-levels -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.propositions ``` diff --git a/src/foundation/product-decompositions-subuniverse.lagda.md b/src/foundation/product-decompositions-subuniverse.lagda.md index dcedaf6118..cb4513fe87 100644 --- a/src/foundation/product-decompositions-subuniverse.lagda.md +++ b/src/foundation/product-decompositions-subuniverse.lagda.md @@ -1,28 +1,23 @@ # Product decompositions of types in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - foundation.product-decompositions-subuniverse - (funext : function-extensionality) - where +module foundation.product-decompositions-subuniverse where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.dependent-products-propositions funext -open import foundation.equivalences funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.subuniverses funext +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions +open import foundation.equivalences +open import foundation.raising-universe-levels-unit-type +open import foundation.subuniverses open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/products-binary-relations.lagda.md b/src/foundation/products-binary-relations.lagda.md index 8c051bf627..93f4ce0c07 100644 --- a/src/foundation/products-binary-relations.lagda.md +++ b/src/foundation/products-binary-relations.lagda.md @@ -1,18 +1,13 @@ # Products of binary relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.products-binary-relations - (funext : function-extensionality) - where +module foundation.products-binary-relations where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/products-equivalence-relations.lagda.md b/src/foundation/products-equivalence-relations.lagda.md index 73bb6f7de8..37e2364b6d 100644 --- a/src/foundation/products-equivalence-relations.lagda.md +++ b/src/foundation/products-equivalence-relations.lagda.md @@ -1,24 +1,19 @@ # Products of equivalence relataions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.products-equivalence-relations - (funext : function-extensionality) - where +module foundation.products-equivalence-relations where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.products-binary-relations funext +open import foundation.products-binary-relations open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations ```
diff --git a/src/foundation/products-of-tuples-of-types.lagda.md b/src/foundation/products-of-tuples-of-types.lagda.md index 64591a9c2b..0fc4d95508 100644 --- a/src/foundation/products-of-tuples-of-types.lagda.md +++ b/src/foundation/products-of-tuples-of-types.lagda.md @@ -1,12 +1,7 @@ # Products of tuples of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.products-of-tuples-of-types - (funext : function-extensionality) - where +module foundation.products-of-tuples-of-types where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.tuples-of-types funext +open import foundation.tuples-of-types open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/products-pullbacks.lagda.md b/src/foundation/products-pullbacks.lagda.md index 7cf32c29b7..acd174310d 100644 --- a/src/foundation/products-pullbacks.lagda.md +++ b/src/foundation/products-pullbacks.lagda.md @@ -1,25 +1,20 @@ # Products of pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.products-pullbacks - (funext : function-extensionality) - where +module foundation.products-pullbacks where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types funext -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext -open import foundation.pullbacks funext -open import foundation.standard-pullbacks funext +open import foundation.functoriality-cartesian-product-types +open import foundation.inhabited-types +open import foundation.propositional-truncations +open import foundation.pullbacks +open import foundation.standard-pullbacks open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels @@ -29,7 +24,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/products-unordered-pairs-of-types.lagda.md b/src/foundation/products-unordered-pairs-of-types.lagda.md index 9e3fe90acb..73d194ded8 100644 --- a/src/foundation/products-unordered-pairs-of-types.lagda.md +++ b/src/foundation/products-unordered-pairs-of-types.lagda.md @@ -1,33 +1,28 @@ # Products of unordered pairs of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.products-unordered-pairs-of-types - (funext : function-extensionality) - where +module foundation.products-unordered-pairs-of-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.symmetric-operations funext +open import foundation.dependent-universal-property-equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.symmetric-operations open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.unordered-pairs funext -open import foundation.unordered-pairs funext-of-types +open import foundation.unordered-pairs +open import foundation.unordered-pairs-of-types open import foundation-core.cartesian-product-types open import foundation-core.equivalences open import foundation-core.function-types -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.universal-property-standard-finite-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.universal-property-standard-finite-types ```
diff --git a/src/foundation/products-unordered-tuples-of-types.lagda.md b/src/foundation/products-unordered-tuples-of-types.lagda.md index ccceace7d7..c33e6374ef 100644 --- a/src/foundation/products-unordered-tuples-of-types.lagda.md +++ b/src/foundation/products-unordered-tuples-of-types.lagda.md @@ -1,12 +1,7 @@ # Products of unordered tuples of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.products-unordered-tuples-of-types - (funext : function-extensionality) - where +module foundation.products-unordered-tuples-of-types where ```
Imports @@ -15,16 +10,16 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types funext -open import foundation.universal-property-maybe funext +open import foundation.functoriality-dependent-function-types +open import foundation.universal-property-maybe open import foundation.universe-levels -open import foundation.unordered-tuples funext -open import foundation.unordered-tuples funext-of-types +open import foundation.unordered-tuples +open import foundation.unordered-tuples-of-types open import foundation-core.cartesian-product-types open import foundation-core.equivalences -open import univalent-combinatorics.complements-isolated-elements funext +open import univalent-combinatorics.complements-isolated-elements ```
diff --git a/src/foundation/projective-types.lagda.md b/src/foundation/projective-types.lagda.md index 30fea2599e..f537366853 100644 --- a/src/foundation/projective-types.lagda.md +++ b/src/foundation/projective-types.lagda.md @@ -1,12 +1,7 @@ # Projective types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.projective-types - (funext : function-extensionality) - where +module foundation.projective-types where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-maps funext -open import foundation.postcomposition-functions funext -open import foundation.surjective-maps funext +open import foundation.connected-maps +open import foundation.postcomposition-functions +open import foundation.surjective-maps open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/foundation/proper-subtypes.lagda.md b/src/foundation/proper-subtypes.lagda.md index d1183221ee..2ca5864332 100644 --- a/src/foundation/proper-subtypes.lagda.md +++ b/src/foundation/proper-subtypes.lagda.md @@ -1,23 +1,18 @@ # Proper subsets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.proper-subtypes - (funext : function-extensionality) - where +module foundation.proper-subtypes where ```
Imports ```agda -open import foundation.complements-subtypes funext -open import foundation.inhabited-subtypes funext +open import foundation.complements-subtypes +open import foundation.inhabited-subtypes open import foundation.universe-levels open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/propositional-extensionality.lagda.md b/src/foundation/propositional-extensionality.lagda.md index 7965ff0291..3d3e72c471 100644 --- a/src/foundation/propositional-extensionality.lagda.md +++ b/src/foundation/propositional-extensionality.lagda.md @@ -1,35 +1,30 @@ # Propositional extensionality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.propositional-extensionality - (funext : function-extensionality) - where +module foundation.propositional-extensionality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.dependent-products-propositions funext -open import foundation.empty-types funext +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions +open import foundation.empty-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.postcomposition-functions funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.postcomposition-functions +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.subtype-identity-principle open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type -open import foundation.univalence funext -open import foundation.univalent-type-families funext -open import foundation.universal-property-contractible-types funext -open import foundation.universal-property-empty-type funext +open import foundation.univalence +open import foundation.univalent-type-families +open import foundation.universal-property-contractible-types +open import foundation.universal-property-empty-type open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/propositional-maps.lagda.md b/src/foundation/propositional-maps.lagda.md index 3e12f14837..00de80bd25 100644 --- a/src/foundation/propositional-maps.lagda.md +++ b/src/foundation/propositional-maps.lagda.md @@ -1,12 +1,7 @@ # Propositional maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.propositional-maps - (funext : function-extensionality) - where +module foundation.propositional-maps where open import foundation-core.propositional-maps public ``` @@ -15,10 +10,10 @@ open import foundation-core.propositional-maps public ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext -open import foundation.logical-equivalences funext -open import foundation.truncated-maps funext +open import foundation.dependent-products-propositions +open import foundation.embeddings +open import foundation.logical-equivalences +open import foundation.truncated-maps open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/propositional-resizing.lagda.md b/src/foundation/propositional-resizing.lagda.md index 5c4017d869..22cb73035d 100644 --- a/src/foundation/propositional-resizing.lagda.md +++ b/src/foundation/propositional-resizing.lagda.md @@ -1,25 +1,20 @@ # Propositional resizing ```agda -open import foundation.function-extensionality-axiom - -module - foundation.propositional-resizing - (funext : function-extensionality) - where +module foundation.propositional-resizing where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-propositions open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.propositions -open import foundation-core.small-types funext -open import foundation-core.subtypes funext +open import foundation-core.small-types +open import foundation-core.subtypes ```
diff --git a/src/foundation/propositional-truncations.lagda.md b/src/foundation/propositional-truncations.lagda.md index 4c48cc036f..c9ae9be7fc 100644 --- a/src/foundation/propositional-truncations.lagda.md +++ b/src/foundation/propositional-truncations.lagda.md @@ -1,12 +1,7 @@ # Propositional truncations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.propositional-truncations - (funext : function-extensionality) - where +module foundation.propositional-truncations where ```
Imports @@ -14,12 +9,12 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.truncations funext -open import foundation.universal-property-propositional-truncation funext +open import foundation.dependent-products-propositions +open import foundation.functoriality-cartesian-product-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.truncations +open import foundation.universal-property-propositional-truncation open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/propositions.lagda.md b/src/foundation/propositions.lagda.md index 3df756f6f0..75b2a12684 100644 --- a/src/foundation/propositions.lagda.md +++ b/src/foundation/propositions.lagda.md @@ -1,25 +1,20 @@ # Propositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.propositions - (funext : function-extensionality) - where +module foundation.propositions where open import foundation-core.propositions public -open import foundation.dependent-products-propositions funext public +open import foundation.dependent-products-propositions public ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.logical-equivalences funext -open import foundation.retracts-of-types funext +open import foundation.fibers-of-maps +open import foundation.logical-equivalences +open import foundation.retracts-of-types open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/pullback-cones.lagda.md b/src/foundation/pullback-cones.lagda.md index 648277cb32..5a098e4403 100644 --- a/src/foundation/pullback-cones.lagda.md +++ b/src/foundation/pullback-cones.lagda.md @@ -1,34 +1,29 @@ # Pullback cones ```agda -open import foundation.function-extensionality-axiom - -module - foundation.pullback-cones - (funext : function-extensionality) - where +module foundation.pullback-cones where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cartesian-product-types +open import foundation.cones-over-cospan-diagrams open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.pullbacks funext -open import foundation.standard-pullbacks funext +open import foundation.identity-types +open import foundation.pullbacks +open import foundation.standard-pullbacks open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-cartesian-product-types open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/pullbacks-subtypes.lagda.md b/src/foundation/pullbacks-subtypes.lagda.md index a963732d28..f2f6b26b72 100644 --- a/src/foundation/pullbacks-subtypes.lagda.md +++ b/src/foundation/pullbacks-subtypes.lagda.md @@ -1,27 +1,22 @@ # Pullbacks of subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.pullbacks-subtypes - (funext : function-extensionality) - where +module foundation.pullbacks-subtypes where ```
Imports ```agda -open import foundation.logical-equivalences funext -open import foundation.powersets funext +open import foundation.logical-equivalences +open import foundation.powersets open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders ```
diff --git a/src/foundation/pullbacks.lagda.md b/src/foundation/pullbacks.lagda.md index ace892e282..db2de5b6a1 100644 --- a/src/foundation/pullbacks.lagda.md +++ b/src/foundation/pullbacks.lagda.md @@ -1,14 +1,9 @@ # Pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.pullbacks - (funext : function-extensionality) - where +module foundation.pullbacks where -open import foundation-core.pullbacks funext public +open import foundation-core.pullbacks public ```
Imports @@ -16,17 +11,17 @@ open import foundation-core.pullbacks funext public ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-cubes-of-maps funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.commuting-cubes-of-maps +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.dependent-sums-pullbacks funext -open import foundation.descent-equivalences funext +open import foundation.dependent-sums-pullbacks +open import foundation.descent-equivalences open import foundation.equality-cartesian-product-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.standard-pullbacks funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.standard-pullbacks +open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/quasicoherently-idempotent-maps.lagda.md b/src/foundation/quasicoherently-idempotent-maps.lagda.md index 8eb8001436..0cda3d0440 100644 --- a/src/foundation/quasicoherently-idempotent-maps.lagda.md +++ b/src/foundation/quasicoherently-idempotent-maps.lagda.md @@ -1,32 +1,27 @@ # Quasicoherently idempotent maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.quasicoherently-idempotent-maps - (funext : function-extensionality) - where +module foundation.quasicoherently-idempotent-maps where ```
Imports ```agda -open import foundation.1-types funext +open import foundation.1-types open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-homotopies open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equality-dependent-pair-types funext +open import foundation.dependent-products-propositions +open import foundation.equality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-algebra -open import foundation.homotopy-induction funext -open import foundation.idempotent-maps funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext +open import foundation.homotopy-induction +open import foundation.idempotent-maps +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition @@ -39,8 +34,8 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.sets -open import synthetic-homotopy-theory.circle funext -open import synthetic-homotopy-theory.loop-homotopy-circle funext +open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.loop-homotopy-circle ```
diff --git a/src/foundation/raising-universe-levels-booleans.lagda.md b/src/foundation/raising-universe-levels-booleans.lagda.md index c904cc43e7..a94fd6c0e0 100644 --- a/src/foundation/raising-universe-levels-booleans.lagda.md +++ b/src/foundation/raising-universe-levels-booleans.lagda.md @@ -1,18 +1,13 @@ # Raising universe levels of the booleans ```agda -open import foundation.function-extensionality-axiom - -module - foundation.raising-universe-levels-booleans - (funext : function-extensionality) - where +module foundation.raising-universe-levels-booleans where ```
Imports ```agda -open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels open import foundation.universe-levels open import foundation-core.booleans diff --git a/src/foundation/raising-universe-levels-unit-type.lagda.md b/src/foundation/raising-universe-levels-unit-type.lagda.md index 4b5e5bb9a8..c8315fa606 100644 --- a/src/foundation/raising-universe-levels-unit-type.lagda.md +++ b/src/foundation/raising-universe-levels-unit-type.lagda.md @@ -1,12 +1,7 @@ # Raising universe levels for the unit type ```agda -open import foundation.function-extensionality-axiom - -module - foundation.raising-universe-levels-unit-type - (funext : function-extensionality) - where +module foundation.raising-universe-levels-unit-type where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.raising-universe-levels funext +open import foundation.raising-universe-levels open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/raising-universe-levels.lagda.md b/src/foundation/raising-universe-levels.lagda.md index 1516f42d0b..052c944420 100644 --- a/src/foundation/raising-universe-levels.lagda.md +++ b/src/foundation/raising-universe-levels.lagda.md @@ -1,12 +1,7 @@ # Raising universe levels ```agda -open import foundation.function-extensionality-axiom - -module - foundation.raising-universe-levels - (funext : function-extensionality) - where +module foundation.raising-universe-levels where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.univalence funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.univalence open import foundation.universe-levels open import foundation-core.contractible-types @@ -27,7 +22,7 @@ open import foundation-core.homotopies open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/reflecting-maps-equivalence-relations.lagda.md b/src/foundation/reflecting-maps-equivalence-relations.lagda.md index 9f794d93b0..dda9020f8c 100644 --- a/src/foundation/reflecting-maps-equivalence-relations.lagda.md +++ b/src/foundation/reflecting-maps-equivalence-relations.lagda.md @@ -1,26 +1,21 @@ # Reflecting maps for equivalence relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.reflecting-maps-equivalence-relations - (funext : function-extensionality) - where +module foundation.reflecting-maps-equivalence-relations where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.effective-maps-equivalence-relations funext +open import foundation.dependent-products-propositions +open import foundation.effective-maps-equivalence-relations open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext +open import foundation.homotopy-induction open import foundation.subtype-identity-principle open import foundation.universe-levels -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/reflexive-relations.lagda.md b/src/foundation/reflexive-relations.lagda.md index b29536521c..0953b7c3f4 100644 --- a/src/foundation/reflexive-relations.lagda.md +++ b/src/foundation/reflexive-relations.lagda.md @@ -1,19 +1,14 @@ # Reflexive relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.reflexive-relations - (funext : function-extensionality) - where +module foundation.reflexive-relations where ```
Imports ```agda open import foundation.binary-dependent-identifications -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md b/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md index 4567c1f572..c830446ce5 100644 --- a/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md +++ b/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md @@ -9,30 +9,30 @@ module
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.connected-maps funext -open import foundation.connected-types funext +open import foundation.0-connected-types +open import foundation.connected-maps +open import foundation.connected-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fiber-inclusions funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.functoriality-truncation funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.logical-equivalences funext -open import foundation.maps-in-subuniverses funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.separated-types-subuniverses funext -open import foundation.structured-equality-duality funext -open import foundation.subuniverses funext -open import foundation.surjective-maps funext -open import foundation.truncated-maps funext -open import foundation.truncated-types funext +open import foundation.equivalences +open import foundation.fiber-inclusions +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-propositional-truncation +open import foundation.functoriality-truncation +open import foundation.homotopies +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.logical-equivalences +open import foundation.maps-in-subuniverses +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.separated-types-subuniverses +open import foundation.structured-equality-duality +open import foundation.subuniverses +open import foundation.surjective-maps +open import foundation.truncated-maps +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels ``` @@ -89,12 +89,7 @@ agda-unimath. ### The extended fundamental theorem of identity types ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {l1 l2 l3 : Level} (𝒫 : subuniverse (l1 ⊔ l2) l3) {A : UU l1} (a : A) {B : A → UU l2} where diff --git a/src/foundation/relaxed-sigma-decompositions.lagda.md b/src/foundation/relaxed-sigma-decompositions.lagda.md index 4076fe726c..9280f10597 100644 --- a/src/foundation/relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/relaxed-sigma-decompositions.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.relaxed-sigma-decompositions - (funext : function-extensionality) - where +module foundation.relaxed-sigma-decompositions where ```
Imports @@ -16,14 +11,14 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext +open import foundation.dependent-products-contractible-types +open import foundation.equivalence-extensionality +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.transposition-identifications-along-equivalences open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/repetitions-of-values.lagda.md b/src/foundation/repetitions-of-values.lagda.md index 790013c514..cbecce73b5 100644 --- a/src/foundation/repetitions-of-values.lagda.md +++ b/src/foundation/repetitions-of-values.lagda.md @@ -1,12 +1,7 @@ # Repetitions of values of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.repetitions-of-values - (funext : function-extensionality) - where +module foundation.repetitions-of-values where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.pairs-of-distinct-elements funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.pairs-of-distinct-elements open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies diff --git a/src/foundation/repetitions-sequences.lagda.md b/src/foundation/repetitions-sequences.lagda.md index 7a05dd2225..c52b33a71d 100644 --- a/src/foundation/repetitions-sequences.lagda.md +++ b/src/foundation/repetitions-sequences.lagda.md @@ -1,25 +1,20 @@ # Repetitions in sequences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.repetitions-sequences - (funext : function-extensionality) - where +module foundation.repetitions-sequences where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers funext +open import elementary-number-theory.strictly-ordered-pairs-of-natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.negated-equality funext -open import foundation.pairs-of-distinct-elements funext -open import foundation.repetitions-of-values funext +open import foundation.negated-equality +open import foundation.pairs-of-distinct-elements +open import foundation.repetitions-of-values open import foundation.sequences open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/replacement.lagda.md b/src/foundation/replacement.lagda.md index 41f27cbe3b..f399430bcb 100644 --- a/src/foundation/replacement.lagda.md +++ b/src/foundation/replacement.lagda.md @@ -1,22 +1,17 @@ # The type theoretic replacement axiom ```agda -open import foundation.function-extensionality-axiom - -module - foundation.replacement - (funext : function-extensionality) - where +module foundation.replacement where ```
Imports ```agda -open import foundation.images funext -open import foundation.locally-small-types funext +open import foundation.images +open import foundation.locally-small-types open import foundation.universe-levels -open import foundation-core.small-types funext +open import foundation-core.small-types ```
diff --git a/src/foundation/retractions.lagda.md b/src/foundation/retractions.lagda.md index c5fa68eb0d..afabb0426b 100644 --- a/src/foundation/retractions.lagda.md +++ b/src/foundation/retractions.lagda.md @@ -1,12 +1,7 @@ # Retractions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.retractions - (funext : function-extensionality) - where +module foundation.retractions where open import foundation-core.retractions public ``` @@ -15,9 +10,9 @@ open import foundation-core.retractions public ```agda open import foundation.action-on-identifications-functions -open import foundation.coslice funext +open import foundation.coslice open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext +open import foundation.dependent-products-truncated-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/retracts-of-maps.lagda.md b/src/foundation/retracts-of-maps.lagda.md index 878bf112f5..4a6ba64557 100644 --- a/src/foundation/retracts-of-maps.lagda.md +++ b/src/foundation/retracts-of-maps.lagda.md @@ -1,35 +1,29 @@ # Retracts of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.retracts-of-maps - (funext : function-extensionality) - where +module foundation.retracts-of-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-prisms-of-maps funext -open import foundation.commuting-triangles-of-morphisms-arrows funext +open import foundation.commuting-prisms-of-maps +open import foundation.commuting-triangles-of-morphisms-arrows open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-fibers-of-maps funext -open import foundation.homotopies-morphisms-arrows funext +open import foundation.diagonal-maps-of-types +open import foundation.function-extensionality +open import foundation.functoriality-fibers-of-maps +open import foundation.homotopies-morphisms-arrows open import foundation.homotopy-algebra -open import foundation.morphisms-arrows funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-functions funext -open import foundation.retracts-of-types funext +open import foundation.morphisms-arrows +open import foundation.postcomposition-functions +open import foundation.precomposition-functions +open import foundation.retracts-of-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.constant-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps diff --git a/src/foundation/retracts-of-types.lagda.md b/src/foundation/retracts-of-types.lagda.md index 3d81ed7742..e180da55c5 100644 --- a/src/foundation/retracts-of-types.lagda.md +++ b/src/foundation/retracts-of-types.lagda.md @@ -1,12 +1,7 @@ # Retracts of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.retracts-of-types - (funext : function-extensionality) - where +module foundation.retracts-of-types where open import foundation-core.retracts-of-types public ``` @@ -15,16 +10,15 @@ open import foundation-core.retracts-of-types public ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - +open import foundation.equivalences +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.homotopy-induction funext -open import foundation.logical-equivalences funext +open import foundation.homotopy-induction +open import foundation.logical-equivalences open import foundation.structure-identity-principle -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/sections.lagda.md b/src/foundation/sections.lagda.md index d978649891..0ec87899b6 100644 --- a/src/foundation/sections.lagda.md +++ b/src/foundation/sections.lagda.md @@ -1,12 +1,7 @@ # Sections ```agda -open import foundation.function-extensionality-axiom - -module - foundation.sections - (funext : function-extensionality) - where +module foundation.sections where open import foundation-core.sections public ``` @@ -15,11 +10,10 @@ open import foundation-core.sections public ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-homotopies open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.function-extensionality funext - +open import foundation.dependent-products-contractible-types +open import foundation.function-extensionality open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/separated-types-subuniverses.lagda.md b/src/foundation/separated-types-subuniverses.lagda.md index 4cc9ff08b8..cb0571d472 100644 --- a/src/foundation/separated-types-subuniverses.lagda.md +++ b/src/foundation/separated-types-subuniverses.lagda.md @@ -1,19 +1,14 @@ # Types separated at subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - foundation.separated-types-subuniverses - (funext : function-extensionality) - where +module foundation.separated-types-subuniverses where ```
Imports ```agda -open import foundation.dependent-products-propositions funext -open import foundation.subuniverses funext +open import foundation.dependent-products-propositions +open import foundation.subuniverses open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/sequential-limits.lagda.md b/src/foundation/sequential-limits.lagda.md index c37321519a..f2891ee0db 100644 --- a/src/foundation/sequential-limits.lagda.md +++ b/src/foundation/sequential-limits.lagda.md @@ -1,12 +1,7 @@ # Sequential limits ```agda -open import foundation.function-extensionality-axiom - -module - foundation.sequential-limits - (funext : function-extensionality) - where +module foundation.sequential-limits where ```
Imports @@ -15,15 +10,15 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cones-over-inverse-sequential-diagrams funext +open import foundation.cones-over-inverse-sequential-diagrams open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.inverse-sequential-diagrams funext +open import foundation.homotopy-induction +open import foundation.inverse-sequential-diagrams open import foundation.structure-identity-principle -open import foundation.universal-property-sequential-limits funext +open import foundation.universal-property-sequential-limits open import foundation.universe-levels open import foundation-core.commuting-squares-of-homotopies diff --git a/src/foundation/set-presented-types.lagda.md b/src/foundation/set-presented-types.lagda.md index d5b6a411a5..ae88a8fae8 100644 --- a/src/foundation/set-presented-types.lagda.md +++ b/src/foundation/set-presented-types.lagda.md @@ -1,36 +1,31 @@ # Set presented types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.set-presented-types - (funext : function-extensionality) - where +module foundation.set-presented-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equality-coproduct-types funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.fibers-of-maps funext -open import foundation.functoriality-coproduct-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.injective-maps funext -open import foundation.propositional-truncations funext -open import foundation.set-truncations funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.dependent-products-propositions +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equality-coproduct-types +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.fibers-of-maps +open import foundation.functoriality-coproduct-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.images +open import foundation.injective-maps +open import foundation.propositional-truncations +open import foundation.set-truncations +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/set-quotients.lagda.md b/src/foundation/set-quotients.lagda.md index 3cd4071dff..883cf8111f 100644 --- a/src/foundation/set-quotients.lagda.md +++ b/src/foundation/set-quotients.lagda.md @@ -1,12 +1,7 @@ # Set quotients ```agda -open import foundation.function-extensionality-axiom - -module - foundation.set-quotients - (funext : function-extensionality) - where +module foundation.set-quotients where ```
Imports @@ -14,30 +9,31 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.effective-maps-equivalence-relations funext -open import foundation.embeddings funext -open import foundation.equivalence-classes funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.inhabited-subtypes funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.sets funext -open import foundation.slice funext -open import foundation.surjective-maps funext -open import foundation.uniqueness-set-quotients funext -open import foundation.universal-property-image funext -open import foundation.universal-property-set-quotients funext +open import foundation.dependent-products-propositions +open import foundation.effective-maps-equivalence-relations +open import foundation.embeddings +open import foundation.equivalence-classes +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.inhabited-subtypes +open import foundation.reflecting-maps-equivalence-relations +open import foundation.sets +open import foundation.slice +open import foundation.surjective-maps +open import foundation.uniqueness-set-quotients +open import foundation.universal-property-image +open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.homotopies open import foundation-core.propositions -open import foundation-core.small-types funext -open import foundation-core.subtypes funext +open import foundation-core.small-types +open import foundation-core.subtypes ```
diff --git a/src/foundation/set-truncations.lagda.md b/src/foundation/set-truncations.lagda.md index 8eb92139c8..154cc2d2b5 100644 --- a/src/foundation/set-truncations.lagda.md +++ b/src/foundation/set-truncations.lagda.md @@ -3,36 +3,31 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.set-truncations - (funext : function-extensionality) - where +module foundation.set-truncations where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations funext -open import foundation.equality-coproduct-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.mere-equality funext -open import foundation.postcomposition-functions funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.sets funext -open import foundation.slice funext -open import foundation.surjective-maps funext -open import foundation.truncations funext -open import foundation.uniqueness-set-truncations funext +open import foundation.effective-maps-equivalence-relations +open import foundation.equality-coproduct-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.mere-equality +open import foundation.postcomposition-functions +open import foundation.reflecting-maps-equivalence-relations +open import foundation.sets +open import foundation.slice +open import foundation.surjective-maps +open import foundation.truncations +open import foundation.uniqueness-set-truncations open import foundation.unit-type -open import foundation.universal-property-coproduct-types funext -open import foundation.universal-property-dependent-pair-types funext -open import foundation.universal-property-image funext -open import foundation.universal-property-set-quotients funext -open import foundation.universal-property-set-truncation funext +open import foundation.universal-property-coproduct-types +open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-image +open import foundation.universal-property-set-quotients +open import foundation.universal-property-set-truncation open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -42,7 +37,7 @@ open import foundation-core.embeddings open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/sets.lagda.md b/src/foundation/sets.lagda.md index 98b29c759f..f486be35a9 100644 --- a/src/foundation/sets.lagda.md +++ b/src/foundation/sets.lagda.md @@ -1,12 +1,7 @@ # Sets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.sets - (funext : function-extensionality) - where +module foundation.sets where open import foundation-core.sets public ``` @@ -14,16 +9,16 @@ open import foundation-core.sets public
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.logical-equivalences funext -open import foundation.subuniverses funext -open import foundation.truncated-types funext -open import foundation.univalent-type-families funext +open import foundation.dependent-products-truncated-types +open import foundation.logical-equivalences +open import foundation.subuniverses +open import foundation.truncated-types +open import foundation.univalent-type-families open import foundation.universe-levels -open import foundation-core.1-types funext +open import foundation-core.1-types open import foundation-core.cartesian-product-types open import foundation-core.embeddings open import foundation-core.equivalences @@ -32,7 +27,7 @@ open import foundation-core.injective-maps open import foundation-core.precomposition-functions open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families open import foundation-core.truncation-levels ``` diff --git a/src/foundation/sigma-closed-subuniverses.lagda.md b/src/foundation/sigma-closed-subuniverses.lagda.md index b9ce18011c..29e8d7b87a 100644 --- a/src/foundation/sigma-closed-subuniverses.lagda.md +++ b/src/foundation/sigma-closed-subuniverses.lagda.md @@ -1,19 +1,14 @@ # Σ-closed subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - foundation.sigma-closed-subuniverses - (funext : function-extensionality) - where +module foundation.sigma-closed-subuniverses where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.subuniverses funext +open import foundation.subuniverses open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/sigma-decomposition-subuniverse.lagda.md b/src/foundation/sigma-decomposition-subuniverse.lagda.md index 168d2c9160..ef0e6e73f6 100644 --- a/src/foundation/sigma-decomposition-subuniverse.lagda.md +++ b/src/foundation/sigma-decomposition-subuniverse.lagda.md @@ -1,20 +1,15 @@ # Σ-decompositions of types into types in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - foundation.sigma-decomposition-subuniverse - (funext : function-extensionality) - where +module foundation.sigma-decomposition-subuniverse where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.relaxed-sigma-decompositions funext -open import foundation.subuniverses funext +open import foundation.relaxed-sigma-decompositions +open import foundation.subuniverses open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/sigma-decompositions.lagda.md b/src/foundation/sigma-decompositions.lagda.md index 6ba7a4e9cf..b3c759f936 100644 --- a/src/foundation/sigma-decompositions.lagda.md +++ b/src/foundation/sigma-decompositions.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.sigma-decompositions - (funext : function-extensionality) - where +module foundation.sigma-decompositions where ```
Imports @@ -16,17 +11,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext +open import foundation.dependent-products-contractible-types +open import foundation.equivalence-extensionality +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.inhabited-types +open import foundation.propositional-truncations +open import foundation.sets open import foundation.structure-identity-principle -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.transposition-identifications-along-equivalences open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/singleton-subtypes.lagda.md b/src/foundation/singleton-subtypes.lagda.md index 655f085729..b624eca1cc 100644 --- a/src/foundation/singleton-subtypes.lagda.md +++ b/src/foundation/singleton-subtypes.lagda.md @@ -1,29 +1,24 @@ # Singleton subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.singleton-subtypes - (funext : function-extensionality) - where +module foundation.singleton-subtypes where ```
Imports ```agda -open import foundation.connected-components funext -open import foundation.contractible-types funext +open import foundation.connected-components +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation funext -open import foundation.images-subtypes funext -open import foundation.inhabited-subtypes funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.functoriality-propositional-truncation +open import foundation.images-subtypes +open import foundation.inhabited-subtypes +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.sets open import foundation.singleton-induction -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/slice.lagda.md b/src/foundation/slice.lagda.md index bd0e0c899a..621d6af8f9 100644 --- a/src/foundation/slice.lagda.md +++ b/src/foundation/slice.lagda.md @@ -1,30 +1,24 @@ # Morphisms in the slice category of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.slice - (funext : function-extensionality) - where +module foundation.slice where ```
Imports ```agda -open import foundation.commuting-triangles-of-homotopies funext +open import foundation.commuting-triangles-of-homotopies open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - +open import foundation.dependent-products-propositions +open import foundation.equivalences +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.logical-equivalences funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.logical-equivalences open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -41,7 +35,7 @@ open import foundation-core.propositions open import foundation-core.torsorial-type-families open import foundation-core.type-theoretic-principle-of-choice -open import trees.polynomial-endofunctors funext +open import trees.polynomial-endofunctors ```
diff --git a/src/foundation/small-maps.lagda.md b/src/foundation/small-maps.lagda.md index 9f5131f628..4084071783 100644 --- a/src/foundation/small-maps.lagda.md +++ b/src/foundation/small-maps.lagda.md @@ -1,27 +1,22 @@ # Small maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.small-maps - (funext : function-extensionality) - where +module foundation.small-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.locally-small-types funext -open import foundation.retracts-of-maps funext -open import foundation.split-idempotent-maps funext +open import foundation.dependent-products-propositions +open import foundation.locally-small-types +open import foundation.retracts-of-maps +open import foundation.split-idempotent-maps open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.propositions -open import foundation-core.small-types funext +open import foundation-core.small-types ```
diff --git a/src/foundation/small-types.lagda.md b/src/foundation/small-types.lagda.md index ead1b928bf..2d60593a75 100644 --- a/src/foundation/small-types.lagda.md +++ b/src/foundation/small-types.lagda.md @@ -1,26 +1,21 @@ # Small types ```agda -open import foundation.function-extensionality-axiom +module foundation.small-types where -module - foundation.small-types - (funext : function-extensionality) - where - -open import foundation-core.small-types funext public +open import foundation-core.small-types public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.images funext -open import foundation.locally-small-types funext -open import foundation.replacement funext -open import foundation.surjective-maps funext -open import foundation.uniqueness-image funext -open import foundation.universal-property-image funext +open import foundation.images +open import foundation.locally-small-types +open import foundation.replacement +open import foundation.surjective-maps +open import foundation.uniqueness-image +open import foundation.universal-property-image open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/small-universes.lagda.md b/src/foundation/small-universes.lagda.md index f73e0ee038..fda8cb43a0 100644 --- a/src/foundation/small-universes.lagda.md +++ b/src/foundation/small-universes.lagda.md @@ -1,12 +1,7 @@ # Small universes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.small-universes - (funext : function-extensionality) - where +module foundation.small-universes where ```
Imports @@ -15,7 +10,7 @@ module open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.small-types funext +open import foundation-core.small-types ```
diff --git a/src/foundation/span-diagrams.lagda.md b/src/foundation/span-diagrams.lagda.md index 9738936202..3356a17241 100644 --- a/src/foundation/span-diagrams.lagda.md +++ b/src/foundation/span-diagrams.lagda.md @@ -1,19 +1,14 @@ # Span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.span-diagrams - (funext : function-extensionality) - where +module foundation.span-diagrams where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.morphisms-arrows funext +open import foundation.morphisms-arrows open import foundation.spans open import foundation.universe-levels ``` diff --git a/src/foundation/spans-of-spans.lagda.md b/src/foundation/spans-of-spans.lagda.md index 6e228fe989..792737abe6 100644 --- a/src/foundation/spans-of-spans.lagda.md +++ b/src/foundation/spans-of-spans.lagda.md @@ -1,20 +1,15 @@ # Spans of spans ```agda -open import foundation.function-extensionality-axiom - -module - foundation.spans-of-spans - (funext : function-extensionality) - where +module foundation.spans-of-spans where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.spans open import foundation.universe-levels diff --git a/src/foundation/split-idempotent-maps.lagda.md b/src/foundation/split-idempotent-maps.lagda.md index 6e775f6a01..e3a320b622 100644 --- a/src/foundation/split-idempotent-maps.lagda.md +++ b/src/foundation/split-idempotent-maps.lagda.md @@ -1,12 +1,7 @@ # Split idempotent maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.split-idempotent-maps - (funext : function-extensionality) - where +module foundation.split-idempotent-maps where ```
Imports @@ -14,29 +9,29 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fixed-points-endofunctions open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.homotopy-induction funext -open import foundation.idempotent-maps funext -open import foundation.inverse-sequential-diagrams funext -open import foundation.locally-small-types funext -open import foundation.path-cosplit-maps funext -open import foundation.quasicoherently-idempotent-maps funext -open import foundation.retracts-of-types funext -open import foundation.sequential-limits funext +open import foundation.homotopy-induction +open import foundation.idempotent-maps +open import foundation.inverse-sequential-diagrams +open import foundation.locally-small-types +open import foundation.path-cosplit-maps +open import foundation.quasicoherently-idempotent-maps +open import foundation.retracts-of-types +open import foundation.sequential-limits open import foundation.structure-identity-principle open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import foundation.weakly-constant-maps funext +open import foundation.weakly-constant-maps open import foundation.whiskering-homotopies-composition open import foundation-core.commuting-squares-of-homotopies @@ -49,7 +44,7 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.sections open import foundation-core.sets -open import foundation-core.small-types funext +open import foundation-core.small-types open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/standard-apartness-relations.lagda.md b/src/foundation/standard-apartness-relations.lagda.md index 0cb656f8cb..3a3df40ac0 100644 --- a/src/foundation/standard-apartness-relations.lagda.md +++ b/src/foundation/standard-apartness-relations.lagda.md @@ -1,24 +1,19 @@ # Standard apartness relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.standard-apartness-relations - (funext : function-extensionality) - where +module foundation.standard-apartness-relations where ```
Imports ```agda -open import foundation.apartness-relations funext -open import foundation.decidable-types funext +open import foundation.apartness-relations +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.law-of-excluded-middle funext -open import foundation.logical-equivalences funext -open import foundation.negated-equality funext -open import foundation.tight-apartness-relations funext +open import foundation.law-of-excluded-middle +open import foundation.logical-equivalences +open import foundation.negated-equality +open import foundation.tight-apartness-relations open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/standard-pullbacks.lagda.md b/src/foundation/standard-pullbacks.lagda.md index 350bb426a1..8f0db009ca 100644 --- a/src/foundation/standard-pullbacks.lagda.md +++ b/src/foundation/standard-pullbacks.lagda.md @@ -1,28 +1,23 @@ # Standard pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.standard-pullbacks - (funext : function-extensionality) - where +module foundation.standard-pullbacks where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.diagonal-maps-cartesian-products-of-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences @@ -32,7 +27,7 @@ open import foundation-core.homotopies open import foundation-core.retractions open import foundation-core.sections open import foundation-core.type-theoretic-principle-of-choice -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks open import foundation-core.whiskering-identifications-concatenation ``` diff --git a/src/foundation/standard-ternary-pullbacks.lagda.md b/src/foundation/standard-ternary-pullbacks.lagda.md index 8aeefb1d20..6ca4fd1596 100644 --- a/src/foundation/standard-ternary-pullbacks.lagda.md +++ b/src/foundation/standard-ternary-pullbacks.lagda.md @@ -1,28 +1,23 @@ # Standard ternary pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.standard-ternary-pullbacks - (funext : function-extensionality) - where +module foundation.standard-ternary-pullbacks where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.diagonal-maps-cartesian-products-of-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences @@ -32,7 +27,7 @@ open import foundation-core.homotopies open import foundation-core.retractions open import foundation-core.sections open import foundation-core.type-theoretic-principle-of-choice -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks open import foundation-core.whiskering-identifications-concatenation ``` diff --git a/src/foundation/strict-symmetrization-binary-relations.lagda.md b/src/foundation/strict-symmetrization-binary-relations.lagda.md index 8e0b26ad29..1c316d7ad4 100644 --- a/src/foundation/strict-symmetrization-binary-relations.lagda.md +++ b/src/foundation/strict-symmetrization-binary-relations.lagda.md @@ -1,20 +1,15 @@ # Strict symmetrization of binary relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.strict-symmetrization-binary-relations - (funext : function-extensionality) - where +module foundation.strict-symmetrization-binary-relations where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.binary-relations funext-with-extensions -open import foundation.binary-relations-with-lifts funext +open import foundation.binary-relations +open import foundation.binary-relations-with-extensions +open import foundation.binary-relations-with-lifts open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/strictly-involutive-identity-types.lagda.md b/src/foundation/strictly-involutive-identity-types.lagda.md index 5e1d22cbc2..f6cd949dd5 100644 --- a/src/foundation/strictly-involutive-identity-types.lagda.md +++ b/src/foundation/strictly-involutive-identity-types.lagda.md @@ -1,12 +1,7 @@ # Strictly involutive identity types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.strictly-involutive-identity-types - (funext : function-extensionality) - where +module foundation.strictly-involutive-identity-types where ```
Imports @@ -16,13 +11,13 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality funext - -open import foundation.multivariable-homotopies funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.multivariable-homotopies open import foundation.strictly-right-unital-concatenation-identifications open import foundation.telescopes -open import foundation.univalence funext -open import foundation.universal-property-identity-systems funext +open import foundation.univalence +open import foundation.universal-property-identity-systems open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/strong-preunivalence.lagda.md b/src/foundation/strong-preunivalence.lagda.md index 2148624632..051e55fa52 100644 --- a/src/foundation/strong-preunivalence.lagda.md +++ b/src/foundation/strong-preunivalence.lagda.md @@ -1,28 +1,23 @@ # The strong preunivalence axiom ```agda -open import foundation.function-extensionality-axiom - -module - foundation.strong-preunivalence - (funext : function-extensionality) - where +module foundation.strong-preunivalence where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.preunivalence funext -open import foundation.propositional-maps funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.small-types funext -open import foundation.structured-equality-duality funext -open import foundation.univalence funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.preunivalence +open import foundation.propositional-maps +open import foundation.propositions +open import foundation.sets +open import foundation.small-types +open import foundation.structured-equality-duality +open import foundation.univalence open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/strongly-extensional-maps.lagda.md b/src/foundation/strongly-extensional-maps.lagda.md index 6a902e9b19..9b5bfa198f 100644 --- a/src/foundation/strongly-extensional-maps.lagda.md +++ b/src/foundation/strongly-extensional-maps.lagda.md @@ -1,18 +1,13 @@ # Strongly extensional maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.strongly-extensional-maps - (funext : function-extensionality) - where +module foundation.strongly-extensional-maps where ```
Imports ```agda -open import foundation.apartness-relations funext +open import foundation.apartness-relations open import foundation.universe-levels ``` diff --git a/src/foundation/structure.lagda.md b/src/foundation/structure.lagda.md index 15969aa801..6a5b9217b7 100644 --- a/src/foundation/structure.lagda.md +++ b/src/foundation/structure.lagda.md @@ -1,19 +1,14 @@ # Structure ```agda -open import foundation.function-extensionality-axiom - -module - foundation.structure - (funext : function-extensionality) - where +module foundation.structure where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/structured-equality-duality.lagda.md b/src/foundation/structured-equality-duality.lagda.md index 4ce8de15f0..534bf63cd7 100644 --- a/src/foundation/structured-equality-duality.lagda.md +++ b/src/foundation/structured-equality-duality.lagda.md @@ -1,24 +1,19 @@ # Structured equality duality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.structured-equality-duality - (funext : function-extensionality) - where +module foundation.structured-equality-duality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.maps-in-subuniverses funext -open import foundation.separated-types-subuniverses funext -open import foundation.structure funext -open import foundation.subuniverses funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.maps-in-subuniverses +open import foundation.separated-types-subuniverses +open import foundation.structure +open import foundation.subuniverses open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/structured-type-duality.lagda.md b/src/foundation/structured-type-duality.lagda.md index 188e375c32..e7d04bcb07 100644 --- a/src/foundation/structured-type-duality.lagda.md +++ b/src/foundation/structured-type-duality.lagda.md @@ -1,28 +1,23 @@ # Structured type duality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.structured-type-duality - (funext : function-extensionality) - where +module foundation.structured-type-duality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.structure funext +open import foundation.equivalences +open import foundation.structure open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-duality funext -open import foundation.univalence funext +open import foundation.type-duality +open import foundation.univalence open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.type-theoretic-principle-of-choice ``` diff --git a/src/foundation/subtype-duality.lagda.md b/src/foundation/subtype-duality.lagda.md index fd1118c059..abd64501e7 100644 --- a/src/foundation/subtype-duality.lagda.md +++ b/src/foundation/subtype-duality.lagda.md @@ -1,22 +1,17 @@ # Subtype duality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.subtype-duality - (funext : function-extensionality) - where +module foundation.subtype-duality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-types funext -open import foundation.propositional-maps funext -open import foundation.structured-type-duality funext -open import foundation.surjective-maps funext +open import foundation.inhabited-types +open import foundation.propositional-maps +open import foundation.structured-type-duality +open import foundation.surjective-maps open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/subtypes.lagda.md b/src/foundation/subtypes.lagda.md index e62aa97232..20def667fe 100644 --- a/src/foundation/subtypes.lagda.md +++ b/src/foundation/subtypes.lagda.md @@ -1,26 +1,21 @@ # Subtypes ```agda -open import foundation.function-extensionality-axiom +module foundation.subtypes where -module - foundation.subtypes - (funext : function-extensionality) - where - -open import foundation-core.subtypes funext public +open import foundation-core.subtypes public ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext -open import foundation.equality-dependent-function-types funext +open import foundation.dependent-products-propositions +open import foundation.embeddings +open import foundation.equality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences funext -open import foundation.propositional-extensionality funext +open import foundation.logical-equivalences +open import foundation.propositional-extensionality open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/subuniverses.lagda.md b/src/foundation/subuniverses.lagda.md index 1bb3f6ee17..ddeb1e28d6 100644 --- a/src/foundation/subuniverses.lagda.md +++ b/src/foundation/subuniverses.lagda.md @@ -1,23 +1,18 @@ # Subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - foundation.subuniverses - (funext : function-extensionality) - where +module foundation.subuniverses where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.subtype-identity-principle -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.contractible-types @@ -26,7 +21,7 @@ open import foundation-core.fibers-of-maps open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/surjective-maps.lagda.md b/src/foundation/surjective-maps.lagda.md index a2fcd62661..6296eb39df 100644 --- a/src/foundation/surjective-maps.lagda.md +++ b/src/foundation/surjective-maps.lagda.md @@ -1,38 +1,33 @@ # Surjective maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.surjective-maps - (funext : function-extensionality) - where +module foundation.surjective-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.connected-maps funext -open import foundation.contractible-types funext +open import foundation.connected-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.embeddings funext +open import foundation.dependent-products-propositions +open import foundation.embeddings open import foundation.equality-cartesian-product-types -open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-cartesian-product-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.postcomposition-dependent-functions funext -open import foundation.propositional-truncations funext +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.postcomposition-dependent-functions +open import foundation.propositional-truncations open import foundation.split-surjective-maps open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.truncated-types funext -open import foundation.univalence funext -open import foundation.universal-property-family-of-fibers-of-maps funext -open import foundation.universal-property-propositional-truncation funext +open import foundation.truncated-types +open import foundation.univalence +open import foundation.universal-property-family-of-fibers-of-maps +open import foundation.universal-property-propositional-truncation open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -42,19 +37,19 @@ open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.homotopies open import foundation-core.precomposition-dependent-functions open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sections open import foundation-core.sets -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncation-levels -open import orthogonal-factorization-systems.extensions-maps funext +open import orthogonal-factorization-systems.extensions-maps ```
diff --git a/src/foundation/symmetric-binary-relations.lagda.md b/src/foundation/symmetric-binary-relations.lagda.md index 47b07f6c8d..19d488fdc8 100644 --- a/src/foundation/symmetric-binary-relations.lagda.md +++ b/src/foundation/symmetric-binary-relations.lagda.md @@ -1,25 +1,21 @@ # Symmetric binary relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.symmetric-binary-relations - (funext : function-extensionality) - where +module foundation.symmetric-binary-relations where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.morphisms-binary-relations funext -open import foundation.symmetric-operations funext +open import foundation.equivalence-extensionality +open import foundation.function-extensionality-axiom +open import foundation.morphisms-binary-relations +open import foundation.symmetric-operations open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs open import foundation-core.equivalences open import foundation-core.function-types @@ -27,7 +23,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.transport-along-identifications -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/symmetric-cores-binary-relations.lagda.md b/src/foundation/symmetric-cores-binary-relations.lagda.md index 17f920d654..95c56d21dd 100644 --- a/src/foundation/symmetric-cores-binary-relations.lagda.md +++ b/src/foundation/symmetric-cores-binary-relations.lagda.md @@ -1,30 +1,25 @@ # Symmetric cores of binary relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.symmetric-cores-binary-relations - (funext : function-extensionality) - where +module foundation.symmetric-cores-binary-relations where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.morphisms-binary-relations funext -open import foundation.postcomposition-functions funext -open import foundation.symmetric-binary-relations funext +open import foundation.binary-relations +open import foundation.morphisms-binary-relations +open import foundation.postcomposition-functions +open import foundation.symmetric-binary-relations open import foundation.transport-along-identifications -open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.type-arithmetic-dependent-function-types open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/symmetric-difference.lagda.md b/src/foundation/symmetric-difference.lagda.md index f605a3b0f4..13308cf30a 100644 --- a/src/foundation/symmetric-difference.lagda.md +++ b/src/foundation/symmetric-difference.lagda.md @@ -1,31 +1,26 @@ # Symmetric difference of subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.symmetric-difference - (funext : function-extensionality) - where +module foundation.symmetric-difference where ```
Imports ```agda -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.exclusive-sum funext -open import foundation.intersections-subtypes funext +open import foundation.exclusive-sum +open import foundation.intersections-subtypes open import foundation.universe-levels open import foundation-core.coproduct-types -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.transport-along-identifications ``` diff --git a/src/foundation/symmetric-identity-types.lagda.md b/src/foundation/symmetric-identity-types.lagda.md index 688a7e1e21..7b34c892e3 100644 --- a/src/foundation/symmetric-identity-types.lagda.md +++ b/src/foundation/symmetric-identity-types.lagda.md @@ -1,12 +1,7 @@ # The symmetric identity types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.symmetric-identity-types - (funext : function-extensionality) - where +module foundation.symmetric-identity-types where ```
Imports @@ -14,15 +9,14 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.functoriality-dependent-function-types funext +open import foundation.function-extensionality +open import foundation.functoriality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs open import foundation-core.contractible-types open import foundation-core.coproduct-types @@ -33,7 +27,7 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.torsorial-type-families -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/symmetric-operations.lagda.md b/src/foundation/symmetric-operations.lagda.md index 69d03ebdb9..317c977990 100644 --- a/src/foundation/symmetric-operations.lagda.md +++ b/src/foundation/symmetric-operations.lagda.md @@ -1,12 +1,7 @@ # Symmetric operations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.symmetric-operations - (funext : function-extensionality) - where +module foundation.symmetric-operations where ```
Imports @@ -15,16 +10,15 @@ module open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalence-extensionality funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-coproduct-types funext +open import foundation.dependent-products-propositions +open import foundation.equivalence-extensionality +open import foundation.function-extensionality +open import foundation.functoriality-coproduct-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.propositional-truncations funext -open import foundation.universal-property-propositional-truncation-into-sets funext +open import foundation.propositional-truncations +open import foundation.universal-property-propositional-truncation-into-sets open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs open import foundation-core.coproduct-types open import foundation-core.equivalences @@ -33,12 +27,12 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/terminal-spans-families-of-types.lagda.md b/src/foundation/terminal-spans-families-of-types.lagda.md index 830c19b404..697d998b8e 100644 --- a/src/foundation/terminal-spans-families-of-types.lagda.md +++ b/src/foundation/terminal-spans-families-of-types.lagda.md @@ -1,18 +1,13 @@ # Terminal spans on families of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.terminal-spans-families-of-types - (funext : function-extensionality) - where +module foundation.terminal-spans-families-of-types where ```
Imports ```agda -open import foundation.morphisms-spans-families-of-types funext +open import foundation.morphisms-spans-families-of-types open import foundation.spans-families-of-types open import foundation.universe-levels diff --git a/src/foundation/tight-apartness-relations.lagda.md b/src/foundation/tight-apartness-relations.lagda.md index 7fb6473906..f848664137 100644 --- a/src/foundation/tight-apartness-relations.lagda.md +++ b/src/foundation/tight-apartness-relations.lagda.md @@ -1,23 +1,17 @@ # Tight apartness relations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.tight-apartness-relations - (funext : function-extensionality) - where +module foundation.tight-apartness-relations where ```
Imports ```agda -open import foundation.apartness-relations funext -open import foundation.binary-relations funext +open import foundation.apartness-relations +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.propositional-truncations funext +open import foundation.function-extensionality +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/torsorial-type-families.lagda.md b/src/foundation/torsorial-type-families.lagda.md index 0618fff39d..0929568e83 100644 --- a/src/foundation/torsorial-type-families.lagda.md +++ b/src/foundation/torsorial-type-families.lagda.md @@ -1,12 +1,7 @@ # Torsorial type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.torsorial-type-families - (funext : function-extensionality) - where +module foundation.torsorial-type-families where open import foundation-core.torsorial-type-families public ``` @@ -14,11 +9,11 @@ open import foundation-core.torsorial-type-families public
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.logical-equivalences funext -open import foundation.universal-property-identity-types funext +open import foundation.logical-equivalences +open import foundation.universal-property-identity-types open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/total-partial-functions.lagda.md b/src/foundation/total-partial-functions.lagda.md index 13df6f2194..7b1083887d 100644 --- a/src/foundation/total-partial-functions.lagda.md +++ b/src/foundation/total-partial-functions.lagda.md @@ -1,19 +1,14 @@ # Total partial functions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.total-partial-functions - (funext : function-extensionality) - where +module foundation.total-partial-functions where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-propositions open import foundation.partial-functions open import foundation.universe-levels diff --git a/src/foundation/transfinite-cocomposition-of-maps.lagda.md b/src/foundation/transfinite-cocomposition-of-maps.lagda.md index 6dba5a2eeb..9d3f7d02ca 100644 --- a/src/foundation/transfinite-cocomposition-of-maps.lagda.md +++ b/src/foundation/transfinite-cocomposition-of-maps.lagda.md @@ -1,19 +1,14 @@ # Transfinite cocomposition of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.transfinite-cocomposition-of-maps - (funext : function-extensionality) - where +module foundation.transfinite-cocomposition-of-maps where ```
Imports ```agda -open import foundation.inverse-sequential-diagrams funext -open import foundation.sequential-limits funext +open import foundation.inverse-sequential-diagrams +open import foundation.sequential-limits open import foundation.universe-levels ``` diff --git a/src/foundation/transport-along-equivalences.lagda.md b/src/foundation/transport-along-equivalences.lagda.md index c44902f1b1..f46c28bfa9 100644 --- a/src/foundation/transport-along-equivalences.lagda.md +++ b/src/foundation/transport-along-equivalences.lagda.md @@ -1,28 +1,22 @@ # Transport along equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.transport-along-equivalences - (funext : function-extensionality) - where +module foundation.transport-along-equivalences where ```
Imports ```agda -open import foundation.action-on-equivalences-functions funext -open import foundation.action-on-equivalences-type-families funext +open import foundation.action-on-equivalences-functions +open import foundation.action-on-equivalences-type-families open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalence-induction funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - +open import foundation.equivalence-extensionality +open import foundation.equivalence-induction +open import foundation.equivalences +open import foundation.function-extensionality open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.commuting-triangles-of-maps diff --git a/src/foundation/transport-along-higher-identifications.lagda.md b/src/foundation/transport-along-higher-identifications.lagda.md index b5db400ea0..f031e7713c 100644 --- a/src/foundation/transport-along-higher-identifications.lagda.md +++ b/src/foundation/transport-along-higher-identifications.lagda.md @@ -1,27 +1,22 @@ # Transport along higher identifications ```agda -open import foundation.function-extensionality-axiom - -module - foundation.transport-along-higher-identifications - (funext : function-extensionality) - where +module foundation.transport-along-higher-identifications where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-identifications funext -open import foundation.function-types funext -open import foundation.homotopies funext +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-identifications +open import foundation.function-types +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.path-algebra funext +open import foundation.path-algebra open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation open import foundation-core.identity-types open import foundation-core.transport-along-identifications diff --git a/src/foundation/transport-along-homotopies.lagda.md b/src/foundation/transport-along-homotopies.lagda.md index 0e41ff7d8a..8308d97123 100644 --- a/src/foundation/transport-along-homotopies.lagda.md +++ b/src/foundation/transport-along-homotopies.lagda.md @@ -1,22 +1,17 @@ # Transport along homotopies ```agda -open import foundation.function-extensionality-axiom - -module - foundation.transport-along-homotopies - (funext : function-extensionality) - where +module foundation.transport-along-homotopies where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-extensionality funext - -open import foundation.homotopy-induction funext -open import foundation.transport-along-higher-identifications funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.homotopy-induction +open import foundation.transport-along-higher-identifications open import foundation.universe-levels open import foundation-core.homotopies diff --git a/src/foundation/transport-split-type-families.lagda.md b/src/foundation/transport-split-type-families.lagda.md index 7358b6596b..ff883a366f 100644 --- a/src/foundation/transport-split-type-families.lagda.md +++ b/src/foundation/transport-split-type-families.lagda.md @@ -1,25 +1,20 @@ # Transport-split type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.transport-split-type-families - (funext : function-extensionality) - where +module foundation.transport-split-type-families where ```
Imports ```agda -open import foundation.equivalence-injective-type-families funext -open import foundation.equivalences funext +open import foundation.equivalence-injective-type-families +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.iterated-dependent-product-types funext +open import foundation.iterated-dependent-product-types open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalent-type-families funext -open import foundation.universal-property-identity-systems funext +open import foundation.univalent-type-families +open import foundation.universal-property-identity-systems open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/transposition-identifications-along-equivalences.lagda.md b/src/foundation/transposition-identifications-along-equivalences.lagda.md index 1981015681..9870736681 100644 --- a/src/foundation/transposition-identifications-along-equivalences.lagda.md +++ b/src/foundation/transposition-identifications-along-equivalences.lagda.md @@ -1,20 +1,15 @@ # Transposing identifications along equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.transposition-identifications-along-equivalences - (funext : function-extensionality) - where +module foundation.transposition-identifications-along-equivalences where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-identifications funext -open import foundation.identity-types funext +open import foundation.commuting-triangles-of-identifications +open import foundation.identity-types open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/transposition-identifications-along-retractions.lagda.md b/src/foundation/transposition-identifications-along-retractions.lagda.md index f0bfecbc2a..2dfe11e3cb 100644 --- a/src/foundation/transposition-identifications-along-retractions.lagda.md +++ b/src/foundation/transposition-identifications-along-retractions.lagda.md @@ -1,12 +1,7 @@ # Transposing identifications along retractions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.transposition-identifications-along-retractions - (funext : function-extensionality) - where +module foundation.transposition-identifications-along-retractions where ```
@@ -14,8 +9,7 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/transposition-identifications-along-sections.lagda.md b/src/foundation/transposition-identifications-along-sections.lagda.md index a1ede27639..9cffc6452a 100644 --- a/src/foundation/transposition-identifications-along-sections.lagda.md +++ b/src/foundation/transposition-identifications-along-sections.lagda.md @@ -1,12 +1,7 @@ # Transposing identifications along sections ```agda -open import foundation.function-extensionality-axiom - -module - foundation.transposition-identifications-along-sections - (funext : function-extensionality) - where +module foundation.transposition-identifications-along-sections where ```
@@ -14,8 +9,7 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/transposition-span-diagrams.lagda.md b/src/foundation/transposition-span-diagrams.lagda.md index 12b150c1af..1d9df617ee 100644 --- a/src/foundation/transposition-span-diagrams.lagda.md +++ b/src/foundation/transposition-span-diagrams.lagda.md @@ -1,12 +1,7 @@ # Transposition of span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - foundation.transposition-span-diagrams - (funext : function-extensionality) - where +module foundation.transposition-span-diagrams where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.dependent-pair-types open import foundation.opposite-spans -open import foundation.span-diagrams funext +open import foundation.span-diagrams open import foundation.spans open import foundation.universe-levels ``` diff --git a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md index 5930f3e499..905d56a633 100644 --- a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md @@ -1,22 +1,17 @@ # Trivial relaxed Σ-decompositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.trivial-relaxed-sigma-decompositions - (funext : function-extensionality) - where +module foundation.trivial-relaxed-sigma-decompositions where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.raising-universe-levels-unit-type funext -open import foundation.relaxed-sigma-decompositions funext -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions +open import foundation.transposition-identifications-along-equivalences open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels @@ -26,7 +21,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/trivial-sigma-decompositions.lagda.md b/src/foundation/trivial-sigma-decompositions.lagda.md index 1863f92e63..d7a099583f 100644 --- a/src/foundation/trivial-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-sigma-decompositions.lagda.md @@ -1,26 +1,21 @@ # Trivial Σ-decompositions ```agda -open import foundation.function-extensionality-axiom - -module - foundation.trivial-sigma-decompositions - (funext : function-extensionality) - where +module foundation.trivial-sigma-decompositions where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation funext -open import foundation.inhabited-types funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sigma-decompositions funext -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.functoriality-propositional-truncation +open import foundation.inhabited-types +open import foundation.raising-universe-levels-unit-type +open import foundation.sigma-decompositions +open import foundation.transposition-identifications-along-equivalences open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.unit-type open import foundation.universe-levels @@ -30,7 +25,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/truncated-equality.lagda.md b/src/foundation/truncated-equality.lagda.md index 25d8f7c1d6..c88cab61f7 100644 --- a/src/foundation/truncated-equality.lagda.md +++ b/src/foundation/truncated-equality.lagda.md @@ -1,18 +1,13 @@ # Truncated equality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.truncated-equality - (funext : function-extensionality) - where +module foundation.truncated-equality where ```
Imports ```agda -open import foundation.truncations funext +open import foundation.truncations open import foundation.universe-levels open import foundation-core.identity-types diff --git a/src/foundation/truncated-maps.lagda.md b/src/foundation/truncated-maps.lagda.md index b8c1940299..05f95a7187 100644 --- a/src/foundation/truncated-maps.lagda.md +++ b/src/foundation/truncated-maps.lagda.md @@ -1,29 +1,24 @@ # Truncated maps ```agda -open import foundation.function-extensionality-axiom +module foundation.truncated-maps where -module - foundation.truncated-maps - (funext : function-extensionality) - where - -open import foundation.dependent-products-truncated-types funext public -open import foundation-core.truncated-maps funext public +open import foundation.dependent-products-truncated-types public +open import foundation-core.truncated-maps public ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.functoriality-fibers-of-maps funext +open import foundation.dependent-products-propositions +open import foundation.functoriality-fibers-of-maps open import foundation.universe-levels open import foundation-core.fibers-of-maps open import foundation-core.propositions -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks open import foundation-core.truncated-types open import foundation-core.truncation-levels ``` diff --git a/src/foundation/truncated-types.lagda.md b/src/foundation/truncated-types.lagda.md index 64436f7f0d..4233ee729d 100644 --- a/src/foundation/truncated-types.lagda.md +++ b/src/foundation/truncated-types.lagda.md @@ -1,15 +1,10 @@ # Truncated types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.truncated-types - (funext : function-extensionality) - where +module foundation.truncated-types where open import foundation-core.truncated-types public -open import foundation.dependent-products-truncated-types funext public +open import foundation.dependent-products-truncated-types public ```
Imports @@ -18,17 +13,17 @@ open import foundation.dependent-products-truncated-types funext public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.logical-equivalences funext +open import foundation.equivalences +open import foundation.logical-equivalences open import foundation.subtype-identity-principle open import foundation.truncation-levels -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.embeddings open import foundation-core.identity-types open import foundation-core.propositions -open import foundation-core.subtypes funext +open import foundation-core.subtypes open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/truncation-equivalences.lagda.md b/src/foundation/truncation-equivalences.lagda.md index c2a4c41d62..95d6169280 100644 --- a/src/foundation/truncation-equivalences.lagda.md +++ b/src/foundation/truncation-equivalences.lagda.md @@ -1,32 +1,27 @@ # `k`-Equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.truncation-equivalences - (funext : function-extensionality) - where +module foundation.truncation-equivalences where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.connected-maps funext -open import foundation.connected-types funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.connected-maps +open import foundation.connected-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.functoriality-truncation funext -open import foundation.identity-types funext -open import foundation.precomposition-functions-into-subuniverses funext -open import foundation.propositional-truncations funext -open import foundation.truncations funext +open import foundation.dependent-products-truncated-types +open import foundation.functoriality-truncation +open import foundation.identity-types +open import foundation.precomposition-functions-into-subuniverses +open import foundation.propositional-truncations +open import foundation.truncations open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-dependent-pair-types funext -open import foundation.universal-property-equivalences funext -open import foundation.universal-property-truncation funext +open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-equivalences +open import foundation.universal-property-truncation open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/truncation-images-of-maps.lagda.md b/src/foundation/truncation-images-of-maps.lagda.md index 4d320800b2..2aa88a1be2 100644 --- a/src/foundation/truncation-images-of-maps.lagda.md +++ b/src/foundation/truncation-images-of-maps.lagda.md @@ -1,31 +1,26 @@ # Truncation images of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.truncation-images-of-maps - (funext : function-extensionality) - where +module foundation.truncation-images-of-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.connected-maps funext +open import foundation.connected-maps open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.functoriality-truncation funext -open import foundation.identity-types funext -open import foundation.truncations funext +open import foundation.fibers-of-maps +open import foundation.functoriality-truncation +open import foundation.identity-types +open import foundation.truncations open import foundation.universe-levels open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.transport-along-identifications -open import foundation-core.truncated-maps funext +open import foundation-core.truncated-maps open import foundation-core.truncation-levels ``` diff --git a/src/foundation/truncation-modalities.lagda.md b/src/foundation/truncation-modalities.lagda.md index 90470ac5de..4c38c783fb 100644 --- a/src/foundation/truncation-modalities.lagda.md +++ b/src/foundation/truncation-modalities.lagda.md @@ -1,25 +1,20 @@ # The truncation modalities ```agda -open import foundation.function-extensionality-axiom - -module - foundation.truncation-modalities - (funext : function-extensionality) - where +module foundation.truncation-modalities where ```
Imports ```agda -open import foundation.truncations funext +open import foundation.truncations open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.truncation-levels -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.uniquely-eliminating-modalities ```
diff --git a/src/foundation/truncations.lagda.md b/src/foundation/truncations.lagda.md index 4aaa890fce..d7bed98e65 100644 --- a/src/foundation/truncations.lagda.md +++ b/src/foundation/truncations.lagda.md @@ -1,27 +1,22 @@ # Truncations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.truncations - (funext : function-extensionality) - where +module foundation.truncations where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.functoriality-dependent-function-types funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.functoriality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.truncated-types funext -open import foundation.universal-property-dependent-pair-types funext +open import foundation.identity-types +open import foundation.truncated-types +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -35,7 +30,7 @@ open import foundation-core.homotopies open import foundation-core.propositions open import foundation-core.torsorial-type-families open import foundation-core.truncation-levels -open import foundation-core.universal-property-truncation funext +open import foundation-core.universal-property-truncation ```
diff --git a/src/foundation/tuples-of-types.lagda.md b/src/foundation/tuples-of-types.lagda.md index 3b9bc8ee2f..49b8e03fc5 100644 --- a/src/foundation/tuples-of-types.lagda.md +++ b/src/foundation/tuples-of-types.lagda.md @@ -1,12 +1,7 @@ # Tuples of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.tuples-of-types - (funext : function-extensionality) - where +module foundation.tuples-of-types where ```
Imports @@ -16,7 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/type-arithmetic-coproduct-types.lagda.md b/src/foundation/type-arithmetic-coproduct-types.lagda.md index 77379c8cee..4bfa836a20 100644 --- a/src/foundation/type-arithmetic-coproduct-types.lagda.md +++ b/src/foundation/type-arithmetic-coproduct-types.lagda.md @@ -1,20 +1,15 @@ # Type arithmetic for coproduct types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.type-arithmetic-coproduct-types - (funext : function-extensionality) - where +module foundation.type-arithmetic-coproduct-types where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types funext +open import foundation.equality-coproduct-types open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/type-arithmetic-dependent-function-types.lagda.md b/src/foundation/type-arithmetic-dependent-function-types.lagda.md index 98993d5d4d..27533716f7 100644 --- a/src/foundation/type-arithmetic-dependent-function-types.lagda.md +++ b/src/foundation/type-arithmetic-dependent-function-types.lagda.md @@ -1,12 +1,7 @@ # Type arithmetic with dependent function types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.type-arithmetic-dependent-function-types - (funext : function-extensionality) - where +module foundation.type-arithmetic-dependent-function-types where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-function-types funext +open import foundation.functoriality-dependent-function-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/type-arithmetic-empty-type.lagda.md b/src/foundation/type-arithmetic-empty-type.lagda.md index 28df76dcbe..3e65340797 100644 --- a/src/foundation/type-arithmetic-empty-type.lagda.md +++ b/src/foundation/type-arithmetic-empty-type.lagda.md @@ -1,18 +1,13 @@ # Type arithmetic with the empty type ```agda -open import foundation.function-extensionality-axiom - -module - foundation.type-arithmetic-empty-type - (funext : function-extensionality) - where +module foundation.type-arithmetic-empty-type where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/type-arithmetic-standard-pullbacks.lagda.md b/src/foundation/type-arithmetic-standard-pullbacks.lagda.md index a73a6743f1..09335074fa 100644 --- a/src/foundation/type-arithmetic-standard-pullbacks.lagda.md +++ b/src/foundation/type-arithmetic-standard-pullbacks.lagda.md @@ -1,22 +1,17 @@ # Type arithmetic with standard pullbacks ```agda -open import foundation.function-extensionality-axiom - -module - foundation.type-arithmetic-standard-pullbacks - (funext : function-extensionality) - where +module foundation.type-arithmetic-standard-pullbacks where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.standard-pullbacks funext -open import foundation.standard-ternary-pullbacks funext +open import foundation.equality-dependent-pair-types +open import foundation.standard-pullbacks +open import foundation.standard-ternary-pullbacks open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/foundation/type-duality.lagda.md b/src/foundation/type-duality.lagda.md index 61ca8cdeda..50d1ca1b70 100644 --- a/src/foundation/type-duality.lagda.md +++ b/src/foundation/type-duality.lagda.md @@ -1,12 +1,7 @@ # Type duality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.type-duality - (funext : function-extensionality) - where +module foundation.type-duality where ```
Imports @@ -14,17 +9,16 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - +open import foundation.equivalences +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.locally-small-types funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.slice funext +open import foundation.locally-small-types +open import foundation.raising-universe-levels-unit-type +open import foundation.slice open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence funext -open import foundation.universal-property-equivalences funext +open import foundation.univalence +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.contractible-maps @@ -32,15 +26,15 @@ open import foundation-core.contractible-types open import foundation-core.embeddings open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.injective-maps -open import foundation-core.small-types funext +open import foundation-core.small-types open import foundation-core.torsorial-type-families -open import trees.polynomial-endofunctors funext +open import trees.polynomial-endofunctors ```
diff --git a/src/foundation/type-theoretic-principle-of-choice.lagda.md b/src/foundation/type-theoretic-principle-of-choice.lagda.md index 73a5beb31f..984e3fd557 100644 --- a/src/foundation/type-theoretic-principle-of-choice.lagda.md +++ b/src/foundation/type-theoretic-principle-of-choice.lagda.md @@ -1,12 +1,7 @@ # The type theoretic principle of choice ```agda -open import foundation.function-extensionality-axiom - -module - foundation.type-theoretic-principle-of-choice - (funext : function-extensionality) - where +module foundation.type-theoretic-principle-of-choice where open import foundation-core.type-theoretic-principle-of-choice public ``` @@ -15,8 +10,7 @@ open import foundation-core.type-theoretic-principle-of-choice public ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.implicit-function-types open import foundation.structure-identity-principle open import foundation.universe-levels diff --git a/src/foundation/uniformly-decidable-type-families.lagda.md b/src/foundation/uniformly-decidable-type-families.lagda.md index e2118e8af6..9beb5f6b51 100644 --- a/src/foundation/uniformly-decidable-type-families.lagda.md +++ b/src/foundation/uniformly-decidable-type-families.lagda.md @@ -1,31 +1,26 @@ # Uniformly decidable type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.uniformly-decidable-type-families - (funext : function-extensionality) - where +module foundation.uniformly-decidable-type-families where ```
Imports ```agda -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.dependent-products-truncated-types funext -open import foundation.equality-coproduct-types funext -open import foundation.inhabited-types funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.truncated-types funext +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-truncated-types +open import foundation.equality-coproduct-types +open import foundation.inhabited-types +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.truncated-types open import foundation.truncation-levels -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/unions-subtypes.lagda.md b/src/foundation/unions-subtypes.lagda.md index 0d98ac4e8c..a3ae84790a 100644 --- a/src/foundation/unions-subtypes.lagda.md +++ b/src/foundation/unions-subtypes.lagda.md @@ -1,32 +1,27 @@ # Unions of subtypes ```agda -open import foundation.function-extensionality-axiom - -module - foundation.unions-subtypes - (funext : function-extensionality) - where +module foundation.unions-subtypes where ```
Imports ```agda -open import foundation.decidable-subtypes funext +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.large-locale-of-subtypes funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext +open import foundation.disjunction +open import foundation.large-locale-of-subtypes +open import foundation.powersets +open import foundation.propositional-truncations open import foundation.universe-levels -open import foundation-core.subtypes funext +open import foundation-core.subtypes -open import logic.de-morgan-propositions funext -open import logic.de-morgan-subtypes funext -open import logic.double-negation-stable-subtypes funext +open import logic.de-morgan-propositions +open import logic.de-morgan-subtypes +open import logic.double-negation-stable-subtypes -open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.least-upper-bounds-large-posets ```
diff --git a/src/foundation/uniqueness-image.lagda.md b/src/foundation/uniqueness-image.lagda.md index f7a3962959..4711b5a4d1 100644 --- a/src/foundation/uniqueness-image.lagda.md +++ b/src/foundation/uniqueness-image.lagda.md @@ -1,23 +1,18 @@ # Uniqueness of the image of a map ```agda -open import foundation.function-extensionality-axiom - -module - foundation.uniqueness-image - (funext : function-extensionality) - where +module foundation.uniqueness-image where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.images funext -open import foundation.slice funext +open import foundation.equivalences +open import foundation.images +open import foundation.slice open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-image funext +open import foundation.universal-property-image open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/uniqueness-quantification.lagda.md b/src/foundation/uniqueness-quantification.lagda.md index 08f9d9b66d..dbbce2a023 100644 --- a/src/foundation/uniqueness-quantification.lagda.md +++ b/src/foundation/uniqueness-quantification.lagda.md @@ -1,19 +1,14 @@ # Uniqueness quantification ```agda -open import foundation.function-extensionality-axiom - -module - foundation.uniqueness-quantification - (funext : function-extensionality) - where +module foundation.uniqueness-quantification where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/uniqueness-set-quotients.lagda.md b/src/foundation/uniqueness-set-quotients.lagda.md index 7b375f4933..386076acce 100644 --- a/src/foundation/uniqueness-set-quotients.lagda.md +++ b/src/foundation/uniqueness-set-quotients.lagda.md @@ -1,12 +1,7 @@ # The uniqueness of set quotients ```agda -open import foundation.function-extensionality-axiom - -module - foundation.uniqueness-set-quotients - (funext : function-extensionality) - where +module foundation.uniqueness-set-quotients where ```
Imports @@ -14,17 +9,18 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.reflecting-maps-equivalence-relations +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.universal-property-equivalences funext -open import foundation.universal-property-set-quotients funext +open import foundation.universal-property-equivalences +open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.contractible-types -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/uniqueness-set-truncations.lagda.md b/src/foundation/uniqueness-set-truncations.lagda.md index d30e5dd395..604c442e9f 100644 --- a/src/foundation/uniqueness-set-truncations.lagda.md +++ b/src/foundation/uniqueness-set-truncations.lagda.md @@ -1,22 +1,17 @@ # Uniqueness of set truncations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.uniqueness-set-truncations - (funext : function-extensionality) - where +module foundation.uniqueness-set-truncations where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.mere-equality funext -open import foundation.sets funext -open import foundation.uniqueness-set-quotients funext -open import foundation.universal-property-set-truncation funext +open import foundation.mere-equality +open import foundation.sets +open import foundation.uniqueness-set-quotients +open import foundation.universal-property-set-truncation open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/uniqueness-truncation.lagda.md b/src/foundation/uniqueness-truncation.lagda.md index 05ac46d0f5..d14c70219d 100644 --- a/src/foundation/uniqueness-truncation.lagda.md +++ b/src/foundation/uniqueness-truncation.lagda.md @@ -1,18 +1,13 @@ # Uniqueness of the truncations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.uniqueness-truncation - (funext : function-extensionality) - where +module foundation.uniqueness-truncation where ```
Imports ```agda -open import foundation.dependent-products-truncated-types funext +open import foundation.dependent-products-truncated-types open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/foundation/univalence-implies-function-extensionality.lagda.md b/src/foundation/univalence-implies-function-extensionality.lagda.md index 63958f244c..a0d8b50ddc 100644 --- a/src/foundation/univalence-implies-function-extensionality.lagda.md +++ b/src/foundation/univalence-implies-function-extensionality.lagda.md @@ -1,23 +1,19 @@ # The univalence axiom implies function extensionality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.univalence-implies-function-extensionality - (funext : function-extensionality) - where +module foundation.univalence-implies-function-extensionality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalence-induction funext -open import foundation.postcomposition-functions funext +open import foundation.equivalence-induction +open import foundation.function-extensionality-axiom +open import foundation.postcomposition-functions open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import foundation.weak-function-extensionality funext +open import foundation.weak-function-extensionality open import foundation-core.contractible-maps open import foundation-core.contractible-types diff --git a/src/foundation/univalence.lagda.md b/src/foundation/univalence.lagda.md index 657bab60cc..7b5a2bf621 100644 --- a/src/foundation/univalence.lagda.md +++ b/src/foundation/univalence.lagda.md @@ -1,12 +1,7 @@ # The univalence axiom ```agda -open import foundation.function-extensionality-axiom - -module - foundation.univalence - (funext : function-extensionality) - where +module foundation.univalence where open import foundation-core.univalence public ``` @@ -16,8 +11,8 @@ open import foundation-core.univalence public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation/univalent-type-families.lagda.md b/src/foundation/univalent-type-families.lagda.md index 1364a89300..0a3999846c 100644 --- a/src/foundation/univalent-type-families.lagda.md +++ b/src/foundation/univalent-type-families.lagda.md @@ -1,12 +1,7 @@ # Univalent type families ```agda -open import foundation.function-extensionality-axiom - -module - foundation.univalent-type-families - (funext : function-extensionality) - where +module foundation.univalent-type-families where ```
Imports @@ -14,17 +9,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-systems -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.subuniverses funext +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.subuniverses open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalence funext -open import foundation.universal-property-identity-systems funext +open import foundation.univalence +open import foundation.universal-property-identity-systems open import foundation.universe-levels open import foundation-core.embeddings diff --git a/src/foundation/universal-property-booleans.lagda.md b/src/foundation/universal-property-booleans.lagda.md index 1c2bb788a2..bcb23bb57a 100644 --- a/src/foundation/universal-property-booleans.lagda.md +++ b/src/foundation/universal-property-booleans.lagda.md @@ -1,12 +1,7 @@ # The universal property of booleans ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-booleans - (funext : function-extensionality) - where +module foundation.universal-property-booleans where ```
Imports @@ -14,8 +9,7 @@ module ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.universe-levels open import foundation-core.booleans diff --git a/src/foundation/universal-property-cartesian-product-types.lagda.md b/src/foundation/universal-property-cartesian-product-types.lagda.md index 3bb8c4c0be..c2053eae40 100644 --- a/src/foundation/universal-property-cartesian-product-types.lagda.md +++ b/src/foundation/universal-property-cartesian-product-types.lagda.md @@ -1,23 +1,18 @@ # The universal properties of cartesian product types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-cartesian-product-types - (funext : function-extensionality) - where +module foundation.universal-property-cartesian-product-types where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.logical-equivalences funext -open import foundation.standard-pullbacks funext +open import foundation.logical-equivalences +open import foundation.standard-pullbacks open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -26,10 +21,10 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks open import foundation-core.retractions open import foundation-core.sections -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/universal-property-contractible-types.lagda.md b/src/foundation/universal-property-contractible-types.lagda.md index c02455b43f..d73ff1f0f2 100644 --- a/src/foundation/universal-property-contractible-types.lagda.md +++ b/src/foundation/universal-property-contractible-types.lagda.md @@ -1,12 +1,7 @@ # Universal property of contractible types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-contractible-types - (funext : function-extensionality) - where +module foundation.universal-property-contractible-types where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.singleton-induction open import foundation.universe-levels diff --git a/src/foundation/universal-property-coproduct-types.lagda.md b/src/foundation/universal-property-coproduct-types.lagda.md index f353140115..893e864163 100644 --- a/src/foundation/universal-property-coproduct-types.lagda.md +++ b/src/foundation/universal-property-coproduct-types.lagda.md @@ -1,12 +1,7 @@ # The universal property of coproduct types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-coproduct-types - (funext : function-extensionality) - where +module foundation.universal-property-coproduct-types where ```
Imports @@ -14,9 +9,8 @@ module ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality funext - -open import foundation.universal-property-equivalences funext +open import foundation.function-extensionality +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/universal-property-dependent-function-types.lagda.md b/src/foundation/universal-property-dependent-function-types.lagda.md index fcbbf8ce0a..9f7b72e52a 100644 --- a/src/foundation/universal-property-dependent-function-types.lagda.md +++ b/src/foundation/universal-property-dependent-function-types.lagda.md @@ -1,29 +1,23 @@ # The universal property of dependent function types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-dependent-function-types - (funext : function-extensionality) - where +module foundation.universal-property-dependent-function-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext +open import foundation.function-extensionality +open import foundation.identity-types open import foundation.spans-families-of-types -open import foundation.terminal-spans-families-of-types funext +open import foundation.terminal-spans-families-of-types open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types ``` diff --git a/src/foundation/universal-property-dependent-pair-types.lagda.md b/src/foundation/universal-property-dependent-pair-types.lagda.md index 1374eae79b..dcd8364df1 100644 --- a/src/foundation/universal-property-dependent-pair-types.lagda.md +++ b/src/foundation/universal-property-dependent-pair-types.lagda.md @@ -1,20 +1,14 @@ # The universal property of dependent pair types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-dependent-pair-types - (funext : function-extensionality) - where +module foundation.universal-property-dependent-pair-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/universal-property-empty-type.lagda.md b/src/foundation/universal-property-empty-type.lagda.md index 4421e9fe8b..c3fe4f7374 100644 --- a/src/foundation/universal-property-empty-type.lagda.md +++ b/src/foundation/universal-property-empty-type.lagda.md @@ -1,21 +1,15 @@ # The universal property of the empty type ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-empty-type - (funext : function-extensionality) - where +module foundation.universal-property-empty-type where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.universal-property-equivalences funext +open import foundation.function-extensionality +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/foundation/universal-property-equivalences.lagda.md b/src/foundation/universal-property-equivalences.lagda.md index 7611184631..4f4300ef98 100644 --- a/src/foundation/universal-property-equivalences.lagda.md +++ b/src/foundation/universal-property-equivalences.lagda.md @@ -1,20 +1,15 @@ # The universal property of equivalences ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-equivalences - (funext : function-extensionality) - where +module foundation.universal-property-equivalences where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.precomposition-functions-into-subuniverses funext +open import foundation.dependent-universal-property-equivalences +open import foundation.precomposition-functions-into-subuniverses open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md index 40f1377b76..82c10540aa 100644 --- a/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md +++ b/src/foundation/universal-property-family-of-fibers-of-maps.lagda.md @@ -1,12 +1,7 @@ # The universal property of the family of fibers of maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-family-of-fibers-of-maps - (funext : function-extensionality) - where +module foundation.universal-property-family-of-fibers-of-maps where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.families-of-equivalences funext -open import foundation.function-extensionality funext - +open import foundation.families-of-equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.subtype-identity-principle open import foundation.universe-levels @@ -26,7 +21,7 @@ open import foundation-core.diagonal-maps-of-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types @@ -34,8 +29,8 @@ open import foundation-core.precomposition-dependent-functions open import foundation-core.retractions open import foundation-core.sections -open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements funext -open import orthogonal-factorization-systems.lifts-families-of-elements funext +open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements ```
diff --git a/src/foundation/universal-property-fiber-products.lagda.md b/src/foundation/universal-property-fiber-products.lagda.md index a403c1787c..9c0b864ad8 100644 --- a/src/foundation/universal-property-fiber-products.lagda.md +++ b/src/foundation/universal-property-fiber-products.lagda.md @@ -1,21 +1,16 @@ # The universal property of fiber products ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-fiber-products - (funext : function-extensionality) - where +module foundation.universal-property-fiber-products where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.standard-pullbacks funext +open import foundation.standard-pullbacks open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -26,8 +21,8 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types -open import foundation-core.pullbacks funext -open import foundation-core.universal-property-pullbacks funext +open import foundation-core.pullbacks +open import foundation-core.universal-property-pullbacks ```
diff --git a/src/foundation/universal-property-identity-systems.lagda.md b/src/foundation/universal-property-identity-systems.lagda.md index 39be921752..b0e32181a0 100644 --- a/src/foundation/universal-property-identity-systems.lagda.md +++ b/src/foundation/universal-property-identity-systems.lagda.md @@ -1,12 +1,7 @@ # The universal property of identity systems ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-identity-systems - (funext : function-extensionality) - where +module foundation.universal-property-identity-systems where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.dependent-pair-types open import foundation.identity-systems -open import foundation.universal-property-contractible-types funext -open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-contractible-types +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/universal-property-identity-types.lagda.md b/src/foundation/universal-property-identity-types.lagda.md index daba01e9c9..1e4268ca8f 100644 --- a/src/foundation/universal-property-identity-types.lagda.md +++ b/src/foundation/universal-property-identity-types.lagda.md @@ -1,12 +1,7 @@ # The universal property of identity types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-identity-types - (funext : function-extensionality) - where +module foundation.universal-property-identity-types where ```
Imports @@ -14,19 +9,18 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.dependent-universal-property-equivalences funext -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.full-subtypes funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-dependent-function-types funext +open import foundation.dependent-products-propositions +open import foundation.dependent-universal-property-equivalences +open import foundation.embeddings +open import foundation.equivalences +open import foundation.full-subtypes +open import foundation.function-extensionality +open import foundation.functoriality-dependent-function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.preunivalence funext -open import foundation.univalence funext +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.preunivalence +open import foundation.univalence open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/universal-property-image.lagda.md b/src/foundation/universal-property-image.lagda.md index 8a945fb291..d3ce89ffd0 100644 --- a/src/foundation/universal-property-image.lagda.md +++ b/src/foundation/universal-property-image.lagda.md @@ -1,26 +1,21 @@ # The universal property of the image of a map ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-image - (funext : function-extensionality) - where +module foundation.universal-property-image where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.images funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.slice funext -open import foundation.surjective-maps funext +open import foundation.embeddings +open import foundation.images +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.slice +open import foundation.surjective-maps open import foundation.transport-along-identifications -open import foundation.universal-property-family-of-fibers-of-maps funext +open import foundation.universal-property-family-of-fibers-of-maps open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -29,7 +24,7 @@ open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types @@ -37,7 +32,7 @@ open import foundation-core.injective-maps open import foundation-core.propositional-maps open import foundation-core.propositions open import foundation-core.sections -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/universal-property-maybe.lagda.md b/src/foundation/universal-property-maybe.lagda.md index 27564028ad..f55128fdfa 100644 --- a/src/foundation/universal-property-maybe.lagda.md +++ b/src/foundation/universal-property-maybe.lagda.md @@ -1,20 +1,14 @@ # The universal property of the maybe monad ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-maybe - (funext : function-extensionality) - where +module foundation.universal-property-maybe where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.universe-levels open import foundation-core.cartesian-product-types diff --git a/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md b/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md index 2ae5b12dc0..124181f37d 100644 --- a/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md +++ b/src/foundation/universal-property-propositional-truncation-into-sets.lagda.md @@ -1,12 +1,7 @@ # The universal property of propositional truncations with respect to sets ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-propositional-truncation-into-sets - (funext : function-extensionality) - where +module foundation.universal-property-propositional-truncation-into-sets where ```
Imports @@ -14,11 +9,10 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.propositional-truncations funext +open import foundation.function-extensionality +open import foundation.propositional-truncations open import foundation.universe-levels -open import foundation.weakly-constant-maps funext +open import foundation.weakly-constant-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps @@ -27,7 +21,7 @@ open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import foundation-core.subtypes funext +open import foundation-core.subtypes ```
diff --git a/src/foundation/universal-property-propositional-truncation.lagda.md b/src/foundation/universal-property-propositional-truncation.lagda.md index ed662964de..1cadb2f5f2 100644 --- a/src/foundation/universal-property-propositional-truncation.lagda.md +++ b/src/foundation/universal-property-propositional-truncation.lagda.md @@ -1,35 +1,29 @@ # The universal property of propositional truncations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-propositional-truncation - (funext : function-extensionality) - where +module foundation.universal-property-propositional-truncation where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-cartesian-product-types funext -open import foundation.logical-equivalences funext -open import foundation.precomposition-functions-into-subuniverses funext +open import foundation.dependent-products-propositions +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.functoriality-cartesian-product-types +open import foundation.logical-equivalences +open import foundation.precomposition-functions-into-subuniverses open import foundation.subtype-identity-principle open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types funext -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types diff --git a/src/foundation/universal-property-pullbacks.lagda.md b/src/foundation/universal-property-pullbacks.lagda.md index 3fe1ee145a..0b97e575fa 100644 --- a/src/foundation/universal-property-pullbacks.lagda.md +++ b/src/foundation/universal-property-pullbacks.lagda.md @@ -1,28 +1,23 @@ # The universal property of pullbacks ```agda -open import foundation.function-extensionality-axiom +module foundation.universal-property-pullbacks where -module - foundation.universal-property-pullbacks - (funext : function-extensionality) - where - -open import foundation-core.universal-property-pullbacks funext public +open import foundation-core.universal-property-pullbacks public ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.subtype-identity-principle open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.function-types -open import foundation-core.pullbacks funext +open import foundation-core.pullbacks ```
diff --git a/src/foundation/universal-property-sequential-limits.lagda.md b/src/foundation/universal-property-sequential-limits.lagda.md index d2b09b774d..d7377fae19 100644 --- a/src/foundation/universal-property-sequential-limits.lagda.md +++ b/src/foundation/universal-property-sequential-limits.lagda.md @@ -1,23 +1,18 @@ # The universal property of sequential limits ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-sequential-limits - (funext : function-extensionality) - where +module foundation.universal-property-sequential-limits where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-inverse-sequential-diagrams funext +open import foundation.cones-over-inverse-sequential-diagrams open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.inverse-sequential-diagrams funext -open import foundation.postcomposition-functions funext +open import foundation.equivalences +open import foundation.inverse-sequential-diagrams +open import foundation.postcomposition-functions open import foundation.subtype-identity-principle open import foundation.universe-levels diff --git a/src/foundation/universal-property-set-quotients.lagda.md b/src/foundation/universal-property-set-quotients.lagda.md index 747d57b3d4..8ff5cf6b79 100644 --- a/src/foundation/universal-property-set-quotients.lagda.md +++ b/src/foundation/universal-property-set-quotients.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-set-quotients - (funext : function-extensionality) - where +module foundation.universal-property-set-quotients where ```
Imports @@ -16,28 +11,28 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.dependent-universal-property-equivalences funext -open import foundation.effective-maps-equivalence-relations funext -open import foundation.epimorphisms-with-respect-to-sets funext -open import foundation.equivalence-classes funext -open import foundation.existential-quantification funext -open import foundation.function-extensionality funext - +open import foundation.dependent-products-propositions +open import foundation.dependent-universal-property-equivalences +open import foundation.effective-maps-equivalence-relations +open import foundation.epimorphisms-with-respect-to-sets +open import foundation.equivalence-classes +open import foundation.existential-quantification +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.injective-maps funext -open import foundation.locally-small-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.sets funext -open import foundation.surjective-maps funext +open import foundation.identity-types +open import foundation.images +open import foundation.injective-maps +open import foundation.locally-small-types +open import foundation.logical-equivalences +open import foundation.propositional-extensionality +open import foundation.propositional-truncations +open import foundation.reflecting-maps-equivalence-relations +open import foundation.sets +open import foundation.surjective-maps open import foundation.transport-along-identifications -open import foundation.universal-property-dependent-pair-types funext -open import foundation.universal-property-image funext +open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-image open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -46,7 +41,7 @@ open import foundation-core.commuting-triangles-of-maps open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.embeddings -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.fibers-of-maps open import foundation-core.function-types @@ -54,8 +49,8 @@ open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.propositional-maps open import foundation-core.propositions -open import foundation-core.small-types funext -open import foundation-core.subtypes funext +open import foundation-core.small-types +open import foundation-core.subtypes open import foundation-core.torsorial-type-families open import foundation-core.type-theoretic-principle-of-choice open import foundation-core.univalence diff --git a/src/foundation/universal-property-set-truncation.lagda.md b/src/foundation/universal-property-set-truncation.lagda.md index 1ac282d263..c6a4069b7b 100644 --- a/src/foundation/universal-property-set-truncation.lagda.md +++ b/src/foundation/universal-property-set-truncation.lagda.md @@ -1,26 +1,20 @@ # The universal property of set truncations ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-set-truncation - (funext : function-extensionality) - where +module foundation.universal-property-set-truncation where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.mere-equality funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.mere-equality +open import foundation.reflecting-maps-equivalence-relations +open import foundation.sets open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-equivalences funext -open import foundation.universal-property-set-quotients funext +open import foundation.universal-property-equivalences +open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation-core.contractible-maps diff --git a/src/foundation/universal-property-truncation.lagda.md b/src/foundation/universal-property-truncation.lagda.md index fe3a531d07..3a47918c45 100644 --- a/src/foundation/universal-property-truncation.lagda.md +++ b/src/foundation/universal-property-truncation.lagda.md @@ -1,37 +1,31 @@ # The universal property of truncations ```agda -open import foundation.function-extensionality-axiom +module foundation.universal-property-truncation where -module - foundation.universal-property-truncation - (funext : function-extensionality) - where - -open import foundation-core.universal-property-truncation funext public +open import foundation-core.universal-property-truncation public ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-contractible-types funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.surjective-maps funext -open import foundation.type-arithmetic-dependent-function-types funext -open import foundation.universal-property-dependent-pair-types funext -open import foundation.universal-property-identity-types funext +open import foundation.dependent-products-contractible-types +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.surjective-maps +open import foundation.type-arithmetic-dependent-function-types +open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-identity-types open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.equivalences open import foundation-core.fibers-of-maps -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.torsorial-type-families open import foundation-core.truncated-types diff --git a/src/foundation/universal-property-unit-type.lagda.md b/src/foundation/universal-property-unit-type.lagda.md index 823ca72740..20149383b1 100644 --- a/src/foundation/universal-property-unit-type.lagda.md +++ b/src/foundation/universal-property-unit-type.lagda.md @@ -1,12 +1,7 @@ # The universal property of the unit type ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-property-unit-type - (funext : function-extensionality) - where +module foundation.universal-property-unit-type where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-contractible-types funext -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-contractible-types +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.constant-maps diff --git a/src/foundation/universal-quantification.lagda.md b/src/foundation/universal-quantification.lagda.md index 043f646f4a..63a9a9e0e7 100644 --- a/src/foundation/universal-quantification.lagda.md +++ b/src/foundation/universal-quantification.lagda.md @@ -1,22 +1,17 @@ # Universal quantification ```agda -open import foundation.function-extensionality-axiom - -module - foundation.universal-quantification - (funext : function-extensionality) - where +module foundation.universal-quantification where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext +open import foundation.dependent-products-propositions open import foundation.evaluation-functions -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.logical-equivalences +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/unordered-pairs-of-types.lagda.md b/src/foundation/unordered-pairs-of-types.lagda.md index fd833b65f2..ccefe96921 100644 --- a/src/foundation/unordered-pairs-of-types.lagda.md +++ b/src/foundation/unordered-pairs-of-types.lagda.md @@ -1,12 +1,7 @@ # Unordered pairs of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.unordered-pairs-of-types - (funext : function-extensionality) - where +module foundation.unordered-pairs-of-types where ```
Imports @@ -15,15 +10,15 @@ module open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.torsorial-type-families -open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.2-element-types ```
diff --git a/src/foundation/unordered-pairs.lagda.md b/src/foundation/unordered-pairs.lagda.md index 14a446f15c..764054eed8 100644 --- a/src/foundation/unordered-pairs.lagda.md +++ b/src/foundation/unordered-pairs.lagda.md @@ -1,35 +1,29 @@ # Unordered pairs of elements in a type ```agda -open import foundation.function-extensionality-axiom - -module - foundation.unordered-pairs - (funext : function-extensionality) - where +module foundation.unordered-pairs where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-types funext -open import foundation.decidable-equality funext +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-types +open import foundation.decidable-equality open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-extensionality funext - +open import foundation.dependent-universal-property-equivalences +open import foundation.existential-quantification +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.mere-equivalences funext -open import foundation.postcomposition-functions funext -open import foundation.propositional-truncations funext +open import foundation.homotopy-induction +open import foundation.mere-equivalences +open import foundation.postcomposition-functions +open import foundation.propositional-truncations open import foundation.structure-identity-principle -open import foundation.type-arithmetic-dependent-function-types funext -open import foundation.universal-property-contractible-types funext -open import foundation.universal-property-dependent-pair-types funext +open import foundation.type-arithmetic-dependent-function-types +open import foundation.universal-property-contractible-types +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -38,7 +32,7 @@ open import foundation-core.coproduct-types open import foundation-core.embeddings open import foundation-core.equivalences open import foundation-core.function-types -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies open import foundation-core.identity-types @@ -47,11 +41,11 @@ open import foundation-core.propositions open import foundation-core.sets open import foundation-core.torsorial-type-families -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext -open import univalent-combinatorics.universal-property-standard-finite-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.universal-property-standard-finite-types ```
diff --git a/src/foundation/unordered-tuples-of-types.lagda.md b/src/foundation/unordered-tuples-of-types.lagda.md index 58aea7bda5..b208cabd92 100644 --- a/src/foundation/unordered-tuples-of-types.lagda.md +++ b/src/foundation/unordered-tuples-of-types.lagda.md @@ -1,12 +1,7 @@ # Unordered tuples of types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.unordered-tuples-of-types - (funext : function-extensionality) - where +module foundation.unordered-tuples-of-types where ```
Imports @@ -17,15 +12,15 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.structure-identity-principle -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import foundation.unordered-tuples funext +open import foundation.unordered-tuples open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.torsorial-type-families -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/foundation/unordered-tuples.lagda.md b/src/foundation/unordered-tuples.lagda.md index a857805559..d3ce033256 100644 --- a/src/foundation/unordered-tuples.lagda.md +++ b/src/foundation/unordered-tuples.lagda.md @@ -1,12 +1,7 @@ # Unordered `n`-tuples of elements in a type ```agda -open import foundation.function-extensionality-axiom - -module - foundation.unordered-tuples - (funext : function-extensionality) - where +module foundation.unordered-tuples where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types funext -open import foundation.decidable-equality funext +open import foundation.1-types +open import foundation.decidable-equality open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext +open import foundation.dependent-products-truncated-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.postcomposition-functions funext +open import foundation.homotopy-induction +open import foundation.postcomposition-functions open import foundation.structure-identity-principle -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels open import foundation.whiskering-homotopies-composition @@ -35,10 +30,10 @@ open import foundation-core.identity-types open import foundation-core.sets open import foundation-core.torsorial-type-families -open import univalent-combinatorics.complements-isolated-elements funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.complements-isolated-elements +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/vectors-set-quotients.lagda.md b/src/foundation/vectors-set-quotients.lagda.md index d979430018..d9652fc385 100644 --- a/src/foundation/vectors-set-quotients.lagda.md +++ b/src/foundation/vectors-set-quotients.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - foundation.vectors-set-quotients - (funext : function-extensionality) - where +module foundation.vectors-set-quotients where ```
Imports @@ -17,26 +12,26 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-products-set-quotients funext +open import foundation.cartesian-products-set-quotients open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-extensionality funext - -open import foundation.multivariable-operations funext -open import foundation.products-equivalence-relations funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.set-quotients funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.multivariable-operations +open import foundation.products-equivalence-relations +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type +open import foundation.reflecting-maps-equivalence-relations +open import foundation.set-quotients +open import foundation.sets open import foundation.unit-type -open import foundation.universal-property-set-quotients funext +open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.coproduct-types open import foundation-core.equality-dependent-pair-types -open import foundation-core.equivalence-relations funext +open import foundation-core.equivalence-relations open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies @@ -45,9 +40,9 @@ open import foundation-core.propositions open import foundation-core.retractions open import foundation-core.sections -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/foundation/vertical-composition-spans-of-spans.lagda.md b/src/foundation/vertical-composition-spans-of-spans.lagda.md index dffbda6cba..785b482745 100644 --- a/src/foundation/vertical-composition-spans-of-spans.lagda.md +++ b/src/foundation/vertical-composition-spans-of-spans.lagda.md @@ -1,32 +1,27 @@ # Vertical composition of spans of spans ```agda -open import foundation.function-extensionality-axiom - -module - foundation.vertical-composition-spans-of-spans - (funext : function-extensionality) - where +module foundation.vertical-composition-spans-of-spans where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps funext -open import foundation.composition-spans funext +open import foundation.commuting-triangles-of-maps +open import foundation.composition-spans open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.equivalences-spans funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.morphisms-arrows funext +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.equivalences-spans +open import foundation.homotopies +open import foundation.identity-types +open import foundation.morphisms-arrows open import foundation.morphisms-spans -open import foundation.pullbacks funext +open import foundation.pullbacks open import foundation.spans -open import foundation.spans-of-spans funext -open import foundation.standard-pullbacks funext -open import foundation.type-arithmetic-standard-pullbacks funext +open import foundation.spans-of-spans +open import foundation.standard-pullbacks +open import foundation.type-arithmetic-standard-pullbacks open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/foundation/weak-function-extensionality.lagda.md b/src/foundation/weak-function-extensionality.lagda.md index 06c9312502..39801af669 100644 --- a/src/foundation/weak-function-extensionality.lagda.md +++ b/src/foundation/weak-function-extensionality.lagda.md @@ -1,21 +1,17 @@ # Weak function extensionality ```agda -open import foundation.function-extensionality-axiom - -module - foundation.weak-function-extensionality - (funext : function-extensionality) - where +module foundation.weak-function-extensionality where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels diff --git a/src/foundation/weak-limited-principle-of-omniscience.lagda.md b/src/foundation/weak-limited-principle-of-omniscience.lagda.md index 19ced2b51c..abef45248f 100644 --- a/src/foundation/weak-limited-principle-of-omniscience.lagda.md +++ b/src/foundation/weak-limited-principle-of-omniscience.lagda.md @@ -1,12 +1,7 @@ # The weak limited principle of omniscience ```agda -open import foundation.function-extensionality-axiom - -module - foundation.weak-limited-principle-of-omniscience - (funext : function-extensionality) - where +module foundation.weak-limited-principle-of-omniscience where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.disjunction funext -open import foundation.negation funext -open import foundation.universal-quantification funext +open import foundation.disjunction +open import foundation.negation +open import foundation.universal-quantification open import foundation.universe-levels open import foundation-core.booleans -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.propositions open import foundation-core.sets ``` diff --git a/src/foundation/weakly-constant-maps.lagda.md b/src/foundation/weakly-constant-maps.lagda.md index 0c48713b47..e2d2c88d58 100644 --- a/src/foundation/weakly-constant-maps.lagda.md +++ b/src/foundation/weakly-constant-maps.lagda.md @@ -1,12 +1,7 @@ # Weakly constant maps ```agda -open import foundation.function-extensionality-axiom - -module - foundation.weakly-constant-maps - (funext : function-extensionality) - where +module foundation.weakly-constant-maps where ```
Imports @@ -15,8 +10,8 @@ module open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext +open import foundation.identity-types +open import foundation.iterated-dependent-product-types open import foundation.telescopes open import foundation.universe-levels diff --git a/src/foundation/whiskering-homotopies-concatenation.lagda.md b/src/foundation/whiskering-homotopies-concatenation.lagda.md index d84e1d82d0..ef61dcad5c 100644 --- a/src/foundation/whiskering-homotopies-concatenation.lagda.md +++ b/src/foundation/whiskering-homotopies-concatenation.lagda.md @@ -1,12 +1,7 @@ # Whiskering homotopies with respect to concatenation ```agda -open import foundation.function-extensionality-axiom - -module - foundation.whiskering-homotopies-concatenation - (funext : function-extensionality) - where +module foundation.whiskering-homotopies-concatenation where open import foundation-core.whiskering-homotopies-concatenation public ``` @@ -15,10 +10,10 @@ open import foundation-core.whiskering-homotopies-concatenation public ```agda open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation open import foundation-core.equivalences -open import foundation-core.functoriality-dependent-function-types funext +open import foundation-core.functoriality-dependent-function-types open import foundation-core.homotopies ``` diff --git a/src/foundation/whiskering-identifications-concatenation.lagda.md b/src/foundation/whiskering-identifications-concatenation.lagda.md index 79c68c4137..c37fbc64cc 100644 --- a/src/foundation/whiskering-identifications-concatenation.lagda.md +++ b/src/foundation/whiskering-identifications-concatenation.lagda.md @@ -1,12 +1,7 @@ # Whiskering identifications with respect to concatenation ```agda -open import foundation.function-extensionality-axiom - -module - foundation.whiskering-identifications-concatenation - (funext : function-extensionality) - where +module foundation.whiskering-identifications-concatenation where open import foundation-core.whiskering-identifications-concatenation public ``` @@ -15,7 +10,7 @@ open import foundation-core.whiskering-identifications-concatenation public ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels open import foundation-core.equivalences diff --git a/src/foundation/wild-category-of-types.lagda.md b/src/foundation/wild-category-of-types.lagda.md index 6e496cd7e4..60277a29a4 100644 --- a/src/foundation/wild-category-of-types.lagda.md +++ b/src/foundation/wild-category-of-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - foundation.wild-category-of-types - (funext : function-extensionality) - where +module foundation.wild-category-of-types where ```
Imports @@ -16,11 +11,11 @@ module ```agda open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.globular-type-of-functions funext -open import foundation.homotopies funext -open import foundation.isomorphisms-of-sets funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.globular-type-of-functions +open import foundation.homotopies +open import foundation.isomorphisms-of-sets +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels open import foundation-core.contractible-types @@ -31,13 +26,13 @@ open import foundation-core.identity-types open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.large-reflexive-globular-types funext -open import globular-types.large-transitive-globular-types funext -open import globular-types.reflexive-globular-types funext -open import globular-types.transitive-globular-types funext +open import globular-types.large-reflexive-globular-types +open import globular-types.large-transitive-globular-types +open import globular-types.reflexive-globular-types +open import globular-types.transitive-globular-types -open import wild-category-theory.noncoherent-large-omega-precategories funext -open import wild-category-theory.noncoherent-omega-precategories funext +open import wild-category-theory.noncoherent-large-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories ```
diff --git a/src/foundation/yoneda-identity-types.lagda.md b/src/foundation/yoneda-identity-types.lagda.md index 74133c02d2..f9064f5122 100644 --- a/src/foundation/yoneda-identity-types.lagda.md +++ b/src/foundation/yoneda-identity-types.lagda.md @@ -1,12 +1,7 @@ # Yoneda identity types ```agda -open import foundation.function-extensionality-axiom - -module - foundation.yoneda-identity-types - (funext : function-extensionality) - where +module foundation.yoneda-identity-types where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.multivariable-homotopies funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.multivariable-homotopies open import foundation.strictly-right-unital-concatenation-identifications open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalence funext -open import foundation.universal-property-identity-systems funext +open import foundation.univalence +open import foundation.universal-property-identity-systems open import foundation.universe-levels open import foundation-core.contractible-types diff --git a/src/globular-types.lagda.md b/src/globular-types.lagda.md index 688a7344ee..260995b614 100644 --- a/src/globular-types.lagda.md +++ b/src/globular-types.lagda.md @@ -7,66 +7,61 @@ ## Modules in the globular types namespace ```agda -open import foundation.function-extensionality-axiom +module globular-types where -module - globular-types - (funext : function-extensionality) - where - -open import globular-types.base-change-dependent-globular-types funext public -open import globular-types.base-change-dependent-reflexive-globular-types funext public -open import globular-types.binary-dependent-globular-types funext public -open import globular-types.binary-dependent-reflexive-globular-types funext public +open import globular-types.base-change-dependent-globular-types public +open import globular-types.base-change-dependent-reflexive-globular-types public +open import globular-types.binary-dependent-globular-types public +open import globular-types.binary-dependent-reflexive-globular-types public open import globular-types.binary-globular-maps public -open import globular-types.colax-reflexive-globular-maps funext public -open import globular-types.colax-transitive-globular-maps funext public +open import globular-types.colax-reflexive-globular-maps public +open import globular-types.colax-transitive-globular-maps public open import globular-types.composition-structure-globular-types public open import globular-types.constant-globular-types public -open import globular-types.dependent-globular-types funext public -open import globular-types.dependent-reflexive-globular-types funext public -open import globular-types.dependent-sums-globular-types funext public -open import globular-types.discrete-dependent-reflexive-globular-types funext public -open import globular-types.discrete-globular-types funext public -open import globular-types.discrete-reflexive-globular-types funext public -open import globular-types.empty-globular-types funext public -open import globular-types.equality-globular-types funext public -open import globular-types.exponentials-globular-types funext public -open import globular-types.fibers-globular-maps funext public -open import globular-types.globular-equivalences funext public -open import globular-types.globular-maps funext public +open import globular-types.dependent-globular-types public +open import globular-types.dependent-reflexive-globular-types public +open import globular-types.dependent-sums-globular-types public +open import globular-types.discrete-dependent-reflexive-globular-types public +open import globular-types.discrete-globular-types public +open import globular-types.discrete-reflexive-globular-types public +open import globular-types.empty-globular-types public +open import globular-types.equality-globular-types public +open import globular-types.exponentials-globular-types public +open import globular-types.fibers-globular-maps public +open import globular-types.globular-equivalences public +open import globular-types.globular-maps public open import globular-types.globular-types public -open import globular-types.large-colax-reflexive-globular-maps funext public -open import globular-types.large-colax-transitive-globular-maps funext public -open import globular-types.large-globular-maps funext public +open import globular-types.large-colax-reflexive-globular-maps public +open import globular-types.large-colax-transitive-globular-maps public +open import globular-types.large-globular-maps public open import globular-types.large-globular-types public -open import globular-types.large-lax-reflexive-globular-maps funext public -open import globular-types.large-lax-transitive-globular-maps funext public -open import globular-types.large-reflexive-globular-maps funext public -open import globular-types.large-reflexive-globular-types funext public -open import globular-types.large-symmetric-globular-types funext public -open import globular-types.large-transitive-globular-maps funext public -open import globular-types.large-transitive-globular-types funext public -open import globular-types.lax-reflexive-globular-maps funext public -open import globular-types.lax-transitive-globular-maps funext public -open import globular-types.points-globular-types funext public -open import globular-types.points-reflexive-globular-types funext public -open import globular-types.pointwise-extensions-binary-families-globular-types funext public -open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types funext public -open import globular-types.pointwise-extensions-families-globular-types funext public -open import globular-types.pointwise-extensions-families-reflexive-globular-types funext public -open import globular-types.products-families-of-globular-types funext public -open import globular-types.reflexive-globular-equivalences funext public -open import globular-types.reflexive-globular-maps funext public -open import globular-types.reflexive-globular-types funext public -open import globular-types.sections-dependent-globular-types funext public -open import globular-types.superglobular-types funext public -open import globular-types.symmetric-globular-types funext public -open import globular-types.terminal-globular-types funext public -open import globular-types.transitive-globular-maps funext public -open import globular-types.transitive-globular-types funext public +open import globular-types.large-lax-reflexive-globular-maps public +open import globular-types.large-lax-transitive-globular-maps public +open import globular-types.large-reflexive-globular-maps public +open import globular-types.large-reflexive-globular-types public +open import globular-types.large-symmetric-globular-types public +open import globular-types.large-transitive-globular-maps public +open import globular-types.large-transitive-globular-types public +open import globular-types.lax-reflexive-globular-maps public +open import globular-types.lax-transitive-globular-maps public +open import globular-types.points-globular-types public +open import globular-types.points-reflexive-globular-types public +open import globular-types.pointwise-extensions-binary-families-globular-types public +open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types public +open import globular-types.pointwise-extensions-families-globular-types public +open import globular-types.pointwise-extensions-families-reflexive-globular-types public +open import globular-types.products-families-of-globular-types public +open import globular-types.reflexive-globular-equivalences public +open import globular-types.reflexive-globular-maps public +open import globular-types.reflexive-globular-types public +open import globular-types.sections-dependent-globular-types public +open import globular-types.superglobular-types public +open import globular-types.symmetric-globular-types public +open import globular-types.terminal-globular-types public +open import globular-types.transitive-globular-maps public +open import globular-types.transitive-globular-types public open import globular-types.unit-globular-type public -open import globular-types.unit-reflexive-globular-type funext public -open import globular-types.universal-globular-type funext public -open import globular-types.universal-reflexive-globular-type funext public +open import globular-types.unit-reflexive-globular-type public +open import globular-types.universal-globular-type public +open import globular-types.universal-reflexive-globular-type public ``` diff --git a/src/globular-types/base-change-dependent-globular-types.lagda.md b/src/globular-types/base-change-dependent-globular-types.lagda.md index d000158db8..c0408459c0 100644 --- a/src/globular-types/base-change-dependent-globular-types.lagda.md +++ b/src/globular-types/base-change-dependent-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.base-change-dependent-globular-types - (funext : function-extensionality) - where +module globular-types.base-change-dependent-globular-types where ```
Imports @@ -16,8 +11,8 @@ module ```agda open import foundation.universe-levels -open import globular-types.dependent-globular-types funext -open import globular-types.globular-maps funext +open import globular-types.dependent-globular-types +open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md b/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md index 709a13fd92..f1507037dd 100644 --- a/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/base-change-dependent-reflexive-globular-types.lagda.md @@ -3,27 +3,22 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.base-change-dependent-reflexive-globular-types - (funext : function-extensionality) - where +module globular-types.base-change-dependent-reflexive-globular-types where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import globular-types.base-change-dependent-globular-types funext -open import globular-types.dependent-globular-types funext -open import globular-types.dependent-reflexive-globular-types funext +open import globular-types.base-change-dependent-globular-types +open import globular-types.dependent-globular-types +open import globular-types.dependent-reflexive-globular-types open import globular-types.globular-types -open import globular-types.reflexive-globular-maps funext -open import globular-types.reflexive-globular-types funext +open import globular-types.reflexive-globular-maps +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/binary-dependent-globular-types.lagda.md b/src/globular-types/binary-dependent-globular-types.lagda.md index 0ac6db2f7a..de718af1c3 100644 --- a/src/globular-types/binary-dependent-globular-types.lagda.md +++ b/src/globular-types/binary-dependent-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.binary-dependent-globular-types - (funext : function-extensionality) - where +module globular-types.binary-dependent-globular-types where ```
Imports @@ -17,7 +12,7 @@ module open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.points-globular-types funext +open import globular-types.points-globular-types ```
diff --git a/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md b/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md index 4d9d40343a..234b035227 100644 --- a/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/binary-dependent-reflexive-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.binary-dependent-reflexive-globular-types - (funext : function-extensionality) - where +module globular-types.binary-dependent-reflexive-globular-types where ```
Imports @@ -16,10 +11,10 @@ module ```agda open import foundation.universe-levels -open import globular-types.binary-dependent-globular-types funext +open import globular-types.binary-dependent-globular-types open import globular-types.globular-types -open import globular-types.points-reflexive-globular-types funext -open import globular-types.reflexive-globular-types funext +open import globular-types.points-reflexive-globular-types +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/colax-reflexive-globular-maps.lagda.md b/src/globular-types/colax-reflexive-globular-maps.lagda.md index ddd1b65791..1e834a12a5 100644 --- a/src/globular-types/colax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/colax-reflexive-globular-maps.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.colax-reflexive-globular-maps - (funext : function-extensionality) - where +module globular-types.colax-reflexive-globular-maps where ```
Imports @@ -16,8 +11,8 @@ module ```agda open import foundation.universe-levels -open import globular-types.globular-maps funext -open import globular-types.reflexive-globular-types funext +open import globular-types.globular-maps +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/colax-transitive-globular-maps.lagda.md b/src/globular-types/colax-transitive-globular-maps.lagda.md index 8f037f92c4..cb012086d5 100644 --- a/src/globular-types/colax-transitive-globular-maps.lagda.md +++ b/src/globular-types/colax-transitive-globular-maps.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.colax-transitive-globular-maps - (funext : function-extensionality) - where +module globular-types.colax-transitive-globular-maps where ```
Imports @@ -16,8 +11,8 @@ module ```agda open import foundation.universe-levels -open import globular-types.globular-maps funext -open import globular-types.transitive-globular-types funext +open import globular-types.globular-maps +open import globular-types.transitive-globular-types ```
diff --git a/src/globular-types/dependent-globular-types.lagda.md b/src/globular-types/dependent-globular-types.lagda.md index 8f8725a6e1..41d4806001 100644 --- a/src/globular-types/dependent-globular-types.lagda.md +++ b/src/globular-types/dependent-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.dependent-globular-types - (funext : function-extensionality) - where +module globular-types.dependent-globular-types where ```
Imports @@ -18,7 +13,7 @@ open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.points-globular-types funext +open import globular-types.points-globular-types ```
diff --git a/src/globular-types/dependent-reflexive-globular-types.lagda.md b/src/globular-types/dependent-reflexive-globular-types.lagda.md index dd5c0ec871..b82c493c5e 100644 --- a/src/globular-types/dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/dependent-reflexive-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.dependent-reflexive-globular-types - (funext : function-extensionality) - where +module globular-types.dependent-reflexive-globular-types where ```
Imports @@ -17,10 +12,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.dependent-globular-types funext +open import globular-types.dependent-globular-types open import globular-types.globular-types -open import globular-types.points-reflexive-globular-types funext -open import globular-types.reflexive-globular-types funext +open import globular-types.points-reflexive-globular-types +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/dependent-sums-globular-types.lagda.md b/src/globular-types/dependent-sums-globular-types.lagda.md index 83e39e0b54..ead7b91cb5 100644 --- a/src/globular-types/dependent-sums-globular-types.lagda.md +++ b/src/globular-types/dependent-sums-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.dependent-sums-globular-types - (funext : function-extensionality) - where +module globular-types.dependent-sums-globular-types where ```
Imports @@ -17,11 +12,11 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.base-change-dependent-globular-types funext -open import globular-types.dependent-globular-types funext -open import globular-types.globular-maps funext +open import globular-types.base-change-dependent-globular-types +open import globular-types.dependent-globular-types +open import globular-types.globular-maps open import globular-types.globular-types -open import globular-types.sections-dependent-globular-types funext +open import globular-types.sections-dependent-globular-types ```
diff --git a/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md b/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md index b002492c96..782d45590d 100644 --- a/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md +++ b/src/globular-types/discrete-dependent-reflexive-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.discrete-dependent-reflexive-globular-types - (funext : function-extensionality) - where +module globular-types.discrete-dependent-reflexive-globular-types where ```
Imports @@ -16,10 +11,10 @@ module ```agda open import foundation.universe-levels -open import globular-types.dependent-reflexive-globular-types funext -open import globular-types.discrete-reflexive-globular-types funext -open import globular-types.points-reflexive-globular-types funext -open import globular-types.reflexive-globular-types funext +open import globular-types.dependent-reflexive-globular-types +open import globular-types.discrete-reflexive-globular-types +open import globular-types.points-reflexive-globular-types +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/discrete-globular-types.lagda.md b/src/globular-types/discrete-globular-types.lagda.md index 8883dade06..77b4dd1141 100644 --- a/src/globular-types/discrete-globular-types.lagda.md +++ b/src/globular-types/discrete-globular-types.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.discrete-globular-types - (funext : function-extensionality) - where +module globular-types.discrete-globular-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.discrete-binary-relations funext -open import foundation.propositions funext +open import foundation.discrete-binary-relations +open import foundation.propositions open import foundation.universe-levels -open import globular-types.empty-globular-types funext +open import globular-types.empty-globular-types open import globular-types.globular-types ``` diff --git a/src/globular-types/discrete-reflexive-globular-types.lagda.md b/src/globular-types/discrete-reflexive-globular-types.lagda.md index cbd898c3ff..9e45c68d20 100644 --- a/src/globular-types/discrete-reflexive-globular-types.lagda.md +++ b/src/globular-types/discrete-reflexive-globular-types.lagda.md @@ -3,25 +3,20 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.discrete-reflexive-globular-types - (funext : function-extensionality) - where +module globular-types.discrete-reflexive-globular-types where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.reflexive-globular-types funext -open import globular-types.symmetric-globular-types funext -open import globular-types.transitive-globular-types funext +open import globular-types.reflexive-globular-types +open import globular-types.symmetric-globular-types +open import globular-types.transitive-globular-types ```
diff --git a/src/globular-types/empty-globular-types.lagda.md b/src/globular-types/empty-globular-types.lagda.md index f612cfcc1a..9e19f67f78 100644 --- a/src/globular-types/empty-globular-types.lagda.md +++ b/src/globular-types/empty-globular-types.lagda.md @@ -3,18 +3,13 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.empty-globular-types - (funext : function-extensionality) - where +module globular-types.empty-globular-types where ```
Imports ```agda -open import foundation.empty-types funext +open import foundation.empty-types open import foundation.universe-levels open import globular-types.constant-globular-types diff --git a/src/globular-types/equality-globular-types.lagda.md b/src/globular-types/equality-globular-types.lagda.md index 92ae709ea6..a93f6bde6f 100644 --- a/src/globular-types/equality-globular-types.lagda.md +++ b/src/globular-types/equality-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.equality-globular-types - (funext : function-extensionality) - where +module globular-types.equality-globular-types where ```
Imports @@ -16,13 +11,13 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-homotopies funext -open import foundation.cartesian-product-types funext +open import foundation.binary-homotopies +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.identity-types +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels open import foundation-core.coherently-invertible-maps diff --git a/src/globular-types/exponentials-globular-types.lagda.md b/src/globular-types/exponentials-globular-types.lagda.md index a6e30ae583..85458109da 100644 --- a/src/globular-types/exponentials-globular-types.lagda.md +++ b/src/globular-types/exponentials-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.exponentials-globular-types - (funext : function-extensionality) - where +module globular-types.exponentials-globular-types where ```
Imports @@ -17,9 +12,9 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types -open import globular-types.products-families-of-globular-types funext +open import globular-types.products-families-of-globular-types ```
diff --git a/src/globular-types/fibers-globular-maps.lagda.md b/src/globular-types/fibers-globular-maps.lagda.md index 21ece5fd89..62022c561b 100644 --- a/src/globular-types/fibers-globular-maps.lagda.md +++ b/src/globular-types/fibers-globular-maps.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.fibers-globular-maps - (funext : function-extensionality) - where +module globular-types.fibers-globular-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.identity-types funext +open import foundation.fibers-of-maps +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.dependent-globular-types funext -open import globular-types.globular-maps funext +open import globular-types.dependent-globular-types +open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/globular-equivalences.lagda.md b/src/globular-types/globular-equivalences.lagda.md index 14f5f46142..5afece9603 100644 --- a/src/globular-types/globular-equivalences.lagda.md +++ b/src/globular-types/globular-equivalences.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.globular-equivalences - (funext : function-extensionality) - where +module globular-types.globular-equivalences where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/globular-maps.lagda.md b/src/globular-types/globular-maps.lagda.md index 44bbe7cd7b..4cdc042698 100644 --- a/src/globular-types/globular-maps.lagda.md +++ b/src/globular-types/globular-maps.lagda.md @@ -3,20 +3,15 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.globular-maps - (funext : function-extensionality) - where +module globular-types.globular-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels open import globular-types.globular-types diff --git a/src/globular-types/large-colax-reflexive-globular-maps.lagda.md b/src/globular-types/large-colax-reflexive-globular-maps.lagda.md index adff192737..a293af9b2d 100644 --- a/src/globular-types/large-colax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/large-colax-reflexive-globular-maps.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-colax-reflexive-globular-maps - (funext : function-extensionality) - where +module globular-types.large-colax-reflexive-globular-maps where ```
Imports ```agda -open import foundation.function-types funext +open import foundation.function-types open import foundation.universe-levels -open import globular-types.colax-reflexive-globular-maps funext -open import globular-types.large-globular-maps funext -open import globular-types.large-reflexive-globular-types funext -open import globular-types.reflexive-globular-types funext +open import globular-types.colax-reflexive-globular-maps +open import globular-types.large-globular-maps +open import globular-types.large-reflexive-globular-types +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/large-colax-transitive-globular-maps.lagda.md b/src/globular-types/large-colax-transitive-globular-maps.lagda.md index 96479e7cfe..89aa77b7db 100644 --- a/src/globular-types/large-colax-transitive-globular-maps.lagda.md +++ b/src/globular-types/large-colax-transitive-globular-maps.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-colax-transitive-globular-maps - (funext : function-extensionality) - where +module globular-types.large-colax-transitive-globular-maps where ```
Imports ```agda -open import foundation.function-types funext +open import foundation.function-types open import foundation.universe-levels -open import globular-types.colax-transitive-globular-maps funext -open import globular-types.large-globular-maps funext -open import globular-types.large-transitive-globular-types funext -open import globular-types.transitive-globular-types funext +open import globular-types.colax-transitive-globular-maps +open import globular-types.large-globular-maps +open import globular-types.large-transitive-globular-types +open import globular-types.transitive-globular-types ```
diff --git a/src/globular-types/large-globular-maps.lagda.md b/src/globular-types/large-globular-maps.lagda.md index 79ff02150b..de2899cac3 100644 --- a/src/globular-types/large-globular-maps.lagda.md +++ b/src/globular-types/large-globular-maps.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-globular-maps - (funext : function-extensionality) - where +module globular-types.large-globular-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types open import globular-types.large-globular-types ``` diff --git a/src/globular-types/large-lax-reflexive-globular-maps.lagda.md b/src/globular-types/large-lax-reflexive-globular-maps.lagda.md index 47fe404b1d..4bde0a6526 100644 --- a/src/globular-types/large-lax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/large-lax-reflexive-globular-maps.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-lax-reflexive-globular-maps - (funext : function-extensionality) - where +module globular-types.large-lax-reflexive-globular-maps where ```
Imports ```agda -open import foundation.function-types funext +open import foundation.function-types open import foundation.universe-levels -open import globular-types.large-globular-maps funext -open import globular-types.large-reflexive-globular-types funext -open import globular-types.lax-reflexive-globular-maps funext -open import globular-types.reflexive-globular-types funext +open import globular-types.large-globular-maps +open import globular-types.large-reflexive-globular-types +open import globular-types.lax-reflexive-globular-maps +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/large-lax-transitive-globular-maps.lagda.md b/src/globular-types/large-lax-transitive-globular-maps.lagda.md index e41dd02a81..d2534bf35f 100644 --- a/src/globular-types/large-lax-transitive-globular-maps.lagda.md +++ b/src/globular-types/large-lax-transitive-globular-maps.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-lax-transitive-globular-maps - (funext : function-extensionality) - where +module globular-types.large-lax-transitive-globular-maps where ```
Imports ```agda -open import foundation.function-types funext +open import foundation.function-types open import foundation.universe-levels -open import globular-types.large-globular-maps funext -open import globular-types.large-transitive-globular-types funext -open import globular-types.lax-transitive-globular-maps funext -open import globular-types.transitive-globular-types funext +open import globular-types.large-globular-maps +open import globular-types.large-transitive-globular-types +open import globular-types.lax-transitive-globular-maps +open import globular-types.transitive-globular-types ```
diff --git a/src/globular-types/large-reflexive-globular-maps.lagda.md b/src/globular-types/large-reflexive-globular-maps.lagda.md index a5278af3a8..38cada0b7b 100644 --- a/src/globular-types/large-reflexive-globular-maps.lagda.md +++ b/src/globular-types/large-reflexive-globular-maps.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-reflexive-globular-maps - (funext : function-extensionality) - where +module globular-types.large-reflexive-globular-maps where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.large-globular-maps funext -open import globular-types.large-reflexive-globular-types funext -open import globular-types.reflexive-globular-maps funext -open import globular-types.reflexive-globular-types funext +open import globular-types.large-globular-maps +open import globular-types.large-reflexive-globular-types +open import globular-types.reflexive-globular-maps +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/large-reflexive-globular-types.lagda.md b/src/globular-types/large-reflexive-globular-types.lagda.md index 143220a0b8..5c87033440 100644 --- a/src/globular-types/large-reflexive-globular-types.lagda.md +++ b/src/globular-types/large-reflexive-globular-types.lagda.md @@ -3,25 +3,20 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-reflexive-globular-types - (funext : function-extensionality) - where +module globular-types.large-reflexive-globular-types where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.large-binary-relations funext +open import foundation.binary-relations +open import foundation.large-binary-relations open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.large-globular-maps funext +open import globular-types.large-globular-maps open import globular-types.large-globular-types -open import globular-types.reflexive-globular-types funext +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/large-symmetric-globular-types.lagda.md b/src/globular-types/large-symmetric-globular-types.lagda.md index fd2a165495..02e84ade5f 100644 --- a/src/globular-types/large-symmetric-globular-types.lagda.md +++ b/src/globular-types/large-symmetric-globular-types.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-symmetric-globular-types - (funext : function-extensionality) - where +module globular-types.large-symmetric-globular-types where ```
Imports ```agda -open import foundation.large-binary-relations funext +open import foundation.large-binary-relations open import foundation.universe-levels open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.symmetric-globular-types funext +open import globular-types.symmetric-globular-types ```
diff --git a/src/globular-types/large-transitive-globular-maps.lagda.md b/src/globular-types/large-transitive-globular-maps.lagda.md index 6e5d4245c4..c4800f5c99 100644 --- a/src/globular-types/large-transitive-globular-maps.lagda.md +++ b/src/globular-types/large-transitive-globular-maps.lagda.md @@ -3,26 +3,21 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-transitive-globular-maps - (funext : function-extensionality) - where +module globular-types.large-transitive-globular-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.large-globular-maps funext -open import globular-types.large-transitive-globular-types funext -open import globular-types.transitive-globular-maps funext -open import globular-types.transitive-globular-types funext +open import globular-types.large-globular-maps +open import globular-types.large-transitive-globular-types +open import globular-types.transitive-globular-maps +open import globular-types.transitive-globular-types ```
diff --git a/src/globular-types/large-transitive-globular-types.lagda.md b/src/globular-types/large-transitive-globular-types.lagda.md index b34f28e915..7981f454ba 100644 --- a/src/globular-types/large-transitive-globular-types.lagda.md +++ b/src/globular-types/large-transitive-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.large-transitive-globular-types - (funext : function-extensionality) - where +module globular-types.large-transitive-globular-types where ```
Imports @@ -17,9 +12,9 @@ module open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.large-globular-maps funext +open import globular-types.large-globular-maps open import globular-types.large-globular-types -open import globular-types.transitive-globular-types funext +open import globular-types.transitive-globular-types ```
diff --git a/src/globular-types/lax-reflexive-globular-maps.lagda.md b/src/globular-types/lax-reflexive-globular-maps.lagda.md index 89cb31719d..910fa5260d 100644 --- a/src/globular-types/lax-reflexive-globular-maps.lagda.md +++ b/src/globular-types/lax-reflexive-globular-maps.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.lax-reflexive-globular-maps - (funext : function-extensionality) - where +module globular-types.lax-reflexive-globular-maps where ```
Imports @@ -16,8 +11,8 @@ module ```agda open import foundation.universe-levels -open import globular-types.globular-maps funext -open import globular-types.reflexive-globular-types funext +open import globular-types.globular-maps +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/lax-transitive-globular-maps.lagda.md b/src/globular-types/lax-transitive-globular-maps.lagda.md index e6a8ff4cac..d06760ce39 100644 --- a/src/globular-types/lax-transitive-globular-maps.lagda.md +++ b/src/globular-types/lax-transitive-globular-maps.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.lax-transitive-globular-maps - (funext : function-extensionality) - where +module globular-types.lax-transitive-globular-maps where ```
Imports @@ -16,8 +11,8 @@ module ```agda open import foundation.universe-levels -open import globular-types.globular-maps funext -open import globular-types.transitive-globular-types funext +open import globular-types.globular-maps +open import globular-types.transitive-globular-types ```
diff --git a/src/globular-types/points-globular-types.lagda.md b/src/globular-types/points-globular-types.lagda.md index 7d1dbb0af4..94e81c6f56 100644 --- a/src/globular-types/points-globular-types.lagda.md +++ b/src/globular-types/points-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.points-globular-types - (funext : function-extensionality) - where +module globular-types.points-globular-types where ```
Imports @@ -17,7 +12,7 @@ module open import foundation.unit-type open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types open import globular-types.unit-globular-type ``` diff --git a/src/globular-types/points-reflexive-globular-types.lagda.md b/src/globular-types/points-reflexive-globular-types.lagda.md index 4f0fe2e779..c18a467757 100644 --- a/src/globular-types/points-reflexive-globular-types.lagda.md +++ b/src/globular-types/points-reflexive-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.points-reflexive-globular-types - (funext : function-extensionality) - where +module globular-types.points-reflexive-globular-types where ```
Imports @@ -16,8 +11,8 @@ module ```agda open import foundation.universe-levels -open import globular-types.points-globular-types funext -open import globular-types.reflexive-globular-types funext +open import globular-types.points-globular-types +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md b/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md index b1cc9ec0ba..904d9b312f 100644 --- a/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-binary-families-globular-types.lagda.md @@ -14,10 +14,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.binary-dependent-globular-types funext -open import globular-types.globular-equivalences funext +open import globular-types.binary-dependent-globular-types +open import globular-types.globular-equivalences open import globular-types.globular-types -open import globular-types.points-globular-types funext +open import globular-types.points-globular-types ```
@@ -48,12 +48,7 @@ of `K` if it comes equipped with a family of ### The predicate of being a pointwise extension of a binary family of globular types ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {l1 l2 l3 l4 l5 l6 l7 l8 : Level} {G : Globular-Type l1 l2} {H : Globular-Type l3 l4} (K : 0-cell-Globular-Type G → 0-cell-Globular-Type H → Globular-Type l5 l6) diff --git a/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md b/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md index 1023ced2d4..c593d0e0a3 100644 --- a/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-binary-families-reflexive-globular-types.lagda.md @@ -14,10 +14,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.binary-dependent-reflexive-globular-types funext -open import globular-types.points-reflexive-globular-types funext -open import globular-types.reflexive-globular-equivalences funext -open import globular-types.reflexive-globular-types funext +open import globular-types.binary-dependent-reflexive-globular-types +open import globular-types.points-reflexive-globular-types +open import globular-types.reflexive-globular-equivalences +open import globular-types.reflexive-globular-types ```
@@ -49,12 +49,7 @@ of `K` if it comes equipped with a family of ### The predicate of being a pointwise extension of a binary family of reflexive globular types ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {l1 l2 l3 l4 l5 l6 l7 l8 : Level} {G : Reflexive-Globular-Type l1 l2} {H : Reflexive-Globular-Type l3 l4} (K : diff --git a/src/globular-types/pointwise-extensions-families-globular-types.lagda.md b/src/globular-types/pointwise-extensions-families-globular-types.lagda.md index a531212472..05d14be3df 100644 --- a/src/globular-types/pointwise-extensions-families-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-families-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.pointwise-extensions-families-globular-types - (funext : function-extensionality) - where +module globular-types.pointwise-extensions-families-globular-types where ```
Imports @@ -17,10 +12,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.dependent-globular-types funext -open import globular-types.globular-equivalences funext +open import globular-types.dependent-globular-types +open import globular-types.globular-equivalences open import globular-types.globular-types -open import globular-types.points-globular-types funext +open import globular-types.points-globular-types ```
diff --git a/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md b/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md index 10e14d29a1..195002b2fe 100644 --- a/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md +++ b/src/globular-types/pointwise-extensions-families-reflexive-globular-types.lagda.md @@ -14,13 +14,13 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.dependent-globular-types funext -open import globular-types.dependent-reflexive-globular-types funext +open import globular-types.dependent-globular-types +open import globular-types.dependent-reflexive-globular-types open import globular-types.globular-types -open import globular-types.points-globular-types funext -open import globular-types.points-reflexive-globular-types funext -open import globular-types.reflexive-globular-equivalences funext -open import globular-types.reflexive-globular-types funext +open import globular-types.points-globular-types +open import globular-types.points-reflexive-globular-types +open import globular-types.reflexive-globular-equivalences +open import globular-types.reflexive-globular-types ```
@@ -49,12 +49,7 @@ indexed by the [points](globular-types.points-reflexive-globular-types.md) of ### The predicate of being a pointwise extension of a family of reflexive globular types ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {l1 l2 l3 l4 l5 l6 : Level} {G : Reflexive-Globular-Type l1 l2} (H : 0-cell-Reflexive-Globular-Type G → Reflexive-Globular-Type l3 l4) (K : Dependent-Reflexive-Globular-Type l5 l6 G) diff --git a/src/globular-types/products-families-of-globular-types.lagda.md b/src/globular-types/products-families-of-globular-types.lagda.md index 2f0f276f63..a3c5ae1d63 100644 --- a/src/globular-types/products-families-of-globular-types.lagda.md +++ b/src/globular-types/products-families-of-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.products-families-of-globular-types - (funext : function-extensionality) - where +module globular-types.products-families-of-globular-types where ```
Imports @@ -17,7 +12,7 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/reflexive-globular-equivalences.lagda.md b/src/globular-types/reflexive-globular-equivalences.lagda.md index 6ef59adcc3..8d154f39af 100644 --- a/src/globular-types/reflexive-globular-equivalences.lagda.md +++ b/src/globular-types/reflexive-globular-equivalences.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.reflexive-globular-equivalences - (funext : function-extensionality) - where +module globular-types.reflexive-globular-equivalences where ```
Imports @@ -16,15 +11,15 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-equivalences funext -open import globular-types.globular-maps funext -open import globular-types.reflexive-globular-maps funext -open import globular-types.reflexive-globular-types funext +open import globular-types.globular-equivalences +open import globular-types.globular-maps +open import globular-types.reflexive-globular-maps +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/reflexive-globular-maps.lagda.md b/src/globular-types/reflexive-globular-maps.lagda.md index 3eb226d886..92bd88780a 100644 --- a/src/globular-types/reflexive-globular-maps.lagda.md +++ b/src/globular-types/reflexive-globular-maps.lagda.md @@ -3,22 +3,17 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.reflexive-globular-maps - (funext : function-extensionality) - where +module globular-types.reflexive-globular-maps where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-maps funext -open import globular-types.reflexive-globular-types funext +open import globular-types.globular-maps +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/reflexive-globular-types.lagda.md b/src/globular-types/reflexive-globular-types.lagda.md index 8005795203..8eec1e2951 100644 --- a/src/globular-types/reflexive-globular-types.lagda.md +++ b/src/globular-types/reflexive-globular-types.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.reflexive-globular-types - (funext : function-extensionality) - where +module globular-types.reflexive-globular-types where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/sections-dependent-globular-types.lagda.md b/src/globular-types/sections-dependent-globular-types.lagda.md index eb1340404d..382d8719a1 100644 --- a/src/globular-types/sections-dependent-globular-types.lagda.md +++ b/src/globular-types/sections-dependent-globular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.sections-dependent-globular-types - (funext : function-extensionality) - where +module globular-types.sections-dependent-globular-types where ```
Imports @@ -16,7 +11,7 @@ module ```agda open import foundation.universe-levels -open import globular-types.dependent-globular-types funext +open import globular-types.dependent-globular-types open import globular-types.globular-types ``` diff --git a/src/globular-types/superglobular-types.lagda.md b/src/globular-types/superglobular-types.lagda.md index 6819e1a9fe..eb34024fd4 100644 --- a/src/globular-types/superglobular-types.lagda.md +++ b/src/globular-types/superglobular-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.superglobular-types - (funext : function-extensionality) - where +module globular-types.superglobular-types where ```
Imports @@ -17,12 +12,12 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.binary-dependent-reflexive-globular-types funext +open import globular-types.binary-dependent-reflexive-globular-types open import globular-types.globular-types -open import globular-types.points-reflexive-globular-types funext -open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types funext -open import globular-types.reflexive-globular-equivalences funext -open import globular-types.reflexive-globular-types funext +open import globular-types.points-reflexive-globular-types +open import globular-types.pointwise-extensions-binary-families-reflexive-globular-types +open import globular-types.reflexive-globular-equivalences +open import globular-types.reflexive-globular-types ```
diff --git a/src/globular-types/symmetric-globular-types.lagda.md b/src/globular-types/symmetric-globular-types.lagda.md index a1708f579d..f8b627002c 100644 --- a/src/globular-types/symmetric-globular-types.lagda.md +++ b/src/globular-types/symmetric-globular-types.lagda.md @@ -3,20 +3,15 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.symmetric-globular-types - (funext : function-extensionality) - where +module globular-types.symmetric-globular-types where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels open import globular-types.globular-types diff --git a/src/globular-types/terminal-globular-types.lagda.md b/src/globular-types/terminal-globular-types.lagda.md index 192b92c3a1..b9007c4347 100644 --- a/src/globular-types/terminal-globular-types.lagda.md +++ b/src/globular-types/terminal-globular-types.lagda.md @@ -3,21 +3,16 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.terminal-globular-types - (funext : function-extensionality) - where +module globular-types.terminal-globular-types where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/transitive-globular-maps.lagda.md b/src/globular-types/transitive-globular-maps.lagda.md index 6c330292f1..3d7d093665 100644 --- a/src/globular-types/transitive-globular-maps.lagda.md +++ b/src/globular-types/transitive-globular-maps.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.transitive-globular-maps - (funext : function-extensionality) - where +module globular-types.transitive-globular-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-maps funext -open import globular-types.transitive-globular-types funext +open import globular-types.globular-maps +open import globular-types.transitive-globular-types ```
diff --git a/src/globular-types/transitive-globular-types.lagda.md b/src/globular-types/transitive-globular-types.lagda.md index 4756a13f95..368bad45fc 100644 --- a/src/globular-types/transitive-globular-types.lagda.md +++ b/src/globular-types/transitive-globular-types.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.transitive-globular-types - (funext : function-extensionality) - where +module globular-types.transitive-globular-types where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/unit-reflexive-globular-type.lagda.md b/src/globular-types/unit-reflexive-globular-type.lagda.md index ac0c4127d4..1c3e8752c0 100644 --- a/src/globular-types/unit-reflexive-globular-type.lagda.md +++ b/src/globular-types/unit-reflexive-globular-type.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.unit-reflexive-globular-type - (funext : function-extensionality) - where +module globular-types.unit-reflexive-globular-type where ```
Imports @@ -17,7 +12,7 @@ module open import foundation.unit-type open import foundation.universe-levels -open import globular-types.reflexive-globular-types funext +open import globular-types.reflexive-globular-types open import globular-types.unit-globular-type ``` diff --git a/src/globular-types/universal-globular-type.lagda.md b/src/globular-types/universal-globular-type.lagda.md index ac7317b7c8..2d67afcbf1 100644 --- a/src/globular-types/universal-globular-type.lagda.md +++ b/src/globular-types/universal-globular-type.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.universal-globular-type - (funext : function-extensionality) - where +module globular-types.universal-globular-type where ```
Imports @@ -18,9 +13,9 @@ open import foundation.dependent-pair-types open import foundation.spans open import foundation.universe-levels -open import globular-types.dependent-globular-types funext -open import globular-types.exponentials-globular-types funext -open import globular-types.globular-maps funext +open import globular-types.dependent-globular-types +open import globular-types.exponentials-globular-types +open import globular-types.globular-maps open import globular-types.globular-types ``` diff --git a/src/globular-types/universal-reflexive-globular-type.lagda.md b/src/globular-types/universal-reflexive-globular-type.lagda.md index 92b9da49af..d704e71b34 100644 --- a/src/globular-types/universal-reflexive-globular-type.lagda.md +++ b/src/globular-types/universal-reflexive-globular-type.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - globular-types.universal-reflexive-globular-type - (funext : function-extensionality) - where +module globular-types.universal-reflexive-globular-type where ```
Imports @@ -17,7 +12,7 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import globular-types.reflexive-globular-types funext +open import globular-types.reflexive-globular-types ```
diff --git a/src/graph-theory.lagda.md b/src/graph-theory.lagda.md index c4c8add1ae..c873b5ded2 100644 --- a/src/graph-theory.lagda.md +++ b/src/graph-theory.lagda.md @@ -3,90 +3,85 @@ ## Modules in the graph theory namespace ```agda -open import foundation.function-extensionality-axiom +module graph-theory where -module - graph-theory - (funext : function-extensionality) - where - -open import graph-theory.acyclic-undirected-graphs funext public -open import graph-theory.base-change-dependent-directed-graphs funext public -open import graph-theory.base-change-dependent-reflexive-graphs funext public -open import graph-theory.cartesian-products-directed-graphs funext public -open import graph-theory.cartesian-products-reflexive-graphs funext public -open import graph-theory.circuits-undirected-graphs funext public -open import graph-theory.closed-walks-undirected-graphs funext public -open import graph-theory.complete-bipartite-graphs funext public -open import graph-theory.complete-multipartite-graphs funext public -open import graph-theory.complete-undirected-graphs funext public -open import graph-theory.connected-undirected-graphs funext public -open import graph-theory.cycles-undirected-graphs funext public -open import graph-theory.dependent-directed-graphs funext public -open import graph-theory.dependent-products-directed-graphs funext public -open import graph-theory.dependent-products-reflexive-graphs funext public -open import graph-theory.dependent-reflexive-graphs funext public -open import graph-theory.dependent-sums-directed-graphs funext public -open import graph-theory.dependent-sums-reflexive-graphs funext public -open import graph-theory.directed-graph-duality funext public -open import graph-theory.directed-graph-structures-on-standard-finite-sets funext public -open import graph-theory.directed-graphs funext public -open import graph-theory.discrete-dependent-reflexive-graphs funext public -open import graph-theory.discrete-directed-graphs funext public -open import graph-theory.discrete-reflexive-graphs funext public -open import graph-theory.displayed-large-reflexive-graphs funext public -open import graph-theory.edge-coloured-undirected-graphs funext public -open import graph-theory.embeddings-directed-graphs funext public -open import graph-theory.embeddings-undirected-graphs funext public -open import graph-theory.enriched-undirected-graphs funext public -open import graph-theory.equivalences-dependent-directed-graphs funext public -open import graph-theory.equivalences-dependent-reflexive-graphs funext public -open import graph-theory.equivalences-directed-graphs funext public -open import graph-theory.equivalences-enriched-undirected-graphs funext public -open import graph-theory.equivalences-reflexive-graphs funext public -open import graph-theory.equivalences-undirected-graphs funext public -open import graph-theory.eulerian-circuits-undirected-graphs funext public -open import graph-theory.faithful-morphisms-undirected-graphs funext public -open import graph-theory.fibers-directed-graphs funext public -open import graph-theory.fibers-morphisms-directed-graphs funext public -open import graph-theory.fibers-morphisms-reflexive-graphs funext public -open import graph-theory.finite-graphs funext public -open import graph-theory.geometric-realizations-undirected-graphs funext public -open import graph-theory.higher-directed-graphs funext public -open import graph-theory.hypergraphs funext public -open import graph-theory.internal-hom-directed-graphs funext public -open import graph-theory.large-higher-directed-graphs funext public +open import graph-theory.acyclic-undirected-graphs public +open import graph-theory.base-change-dependent-directed-graphs public +open import graph-theory.base-change-dependent-reflexive-graphs public +open import graph-theory.cartesian-products-directed-graphs public +open import graph-theory.cartesian-products-reflexive-graphs public +open import graph-theory.circuits-undirected-graphs public +open import graph-theory.closed-walks-undirected-graphs public +open import graph-theory.complete-bipartite-graphs public +open import graph-theory.complete-multipartite-graphs public +open import graph-theory.complete-undirected-graphs public +open import graph-theory.connected-undirected-graphs public +open import graph-theory.cycles-undirected-graphs public +open import graph-theory.dependent-directed-graphs public +open import graph-theory.dependent-products-directed-graphs public +open import graph-theory.dependent-products-reflexive-graphs public +open import graph-theory.dependent-reflexive-graphs public +open import graph-theory.dependent-sums-directed-graphs public +open import graph-theory.dependent-sums-reflexive-graphs public +open import graph-theory.directed-graph-duality public +open import graph-theory.directed-graph-structures-on-standard-finite-sets public +open import graph-theory.directed-graphs public +open import graph-theory.discrete-dependent-reflexive-graphs public +open import graph-theory.discrete-directed-graphs public +open import graph-theory.discrete-reflexive-graphs public +open import graph-theory.displayed-large-reflexive-graphs public +open import graph-theory.edge-coloured-undirected-graphs public +open import graph-theory.embeddings-directed-graphs public +open import graph-theory.embeddings-undirected-graphs public +open import graph-theory.enriched-undirected-graphs public +open import graph-theory.equivalences-dependent-directed-graphs public +open import graph-theory.equivalences-dependent-reflexive-graphs public +open import graph-theory.equivalences-directed-graphs public +open import graph-theory.equivalences-enriched-undirected-graphs public +open import graph-theory.equivalences-reflexive-graphs public +open import graph-theory.equivalences-undirected-graphs public +open import graph-theory.eulerian-circuits-undirected-graphs public +open import graph-theory.faithful-morphisms-undirected-graphs public +open import graph-theory.fibers-directed-graphs public +open import graph-theory.fibers-morphisms-directed-graphs public +open import graph-theory.fibers-morphisms-reflexive-graphs public +open import graph-theory.finite-graphs public +open import graph-theory.geometric-realizations-undirected-graphs public +open import graph-theory.higher-directed-graphs public +open import graph-theory.hypergraphs public +open import graph-theory.internal-hom-directed-graphs public +open import graph-theory.large-higher-directed-graphs public open import graph-theory.large-reflexive-graphs public -open import graph-theory.matchings funext public -open import graph-theory.mere-equivalences-undirected-graphs funext public -open import graph-theory.morphisms-dependent-directed-graphs funext public -open import graph-theory.morphisms-directed-graphs funext public -open import graph-theory.morphisms-reflexive-graphs funext public -open import graph-theory.morphisms-undirected-graphs funext public -open import graph-theory.neighbors-undirected-graphs funext public -open import graph-theory.orientations-undirected-graphs funext public -open import graph-theory.paths-undirected-graphs funext public -open import graph-theory.polygons funext public -open import graph-theory.raising-universe-levels-directed-graphs funext public -open import graph-theory.reflecting-maps-undirected-graphs funext public -open import graph-theory.reflexive-graphs funext public -open import graph-theory.regular-undirected-graphs funext public -open import graph-theory.sections-dependent-directed-graphs funext public -open import graph-theory.sections-dependent-reflexive-graphs funext public -open import graph-theory.simple-undirected-graphs funext public -open import graph-theory.stereoisomerism-enriched-undirected-graphs funext public -open import graph-theory.terminal-directed-graphs funext public -open import graph-theory.terminal-reflexive-graphs funext public -open import graph-theory.totally-faithful-morphisms-undirected-graphs funext public -open import graph-theory.trails-directed-graphs funext public -open import graph-theory.trails-undirected-graphs funext public -open import graph-theory.undirected-graph-structures-on-standard-finite-sets funext public -open import graph-theory.undirected-graphs funext public -open import graph-theory.universal-directed-graph funext public -open import graph-theory.universal-reflexive-graph funext public -open import graph-theory.vertex-covers funext public -open import graph-theory.voltage-graphs funext public -open import graph-theory.walks-directed-graphs funext public -open import graph-theory.walks-undirected-graphs funext public -open import graph-theory.wide-displayed-large-reflexive-graphs funext public +open import graph-theory.matchings public +open import graph-theory.mere-equivalences-undirected-graphs public +open import graph-theory.morphisms-dependent-directed-graphs public +open import graph-theory.morphisms-directed-graphs public +open import graph-theory.morphisms-reflexive-graphs public +open import graph-theory.morphisms-undirected-graphs public +open import graph-theory.neighbors-undirected-graphs public +open import graph-theory.orientations-undirected-graphs public +open import graph-theory.paths-undirected-graphs public +open import graph-theory.polygons public +open import graph-theory.raising-universe-levels-directed-graphs public +open import graph-theory.reflecting-maps-undirected-graphs public +open import graph-theory.reflexive-graphs public +open import graph-theory.regular-undirected-graphs public +open import graph-theory.sections-dependent-directed-graphs public +open import graph-theory.sections-dependent-reflexive-graphs public +open import graph-theory.simple-undirected-graphs public +open import graph-theory.stereoisomerism-enriched-undirected-graphs public +open import graph-theory.terminal-directed-graphs public +open import graph-theory.terminal-reflexive-graphs public +open import graph-theory.totally-faithful-morphisms-undirected-graphs public +open import graph-theory.trails-directed-graphs public +open import graph-theory.trails-undirected-graphs public +open import graph-theory.undirected-graph-structures-on-standard-finite-sets public +open import graph-theory.undirected-graphs public +open import graph-theory.universal-directed-graph public +open import graph-theory.universal-reflexive-graph public +open import graph-theory.vertex-covers public +open import graph-theory.voltage-graphs public +open import graph-theory.walks-directed-graphs public +open import graph-theory.walks-undirected-graphs public +open import graph-theory.wide-displayed-large-reflexive-graphs public ``` diff --git a/src/graph-theory/acyclic-undirected-graphs.lagda.md b/src/graph-theory/acyclic-undirected-graphs.lagda.md index 6bf8e4eb8b..300bd4eda8 100644 --- a/src/graph-theory/acyclic-undirected-graphs.lagda.md +++ b/src/graph-theory/acyclic-undirected-graphs.lagda.md @@ -1,12 +1,7 @@ # Acyclic undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.acyclic-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.acyclic-undirected-graphs where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.universe-levels -open import graph-theory.geometric-realizations-undirected-graphs funext -open import graph-theory.reflecting-maps-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.geometric-realizations-undirected-graphs +open import graph-theory.reflecting-maps-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/base-change-dependent-directed-graphs.lagda.md b/src/graph-theory/base-change-dependent-directed-graphs.lagda.md index 7cad3529cf..839b1619cd 100644 --- a/src/graph-theory/base-change-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/base-change-dependent-directed-graphs.lagda.md @@ -1,12 +1,7 @@ # Base change of dependent directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.base-change-dependent-directed-graphs - (funext : function-extensionality) - where +module graph-theory.base-change-dependent-directed-graphs where ```
Imports @@ -15,9 +10,9 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.dependent-directed-graphs +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md b/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md index 9f11a28a05..d1168be9c8 100644 --- a/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/base-change-dependent-reflexive-graphs.lagda.md @@ -1,27 +1,22 @@ # Base change of dependent reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.base-change-dependent-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.base-change-dependent-reflexive-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs funext -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.dependent-reflexive-graphs funext -open import graph-theory.morphisms-reflexive-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.base-change-dependent-directed-graphs +open import graph-theory.dependent-directed-graphs +open import graph-theory.dependent-reflexive-graphs +open import graph-theory.morphisms-reflexive-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/cartesian-products-directed-graphs.lagda.md b/src/graph-theory/cartesian-products-directed-graphs.lagda.md index 5746251702..50840f8b15 100644 --- a/src/graph-theory/cartesian-products-directed-graphs.lagda.md +++ b/src/graph-theory/cartesian-products-directed-graphs.lagda.md @@ -1,23 +1,18 @@ # Cartesian products of directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.cartesian-products-directed-graphs - (funext : function-extensionality) - where +module graph-theory.cartesian-products-directed-graphs where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md b/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md index ee2eba1fc4..f68342b1c5 100644 --- a/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md +++ b/src/graph-theory/cartesian-products-reflexive-graphs.lagda.md @@ -1,27 +1,22 @@ # Cartesian products of reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.cartesian-products-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.cartesian-products-reflexive-graphs where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import graph-theory.cartesian-products-directed-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.morphisms-reflexive-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.cartesian-products-directed-graphs +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.morphisms-reflexive-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/circuits-undirected-graphs.lagda.md b/src/graph-theory/circuits-undirected-graphs.lagda.md index 9338ca4cb8..e3a8ea7dcc 100644 --- a/src/graph-theory/circuits-undirected-graphs.lagda.md +++ b/src/graph-theory/circuits-undirected-graphs.lagda.md @@ -1,12 +1,7 @@ # Circuits in undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.circuits-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.circuits-undirected-graphs where ```
Imports @@ -17,9 +12,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.polygons funext -open import graph-theory.totally-faithful-morphisms-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.polygons +open import graph-theory.totally-faithful-morphisms-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/closed-walks-undirected-graphs.lagda.md b/src/graph-theory/closed-walks-undirected-graphs.lagda.md index 3f6ec3cb82..54484b5def 100644 --- a/src/graph-theory/closed-walks-undirected-graphs.lagda.md +++ b/src/graph-theory/closed-walks-undirected-graphs.lagda.md @@ -1,12 +1,7 @@ # Closed walks in undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.closed-walks-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.closed-walks-undirected-graphs where ```
Imports @@ -17,9 +12,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs funext -open import graph-theory.polygons funext -open import graph-theory.undirected-graphs funext +open import graph-theory.morphisms-undirected-graphs +open import graph-theory.polygons +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/complete-bipartite-graphs.lagda.md b/src/graph-theory/complete-bipartite-graphs.lagda.md index 89b024de4a..d671a66be1 100644 --- a/src/graph-theory/complete-bipartite-graphs.lagda.md +++ b/src/graph-theory/complete-bipartite-graphs.lagda.md @@ -1,29 +1,24 @@ # Complete bipartite graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.complete-bipartite-graphs - (funext : function-extensionality) - where +module graph-theory.complete-bipartite-graphs where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.finite-graphs funext +open import graph-theory.finite-graphs -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.fibers-of-maps funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.fibers-of-maps +open import univalent-combinatorics.finite-types ```
diff --git a/src/graph-theory/complete-multipartite-graphs.lagda.md b/src/graph-theory/complete-multipartite-graphs.lagda.md index 86f03e5e27..eafcab5fa0 100644 --- a/src/graph-theory/complete-multipartite-graphs.lagda.md +++ b/src/graph-theory/complete-multipartite-graphs.lagda.md @@ -1,28 +1,23 @@ # Complete multipartite graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.complete-multipartite-graphs - (funext : function-extensionality) - where +module graph-theory.complete-multipartite-graphs where ```
Imports ```agda open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.finite-graphs funext +open import graph-theory.finite-graphs -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.function-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.function-types ```
diff --git a/src/graph-theory/complete-undirected-graphs.lagda.md b/src/graph-theory/complete-undirected-graphs.lagda.md index e16175238a..6adb8963c1 100644 --- a/src/graph-theory/complete-undirected-graphs.lagda.md +++ b/src/graph-theory/complete-undirected-graphs.lagda.md @@ -1,12 +1,7 @@ # Complete undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.complete-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.complete-undirected-graphs where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.universe-levels -open import graph-theory.complete-multipartite-graphs funext -open import graph-theory.finite-graphs funext +open import graph-theory.complete-multipartite-graphs +open import graph-theory.finite-graphs -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/graph-theory/connected-undirected-graphs.lagda.md b/src/graph-theory/connected-undirected-graphs.lagda.md index 50f6931ec6..fafe80a55b 100644 --- a/src/graph-theory/connected-undirected-graphs.lagda.md +++ b/src/graph-theory/connected-undirected-graphs.lagda.md @@ -1,23 +1,18 @@ # Connected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.connected-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.connected-undirected-graphs where ```
Imports ```agda -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.universe-levels -open import graph-theory.undirected-graphs funext -open import graph-theory.walks-undirected-graphs funext +open import graph-theory.undirected-graphs +open import graph-theory.walks-undirected-graphs ```
diff --git a/src/graph-theory/cycles-undirected-graphs.lagda.md b/src/graph-theory/cycles-undirected-graphs.lagda.md index 9ad87205f2..2dd455a2f4 100644 --- a/src/graph-theory/cycles-undirected-graphs.lagda.md +++ b/src/graph-theory/cycles-undirected-graphs.lagda.md @@ -1,12 +1,7 @@ # Cycles in undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.cycles-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.cycles-undirected-graphs where ```
Imports @@ -17,9 +12,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.embeddings-undirected-graphs funext -open import graph-theory.polygons funext -open import graph-theory.undirected-graphs funext +open import graph-theory.embeddings-undirected-graphs +open import graph-theory.polygons +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/dependent-directed-graphs.lagda.md b/src/graph-theory/dependent-directed-graphs.lagda.md index f865864cad..bd7a43b39d 100644 --- a/src/graph-theory/dependent-directed-graphs.lagda.md +++ b/src/graph-theory/dependent-directed-graphs.lagda.md @@ -1,12 +1,7 @@ # Dependent directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.dependent-directed-graphs - (funext : function-extensionality) - where +module graph-theory.dependent-directed-graphs where ```
Imports @@ -15,7 +10,7 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs funext +open import graph-theory.directed-graphs ```
diff --git a/src/graph-theory/dependent-products-directed-graphs.lagda.md b/src/graph-theory/dependent-products-directed-graphs.lagda.md index 273bbc998c..5e0174ead8 100644 --- a/src/graph-theory/dependent-products-directed-graphs.lagda.md +++ b/src/graph-theory/dependent-products-directed-graphs.lagda.md @@ -1,30 +1,25 @@ # Dependent products of directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.dependent-products-directed-graphs - (funext : function-extensionality) - where +module graph-theory.dependent-products-directed-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs funext -open import graph-theory.cartesian-products-directed-graphs funext -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.sections-dependent-directed-graphs funext +open import graph-theory.base-change-dependent-directed-graphs +open import graph-theory.cartesian-products-directed-graphs +open import graph-theory.dependent-directed-graphs +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.sections-dependent-directed-graphs ```
diff --git a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md index 9612955f7e..562665d1c4 100644 --- a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md @@ -1,12 +1,7 @@ # Dependent products of reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.dependent-products-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.dependent-products-reflexive-graphs where ```
Imports @@ -14,33 +9,33 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-identifications +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import graph-theory.base-change-dependent-reflexive-graphs funext -open import graph-theory.cartesian-products-reflexive-graphs funext -open import graph-theory.dependent-reflexive-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.morphisms-reflexive-graphs funext -open import graph-theory.reflexive-graphs funext -open import graph-theory.sections-dependent-reflexive-graphs funext +open import graph-theory.base-change-dependent-reflexive-graphs +open import graph-theory.cartesian-products-reflexive-graphs +open import graph-theory.dependent-reflexive-graphs +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.morphisms-reflexive-graphs +open import graph-theory.reflexive-graphs +open import graph-theory.sections-dependent-reflexive-graphs ```
diff --git a/src/graph-theory/dependent-reflexive-graphs.lagda.md b/src/graph-theory/dependent-reflexive-graphs.lagda.md index 937d08b635..76136f1504 100644 --- a/src/graph-theory/dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-reflexive-graphs.lagda.md @@ -1,23 +1,18 @@ # Dependent reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.dependent-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.dependent-reflexive-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.dependent-directed-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/dependent-sums-directed-graphs.lagda.md b/src/graph-theory/dependent-sums-directed-graphs.lagda.md index 0090655e84..3c0ab314b5 100644 --- a/src/graph-theory/dependent-sums-directed-graphs.lagda.md +++ b/src/graph-theory/dependent-sums-directed-graphs.lagda.md @@ -1,12 +1,7 @@ # Dependent sums directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.dependent-sums-directed-graphs - (funext : function-extensionality) - where +module graph-theory.dependent-sums-directed-graphs where ```
Imports @@ -15,11 +10,11 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs funext -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.sections-dependent-directed-graphs funext +open import graph-theory.base-change-dependent-directed-graphs +open import graph-theory.dependent-directed-graphs +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.sections-dependent-directed-graphs ```
diff --git a/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md b/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md index e9fb1ecffc..f8b5131441 100644 --- a/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md @@ -1,36 +1,31 @@ # Dependent sums reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.dependent-sums-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.dependent-sums-reflexive-graphs where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import graph-theory.base-change-dependent-reflexive-graphs funext -open import graph-theory.dependent-reflexive-graphs funext -open import graph-theory.dependent-sums-directed-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.discrete-dependent-reflexive-graphs funext -open import graph-theory.discrete-reflexive-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.morphisms-reflexive-graphs funext -open import graph-theory.reflexive-graphs funext -open import graph-theory.sections-dependent-directed-graphs funext -open import graph-theory.sections-dependent-reflexive-graphs funext +open import graph-theory.base-change-dependent-reflexive-graphs +open import graph-theory.dependent-reflexive-graphs +open import graph-theory.dependent-sums-directed-graphs +open import graph-theory.directed-graphs +open import graph-theory.discrete-dependent-reflexive-graphs +open import graph-theory.discrete-reflexive-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.morphisms-reflexive-graphs +open import graph-theory.reflexive-graphs +open import graph-theory.sections-dependent-directed-graphs +open import graph-theory.sections-dependent-reflexive-graphs ```
diff --git a/src/graph-theory/directed-graph-duality.lagda.md b/src/graph-theory/directed-graph-duality.lagda.md index 927cc9b64a..26a89c50fc 100644 --- a/src/graph-theory/directed-graph-duality.lagda.md +++ b/src/graph-theory/directed-graph-duality.lagda.md @@ -1,34 +1,29 @@ # Directed graph duality ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.directed-graph-duality - (funext : function-extensionality) - where +module graph-theory.directed-graph-duality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.dependent-sums-directed-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.equivalences-dependent-directed-graphs funext -open import graph-theory.equivalences-directed-graphs funext -open import graph-theory.fibers-morphisms-directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.dependent-directed-graphs +open import graph-theory.dependent-sums-directed-graphs +open import graph-theory.directed-graphs +open import graph-theory.equivalences-dependent-directed-graphs +open import graph-theory.equivalences-directed-graphs +open import graph-theory.fibers-morphisms-directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md b/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md index 56d7d926b2..79f8ee66f1 100644 --- a/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md +++ b/src/graph-theory/directed-graph-structures-on-standard-finite-sets.lagda.md @@ -1,12 +1,7 @@ # Directed graph structures on standard finite sets ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.directed-graph-structures-on-standard-finite-sets - (funext : function-extensionality) - where +module graph-theory.directed-graph-structures-on-standard-finite-sets where ```
Imports @@ -17,7 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/graph-theory/directed-graphs.lagda.md b/src/graph-theory/directed-graphs.lagda.md index e7f9367184..798b5afeb6 100644 --- a/src/graph-theory/directed-graphs.lagda.md +++ b/src/graph-theory/directed-graphs.lagda.md @@ -1,21 +1,16 @@ # Directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.directed-graphs - (funext : function-extensionality) - where +module graph-theory.directed-graphs where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md b/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md index d25ec3fb85..9d43af0730 100644 --- a/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md @@ -1,23 +1,18 @@ # Discrete dependent reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.discrete-dependent-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.discrete-dependent-reflexive-graphs where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import graph-theory.dependent-reflexive-graphs funext -open import graph-theory.discrete-reflexive-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.dependent-reflexive-graphs +open import graph-theory.discrete-reflexive-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/discrete-directed-graphs.lagda.md b/src/graph-theory/discrete-directed-graphs.lagda.md index a55fe0a3e9..c3ff8a436b 100644 --- a/src/graph-theory/discrete-directed-graphs.lagda.md +++ b/src/graph-theory/discrete-directed-graphs.lagda.md @@ -1,34 +1,29 @@ # Discrete directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.discrete-directed-graphs - (funext : function-extensionality) - where +module graph-theory.discrete-directed-graphs where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.discrete-binary-relations funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.discrete-binary-relations +open import foundation.empty-types +open import foundation.equivalences +open import foundation.homotopies +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.torsorial-type-families -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/discrete-reflexive-graphs.lagda.md b/src/graph-theory/discrete-reflexive-graphs.lagda.md index 9af8d77e65..e750402ea7 100644 --- a/src/graph-theory/discrete-reflexive-graphs.lagda.md +++ b/src/graph-theory/discrete-reflexive-graphs.lagda.md @@ -1,28 +1,23 @@ # Discrete reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.discrete-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.discrete-reflexive-graphs where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.discrete-reflexive-relations funext +open import foundation.discrete-reflexive-relations open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.torsorial-type-families -open import graph-theory.directed-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/displayed-large-reflexive-graphs.lagda.md b/src/graph-theory/displayed-large-reflexive-graphs.lagda.md index 94bd052223..7040f628b1 100644 --- a/src/graph-theory/displayed-large-reflexive-graphs.lagda.md +++ b/src/graph-theory/displayed-large-reflexive-graphs.lagda.md @@ -1,12 +1,7 @@ # Displayed large reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.displayed-large-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.displayed-large-reflexive-graphs where ```
Imports @@ -16,7 +11,7 @@ open import foundation.dependent-pair-types open import foundation.universe-levels open import graph-theory.large-reflexive-graphs -open import graph-theory.reflexive-graphs funext +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/edge-coloured-undirected-graphs.lagda.md b/src/graph-theory/edge-coloured-undirected-graphs.lagda.md index 4a2ba3381c..fe22d6bcf3 100644 --- a/src/graph-theory/edge-coloured-undirected-graphs.lagda.md +++ b/src/graph-theory/edge-coloured-undirected-graphs.lagda.md @@ -1,24 +1,19 @@ # Edge-coloured undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.edge-coloured-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.edge-coloured-undirected-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext +open import foundation.embeddings open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.neighbors-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.neighbors-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/embeddings-directed-graphs.lagda.md b/src/graph-theory/embeddings-directed-graphs.lagda.md index cfd9a759d2..e483f06dc2 100644 --- a/src/graph-theory/embeddings-directed-graphs.lagda.md +++ b/src/graph-theory/embeddings-directed-graphs.lagda.md @@ -1,24 +1,19 @@ # Embeddings of directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.embeddings-directed-graphs - (funext : function-extensionality) - where +module graph-theory.embeddings-directed-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.propositions open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/embeddings-undirected-graphs.lagda.md b/src/graph-theory/embeddings-undirected-graphs.lagda.md index f29cad1f13..db07969f1c 100644 --- a/src/graph-theory/embeddings-undirected-graphs.lagda.md +++ b/src/graph-theory/embeddings-undirected-graphs.lagda.md @@ -1,24 +1,19 @@ # Embeddings of undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.embeddings-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.embeddings-undirected-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.propositions open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.morphisms-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/enriched-undirected-graphs.lagda.md b/src/graph-theory/enriched-undirected-graphs.lagda.md index a9a046e258..1f74332982 100644 --- a/src/graph-theory/enriched-undirected-graphs.lagda.md +++ b/src/graph-theory/enriched-undirected-graphs.lagda.md @@ -1,31 +1,26 @@ # Enriched undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.enriched-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.enriched-undirected-graphs where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.connected-components funext +open import foundation.connected-components open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import graph-theory.neighbors-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.neighbors-undirected-graphs +open import graph-theory.undirected-graphs -open import higher-group-theory.higher-group-actions funext -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-group-actions +open import higher-group-theory.higher-groups ```
diff --git a/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md b/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md index 89ecf974de..2876ea23fa 100644 --- a/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/equivalences-dependent-directed-graphs.lagda.md @@ -1,31 +1,26 @@ # Equivalences of dependent directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.equivalences-dependent-directed-graphs - (funext : function-extensionality) - where +module graph-theory.equivalences-dependent-directed-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.families-of-equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.families-of-equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.directed-graphs funext +open import graph-theory.dependent-directed-graphs +open import graph-theory.directed-graphs ```
diff --git a/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md b/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md index 079cdb41d6..4197698468 100644 --- a/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/equivalences-dependent-reflexive-graphs.lagda.md @@ -1,32 +1,27 @@ # Equivalences of dependent reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.equivalences-dependent-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.equivalences-dependent-reflexive-graphs where ```
Imports ```agda -open import foundation.dependent-identifications funext +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.families-of-equivalences funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.families-of-equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import graph-theory.dependent-reflexive-graphs funext -open import graph-theory.equivalences-dependent-directed-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.dependent-reflexive-graphs +open import graph-theory.equivalences-dependent-directed-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/equivalences-directed-graphs.lagda.md b/src/graph-theory/equivalences-directed-graphs.lagda.md index fd6909a73e..a95e1ea270 100644 --- a/src/graph-theory/equivalences-directed-graphs.lagda.md +++ b/src/graph-theory/equivalences-directed-graphs.lagda.md @@ -1,12 +1,7 @@ # Equivalences of directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.equivalences-directed-graphs - (funext : function-extensionality) - where +module graph-theory.equivalences-directed-graphs where ```
Imports @@ -15,28 +10,28 @@ module open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.torsorial-type-families +open import foundation.transposition-identifications-along-equivalences open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext -open import foundation.univalence funext +open import foundation.type-theoretic-principle-of-choice +open import foundation.univalence open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md b/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md index 2039e13fb8..5655fafc9d 100644 --- a/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md +++ b/src/graph-theory/equivalences-enriched-undirected-graphs.lagda.md @@ -1,34 +1,29 @@ # Equivalences of enriched undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.equivalences-enriched-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.equivalences-enriched-undirected-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.enriched-undirected-graphs funext -open import graph-theory.equivalences-undirected-graphs funext -open import graph-theory.neighbors-undirected-graphs funext +open import graph-theory.enriched-undirected-graphs +open import graph-theory.equivalences-undirected-graphs +open import graph-theory.neighbors-undirected-graphs ```
diff --git a/src/graph-theory/equivalences-reflexive-graphs.lagda.md b/src/graph-theory/equivalences-reflexive-graphs.lagda.md index c693eaba6d..ae2ff0ebab 100644 --- a/src/graph-theory/equivalences-reflexive-graphs.lagda.md +++ b/src/graph-theory/equivalences-reflexive-graphs.lagda.md @@ -1,25 +1,20 @@ # Equivalences of reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.equivalences-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.equivalences-reflexive-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import graph-theory.equivalences-directed-graphs funext -open import graph-theory.morphisms-reflexive-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.equivalences-directed-graphs +open import graph-theory.morphisms-reflexive-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/equivalences-undirected-graphs.lagda.md b/src/graph-theory/equivalences-undirected-graphs.lagda.md index d8553c2fff..4b98ef0d5e 100644 --- a/src/graph-theory/equivalences-undirected-graphs.lagda.md +++ b/src/graph-theory/equivalences-undirected-graphs.lagda.md @@ -1,38 +1,33 @@ # Equivalences of undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.equivalences-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.equivalences-undirected-graphs where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.morphisms-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.morphisms-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md b/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md index 15ce7dc365..5503cf3128 100644 --- a/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md +++ b/src/graph-theory/eulerian-circuits-undirected-graphs.lagda.md @@ -1,12 +1,7 @@ # Eulerian circuits in undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.eulerian-circuits-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.eulerian-circuits-undirected-graphs where ```
Imports @@ -15,13 +10,13 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs funext -open import graph-theory.polygons funext -open import graph-theory.undirected-graphs funext +open import graph-theory.morphisms-undirected-graphs +open import graph-theory.polygons +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md b/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md index a303a3d40d..685ec29151 100644 --- a/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md @@ -1,24 +1,19 @@ # Faithful morphisms of undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.faithful-morphisms-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.faithful-morphisms-undirected-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.propositions open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.morphisms-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/fibers-directed-graphs.lagda.md b/src/graph-theory/fibers-directed-graphs.lagda.md index 36461f54a3..ed82be7273 100644 --- a/src/graph-theory/fibers-directed-graphs.lagda.md +++ b/src/graph-theory/fibers-directed-graphs.lagda.md @@ -1,34 +1,29 @@ # Fibers of directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.fibers-directed-graphs - (funext : function-extensionality) - where +module graph-theory.fibers-directed-graphs where ```
Imports ```agda -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.walks-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.walks-directed-graphs -open import trees.directed-trees funext +open import trees.directed-trees ```
diff --git a/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md b/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md index 766e9b3865..c6e11c4da1 100644 --- a/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md +++ b/src/graph-theory/fibers-morphisms-directed-graphs.lagda.md @@ -1,30 +1,25 @@ # Fibers of morphisms into directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.fibers-morphisms-directed-graphs - (funext : function-extensionality) - where +module graph-theory.fibers-morphisms-directed-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.families-of-equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.families-of-equivalences +open import foundation.fibers-of-maps +open import foundation.identity-types open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.dependent-sums-directed-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.equivalences-dependent-directed-graphs funext -open import graph-theory.equivalences-directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.dependent-directed-graphs +open import graph-theory.dependent-sums-directed-graphs +open import graph-theory.directed-graphs +open import graph-theory.equivalences-dependent-directed-graphs +open import graph-theory.equivalences-directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md b/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md index 4e84053970..8ffde96bc4 100644 --- a/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md +++ b/src/graph-theory/fibers-morphisms-reflexive-graphs.lagda.md @@ -1,12 +1,7 @@ # Fibers of morphisms into reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.fibers-morphisms-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.fibers-morphisms-reflexive-graphs where ```
Imports @@ -14,25 +9,25 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications funext -open import foundation.dependent-identifications funext +open import foundation.commuting-squares-of-identifications +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.families-of-equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.identity-types funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.families-of-equivalences +open import foundation.fibers-of-maps +open import foundation.identity-types open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.dependent-reflexive-graphs funext -open import graph-theory.dependent-sums-reflexive-graphs funext -open import graph-theory.equivalences-dependent-directed-graphs funext -open import graph-theory.equivalences-dependent-reflexive-graphs funext -open import graph-theory.equivalences-reflexive-graphs funext -open import graph-theory.fibers-morphisms-directed-graphs funext -open import graph-theory.morphisms-reflexive-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.dependent-directed-graphs +open import graph-theory.dependent-reflexive-graphs +open import graph-theory.dependent-sums-reflexive-graphs +open import graph-theory.equivalences-dependent-directed-graphs +open import graph-theory.equivalences-dependent-reflexive-graphs +open import graph-theory.equivalences-reflexive-graphs +open import graph-theory.fibers-morphisms-directed-graphs +open import graph-theory.morphisms-reflexive-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/finite-graphs.lagda.md b/src/graph-theory/finite-graphs.lagda.md index c5cd6f2f79..6aff626a25 100644 --- a/src/graph-theory/finite-graphs.lagda.md +++ b/src/graph-theory/finite-graphs.lagda.md @@ -1,28 +1,23 @@ # Finite graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.finite-graphs - (funext : function-extensionality) - where +module graph-theory.finite-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.homotopies open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.undirected-graphs funext +open import graph-theory.undirected-graphs -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md b/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md index df19ae0e8a..bb8fa6abfc 100644 --- a/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md +++ b/src/graph-theory/geometric-realizations-undirected-graphs.lagda.md @@ -1,25 +1,20 @@ # Geometric realizations of undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.geometric-realizations-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.geometric-realizations-undirected-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.symmetric-identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.symmetric-identity-types open import foundation.universe-levels -open import graph-theory.reflecting-maps-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.reflecting-maps-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/higher-directed-graphs.lagda.md b/src/graph-theory/higher-directed-graphs.lagda.md index a73f8d6185..3357611b21 100644 --- a/src/graph-theory/higher-directed-graphs.lagda.md +++ b/src/graph-theory/higher-directed-graphs.lagda.md @@ -1,12 +1,7 @@ # Higher directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.higher-directed-graphs - (funext : function-extensionality) - where +module graph-theory.higher-directed-graphs where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs funext +open import graph-theory.directed-graphs ```
diff --git a/src/graph-theory/hypergraphs.lagda.md b/src/graph-theory/hypergraphs.lagda.md index a55531b153..018e504f13 100644 --- a/src/graph-theory/hypergraphs.lagda.md +++ b/src/graph-theory/hypergraphs.lagda.md @@ -1,12 +1,7 @@ # Hypergraphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.hypergraphs - (funext : function-extensionality) - where +module graph-theory.hypergraphs where ```
Imports @@ -16,7 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation.unordered-tuples funext +open import foundation.unordered-tuples ```
diff --git a/src/graph-theory/internal-hom-directed-graphs.lagda.md b/src/graph-theory/internal-hom-directed-graphs.lagda.md index 23a6834e72..c4625f214c 100644 --- a/src/graph-theory/internal-hom-directed-graphs.lagda.md +++ b/src/graph-theory/internal-hom-directed-graphs.lagda.md @@ -1,27 +1,22 @@ # Internal homs of directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.internal-hom-directed-graphs - (funext : function-extensionality) - where +module graph-theory.internal-hom-directed-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels -open import graph-theory.cartesian-products-directed-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.cartesian-products-directed-graphs +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/large-higher-directed-graphs.lagda.md b/src/graph-theory/large-higher-directed-graphs.lagda.md index 8c01b1b29f..6d805cf1a8 100644 --- a/src/graph-theory/large-higher-directed-graphs.lagda.md +++ b/src/graph-theory/large-higher-directed-graphs.lagda.md @@ -1,12 +1,7 @@ # Large higher directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.large-higher-directed-graphs - (funext : function-extensionality) - where +module graph-theory.large-higher-directed-graphs where ```
Imports @@ -14,17 +9,17 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.raising-universe-levels funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.raising-universe-levels open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.higher-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.higher-directed-graphs ```
diff --git a/src/graph-theory/matchings.lagda.md b/src/graph-theory/matchings.lagda.md index c80a5ead6e..66d2d1cc2c 100644 --- a/src/graph-theory/matchings.lagda.md +++ b/src/graph-theory/matchings.lagda.md @@ -1,29 +1,24 @@ # Matchings ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.matchings - (funext : function-extensionality) - where +module graph-theory.matchings where ```
Imports ```agda -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.undirected-graphs funext +open import graph-theory.undirected-graphs -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md b/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md index 8e240c26a5..9376ae4058 100644 --- a/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md +++ b/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md @@ -1,23 +1,18 @@ # Mere equivalences of undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.mere-equivalences-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.mere-equivalences-undirected-graphs where ```
Imports ```agda -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.universe-levels -open import graph-theory.equivalences-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.equivalences-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md b/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md index 222c55ecec..ef0c365ed0 100644 --- a/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/morphisms-dependent-directed-graphs.lagda.md @@ -1,23 +1,18 @@ # Morphisms of dependent directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.morphisms-dependent-directed-graphs - (funext : function-extensionality) - where +module graph-theory.morphisms-dependent-directed-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext +open import foundation.function-types open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.directed-graphs funext +open import graph-theory.dependent-directed-graphs +open import graph-theory.directed-graphs ```
diff --git a/src/graph-theory/morphisms-directed-graphs.lagda.md b/src/graph-theory/morphisms-directed-graphs.lagda.md index 98b63abf0e..9c85662c76 100644 --- a/src/graph-theory/morphisms-directed-graphs.lagda.md +++ b/src/graph-theory/morphisms-directed-graphs.lagda.md @@ -1,12 +1,7 @@ # Morphisms of directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.morphisms-directed-graphs - (funext : function-extensionality) - where +module graph-theory.morphisms-directed-graphs where ```
Imports @@ -15,19 +10,19 @@ module open import foundation.binary-dependent-identifications open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import graph-theory.directed-graphs funext +open import graph-theory.directed-graphs ```
diff --git a/src/graph-theory/morphisms-reflexive-graphs.lagda.md b/src/graph-theory/morphisms-reflexive-graphs.lagda.md index 3825329b02..855700002e 100644 --- a/src/graph-theory/morphisms-reflexive-graphs.lagda.md +++ b/src/graph-theory/morphisms-reflexive-graphs.lagda.md @@ -1,12 +1,7 @@ # Morphisms of reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.morphisms-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.morphisms-reflexive-graphs where ```
Imports @@ -15,22 +10,22 @@ module open import foundation.action-on-identifications-binary-dependent-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-identifications open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.morphisms-directed-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/morphisms-undirected-graphs.lagda.md b/src/graph-theory/morphisms-undirected-graphs.lagda.md index 09e5dbc957..aa80fba80a 100644 --- a/src/graph-theory/morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/morphisms-undirected-graphs.lagda.md @@ -1,36 +1,31 @@ # Morphisms of undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.morphisms-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.morphisms-undirected-graphs where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.undirected-graphs funext +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/neighbors-undirected-graphs.lagda.md b/src/graph-theory/neighbors-undirected-graphs.lagda.md index 4f23c9a277..9b6fba97e3 100644 --- a/src/graph-theory/neighbors-undirected-graphs.lagda.md +++ b/src/graph-theory/neighbors-undirected-graphs.lagda.md @@ -1,29 +1,24 @@ # Incidence in undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.neighbors-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.neighbors-undirected-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.equivalences-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.equivalences-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/orientations-undirected-graphs.lagda.md b/src/graph-theory/orientations-undirected-graphs.lagda.md index 1a905eaceb..cdabb031fa 100644 --- a/src/graph-theory/orientations-undirected-graphs.lagda.md +++ b/src/graph-theory/orientations-undirected-graphs.lagda.md @@ -1,12 +1,7 @@ # Orientations of undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.orientations-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.orientations-undirected-graphs where ```
Imports @@ -15,9 +10,9 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.undirected-graphs funext +open import graph-theory.undirected-graphs -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/graph-theory/paths-undirected-graphs.lagda.md b/src/graph-theory/paths-undirected-graphs.lagda.md index aaafacb98d..b811c34281 100644 --- a/src/graph-theory/paths-undirected-graphs.lagda.md +++ b/src/graph-theory/paths-undirected-graphs.lagda.md @@ -1,12 +1,7 @@ # Paths in undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.paths-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.paths-undirected-graphs where ```
Imports @@ -15,11 +10,11 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.injective-maps funext +open import foundation.injective-maps open import foundation.universe-levels -open import graph-theory.undirected-graphs funext -open import graph-theory.walks-undirected-graphs funext +open import graph-theory.undirected-graphs +open import graph-theory.walks-undirected-graphs ```
diff --git a/src/graph-theory/polygons.lagda.md b/src/graph-theory/polygons.lagda.md index 0efd1014d9..68f0117f77 100644 --- a/src/graph-theory/polygons.lagda.md +++ b/src/graph-theory/polygons.lagda.md @@ -1,34 +1,29 @@ # Polygons ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.polygons - (funext : function-extensionality) - where +module graph-theory.polygons where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.modular-arithmetic open import elementary-number-theory.natural-numbers -open import foundation.decidable-equality funext +open import foundation.decidable-equality open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.mere-equivalences funext -open import foundation.sets funext +open import foundation.fibers-of-maps +open import foundation.functoriality-propositional-truncation +open import foundation.mere-equivalences +open import foundation.sets open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.equivalences-undirected-graphs funext -open import graph-theory.mere-equivalences-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.equivalences-undirected-graphs +open import graph-theory.mere-equivalences-undirected-graphs +open import graph-theory.undirected-graphs -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md b/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md index ac64b1117d..ff763cffc0 100644 --- a/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md +++ b/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md @@ -1,25 +1,20 @@ # Raising universe levels of directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.raising-universe-levels-directed-graphs - (funext : function-extensionality) - where +module graph-theory.raising-universe-levels-directed-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.raising-universe-levels funext +open import foundation.equivalences +open import foundation.raising-universe-levels open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.equivalences-directed-graphs funext -open import graph-theory.walks-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.equivalences-directed-graphs +open import graph-theory.walks-directed-graphs ```
diff --git a/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md b/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md index c4dfa41d1d..5be62477ee 100644 --- a/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md +++ b/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md @@ -1,25 +1,20 @@ # Reflecting maps of undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.reflecting-maps-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.reflecting-maps-undirected-graphs where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.symmetric-identity-types funext +open import foundation.symmetric-identity-types open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.undirected-graphs funext +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/reflexive-graphs.lagda.md b/src/graph-theory/reflexive-graphs.lagda.md index ebfa77f653..1ab53e86e5 100644 --- a/src/graph-theory/reflexive-graphs.lagda.md +++ b/src/graph-theory/reflexive-graphs.lagda.md @@ -1,12 +1,7 @@ # Reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.reflexive-graphs where ```
Imports @@ -14,11 +9,11 @@ module ```agda open import foundation.binary-dependent-identifications open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.reflexive-relations funext +open import foundation.identity-types +open import foundation.reflexive-relations open import foundation.universe-levels -open import graph-theory.directed-graphs funext +open import graph-theory.directed-graphs ```
diff --git a/src/graph-theory/regular-undirected-graphs.lagda.md b/src/graph-theory/regular-undirected-graphs.lagda.md index b5b08ebc73..295ec95081 100644 --- a/src/graph-theory/regular-undirected-graphs.lagda.md +++ b/src/graph-theory/regular-undirected-graphs.lagda.md @@ -1,23 +1,18 @@ # Regular undirected graph ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.regular-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.regular-undirected-graphs where ```
Imports ```agda -open import foundation.mere-equivalences funext -open import foundation.propositions funext +open import foundation.mere-equivalences +open import foundation.propositions open import foundation.universe-levels -open import graph-theory.neighbors-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.neighbors-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/sections-dependent-directed-graphs.lagda.md b/src/graph-theory/sections-dependent-directed-graphs.lagda.md index 4400e8a100..c8ca8c42d4 100644 --- a/src/graph-theory/sections-dependent-directed-graphs.lagda.md +++ b/src/graph-theory/sections-dependent-directed-graphs.lagda.md @@ -1,31 +1,26 @@ # Sections of dependent directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.sections-dependent-directed-graphs - (funext : function-extensionality) - where +module graph-theory.sections-dependent-directed-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.directed-graphs funext +open import graph-theory.dependent-directed-graphs +open import graph-theory.directed-graphs ```
diff --git a/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md b/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md index ff4182136e..792b3557f8 100644 --- a/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/sections-dependent-reflexive-graphs.lagda.md @@ -1,12 +1,7 @@ # Sections of dependent reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.sections-dependent-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.sections-dependent-reflexive-graphs where ```
Imports @@ -16,24 +11,24 @@ open import foundation.action-on-identifications-binary-dependent-functions open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-identifications open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.reflexive-relations funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.reflexive-relations open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.dependent-reflexive-graphs funext -open import graph-theory.reflexive-graphs funext -open import graph-theory.sections-dependent-directed-graphs funext +open import graph-theory.dependent-reflexive-graphs +open import graph-theory.reflexive-graphs +open import graph-theory.sections-dependent-directed-graphs ```
diff --git a/src/graph-theory/simple-undirected-graphs.lagda.md b/src/graph-theory/simple-undirected-graphs.lagda.md index e7da69dc88..b81f7668e6 100644 --- a/src/graph-theory/simple-undirected-graphs.lagda.md +++ b/src/graph-theory/simple-undirected-graphs.lagda.md @@ -1,27 +1,22 @@ # Simple undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.simple-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.simple-undirected-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.negation +open import foundation.propositions open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.undirected-graphs funext +open import graph-theory.undirected-graphs -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md b/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md index 3c201d24e8..1fd241fbed 100644 --- a/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md +++ b/src/graph-theory/stereoisomerism-enriched-undirected-graphs.lagda.md @@ -1,24 +1,19 @@ # Stereoisomerism for enriched undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.stereoisomerism-enriched-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.stereoisomerism-enriched-undirected-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext +open import foundation.function-types +open import foundation.homotopies open import foundation.universe-levels -open import graph-theory.enriched-undirected-graphs funext -open import graph-theory.equivalences-undirected-graphs funext +open import graph-theory.enriched-undirected-graphs +open import graph-theory.equivalences-undirected-graphs ```
diff --git a/src/graph-theory/terminal-directed-graphs.lagda.md b/src/graph-theory/terminal-directed-graphs.lagda.md index 23a6ff1841..d49804435a 100644 --- a/src/graph-theory/terminal-directed-graphs.lagda.md +++ b/src/graph-theory/terminal-directed-graphs.lagda.md @@ -1,25 +1,20 @@ # Terminal directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.terminal-directed-graphs - (funext : function-extensionality) - where +module graph-theory.terminal-directed-graphs where ```
Idea ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/terminal-reflexive-graphs.lagda.md b/src/graph-theory/terminal-reflexive-graphs.lagda.md index 689794d0bf..31ff8ae60a 100644 --- a/src/graph-theory/terminal-reflexive-graphs.lagda.md +++ b/src/graph-theory/terminal-reflexive-graphs.lagda.md @@ -1,27 +1,22 @@ # Terminal reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.terminal-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.terminal-reflexive-graphs where ```
Idea ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.reflexive-graphs funext -open import graph-theory.morphisms-reflexive-graphs funext -open import graph-theory.terminal-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.reflexive-graphs +open import graph-theory.morphisms-reflexive-graphs +open import graph-theory.terminal-directed-graphs ```
diff --git a/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md b/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md index 2fe137c05b..7127494138 100644 --- a/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/totally-faithful-morphisms-undirected-graphs.lagda.md @@ -1,24 +1,19 @@ # Totally faithful morphisms of undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.totally-faithful-morphisms-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.totally-faithful-morphisms-undirected-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.embeddings +open import foundation.functoriality-dependent-pair-types open import foundation.universe-levels -open import graph-theory.morphisms-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.morphisms-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/graph-theory/trails-directed-graphs.lagda.md b/src/graph-theory/trails-directed-graphs.lagda.md index abcdaf5508..19c803955e 100644 --- a/src/graph-theory/trails-directed-graphs.lagda.md +++ b/src/graph-theory/trails-directed-graphs.lagda.md @@ -1,23 +1,18 @@ # Trails in directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.trails-directed-graphs - (funext : function-extensionality) - where +module graph-theory.trails-directed-graphs where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.injective-maps funext +open import foundation.injective-maps open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.walks-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.walks-directed-graphs ```
diff --git a/src/graph-theory/trails-undirected-graphs.lagda.md b/src/graph-theory/trails-undirected-graphs.lagda.md index f5db11d07a..3aaaa397cc 100644 --- a/src/graph-theory/trails-undirected-graphs.lagda.md +++ b/src/graph-theory/trails-undirected-graphs.lagda.md @@ -1,12 +1,7 @@ # Trails in undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.trails-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.trails-undirected-graphs where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.injective-maps funext -open import foundation.propositions funext +open import foundation.injective-maps +open import foundation.propositions open import foundation.universe-levels -open import graph-theory.undirected-graphs funext -open import graph-theory.walks-undirected-graphs funext +open import graph-theory.undirected-graphs +open import graph-theory.walks-undirected-graphs ```
diff --git a/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md b/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md index 24e3ab01e7..b16324d61e 100644 --- a/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md +++ b/src/graph-theory/undirected-graph-structures-on-standard-finite-sets.lagda.md @@ -1,12 +1,7 @@ # Undirected graph structures on standard finite sets ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.undirected-graph-structures-on-standard-finite-sets - (funext : function-extensionality) - where +module graph-theory.undirected-graph-structures-on-standard-finite-sets where ```
Imports @@ -16,9 +11,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/graph-theory/undirected-graphs.lagda.md b/src/graph-theory/undirected-graphs.lagda.md index 5ceb37a9b3..dda08c3492 100644 --- a/src/graph-theory/undirected-graphs.lagda.md +++ b/src/graph-theory/undirected-graphs.lagda.md @@ -1,25 +1,20 @@ # Undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.undirected-graphs - (funext : function-extensionality) - where +module graph-theory.undirected-graphs where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.directed-graphs funext +open import graph-theory.directed-graphs ```
diff --git a/src/graph-theory/universal-directed-graph.lagda.md b/src/graph-theory/universal-directed-graph.lagda.md index 167fd3c608..d7242623d2 100644 --- a/src/graph-theory/universal-directed-graph.lagda.md +++ b/src/graph-theory/universal-directed-graph.lagda.md @@ -1,12 +1,7 @@ # The universal directed graph ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.universal-directed-graph - (funext : function-extensionality) - where +module graph-theory.universal-directed-graph where ```
Imports @@ -15,11 +10,11 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.base-change-dependent-directed-graphs funext -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.equivalences-dependent-directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.base-change-dependent-directed-graphs +open import graph-theory.dependent-directed-graphs +open import graph-theory.directed-graphs +open import graph-theory.equivalences-dependent-directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/universal-reflexive-graph.lagda.md b/src/graph-theory/universal-reflexive-graph.lagda.md index a0ab6c1819..3b3fd8042f 100644 --- a/src/graph-theory/universal-reflexive-graph.lagda.md +++ b/src/graph-theory/universal-reflexive-graph.lagda.md @@ -1,12 +1,7 @@ # The universal reflexive graph ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.universal-reflexive-graph - (funext : function-extensionality) - where +module graph-theory.universal-reflexive-graph where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.dependent-directed-graphs funext -open import graph-theory.dependent-reflexive-graphs funext -open import graph-theory.directed-graphs funext -open import graph-theory.reflexive-graphs funext +open import graph-theory.dependent-directed-graphs +open import graph-theory.dependent-reflexive-graphs +open import graph-theory.directed-graphs +open import graph-theory.reflexive-graphs ```
diff --git a/src/graph-theory/vertex-covers.lagda.md b/src/graph-theory/vertex-covers.lagda.md index 2dcce33e22..462cda70c8 100644 --- a/src/graph-theory/vertex-covers.lagda.md +++ b/src/graph-theory/vertex-covers.lagda.md @@ -1,29 +1,24 @@ # Vertex covers ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.vertex-covers - (funext : function-extensionality) - where +module graph-theory.vertex-covers where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.undirected-graphs funext +open import graph-theory.undirected-graphs -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/graph-theory/voltage-graphs.lagda.md b/src/graph-theory/voltage-graphs.lagda.md index bf53f23fd5..bc99323d60 100644 --- a/src/graph-theory/voltage-graphs.lagda.md +++ b/src/graph-theory/voltage-graphs.lagda.md @@ -1,12 +1,7 @@ # Voltage graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.voltage-graphs - (funext : function-extensionality) - where +module graph-theory.voltage-graphs where ```
Imports @@ -15,9 +10,9 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.directed-graphs funext +open import graph-theory.directed-graphs -open import group-theory.groups funext +open import group-theory.groups ```
diff --git a/src/graph-theory/walks-directed-graphs.lagda.md b/src/graph-theory/walks-directed-graphs.lagda.md index ea770b217d..b7e9537b73 100644 --- a/src/graph-theory/walks-directed-graphs.lagda.md +++ b/src/graph-theory/walks-directed-graphs.lagda.md @@ -1,12 +1,7 @@ # Walks in directed graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.walks-directed-graphs - (funext : function-extensionality) - where +module graph-theory.walks-directed-graphs where ```
Imports @@ -15,27 +10,27 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.raising-universe-levels funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.raising-universe-levels +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.equivalences-directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.equivalences-directed-graphs +open import graph-theory.morphisms-directed-graphs ```
diff --git a/src/graph-theory/walks-undirected-graphs.lagda.md b/src/graph-theory/walks-undirected-graphs.lagda.md index 80f19afcad..b73510b8b4 100644 --- a/src/graph-theory/walks-undirected-graphs.lagda.md +++ b/src/graph-theory/walks-undirected-graphs.lagda.md @@ -1,41 +1,36 @@ # Walks in undirected graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.walks-undirected-graphs - (funext : function-extensionality) - where +module graph-theory.walks-undirected-graphs where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-coproduct-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.torsorial-type-families +open import foundation.type-arithmetic-coproduct-types open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.undirected-graphs funext +open import graph-theory.undirected-graphs -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md b/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md index 51bb50e037..4392870452 100644 --- a/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md +++ b/src/graph-theory/wide-displayed-large-reflexive-graphs.lagda.md @@ -1,25 +1,20 @@ # Wide displayed large reflexive graphs ```agda -open import foundation.function-extensionality-axiom - -module - graph-theory.wide-displayed-large-reflexive-graphs - (funext : function-extensionality) - where +module graph-theory.wide-displayed-large-reflexive-graphs where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import graph-theory.large-reflexive-graphs -open import graph-theory.reflexive-graphs funext +open import graph-theory.reflexive-graphs ```
diff --git a/src/group-theory.lagda.md b/src/group-theory.lagda.md index 27c6f34059..6d7a7e8e31 100644 --- a/src/group-theory.lagda.md +++ b/src/group-theory.lagda.md @@ -3,208 +3,203 @@ ## Modules in the group theory namespace ```agda -open import foundation.function-extensionality-axiom +module group-theory where -module - group-theory - (funext : function-extensionality) - where - -open import group-theory.abelian-groups funext public -open import group-theory.abelianization-groups funext public -open import group-theory.addition-homomorphisms-abelian-groups funext public -open import group-theory.automorphism-groups funext public -open import group-theory.cartesian-products-abelian-groups funext public -open import group-theory.cartesian-products-concrete-groups funext public -open import group-theory.cartesian-products-groups funext public -open import group-theory.cartesian-products-monoids funext public -open import group-theory.cartesian-products-semigroups funext public -open import group-theory.category-of-abelian-groups funext public +open import group-theory.abelian-groups public +open import group-theory.abelianization-groups public +open import group-theory.addition-homomorphisms-abelian-groups public +open import group-theory.automorphism-groups public +open import group-theory.cartesian-products-abelian-groups public +open import group-theory.cartesian-products-concrete-groups public +open import group-theory.cartesian-products-groups public +open import group-theory.cartesian-products-monoids public +open import group-theory.cartesian-products-semigroups public +open import group-theory.category-of-abelian-groups public open import group-theory.category-of-concrete-groups public -open import group-theory.category-of-group-actions funext public -open import group-theory.category-of-groups funext public -open import group-theory.category-of-orbits-groups funext public -open import group-theory.category-of-semigroups funext public -open import group-theory.cayleys-theorem funext public -open import group-theory.centers-groups funext public -open import group-theory.centers-monoids funext public -open import group-theory.centers-semigroups funext public -open import group-theory.central-elements-groups funext public -open import group-theory.central-elements-monoids funext public -open import group-theory.central-elements-semigroups funext public -open import group-theory.centralizer-subgroups funext public -open import group-theory.characteristic-subgroups funext public -open import group-theory.commutative-monoids funext public -open import group-theory.commutator-subgroups funext public -open import group-theory.commutators-of-elements-groups funext public -open import group-theory.commuting-elements-groups funext public -open import group-theory.commuting-elements-monoids funext public -open import group-theory.commuting-elements-semigroups funext public -open import group-theory.commuting-squares-of-group-homomorphisms funext public -open import group-theory.concrete-group-actions funext public -open import group-theory.concrete-groups funext public -open import group-theory.concrete-monoids funext public -open import group-theory.congruence-relations-abelian-groups funext public -open import group-theory.congruence-relations-commutative-monoids funext public -open import group-theory.congruence-relations-groups funext public -open import group-theory.congruence-relations-monoids funext public -open import group-theory.congruence-relations-semigroups funext public -open import group-theory.conjugation funext public -open import group-theory.conjugation-concrete-groups funext public -open import group-theory.contravariant-pushforward-concrete-group-actions funext public -open import group-theory.cores-monoids funext public -open import group-theory.cyclic-groups funext public -open import group-theory.decidable-subgroups funext public -open import group-theory.dependent-products-abelian-groups funext public -open import group-theory.dependent-products-commutative-monoids funext public -open import group-theory.dependent-products-groups funext public -open import group-theory.dependent-products-monoids funext public -open import group-theory.dependent-products-semigroups funext public -open import group-theory.dihedral-group-construction funext public -open import group-theory.dihedral-groups funext public -open import group-theory.e8-lattice funext public -open import group-theory.elements-of-finite-order-groups funext public -open import group-theory.embeddings-abelian-groups funext public -open import group-theory.embeddings-groups funext public -open import group-theory.endomorphism-rings-abelian-groups funext public -open import group-theory.epimorphisms-groups funext public -open import group-theory.equivalences-concrete-group-actions funext public -open import group-theory.equivalences-concrete-groups funext public -open import group-theory.equivalences-group-actions funext public -open import group-theory.equivalences-semigroups funext public -open import group-theory.exponents-abelian-groups funext public -open import group-theory.exponents-groups funext public -open import group-theory.free-concrete-group-actions funext public -open import group-theory.free-groups-with-one-generator funext public -open import group-theory.full-subgroups funext public -open import group-theory.full-subsemigroups funext public -open import group-theory.function-abelian-groups funext public -open import group-theory.function-commutative-monoids funext public -open import group-theory.function-groups funext public -open import group-theory.function-monoids funext public -open import group-theory.function-semigroups funext public -open import group-theory.functoriality-quotient-groups funext public -open import group-theory.furstenberg-groups funext public -open import group-theory.generating-elements-groups funext public -open import group-theory.generating-sets-groups funext public -open import group-theory.group-actions funext public -open import group-theory.groups funext public -open import group-theory.homomorphisms-abelian-groups funext public -open import group-theory.homomorphisms-commutative-monoids funext public -open import group-theory.homomorphisms-concrete-group-actions funext public -open import group-theory.homomorphisms-concrete-groups funext public -open import group-theory.homomorphisms-generated-subgroups funext public -open import group-theory.homomorphisms-group-actions funext public -open import group-theory.homomorphisms-groups funext public -open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups funext public -open import group-theory.homomorphisms-monoids funext public -open import group-theory.homomorphisms-semigroups funext public -open import group-theory.homotopy-automorphism-groups funext public -open import group-theory.images-of-group-homomorphisms funext public -open import group-theory.images-of-semigroup-homomorphisms funext public -open import group-theory.integer-multiples-of-elements-abelian-groups funext public -open import group-theory.integer-powers-of-elements-groups funext public -open import group-theory.intersections-subgroups-abelian-groups funext public -open import group-theory.intersections-subgroups-groups funext public -open import group-theory.inverse-semigroups funext public -open import group-theory.invertible-elements-monoids funext public -open import group-theory.isomorphisms-abelian-groups funext public -open import group-theory.isomorphisms-concrete-groups funext public -open import group-theory.isomorphisms-group-actions funext public -open import group-theory.isomorphisms-groups funext public -open import group-theory.isomorphisms-monoids funext public -open import group-theory.isomorphisms-semigroups funext public -open import group-theory.iterated-cartesian-products-concrete-groups funext public -open import group-theory.kernels-homomorphisms-abelian-groups funext public -open import group-theory.kernels-homomorphisms-concrete-groups funext public -open import group-theory.kernels-homomorphisms-groups funext public -open import group-theory.large-semigroups funext public -open import group-theory.loop-groups-sets funext public -open import group-theory.mere-equivalences-concrete-group-actions funext public -open import group-theory.mere-equivalences-group-actions funext public -open import group-theory.minkowski-multiplication-commutative-monoids funext public -open import group-theory.minkowski-multiplication-monoids funext public -open import group-theory.minkowski-multiplication-semigroups funext public -open import group-theory.monoid-actions funext public -open import group-theory.monoids funext public -open import group-theory.monomorphisms-concrete-groups funext public -open import group-theory.monomorphisms-groups funext public -open import group-theory.multiples-of-elements-abelian-groups funext public -open import group-theory.nontrivial-groups funext public -open import group-theory.normal-closures-subgroups funext public -open import group-theory.normal-cores-subgroups funext public -open import group-theory.normal-subgroups funext public -open import group-theory.normal-subgroups-concrete-groups funext public -open import group-theory.normal-submonoids funext public -open import group-theory.normal-submonoids-commutative-monoids funext public -open import group-theory.normalizer-subgroups funext public -open import group-theory.nullifying-group-homomorphisms funext public -open import group-theory.opposite-groups funext public -open import group-theory.opposite-semigroups funext public -open import group-theory.orbit-stabilizer-theorem-concrete-groups funext public -open import group-theory.orbits-concrete-group-actions funext public -open import group-theory.orbits-group-actions funext public -open import group-theory.orders-of-elements-groups funext public -open import group-theory.perfect-cores funext public -open import group-theory.perfect-groups funext public -open import group-theory.perfect-subgroups funext public -open import group-theory.powers-of-elements-commutative-monoids funext public -open import group-theory.powers-of-elements-groups funext public -open import group-theory.powers-of-elements-monoids funext public -open import group-theory.precategory-of-commutative-monoids funext public -open import group-theory.precategory-of-concrete-groups funext public -open import group-theory.precategory-of-group-actions funext public -open import group-theory.precategory-of-groups funext public -open import group-theory.precategory-of-monoids funext public -open import group-theory.precategory-of-orbits-monoid-actions funext public -open import group-theory.precategory-of-semigroups funext public -open import group-theory.principal-group-actions funext public -open import group-theory.principal-torsors-concrete-groups funext public -open import group-theory.products-of-elements-monoids funext public -open import group-theory.products-of-tuples-of-elements-commutative-monoids funext public -open import group-theory.pullbacks-subgroups funext public -open import group-theory.pullbacks-subsemigroups funext public -open import group-theory.quotient-groups funext public -open import group-theory.quotient-groups-concrete-groups funext public -open import group-theory.quotients-abelian-groups funext public -open import group-theory.rational-commutative-monoids funext public -open import group-theory.representations-monoids-precategories funext public -open import group-theory.saturated-congruence-relations-commutative-monoids funext public -open import group-theory.saturated-congruence-relations-monoids funext public -open import group-theory.semigroups funext public -open import group-theory.sheargroups funext public -open import group-theory.shriek-concrete-group-actions funext public -open import group-theory.stabilizer-groups funext public -open import group-theory.stabilizer-groups-concrete-group-actions funext public -open import group-theory.subgroups funext public -open import group-theory.subgroups-abelian-groups funext public -open import group-theory.subgroups-concrete-groups funext public -open import group-theory.subgroups-generated-by-elements-groups funext public -open import group-theory.subgroups-generated-by-families-of-elements-groups funext public -open import group-theory.subgroups-generated-by-subsets-groups funext public -open import group-theory.submonoids funext public -open import group-theory.submonoids-commutative-monoids funext public -open import group-theory.subsemigroups funext public -open import group-theory.subsets-abelian-groups funext public -open import group-theory.subsets-commutative-monoids funext public -open import group-theory.subsets-groups funext public -open import group-theory.subsets-monoids funext public -open import group-theory.subsets-semigroups funext public -open import group-theory.substitution-functor-concrete-group-actions funext public -open import group-theory.substitution-functor-group-actions funext public -open import group-theory.surjective-group-homomorphisms funext public -open import group-theory.surjective-semigroup-homomorphisms funext public -open import group-theory.symmetric-concrete-groups funext public -open import group-theory.symmetric-groups funext public -open import group-theory.torsion-elements-groups funext public -open import group-theory.torsion-free-groups funext public -open import group-theory.torsors funext public -open import group-theory.transitive-concrete-group-actions funext public -open import group-theory.transitive-group-actions funext public -open import group-theory.trivial-concrete-groups funext public -open import group-theory.trivial-group-homomorphisms funext public -open import group-theory.trivial-groups funext public -open import group-theory.trivial-subgroups funext public -open import group-theory.unordered-tuples-of-elements-commutative-monoids funext public -open import group-theory.wild-representations-monoids funext public +open import group-theory.category-of-group-actions public +open import group-theory.category-of-groups public +open import group-theory.category-of-orbits-groups public +open import group-theory.category-of-semigroups public +open import group-theory.cayleys-theorem public +open import group-theory.centers-groups public +open import group-theory.centers-monoids public +open import group-theory.centers-semigroups public +open import group-theory.central-elements-groups public +open import group-theory.central-elements-monoids public +open import group-theory.central-elements-semigroups public +open import group-theory.centralizer-subgroups public +open import group-theory.characteristic-subgroups public +open import group-theory.commutative-monoids public +open import group-theory.commutator-subgroups public +open import group-theory.commutators-of-elements-groups public +open import group-theory.commuting-elements-groups public +open import group-theory.commuting-elements-monoids public +open import group-theory.commuting-elements-semigroups public +open import group-theory.commuting-squares-of-group-homomorphisms public +open import group-theory.concrete-group-actions public +open import group-theory.concrete-groups public +open import group-theory.concrete-monoids public +open import group-theory.congruence-relations-abelian-groups public +open import group-theory.congruence-relations-commutative-monoids public +open import group-theory.congruence-relations-groups public +open import group-theory.congruence-relations-monoids public +open import group-theory.congruence-relations-semigroups public +open import group-theory.conjugation public +open import group-theory.conjugation-concrete-groups public +open import group-theory.contravariant-pushforward-concrete-group-actions public +open import group-theory.cores-monoids public +open import group-theory.cyclic-groups public +open import group-theory.decidable-subgroups public +open import group-theory.dependent-products-abelian-groups public +open import group-theory.dependent-products-commutative-monoids public +open import group-theory.dependent-products-groups public +open import group-theory.dependent-products-monoids public +open import group-theory.dependent-products-semigroups public +open import group-theory.dihedral-group-construction public +open import group-theory.dihedral-groups public +open import group-theory.e8-lattice public +open import group-theory.elements-of-finite-order-groups public +open import group-theory.embeddings-abelian-groups public +open import group-theory.embeddings-groups public +open import group-theory.endomorphism-rings-abelian-groups public +open import group-theory.epimorphisms-groups public +open import group-theory.equivalences-concrete-group-actions public +open import group-theory.equivalences-concrete-groups public +open import group-theory.equivalences-group-actions public +open import group-theory.equivalences-semigroups public +open import group-theory.exponents-abelian-groups public +open import group-theory.exponents-groups public +open import group-theory.free-concrete-group-actions public +open import group-theory.free-groups-with-one-generator public +open import group-theory.full-subgroups public +open import group-theory.full-subsemigroups public +open import group-theory.function-abelian-groups public +open import group-theory.function-commutative-monoids public +open import group-theory.function-groups public +open import group-theory.function-monoids public +open import group-theory.function-semigroups public +open import group-theory.functoriality-quotient-groups public +open import group-theory.furstenberg-groups public +open import group-theory.generating-elements-groups public +open import group-theory.generating-sets-groups public +open import group-theory.group-actions public +open import group-theory.groups public +open import group-theory.homomorphisms-abelian-groups public +open import group-theory.homomorphisms-commutative-monoids public +open import group-theory.homomorphisms-concrete-group-actions public +open import group-theory.homomorphisms-concrete-groups public +open import group-theory.homomorphisms-generated-subgroups public +open import group-theory.homomorphisms-group-actions public +open import group-theory.homomorphisms-groups public +open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups public +open import group-theory.homomorphisms-monoids public +open import group-theory.homomorphisms-semigroups public +open import group-theory.homotopy-automorphism-groups public +open import group-theory.images-of-group-homomorphisms public +open import group-theory.images-of-semigroup-homomorphisms public +open import group-theory.integer-multiples-of-elements-abelian-groups public +open import group-theory.integer-powers-of-elements-groups public +open import group-theory.intersections-subgroups-abelian-groups public +open import group-theory.intersections-subgroups-groups public +open import group-theory.inverse-semigroups public +open import group-theory.invertible-elements-monoids public +open import group-theory.isomorphisms-abelian-groups public +open import group-theory.isomorphisms-concrete-groups public +open import group-theory.isomorphisms-group-actions public +open import group-theory.isomorphisms-groups public +open import group-theory.isomorphisms-monoids public +open import group-theory.isomorphisms-semigroups public +open import group-theory.iterated-cartesian-products-concrete-groups public +open import group-theory.kernels-homomorphisms-abelian-groups public +open import group-theory.kernels-homomorphisms-concrete-groups public +open import group-theory.kernels-homomorphisms-groups public +open import group-theory.large-semigroups public +open import group-theory.loop-groups-sets public +open import group-theory.mere-equivalences-concrete-group-actions public +open import group-theory.mere-equivalences-group-actions public +open import group-theory.minkowski-multiplication-commutative-monoids public +open import group-theory.minkowski-multiplication-monoids public +open import group-theory.minkowski-multiplication-semigroups public +open import group-theory.monoid-actions public +open import group-theory.monoids public +open import group-theory.monomorphisms-concrete-groups public +open import group-theory.monomorphisms-groups public +open import group-theory.multiples-of-elements-abelian-groups public +open import group-theory.nontrivial-groups public +open import group-theory.normal-closures-subgroups public +open import group-theory.normal-cores-subgroups public +open import group-theory.normal-subgroups public +open import group-theory.normal-subgroups-concrete-groups public +open import group-theory.normal-submonoids public +open import group-theory.normal-submonoids-commutative-monoids public +open import group-theory.normalizer-subgroups public +open import group-theory.nullifying-group-homomorphisms public +open import group-theory.opposite-groups public +open import group-theory.opposite-semigroups public +open import group-theory.orbit-stabilizer-theorem-concrete-groups public +open import group-theory.orbits-concrete-group-actions public +open import group-theory.orbits-group-actions public +open import group-theory.orders-of-elements-groups public +open import group-theory.perfect-cores public +open import group-theory.perfect-groups public +open import group-theory.perfect-subgroups public +open import group-theory.powers-of-elements-commutative-monoids public +open import group-theory.powers-of-elements-groups public +open import group-theory.powers-of-elements-monoids public +open import group-theory.precategory-of-commutative-monoids public +open import group-theory.precategory-of-concrete-groups public +open import group-theory.precategory-of-group-actions public +open import group-theory.precategory-of-groups public +open import group-theory.precategory-of-monoids public +open import group-theory.precategory-of-orbits-monoid-actions public +open import group-theory.precategory-of-semigroups public +open import group-theory.principal-group-actions public +open import group-theory.principal-torsors-concrete-groups public +open import group-theory.products-of-elements-monoids public +open import group-theory.products-of-tuples-of-elements-commutative-monoids public +open import group-theory.pullbacks-subgroups public +open import group-theory.pullbacks-subsemigroups public +open import group-theory.quotient-groups public +open import group-theory.quotient-groups-concrete-groups public +open import group-theory.quotients-abelian-groups public +open import group-theory.rational-commutative-monoids public +open import group-theory.representations-monoids-precategories public +open import group-theory.saturated-congruence-relations-commutative-monoids public +open import group-theory.saturated-congruence-relations-monoids public +open import group-theory.semigroups public +open import group-theory.sheargroups public +open import group-theory.shriek-concrete-group-actions public +open import group-theory.stabilizer-groups public +open import group-theory.stabilizer-groups-concrete-group-actions public +open import group-theory.subgroups public +open import group-theory.subgroups-abelian-groups public +open import group-theory.subgroups-concrete-groups public +open import group-theory.subgroups-generated-by-elements-groups public +open import group-theory.subgroups-generated-by-families-of-elements-groups public +open import group-theory.subgroups-generated-by-subsets-groups public +open import group-theory.submonoids public +open import group-theory.submonoids-commutative-monoids public +open import group-theory.subsemigroups public +open import group-theory.subsets-abelian-groups public +open import group-theory.subsets-commutative-monoids public +open import group-theory.subsets-groups public +open import group-theory.subsets-monoids public +open import group-theory.subsets-semigroups public +open import group-theory.substitution-functor-concrete-group-actions public +open import group-theory.substitution-functor-group-actions public +open import group-theory.surjective-group-homomorphisms public +open import group-theory.surjective-semigroup-homomorphisms public +open import group-theory.symmetric-concrete-groups public +open import group-theory.symmetric-groups public +open import group-theory.torsion-elements-groups public +open import group-theory.torsion-free-groups public +open import group-theory.torsors public +open import group-theory.transitive-concrete-group-actions public +open import group-theory.transitive-group-actions public +open import group-theory.trivial-concrete-groups public +open import group-theory.trivial-group-homomorphisms public +open import group-theory.trivial-groups public +open import group-theory.trivial-subgroups public +open import group-theory.unordered-tuples-of-elements-commutative-monoids public +open import group-theory.wild-representations-monoids public ``` diff --git a/src/group-theory/abelian-groups.lagda.md b/src/group-theory/abelian-groups.lagda.md index 050d547706..6023e6276d 100644 --- a/src/group-theory/abelian-groups.lagda.md +++ b/src/group-theory/abelian-groups.lagda.md @@ -1,12 +1,7 @@ # Abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.abelian-groups - (funext : function-extensionality) - where +module group-theory.abelian-groups where ```
Imports @@ -14,41 +9,41 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.full-subtypes funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.full-subtypes +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps open import foundation.interchange-law -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.central-elements-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.commutator-subgroups funext -open import group-theory.commutators-of-elements-groups funext -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.monoids funext -open import group-theory.nullifying-group-homomorphisms funext -open import group-theory.pullbacks-subgroups funext -open import group-theory.semigroups funext -open import group-theory.subgroups funext -open import group-theory.subgroups funext-generated-by-families-of-elements-groups -open import group-theory.trivial-subgroups funext - -open import lists.concatenation-lists funext +open import group-theory.central-elements-groups +open import group-theory.commutative-monoids +open import group-theory.commutator-subgroups +open import group-theory.commutators-of-elements-groups +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.monoids +open import group-theory.nullifying-group-homomorphisms +open import group-theory.pullbacks-subgroups +open import group-theory.semigroups +open import group-theory.subgroups +open import group-theory.subgroups-generated-by-families-of-elements-groups +open import group-theory.trivial-subgroups + +open import lists.concatenation-lists open import lists.lists -open import structured-types.pointed-types-equipped-with-automorphisms funext +open import structured-types.pointed-types-equipped-with-automorphisms ```
diff --git a/src/group-theory/abelianization-groups.lagda.md b/src/group-theory/abelianization-groups.lagda.md index c28d0833c9..5698ee542f 100644 --- a/src/group-theory/abelianization-groups.lagda.md +++ b/src/group-theory/abelianization-groups.lagda.md @@ -3,46 +3,41 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - group-theory.abelianization-groups - (funext : function-extensionality) - where +module group-theory.abelianization-groups where ```
Imports ```agda -open import category-theory.adjunctions-large-categories funext -open import category-theory.adjunctions-large-precategories funext -open import category-theory.functors-large-categories funext -open import category-theory.functors-large-precategories funext -open import category-theory.natural-transformations-functors-large-categories funext -open import category-theory.natural-transformations-functors-large-precategories funext - -open import foundation.commuting-squares-of-maps funext +open import category-theory.adjunctions-large-categories +open import category-theory.adjunctions-large-precategories +open import category-theory.functors-large-categories +open import category-theory.functors-large-precategories +open import category-theory.natural-transformations-functors-large-categories +open import category-theory.natural-transformations-functors-large-precategories + +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.set-quotients funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.set-quotients +open import foundation.sets open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import group-theory.abelian-groups funext -open import group-theory.category-of-abelian-groups funext -open import group-theory.category-of-groups funext -open import group-theory.commutator-subgroups funext -open import group-theory.commuting-squares-of-group-homomorphisms funext -open import group-theory.functoriality-quotient-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.normal-subgroups funext -open import group-theory.nullifying-group-homomorphisms funext -open import group-theory.quotient-groups funext +open import group-theory.abelian-groups +open import group-theory.category-of-abelian-groups +open import group-theory.category-of-groups +open import group-theory.commutator-subgroups +open import group-theory.commuting-squares-of-group-homomorphisms +open import group-theory.functoriality-quotient-groups +open import group-theory.groups +open import group-theory.homomorphisms-abelian-groups +open import group-theory.homomorphisms-groups +open import group-theory.normal-subgroups +open import group-theory.nullifying-group-homomorphisms +open import group-theory.quotient-groups ```
diff --git a/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md b/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md index d3de9771ba..8c5fd68978 100644 --- a/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/addition-homomorphisms-abelian-groups.lagda.md @@ -1,12 +1,7 @@ # Pointwise addition of morphisms of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.addition-homomorphisms-abelian-groups - (funext : function-extensionality) - where +module group-theory.addition-homomorphisms-abelian-groups where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.homomorphisms-abelian-groups +open import group-theory.semigroups ```
diff --git a/src/group-theory/automorphism-groups.lagda.md b/src/group-theory/automorphism-groups.lagda.md index 65c6335a6c..668dde054a 100644 --- a/src/group-theory/automorphism-groups.lagda.md +++ b/src/group-theory/automorphism-groups.lagda.md @@ -1,32 +1,27 @@ # Automorphism groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.automorphism-groups - (funext : function-extensionality) - where +module group-theory.automorphism-groups where ```
Imports ```agda -open import foundation.1-types funext -open import foundation.connected-components funext +open import foundation.1-types +open import foundation.connected-components open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.equivalences-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.equivalences-concrete-groups -open import higher-group-theory.automorphism-groups funext -open import higher-group-theory.higher-groups funext +open import higher-group-theory.automorphism-groups +open import higher-group-theory.higher-groups ```
diff --git a/src/group-theory/cartesian-products-abelian-groups.lagda.md b/src/group-theory/cartesian-products-abelian-groups.lagda.md index 21868c8edc..2bf663196b 100644 --- a/src/group-theory/cartesian-products-abelian-groups.lagda.md +++ b/src/group-theory/cartesian-products-abelian-groups.lagda.md @@ -1,12 +1,7 @@ # Cartesian products of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.cartesian-products-abelian-groups - (funext : function-extensionality) - where +module group-theory.cartesian-products-abelian-groups where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.cartesian-products-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.cartesian-products-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/cartesian-products-concrete-groups.lagda.md b/src/group-theory/cartesian-products-concrete-groups.lagda.md index 2280a032ab..a60202281c 100644 --- a/src/group-theory/cartesian-products-concrete-groups.lagda.md +++ b/src/group-theory/cartesian-products-concrete-groups.lagda.md @@ -1,36 +1,31 @@ # Cartesian products of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.cartesian-products-concrete-groups - (funext : function-extensionality) - where +module group-theory.cartesian-products-concrete-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.1-types funext -open import foundation.cartesian-product-types funext +open import foundation.0-connected-types +open import foundation.1-types +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.truncated-types funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.groups funext +open import group-theory.concrete-groups +open import group-theory.groups -open import higher-group-theory.cartesian-products-higher-groups funext -open import higher-group-theory.higher-groups funext +open import higher-group-theory.cartesian-products-higher-groups +open import higher-group-theory.higher-groups open import structured-types.pointed-types ``` diff --git a/src/group-theory/cartesian-products-groups.lagda.md b/src/group-theory/cartesian-products-groups.lagda.md index 43ca52a66a..84748d8b87 100644 --- a/src/group-theory/cartesian-products-groups.lagda.md +++ b/src/group-theory/cartesian-products-groups.lagda.md @@ -1,12 +1,7 @@ # Cartesian products of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.cartesian-products-groups - (funext : function-extensionality) - where +module group-theory.cartesian-products-groups where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.cartesian-products-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.cartesian-products-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/cartesian-products-monoids.lagda.md b/src/group-theory/cartesian-products-monoids.lagda.md index 7880bfd202..c83c132714 100644 --- a/src/group-theory/cartesian-products-monoids.lagda.md +++ b/src/group-theory/cartesian-products-monoids.lagda.md @@ -1,12 +1,7 @@ # Cartesian products of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.cartesian-products-monoids - (funext : function-extensionality) - where +module group-theory.cartesian-products-monoids where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.cartesian-products-semigroups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.cartesian-products-semigroups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/cartesian-products-semigroups.lagda.md b/src/group-theory/cartesian-products-semigroups.lagda.md index a57864f7eb..e14a38dbc2 100644 --- a/src/group-theory/cartesian-products-semigroups.lagda.md +++ b/src/group-theory/cartesian-products-semigroups.lagda.md @@ -1,12 +1,7 @@ # Cartesian products of semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.cartesian-products-semigroups - (funext : function-extensionality) - where +module group-theory.cartesian-products-semigroups where ```
Imports @@ -14,11 +9,11 @@ module ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups ```
diff --git a/src/group-theory/category-of-abelian-groups.lagda.md b/src/group-theory/category-of-abelian-groups.lagda.md index bca9cd26b5..abb1ac4341 100644 --- a/src/group-theory/category-of-abelian-groups.lagda.md +++ b/src/group-theory/category-of-abelian-groups.lagda.md @@ -1,28 +1,23 @@ # The category of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.category-of-abelian-groups - (funext : function-extensionality) - where +module group-theory.category-of-abelian-groups where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.full-large-subcategories funext -open import category-theory.functors-large-categories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.full-large-subcategories +open import category-theory.functors-large-categories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.category-of-groups funext +open import group-theory.abelian-groups +open import group-theory.category-of-groups ```
diff --git a/src/group-theory/category-of-group-actions.lagda.md b/src/group-theory/category-of-group-actions.lagda.md index 08c74e94be..1205990345 100644 --- a/src/group-theory/category-of-group-actions.lagda.md +++ b/src/group-theory/category-of-group-actions.lagda.md @@ -1,32 +1,27 @@ # The category of group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.category-of-group-actions - (funext : function-extensionality) - where +module group-theory.category-of-group-actions where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext -open import group-theory.homomorphisms-group-actions funext -open import group-theory.isomorphisms-group-actions funext -open import group-theory.precategory-of-group-actions funext +open import group-theory.group-actions +open import group-theory.groups +open import group-theory.homomorphisms-group-actions +open import group-theory.isomorphisms-group-actions +open import group-theory.precategory-of-group-actions ```
diff --git a/src/group-theory/category-of-groups.lagda.md b/src/group-theory/category-of-groups.lagda.md index b6c21be780..5b7a7ec268 100644 --- a/src/group-theory/category-of-groups.lagda.md +++ b/src/group-theory/category-of-groups.lagda.md @@ -1,29 +1,24 @@ # The category of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.category-of-groups - (funext : function-extensionality) - where +module group-theory.category-of-groups where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.large-categories funext +open import category-theory.categories +open import category-theory.large-categories -open import foundation.1-types funext -open import foundation.equivalences funext +open import foundation.1-types +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.precategory-of-groups funext +open import group-theory.groups +open import group-theory.isomorphisms-groups +open import group-theory.precategory-of-groups ```
diff --git a/src/group-theory/category-of-orbits-groups.lagda.md b/src/group-theory/category-of-orbits-groups.lagda.md index 93a09223ec..e8ddd2bdc0 100644 --- a/src/group-theory/category-of-orbits-groups.lagda.md +++ b/src/group-theory/category-of-orbits-groups.lagda.md @@ -1,35 +1,30 @@ # The orbit category of a group ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.category-of-orbits-groups - (funext : function-extensionality) - where +module group-theory.category-of-orbits-groups where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.full-large-subcategories funext -open import category-theory.isomorphisms-in-large-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.full-large-subcategories +open import category-theory.isomorphisms-in-large-precategories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.universe-levels -open import group-theory.category-of-group-actions funext -open import group-theory.group-actions funext -open import group-theory.groups funext -open import group-theory.homomorphisms-group-actions funext -open import group-theory.isomorphisms-group-actions funext -open import group-theory.precategory-of-group-actions funext -open import group-theory.transitive-group-actions funext +open import group-theory.category-of-group-actions +open import group-theory.group-actions +open import group-theory.groups +open import group-theory.homomorphisms-group-actions +open import group-theory.isomorphisms-group-actions +open import group-theory.precategory-of-group-actions +open import group-theory.transitive-group-actions ```
diff --git a/src/group-theory/category-of-semigroups.lagda.md b/src/group-theory/category-of-semigroups.lagda.md index 034a13422e..a610b13437 100644 --- a/src/group-theory/category-of-semigroups.lagda.md +++ b/src/group-theory/category-of-semigroups.lagda.md @@ -1,30 +1,25 @@ # The category of semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.category-of-semigroups - (funext : function-extensionality) - where +module group-theory.category-of-semigroups where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.large-categories funext +open import category-theory.categories +open import category-theory.large-categories -open import foundation.1-types funext +open import foundation.1-types open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.isomorphisms-semigroups funext -open import group-theory.precategory-of-semigroups funext -open import group-theory.semigroups funext +open import group-theory.isomorphisms-semigroups +open import group-theory.precategory-of-semigroups +open import group-theory.semigroups ```
diff --git a/src/group-theory/cayleys-theorem.lagda.md b/src/group-theory/cayleys-theorem.lagda.md index bc24466f32..b770b023ac 100644 --- a/src/group-theory/cayleys-theorem.lagda.md +++ b/src/group-theory/cayleys-theorem.lagda.md @@ -1,28 +1,23 @@ # Cayley's theorem ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.cayleys-theorem - (funext : function-extensionality) - where +module group-theory.cayleys-theorem where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalence-extensionality funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.embeddings +open import foundation.equivalence-extensionality +open import foundation.identity-types +open import foundation.injective-maps open import foundation.universe-levels -open import group-theory.embeddings-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.symmetric-groups funext +open import group-theory.embeddings-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.symmetric-groups ```
diff --git a/src/group-theory/centers-groups.lagda.md b/src/group-theory/centers-groups.lagda.md index 2634f73aac..a92e3af960 100644 --- a/src/group-theory/centers-groups.lagda.md +++ b/src/group-theory/centers-groups.lagda.md @@ -1,27 +1,22 @@ # The center of a group ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.centers-groups - (funext : function-extensionality) - where +module group-theory.centers-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.central-elements-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.normal-subgroups funext -open import group-theory.subgroups funext +open import group-theory.central-elements-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.normal-subgroups +open import group-theory.subgroups ```
diff --git a/src/group-theory/centers-monoids.lagda.md b/src/group-theory/centers-monoids.lagda.md index f40e75d76a..39deb28916 100644 --- a/src/group-theory/centers-monoids.lagda.md +++ b/src/group-theory/centers-monoids.lagda.md @@ -1,26 +1,21 @@ # Center of a monoid ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.centers-monoids - (funext : function-extensionality) - where +module group-theory.centers-monoids where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.central-elements-monoids funext -open import group-theory.homomorphisms-monoids funext -open import group-theory.monoids funext -open import group-theory.submonoids funext +open import group-theory.central-elements-monoids +open import group-theory.homomorphisms-monoids +open import group-theory.monoids +open import group-theory.submonoids ```
diff --git a/src/group-theory/centers-semigroups.lagda.md b/src/group-theory/centers-semigroups.lagda.md index 5e24d95ec4..9997e96a0c 100644 --- a/src/group-theory/centers-semigroups.lagda.md +++ b/src/group-theory/centers-semigroups.lagda.md @@ -1,26 +1,21 @@ # Center of a semigroup ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.centers-semigroups - (funext : function-extensionality) - where +module group-theory.centers-semigroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.central-elements-semigroups funext -open import group-theory.homomorphisms-semigroups funext -open import group-theory.semigroups funext -open import group-theory.subsemigroups funext +open import group-theory.central-elements-semigroups +open import group-theory.homomorphisms-semigroups +open import group-theory.semigroups +open import group-theory.subsemigroups ```
diff --git a/src/group-theory/central-elements-groups.lagda.md b/src/group-theory/central-elements-groups.lagda.md index 698682c85b..21cd4b9353 100644 --- a/src/group-theory/central-elements-groups.lagda.md +++ b/src/group-theory/central-elements-groups.lagda.md @@ -1,26 +1,21 @@ # Central elements of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.central-elements-groups - (funext : function-extensionality) - where +module group-theory.central-elements-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.central-elements-monoids funext -open import group-theory.conjugation funext -open import group-theory.groups funext +open import group-theory.central-elements-monoids +open import group-theory.conjugation +open import group-theory.groups ```
diff --git a/src/group-theory/central-elements-monoids.lagda.md b/src/group-theory/central-elements-monoids.lagda.md index a759cd76b5..bece727ced 100644 --- a/src/group-theory/central-elements-monoids.lagda.md +++ b/src/group-theory/central-elements-monoids.lagda.md @@ -1,23 +1,18 @@ # Central elements of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.central-elements-monoids - (funext : function-extensionality) - where +module group-theory.central-elements-monoids where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.central-elements-semigroups funext -open import group-theory.monoids funext +open import group-theory.central-elements-semigroups +open import group-theory.monoids ```
diff --git a/src/group-theory/central-elements-semigroups.lagda.md b/src/group-theory/central-elements-semigroups.lagda.md index 2ade7477b3..cedeca3a11 100644 --- a/src/group-theory/central-elements-semigroups.lagda.md +++ b/src/group-theory/central-elements-semigroups.lagda.md @@ -1,24 +1,19 @@ # Central elements of semirings ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.central-elements-semigroups - (funext : function-extensionality) - where +module group-theory.central-elements-semigroups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups ```
diff --git a/src/group-theory/centralizer-subgroups.lagda.md b/src/group-theory/centralizer-subgroups.lagda.md index e5cff01755..9e44de697c 100644 --- a/src/group-theory/centralizer-subgroups.lagda.md +++ b/src/group-theory/centralizer-subgroups.lagda.md @@ -1,12 +1,7 @@ # Centralizer subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.centralizer-subgroups - (funext : function-extensionality) - where +module group-theory.centralizer-subgroups where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.subgroups +open import group-theory.subsets-groups ```
diff --git a/src/group-theory/characteristic-subgroups.lagda.md b/src/group-theory/characteristic-subgroups.lagda.md index 5073691e85..023e2b5cee 100644 --- a/src/group-theory/characteristic-subgroups.lagda.md +++ b/src/group-theory/characteristic-subgroups.lagda.md @@ -1,24 +1,19 @@ # Characteristic subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.characteristic-subgroups - (funext : function-extensionality) - where +module group-theory.characteristic-subgroups where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.images-of-group-homomorphisms funext -open import group-theory.isomorphisms-groups funext -open import group-theory.subgroups funext +open import group-theory.groups +open import group-theory.images-of-group-homomorphisms +open import group-theory.isomorphisms-groups +open import group-theory.subgroups ```
diff --git a/src/group-theory/commutative-monoids.lagda.md b/src/group-theory/commutative-monoids.lagda.md index 670467cd5c..ad42cb9e4f 100644 --- a/src/group-theory/commutative-monoids.lagda.md +++ b/src/group-theory/commutative-monoids.lagda.md @@ -1,12 +1,7 @@ # Commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.commutative-monoids - (funext : function-extensionality) - where +module group-theory.commutative-monoids where ```
Imports @@ -14,17 +9,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.interchange-law -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets open import foundation.telescopes open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/commutator-subgroups.lagda.md b/src/group-theory/commutator-subgroups.lagda.md index 051b0fbb3b..1300e1e9be 100644 --- a/src/group-theory/commutator-subgroups.lagda.md +++ b/src/group-theory/commutator-subgroups.lagda.md @@ -1,36 +1,31 @@ # Commutator subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.commutator-subgroups - (funext : function-extensionality) - where +module group-theory.commutator-subgroups where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels -open import group-theory.commutators-of-elements-groups funext -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.images-of-group-homomorphisms funext -open import group-theory.normal-subgroups funext -open import group-theory.pullbacks-subgroups funext -open import group-theory.subgroups funext -open import group-theory.subgroups funext-generated-by-families-of-elements-groups -open import group-theory.subgroups-generated-by-subsets-groups funext -open import group-theory.subsets-groups funext +open import group-theory.commutators-of-elements-groups +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.images-of-group-homomorphisms +open import group-theory.normal-subgroups +open import group-theory.pullbacks-subgroups +open import group-theory.subgroups +open import group-theory.subgroups-generated-by-families-of-elements-groups +open import group-theory.subgroups-generated-by-subsets-groups +open import group-theory.subsets-groups ```
diff --git a/src/group-theory/commutators-of-elements-groups.lagda.md b/src/group-theory/commutators-of-elements-groups.lagda.md index ae33e500e3..086b8fcc4d 100644 --- a/src/group-theory/commutators-of-elements-groups.lagda.md +++ b/src/group-theory/commutators-of-elements-groups.lagda.md @@ -1,25 +1,20 @@ # Commutators of elements in groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.commutators-of-elements-groups - (funext : function-extensionality) - where +module group-theory.commutators-of-elements-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.commuting-elements-groups funext -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext +open import group-theory.commuting-elements-groups +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.homomorphisms-groups ```
diff --git a/src/group-theory/commuting-elements-groups.lagda.md b/src/group-theory/commuting-elements-groups.lagda.md index b1c539a3f8..9e76af7d68 100644 --- a/src/group-theory/commuting-elements-groups.lagda.md +++ b/src/group-theory/commuting-elements-groups.lagda.md @@ -1,23 +1,18 @@ # Commuting elements of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.commuting-elements-groups - (funext : function-extensionality) - where +module group-theory.commuting-elements-groups where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.commuting-elements-monoids funext -open import group-theory.groups funext +open import group-theory.commuting-elements-monoids +open import group-theory.groups ```
diff --git a/src/group-theory/commuting-elements-monoids.lagda.md b/src/group-theory/commuting-elements-monoids.lagda.md index 3590439529..3f74bcc1d1 100644 --- a/src/group-theory/commuting-elements-monoids.lagda.md +++ b/src/group-theory/commuting-elements-monoids.lagda.md @@ -1,23 +1,18 @@ # Commuting elements of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.commuting-elements-monoids - (funext : function-extensionality) - where +module group-theory.commuting-elements-monoids where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.commuting-elements-semigroups funext -open import group-theory.monoids funext +open import group-theory.commuting-elements-semigroups +open import group-theory.monoids ```
diff --git a/src/group-theory/commuting-elements-semigroups.lagda.md b/src/group-theory/commuting-elements-semigroups.lagda.md index d0672f59e1..4c5d7998e8 100644 --- a/src/group-theory/commuting-elements-semigroups.lagda.md +++ b/src/group-theory/commuting-elements-semigroups.lagda.md @@ -1,24 +1,19 @@ # Commuting elements of semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.commuting-elements-semigroups - (funext : function-extensionality) - where +module group-theory.commuting-elements-semigroups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups ```
diff --git a/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md b/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md index 6740052c23..e8e02a54ec 100644 --- a/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md +++ b/src/group-theory/commuting-squares-of-group-homomorphisms.lagda.md @@ -1,22 +1,17 @@ # Commuting squares of group homomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.commuting-squares-of-group-homomorphisms - (funext : function-extensionality) - where +module group-theory.commuting-squares-of-group-homomorphisms where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups ```
diff --git a/src/group-theory/concrete-group-actions.lagda.md b/src/group-theory/concrete-group-actions.lagda.md index 8e6fadf7da..a379534da8 100644 --- a/src/group-theory/concrete-group-actions.lagda.md +++ b/src/group-theory/concrete-group-actions.lagda.md @@ -1,23 +1,18 @@ # Concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.concrete-group-actions - (funext : function-extensionality) - where +module group-theory.concrete-group-actions where ```
Imports ```agda -open import foundation.function-types funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.sets open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.concrete-groups funext +open import group-theory.concrete-groups ```
diff --git a/src/group-theory/concrete-groups.lagda.md b/src/group-theory/concrete-groups.lagda.md index 7075446bfc..17b5b67ad6 100644 --- a/src/group-theory/concrete-groups.lagda.md +++ b/src/group-theory/concrete-groups.lagda.md @@ -1,36 +1,31 @@ # Concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.concrete-groups - (funext : function-extensionality) - where +module group-theory.concrete-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.1-types funext +open import foundation.0-connected-types +open import foundation.1-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.truncated-types funext +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.opposite-groups funext -open import group-theory.opposite-semigroups funext -open import group-theory.semigroups funext +open import group-theory.groups +open import group-theory.monoids +open import group-theory.opposite-groups +open import group-theory.opposite-semigroups +open import group-theory.semigroups -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types ``` diff --git a/src/group-theory/concrete-monoids.lagda.md b/src/group-theory/concrete-monoids.lagda.md index aae3ff369a..702c2b25d3 100644 --- a/src/group-theory/concrete-monoids.lagda.md +++ b/src/group-theory/concrete-monoids.lagda.md @@ -1,27 +1,22 @@ # Concrete monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.concrete-monoids - (funext : function-extensionality) - where +module group-theory.concrete-monoids where ```
Imports ```agda -open import category-theory.categories funext +open import category-theory.categories -open import foundation.0-connected-types funext -open import foundation.cartesian-product-types funext +open import foundation.0-connected-types +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.cores-monoids funext -open import group-theory.monoids funext -open import group-theory.torsors funext +open import group-theory.cores-monoids +open import group-theory.monoids +open import group-theory.torsors ```
diff --git a/src/group-theory/congruence-relations-abelian-groups.lagda.md b/src/group-theory/congruence-relations-abelian-groups.lagda.md index ac7ad2bc61..f9f130587d 100644 --- a/src/group-theory/congruence-relations-abelian-groups.lagda.md +++ b/src/group-theory/congruence-relations-abelian-groups.lagda.md @@ -1,27 +1,22 @@ # Congruence relations on abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.congruence-relations-abelian-groups - (funext : function-extensionality) - where +module group-theory.congruence-relations-abelian-groups where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.binary-relations +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.congruence-relations-groups funext +open import group-theory.abelian-groups +open import group-theory.congruence-relations-groups ```
diff --git a/src/group-theory/congruence-relations-commutative-monoids.lagda.md b/src/group-theory/congruence-relations-commutative-monoids.lagda.md index d4c9bc9d88..2b79291e89 100644 --- a/src/group-theory/congruence-relations-commutative-monoids.lagda.md +++ b/src/group-theory/congruence-relations-commutative-monoids.lagda.md @@ -1,27 +1,22 @@ # Congruence relations on commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.congruence-relations-commutative-monoids - (funext : function-extensionality) - where +module group-theory.congruence-relations-commutative-monoids where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.binary-relations +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.congruence-relations-monoids funext +open import group-theory.commutative-monoids +open import group-theory.congruence-relations-monoids ```
diff --git a/src/group-theory/congruence-relations-groups.lagda.md b/src/group-theory/congruence-relations-groups.lagda.md index 60a2e2da69..ca3018bb5d 100644 --- a/src/group-theory/congruence-relations-groups.lagda.md +++ b/src/group-theory/congruence-relations-groups.lagda.md @@ -1,31 +1,26 @@ # Congruence relations on groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.congruence-relations-groups - (funext : function-extensionality) - where +module group-theory.congruence-relations-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.congruence-relations-semigroups funext -open import group-theory.conjugation funext -open import group-theory.groups funext +open import group-theory.congruence-relations-semigroups +open import group-theory.conjugation +open import group-theory.groups ```
diff --git a/src/group-theory/congruence-relations-monoids.lagda.md b/src/group-theory/congruence-relations-monoids.lagda.md index 8639cbe0fa..ce5778b509 100644 --- a/src/group-theory/congruence-relations-monoids.lagda.md +++ b/src/group-theory/congruence-relations-monoids.lagda.md @@ -1,28 +1,23 @@ # Congruence relations on monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.congruence-relations-monoids - (funext : function-extensionality) - where +module group-theory.congruence-relations-monoids where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.congruence-relations-semigroups funext -open import group-theory.monoids funext +open import group-theory.congruence-relations-semigroups +open import group-theory.monoids ```
diff --git a/src/group-theory/congruence-relations-semigroups.lagda.md b/src/group-theory/congruence-relations-semigroups.lagda.md index 24831cd8e9..5ebc48e734 100644 --- a/src/group-theory/congruence-relations-semigroups.lagda.md +++ b/src/group-theory/congruence-relations-semigroups.lagda.md @@ -1,29 +1,24 @@ # Congruence relations on semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.congruence-relations-semigroups - (funext : function-extensionality) - where +module group-theory.congruence-relations-semigroups where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext +open import foundation.equivalence-relations +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups ```
diff --git a/src/group-theory/conjugation-concrete-groups.lagda.md b/src/group-theory/conjugation-concrete-groups.lagda.md index 55ab7f63f0..4b3aa4c395 100644 --- a/src/group-theory/conjugation-concrete-groups.lagda.md +++ b/src/group-theory/conjugation-concrete-groups.lagda.md @@ -1,26 +1,21 @@ # Conjugation on concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.conjugation-concrete-groups - (funext : function-extensionality) - where +module group-theory.conjugation-concrete-groups where ```
Imports ```agda -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.conjugation funext -open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.conjugation +open import group-theory.homomorphisms-concrete-groups -open import higher-group-theory.conjugation funext +open import higher-group-theory.conjugation ```
diff --git a/src/group-theory/conjugation.lagda.md b/src/group-theory/conjugation.lagda.md index 927dfa5700..55baaed82e 100644 --- a/src/group-theory/conjugation.lagda.md +++ b/src/group-theory/conjugation.lagda.md @@ -1,12 +1,7 @@ # Conjugation in groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.conjugation - (funext : function-extensionality) - where +module group-theory.conjugation where ```
Imports @@ -16,24 +11,24 @@ open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.subtypes funext -open import foundation.transposition-identifications-along-retractions funext -open import foundation.transposition-identifications-along-sections funext +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections +open import foundation.subtypes +open import foundation.transposition-identifications-along-retractions +open import foundation.transposition-identifications-along-sections open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.integer-powers-of-elements-groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.subsets-groups funext +open import group-theory.group-actions +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.integer-powers-of-elements-groups +open import group-theory.isomorphisms-groups +open import group-theory.subsets-groups ```
diff --git a/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md b/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md index ef3a41ba66..a9aa640c3c 100644 --- a/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md +++ b/src/group-theory/contravariant-pushforward-concrete-group-actions.lagda.md @@ -1,12 +1,7 @@ # Contravariant pushforwards of concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.contravariant-pushforward-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.contravariant-pushforward-concrete-group-actions where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.homomorphisms-concrete-groups ```
diff --git a/src/group-theory/cores-monoids.lagda.md b/src/group-theory/cores-monoids.lagda.md index 33bb201f66..50328b33a1 100644 --- a/src/group-theory/cores-monoids.lagda.md +++ b/src/group-theory/cores-monoids.lagda.md @@ -1,34 +1,29 @@ # Cores of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.cores-monoids - (funext : function-extensionality) - where +module group-theory.cores-monoids where ```
Imports ```agda -open import category-theory.functors-large-precategories funext +open import category-theory.functors-large-precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-monoids funext -open import group-theory.invertible-elements-monoids funext -open import group-theory.monoids funext -open import group-theory.precategory-of-groups funext -open import group-theory.precategory-of-monoids funext -open import group-theory.semigroups funext -open import group-theory.submonoids funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-monoids +open import group-theory.invertible-elements-monoids +open import group-theory.monoids +open import group-theory.precategory-of-groups +open import group-theory.precategory-of-monoids +open import group-theory.semigroups +open import group-theory.submonoids ```
diff --git a/src/group-theory/cyclic-groups.lagda.md b/src/group-theory/cyclic-groups.lagda.md index 47ada889bb..08c862b1fc 100644 --- a/src/group-theory/cyclic-groups.lagda.md +++ b/src/group-theory/cyclic-groups.lagda.md @@ -1,30 +1,25 @@ # Cyclic groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.cyclic-groups - (funext : function-extensionality) - where +module group-theory.cyclic-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.inhabited-subtypes funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.inhabited-subtypes +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.generating-elements-groups funext -open import group-theory.groups funext +open import group-theory.abelian-groups +open import group-theory.generating-elements-groups +open import group-theory.groups ```
diff --git a/src/group-theory/decidable-subgroups.lagda.md b/src/group-theory/decidable-subgroups.lagda.md index dd5c5ef933..e523eb23cb 100644 --- a/src/group-theory/decidable-subgroups.lagda.md +++ b/src/group-theory/decidable-subgroups.lagda.md @@ -1,36 +1,31 @@ # Decidable subgroups of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.decidable-subgroups - (funext : function-extensionality) - where +module group-theory.decidable-subgroups where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.decidable-subtypes funext +open import foundation.binary-relations +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.semigroups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.semigroups +open import group-theory.subgroups +open import group-theory.subsets-groups ```
diff --git a/src/group-theory/dependent-products-abelian-groups.lagda.md b/src/group-theory/dependent-products-abelian-groups.lagda.md index ce63053a52..94aa816e80 100644 --- a/src/group-theory/dependent-products-abelian-groups.lagda.md +++ b/src/group-theory/dependent-products-abelian-groups.lagda.md @@ -1,29 +1,23 @@ # Dependent products of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.dependent-products-abelian-groups - (funext : function-extensionality) - where +module group-theory.dependent-products-abelian-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.dependent-products-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.dependent-products-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/dependent-products-commutative-monoids.lagda.md b/src/group-theory/dependent-products-commutative-monoids.lagda.md index c0f1835639..6d9fdd11e9 100644 --- a/src/group-theory/dependent-products-commutative-monoids.lagda.md +++ b/src/group-theory/dependent-products-commutative-monoids.lagda.md @@ -1,27 +1,21 @@ # Dependent products of commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.dependent-products-commutative-monoids - (funext : function-extensionality) - where +module group-theory.dependent-products-commutative-monoids where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.dependent-products-monoids funext -open import group-theory.monoids funext +open import group-theory.commutative-monoids +open import group-theory.dependent-products-monoids +open import group-theory.monoids ```
diff --git a/src/group-theory/dependent-products-groups.lagda.md b/src/group-theory/dependent-products-groups.lagda.md index 90daf2af78..6c0d59730a 100644 --- a/src/group-theory/dependent-products-groups.lagda.md +++ b/src/group-theory/dependent-products-groups.lagda.md @@ -1,28 +1,22 @@ # Dependent products of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.dependent-products-groups - (funext : function-extensionality) - where +module group-theory.dependent-products-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.dependent-products-semigroups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.dependent-products-semigroups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/dependent-products-monoids.lagda.md b/src/group-theory/dependent-products-monoids.lagda.md index 504bdf5238..f2602a6622 100644 --- a/src/group-theory/dependent-products-monoids.lagda.md +++ b/src/group-theory/dependent-products-monoids.lagda.md @@ -1,27 +1,21 @@ # Dependent products of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.dependent-products-monoids - (funext : function-extensionality) - where +module group-theory.dependent-products-monoids where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.dependent-products-semigroups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.dependent-products-semigroups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/dependent-products-semigroups.lagda.md b/src/group-theory/dependent-products-semigroups.lagda.md index 987257ff92..5194e020a4 100644 --- a/src/group-theory/dependent-products-semigroups.lagda.md +++ b/src/group-theory/dependent-products-semigroups.lagda.md @@ -1,25 +1,19 @@ # Dependent products of semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.dependent-products-semigroups - (funext : function-extensionality) - where +module group-theory.dependent-products-semigroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups ```
diff --git a/src/group-theory/dihedral-group-construction.lagda.md b/src/group-theory/dihedral-group-construction.lagda.md index 8530ab3444..6aba36c7df 100644 --- a/src/group-theory/dihedral-group-construction.lagda.md +++ b/src/group-theory/dihedral-group-construction.lagda.md @@ -1,29 +1,24 @@ # The dihedral group construction ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.dihedral-group-construction - (funext : function-extensionality) - where +module group-theory.dihedral-group-construction where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.equality-coproduct-types +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/dihedral-groups.lagda.md b/src/group-theory/dihedral-groups.lagda.md index 353ecf5064..83fd4ee34a 100644 --- a/src/group-theory/dihedral-groups.lagda.md +++ b/src/group-theory/dihedral-groups.lagda.md @@ -1,24 +1,19 @@ # The dihedral groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.dihedral-groups - (funext : function-extensionality) - where +module group-theory.dihedral-groups where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.standard-cyclic-groups funext +open import elementary-number-theory.standard-cyclic-groups open import foundation.universe-levels -open import group-theory.dihedral-group-construction funext -open import group-theory.groups funext +open import group-theory.dihedral-group-construction +open import group-theory.groups ```
diff --git a/src/group-theory/e8-lattice.lagda.md b/src/group-theory/e8-lattice.lagda.md index f54f1a79fb..85b7ccc933 100644 --- a/src/group-theory/e8-lattice.lagda.md +++ b/src/group-theory/e8-lattice.lagda.md @@ -1,25 +1,20 @@ # The `E₈`-lattice ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.e8-lattice - (funext : function-extensionality) - where +module group-theory.e8-lattice where ```
Imports ```agda -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers -open import foundation.equality-coproduct-types funext -open import foundation.sets funext +open import foundation.equality-coproduct-types +open import foundation.sets open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/group-theory/elements-of-finite-order-groups.lagda.md b/src/group-theory/elements-of-finite-order-groups.lagda.md index 52ce753ef8..de05cf476b 100644 --- a/src/group-theory/elements-of-finite-order-groups.lagda.md +++ b/src/group-theory/elements-of-finite-order-groups.lagda.md @@ -1,28 +1,23 @@ # Elements of finite order ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.elements-of-finite-order-groups - (funext : function-extensionality) - where +module group-theory.elements-of-finite-order-groups where ```
Imports ```agda -open import elementary-number-theory.group-of-integers funext -open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.group-of-integers +open import elementary-number-theory.nonzero-integers -open import foundation.existential-quantification funext -open import foundation.propositions funext +open import foundation.existential-quantification +open import foundation.propositions open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.orders-of-elements-groups funext -open import group-theory.subgroups funext -open import group-theory.subgroups funext-generated-by-elements-groups +open import group-theory.groups +open import group-theory.orders-of-elements-groups +open import group-theory.subgroups +open import group-theory.subgroups-generated-by-elements-groups ```
diff --git a/src/group-theory/embeddings-abelian-groups.lagda.md b/src/group-theory/embeddings-abelian-groups.lagda.md index 2e027bd62e..9061f2dbe1 100644 --- a/src/group-theory/embeddings-abelian-groups.lagda.md +++ b/src/group-theory/embeddings-abelian-groups.lagda.md @@ -1,24 +1,19 @@ # Embeddings of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.embeddings-abelian-groups - (funext : function-extensionality) - where +module group-theory.embeddings-abelian-groups where ```
Imports ```agda -open import foundation.embeddings funext +open import foundation.embeddings open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.embeddings-groups funext -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.subgroups-abelian-groups funext +open import group-theory.abelian-groups +open import group-theory.embeddings-groups +open import group-theory.homomorphisms-abelian-groups +open import group-theory.subgroups-abelian-groups ```
diff --git a/src/group-theory/embeddings-groups.lagda.md b/src/group-theory/embeddings-groups.lagda.md index c034efab85..9d7b7c5dab 100644 --- a/src/group-theory/embeddings-groups.lagda.md +++ b/src/group-theory/embeddings-groups.lagda.md @@ -1,24 +1,19 @@ # Embeddings of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.embeddings-groups - (funext : function-extensionality) - where +module group-theory.embeddings-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext +open import foundation.embeddings open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.subgroups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.subgroups ```
diff --git a/src/group-theory/endomorphism-rings-abelian-groups.lagda.md b/src/group-theory/endomorphism-rings-abelian-groups.lagda.md index f1e2034d14..d3dfb679a9 100644 --- a/src/group-theory/endomorphism-rings-abelian-groups.lagda.md +++ b/src/group-theory/endomorphism-rings-abelian-groups.lagda.md @@ -1,12 +1,7 @@ # The endomorphism rings of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.endomorphism-rings-abelian-groups - (funext : function-extensionality) - where +module group-theory.endomorphism-rings-abelian-groups where ```
Imports @@ -15,11 +10,11 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.addition-homomorphisms-abelian-groups funext -open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.abelian-groups +open import group-theory.addition-homomorphisms-abelian-groups +open import group-theory.homomorphisms-abelian-groups -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/group-theory/epimorphisms-groups.lagda.md b/src/group-theory/epimorphisms-groups.lagda.md index c590731345..be41b90450 100644 --- a/src/group-theory/epimorphisms-groups.lagda.md +++ b/src/group-theory/epimorphisms-groups.lagda.md @@ -1,26 +1,21 @@ # Epimorphisms in groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.epimorphisms-groups - (funext : function-extensionality) - where +module group-theory.epimorphisms-groups where ```
Imports ```agda -open import category-theory.epimorphisms-in-large-precategories funext +open import category-theory.epimorphisms-in-large-precategories -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.precategory-of-groups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.isomorphisms-groups +open import group-theory.precategory-of-groups ```
diff --git a/src/group-theory/equivalences-concrete-group-actions.lagda.md b/src/group-theory/equivalences-concrete-group-actions.lagda.md index ed39de48f7..27c37431a5 100644 --- a/src/group-theory/equivalences-concrete-group-actions.lagda.md +++ b/src/group-theory/equivalences-concrete-group-actions.lagda.md @@ -1,32 +1,27 @@ # Equivalences of concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.equivalences-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.equivalences-concrete-group-actions where ```
Imports ```agda -open import foundation.1-types funext +open import foundation.1-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.embeddings +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.functoriality-dependent-function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext -open import group-theory.homomorphisms-concrete-group-actions funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups +open import group-theory.homomorphisms-concrete-group-actions ```
diff --git a/src/group-theory/equivalences-concrete-groups.lagda.md b/src/group-theory/equivalences-concrete-groups.lagda.md index 41b0a46531..52676af8d8 100644 --- a/src/group-theory/equivalences-concrete-groups.lagda.md +++ b/src/group-theory/equivalences-concrete-groups.lagda.md @@ -1,30 +1,25 @@ # Equivalences of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.equivalences-concrete-groups - (funext : function-extensionality) - where +module group-theory.equivalences-concrete-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.concrete-groups funext +open import group-theory.concrete-groups -open import higher-group-theory.equivalences-higher-groups funext -open import higher-group-theory.higher-groups funext +open import higher-group-theory.equivalences-higher-groups +open import higher-group-theory.higher-groups ```
diff --git a/src/group-theory/equivalences-group-actions.lagda.md b/src/group-theory/equivalences-group-actions.lagda.md index 03d4a21532..cabae428b7 100644 --- a/src/group-theory/equivalences-group-actions.lagda.md +++ b/src/group-theory/equivalences-group-actions.lagda.md @@ -1,39 +1,34 @@ # Equivalences of group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.equivalences-group-actions - (funext : function-extensionality) - where +module group-theory.equivalences-group-actions where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sets open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext -open import group-theory.homomorphisms-group-actions funext -open import group-theory.homomorphisms-groups funext -open import group-theory.symmetric-groups funext +open import group-theory.group-actions +open import group-theory.groups +open import group-theory.homomorphisms-group-actions +open import group-theory.homomorphisms-groups +open import group-theory.symmetric-groups ```
diff --git a/src/group-theory/equivalences-semigroups.lagda.md b/src/group-theory/equivalences-semigroups.lagda.md index 0928e3a427..b0ec4a907d 100644 --- a/src/group-theory/equivalences-semigroups.lagda.md +++ b/src/group-theory/equivalences-semigroups.lagda.md @@ -1,34 +1,28 @@ # Equivalences between semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.equivalences-semigroups - (funext : function-extensionality) - where +module group-theory.equivalences-semigroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.subtypes +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups funext -open import group-theory.semigroups funext +open import group-theory.homomorphisms-semigroups +open import group-theory.semigroups ```
diff --git a/src/group-theory/exponents-abelian-groups.lagda.md b/src/group-theory/exponents-abelian-groups.lagda.md index 920d194193..1f2bfdd78f 100644 --- a/src/group-theory/exponents-abelian-groups.lagda.md +++ b/src/group-theory/exponents-abelian-groups.lagda.md @@ -1,24 +1,19 @@ # Exponents of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.exponents-abelian-groups - (funext : function-extensionality) - where +module group-theory.exponents-abelian-groups where ```
Imports ```agda -open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.group-of-integers open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.exponents-groups funext -open import group-theory.subgroups-abelian-groups funext +open import group-theory.abelian-groups +open import group-theory.exponents-groups +open import group-theory.subgroups-abelian-groups ```
diff --git a/src/group-theory/exponents-groups.lagda.md b/src/group-theory/exponents-groups.lagda.md index e266800ed5..4df222fea0 100644 --- a/src/group-theory/exponents-groups.lagda.md +++ b/src/group-theory/exponents-groups.lagda.md @@ -1,26 +1,21 @@ # Exponents of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.exponents-groups - (funext : function-extensionality) - where +module group-theory.exponents-groups where ```
Imports ```agda -open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.group-of-integers open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator funext -open import group-theory.groups funext -open import group-theory.intersections-subgroups-groups funext -open import group-theory.kernels-homomorphisms-groups funext -open import group-theory.subgroups funext +open import group-theory.free-groups-with-one-generator +open import group-theory.groups +open import group-theory.intersections-subgroups-groups +open import group-theory.kernels-homomorphisms-groups +open import group-theory.subgroups ```
diff --git a/src/group-theory/free-concrete-group-actions.lagda.md b/src/group-theory/free-concrete-group-actions.lagda.md index 9f76b2fb9b..7eb0462d9f 100644 --- a/src/group-theory/free-concrete-group-actions.lagda.md +++ b/src/group-theory/free-concrete-group-actions.lagda.md @@ -1,27 +1,22 @@ # Free concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.free-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.free-concrete-group-actions where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups -open import higher-group-theory.free-higher-group-actions funext +open import higher-group-theory.free-higher-group-actions ```
diff --git a/src/group-theory/free-groups-with-one-generator.lagda.md b/src/group-theory/free-groups-with-one-generator.lagda.md index 0d8a3204ff..e66fdcf4d7 100644 --- a/src/group-theory/free-groups-with-one-generator.lagda.md +++ b/src/group-theory/free-groups-with-one-generator.lagda.md @@ -1,36 +1,31 @@ # Free groups with one generator ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.free-groups-with-one-generator - (funext : function-extensionality) - where +module group-theory.free-groups-with-one-generator where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.group-of-integers open import elementary-number-theory.integers open import foundation.action-on-identifications-functions -open import foundation.contractible-maps funext +open import foundation.contractible-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.sets +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.integer-powers-of-elements-groups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.integer-powers-of-elements-groups -open import structured-types.initial-pointed-type-equipped-with-automorphism funext +open import structured-types.initial-pointed-type-equipped-with-automorphism ```
diff --git a/src/group-theory/full-subgroups.lagda.md b/src/group-theory/full-subgroups.lagda.md index 3649a9fe91..5200efc0f3 100644 --- a/src/group-theory/full-subgroups.lagda.md +++ b/src/group-theory/full-subgroups.lagda.md @@ -1,28 +1,23 @@ # The full subgroup of a group ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.full-subgroups - (funext : function-extensionality) - where +module group-theory.full-subgroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.full-subtypes funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.full-subtypes +open import foundation.propositions open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.isomorphisms-groups +open import group-theory.subgroups +open import group-theory.subsets-groups ```
diff --git a/src/group-theory/full-subsemigroups.lagda.md b/src/group-theory/full-subsemigroups.lagda.md index 5f028b21b6..507941cd28 100644 --- a/src/group-theory/full-subsemigroups.lagda.md +++ b/src/group-theory/full-subsemigroups.lagda.md @@ -1,29 +1,24 @@ # The full subsemigroup of a semigroup ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.full-subsemigroups - (funext : function-extensionality) - where +module group-theory.full-subsemigroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.full-subtypes funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.full-subtypes +open import foundation.propositions open import foundation.universe-levels -open import group-theory.equivalences-semigroups funext -open import group-theory.homomorphisms-semigroups funext -open import group-theory.isomorphisms-semigroups funext -open import group-theory.semigroups funext -open import group-theory.subsemigroups funext -open import group-theory.subsets-semigroups funext +open import group-theory.equivalences-semigroups +open import group-theory.homomorphisms-semigroups +open import group-theory.isomorphisms-semigroups +open import group-theory.semigroups +open import group-theory.subsemigroups +open import group-theory.subsets-semigroups ```
diff --git a/src/group-theory/function-abelian-groups.lagda.md b/src/group-theory/function-abelian-groups.lagda.md index 517e058567..6836e3eed4 100644 --- a/src/group-theory/function-abelian-groups.lagda.md +++ b/src/group-theory/function-abelian-groups.lagda.md @@ -1,26 +1,21 @@ # Function groups of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.function-abelian-groups - (funext : function-extensionality) - where +module group-theory.function-abelian-groups where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.dependent-products-abelian-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.dependent-products-abelian-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/function-commutative-monoids.lagda.md b/src/group-theory/function-commutative-monoids.lagda.md index 09ffccec4c..57b44087dc 100644 --- a/src/group-theory/function-commutative-monoids.lagda.md +++ b/src/group-theory/function-commutative-monoids.lagda.md @@ -1,24 +1,19 @@ # Function commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.function-commutative-monoids - (funext : function-extensionality) - where +module group-theory.function-commutative-monoids where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.dependent-products-commutative-monoids funext -open import group-theory.monoids funext +open import group-theory.commutative-monoids +open import group-theory.dependent-products-commutative-monoids +open import group-theory.monoids ```
diff --git a/src/group-theory/function-groups.lagda.md b/src/group-theory/function-groups.lagda.md index 23dbecd6aa..b9d8cff7aa 100644 --- a/src/group-theory/function-groups.lagda.md +++ b/src/group-theory/function-groups.lagda.md @@ -1,26 +1,21 @@ # Function groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.function-groups - (funext : function-extensionality) - where +module group-theory.function-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.dependent-products-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.dependent-products-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/function-monoids.lagda.md b/src/group-theory/function-monoids.lagda.md index 59a4b5bc6a..bef75c807a 100644 --- a/src/group-theory/function-monoids.lagda.md +++ b/src/group-theory/function-monoids.lagda.md @@ -1,24 +1,19 @@ # Function monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.function-monoids - (funext : function-extensionality) - where +module group-theory.function-monoids where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.dependent-products-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.dependent-products-monoids +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/group-theory/function-semigroups.lagda.md b/src/group-theory/function-semigroups.lagda.md index e0a4e6c046..06605fc58c 100644 --- a/src/group-theory/function-semigroups.lagda.md +++ b/src/group-theory/function-semigroups.lagda.md @@ -1,23 +1,18 @@ # Function semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.function-semigroups - (funext : function-extensionality) - where +module group-theory.function-semigroups where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.dependent-products-semigroups funext -open import group-theory.semigroups funext +open import group-theory.dependent-products-semigroups +open import group-theory.semigroups ```
diff --git a/src/group-theory/functoriality-quotient-groups.lagda.md b/src/group-theory/functoriality-quotient-groups.lagda.md index e843537518..6b48fc225f 100644 --- a/src/group-theory/functoriality-quotient-groups.lagda.md +++ b/src/group-theory/functoriality-quotient-groups.lagda.md @@ -3,32 +3,27 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - group-theory.functoriality-quotient-groups - (funext : function-extensionality) - where +module group-theory.functoriality-quotient-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.commuting-squares-of-group-homomorphisms funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-groups funext-equipped-with-normal-subgroups -open import group-theory.normal-subgroups funext -open import group-theory.nullifying-group-homomorphisms funext -open import group-theory.quotient-groups funext +open import group-theory.commuting-squares-of-group-homomorphisms +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups +open import group-theory.normal-subgroups +open import group-theory.nullifying-group-homomorphisms +open import group-theory.quotient-groups ```
diff --git a/src/group-theory/furstenberg-groups.lagda.md b/src/group-theory/furstenberg-groups.lagda.md index 695a53a430..a9e760780e 100644 --- a/src/group-theory/furstenberg-groups.lagda.md +++ b/src/group-theory/furstenberg-groups.lagda.md @@ -1,22 +1,17 @@ # Furstenberg groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.furstenberg-groups - (funext : function-extensionality) - where +module group-theory.furstenberg-groups where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/group-theory/generating-elements-groups.lagda.md b/src/group-theory/generating-elements-groups.lagda.md index db998672e7..f0b26019b2 100644 --- a/src/group-theory/generating-elements-groups.lagda.md +++ b/src/group-theory/generating-elements-groups.lagda.md @@ -1,59 +1,54 @@ # Generating elements of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.generating-elements-groups - (funext : function-extensionality) - where +module group-theory.generating-elements-groups where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.injective-maps funext -open import foundation.propositional-maps funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.identity-types +open import foundation.images +open import foundation.injective-maps +open import foundation.propositional-maps +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.sets +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.unit-type open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.addition-homomorphisms-abelian-groups funext -open import group-theory.commuting-elements-groups funext -open import group-theory.conjugation funext -open import group-theory.endomorphism-rings-abelian-groups funext -open import group-theory.free-groups-with-one-generator funext -open import group-theory.full-subgroups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.integer-multiples-of-elements-abelian-groups funext -open import group-theory.integer-powers-of-elements-groups funext -open import group-theory.isomorphisms-abelian-groups funext -open import group-theory.normal-subgroups funext -open import group-theory.quotient-groups funext -open import group-theory.subgroups-generated-by-elements-groups funext -open import group-theory.subsets-groups funext -open import group-theory.trivial-group-homomorphisms funext - -open import ring-theory.integer-multiples-of-elements-rings funext -open import ring-theory.rings funext -open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups funext +open import group-theory.abelian-groups +open import group-theory.addition-homomorphisms-abelian-groups +open import group-theory.commuting-elements-groups +open import group-theory.conjugation +open import group-theory.endomorphism-rings-abelian-groups +open import group-theory.free-groups-with-one-generator +open import group-theory.full-subgroups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.integer-multiples-of-elements-abelian-groups +open import group-theory.integer-powers-of-elements-groups +open import group-theory.isomorphisms-abelian-groups +open import group-theory.normal-subgroups +open import group-theory.quotient-groups +open import group-theory.subgroups-generated-by-elements-groups +open import group-theory.subsets-groups +open import group-theory.trivial-group-homomorphisms + +open import ring-theory.integer-multiples-of-elements-rings +open import ring-theory.rings +open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups ```
diff --git a/src/group-theory/generating-sets-groups.lagda.md b/src/group-theory/generating-sets-groups.lagda.md index dc386022fb..513c92471a 100644 --- a/src/group-theory/generating-sets-groups.lagda.md +++ b/src/group-theory/generating-sets-groups.lagda.md @@ -1,12 +1,7 @@ # Generating sets of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.generating-sets-groups - (funext : function-extensionality) - where +module group-theory.generating-sets-groups where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.universe-levels -open import group-theory.full-subgroups funext -open import group-theory.groups funext -open import group-theory.subgroups-generated-by-subsets-groups funext -open import group-theory.subsets-groups funext +open import group-theory.full-subgroups +open import group-theory.groups +open import group-theory.subgroups-generated-by-subsets-groups +open import group-theory.subsets-groups ```
diff --git a/src/group-theory/group-actions.lagda.md b/src/group-theory/group-actions.lagda.md index 27cbac2328..ae7b61578f 100644 --- a/src/group-theory/group-actions.lagda.md +++ b/src/group-theory/group-actions.lagda.md @@ -1,12 +1,7 @@ # Group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.group-actions - (funext : function-extensionality) - where +module group-theory.group-actions where ```
Imports @@ -14,17 +9,18 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.symmetric-groups funext -open import group-theory.trivial-group-homomorphisms funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.symmetric-groups +open import group-theory.trivial-group-homomorphisms ```
diff --git a/src/group-theory/groups.lagda.md b/src/group-theory/groups.lagda.md index 3c936169c1..ae04f5eb0d 100644 --- a/src/group-theory/groups.lagda.md +++ b/src/group-theory/groups.lagda.md @@ -1,12 +1,7 @@ # Abstract groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.groups - (funext : function-extensionality) - where +module group-theory.groups where ```
Imports @@ -14,35 +9,34 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.involutions funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.involutions +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.invertible-elements-monoids funext -open import group-theory.monoids funext -open import group-theory.products-of-elements-monoids funext -open import group-theory.semigroups funext +open import group-theory.invertible-elements-monoids +open import group-theory.monoids +open import group-theory.products-of-elements-monoids +open import group-theory.semigroups -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import structured-types.h-spaces funext +open import structured-types.h-spaces open import structured-types.pointed-types -open import structured-types.pointed-types-equipped-with-automorphisms funext +open import structured-types.pointed-types-equipped-with-automorphisms ```
diff --git a/src/group-theory/homomorphisms-abelian-groups.lagda.md b/src/group-theory/homomorphisms-abelian-groups.lagda.md index 1930bf59c7..172b824ed0 100644 --- a/src/group-theory/homomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/homomorphisms-abelian-groups.lagda.md @@ -1,32 +1,27 @@ # Homomorphisms of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-abelian-groups - (funext : function-extensionality) - where +module group-theory.homomorphisms-abelian-groups where ```
Imports ```agda -open import category-theory.large-categories funext +open import category-theory.large-categories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.category-of-abelian-groups funext -open import group-theory.homomorphisms-commutative-monoids funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-semigroups funext +open import group-theory.abelian-groups +open import group-theory.category-of-abelian-groups +open import group-theory.homomorphisms-commutative-monoids +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-semigroups ```
diff --git a/src/group-theory/homomorphisms-commutative-monoids.lagda.md b/src/group-theory/homomorphisms-commutative-monoids.lagda.md index 9bd3081a00..b5783ad749 100644 --- a/src/group-theory/homomorphisms-commutative-monoids.lagda.md +++ b/src/group-theory/homomorphisms-commutative-monoids.lagda.md @@ -1,26 +1,21 @@ # Homomorphisms of commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-commutative-monoids - (funext : function-extensionality) - where +module group-theory.homomorphisms-commutative-monoids where ```
Imports ```agda -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.homomorphisms-monoids funext -open import group-theory.homomorphisms-semigroups funext +open import group-theory.commutative-monoids +open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-semigroups ```
diff --git a/src/group-theory/homomorphisms-concrete-group-actions.lagda.md b/src/group-theory/homomorphisms-concrete-group-actions.lagda.md index 4244f46732..62057b8e87 100644 --- a/src/group-theory/homomorphisms-concrete-group-actions.lagda.md +++ b/src/group-theory/homomorphisms-concrete-group-actions.lagda.md @@ -1,32 +1,26 @@ # Morphisms of concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.homomorphisms-concrete-group-actions where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.0-connected-types +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups ```
diff --git a/src/group-theory/homomorphisms-concrete-groups.lagda.md b/src/group-theory/homomorphisms-concrete-groups.lagda.md index f187ff3e1a..d61de489f6 100644 --- a/src/group-theory/homomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/homomorphisms-concrete-groups.lagda.md @@ -1,29 +1,24 @@ # Homomorphisms of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-concrete-groups - (funext : function-extensionality) - where +module group-theory.homomorphisms-concrete-groups where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.sets open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.homomorphisms-groups funext +open import group-theory.concrete-groups +open import group-theory.homomorphisms-groups -open import higher-group-theory.homomorphisms-higher-groups funext +open import higher-group-theory.homomorphisms-higher-groups ```
diff --git a/src/group-theory/homomorphisms-generated-subgroups.lagda.md b/src/group-theory/homomorphisms-generated-subgroups.lagda.md index f7458d93e7..4f2f8359a6 100644 --- a/src/group-theory/homomorphisms-generated-subgroups.lagda.md +++ b/src/group-theory/homomorphisms-generated-subgroups.lagda.md @@ -1,49 +1,44 @@ # Homomorphisms of generated subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-generated-subgroups - (funext : function-extensionality) - where +module group-theory.homomorphisms-generated-subgroups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.embeddings funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.truncated-types funext +open import foundation.dependent-products-truncated-types +open import foundation.embeddings +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.epimorphisms-groups funext -open import group-theory.full-subgroups funext -open import group-theory.generating-sets-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.subgroups funext -open import group-theory.subgroups funext-generated-by-subsets-groups -open import group-theory.subsets-groups funext +open import group-theory.epimorphisms-groups +open import group-theory.full-subgroups +open import group-theory.generating-sets-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.subgroups +open import group-theory.subgroups-generated-by-subsets-groups +open import group-theory.subsets-groups open import lists.lists -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/group-theory/homomorphisms-group-actions.lagda.md b/src/group-theory/homomorphisms-group-actions.lagda.md index 113795f819..7c488f7072 100644 --- a/src/group-theory/homomorphisms-group-actions.lagda.md +++ b/src/group-theory/homomorphisms-group-actions.lagda.md @@ -1,35 +1,30 @@ # Homomorphisms of group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-group-actions - (funext : function-extensionality) - where +module group-theory.homomorphisms-group-actions where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle open import foundation.telescopes -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext +open import group-theory.group-actions +open import group-theory.groups ```
diff --git a/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md b/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md index 70c0274522..824132ed84 100644 --- a/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md +++ b/src/group-theory/homomorphisms-groups-equipped-with-normal-subgroups.lagda.md @@ -1,28 +1,23 @@ # Homomorphisms of groups equipped with normal subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-groups-equipped-with-normal-subgroups - (funext : function-extensionality) - where +module group-theory.homomorphisms-groups-equipped-with-normal-subgroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.normal-subgroups funext -open import group-theory.pullbacks-subgroups funext -open import group-theory.subgroups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.normal-subgroups +open import group-theory.pullbacks-subgroups +open import group-theory.subgroups ```
diff --git a/src/group-theory/homomorphisms-groups.lagda.md b/src/group-theory/homomorphisms-groups.lagda.md index 1d779ab78a..a4e286a07f 100644 --- a/src/group-theory/homomorphisms-groups.lagda.md +++ b/src/group-theory/homomorphisms-groups.lagda.md @@ -1,30 +1,25 @@ # Homomorphisms of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-groups - (funext : function-extensionality) - where +module group-theory.homomorphisms-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-monoids funext -open import group-theory.homomorphisms-semigroups funext +open import group-theory.groups +open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-semigroups ```
diff --git a/src/group-theory/homomorphisms-monoids.lagda.md b/src/group-theory/homomorphisms-monoids.lagda.md index dae6f01976..f8c37265bd 100644 --- a/src/group-theory/homomorphisms-monoids.lagda.md +++ b/src/group-theory/homomorphisms-monoids.lagda.md @@ -1,12 +1,7 @@ # Homomorphisms of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-monoids - (funext : function-extensionality) - where +module group-theory.homomorphisms-monoids where ```
Imports @@ -14,20 +9,20 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups funext -open import group-theory.invertible-elements-monoids funext -open import group-theory.monoids funext +open import group-theory.homomorphisms-semigroups +open import group-theory.invertible-elements-monoids +open import group-theory.monoids ```
diff --git a/src/group-theory/homomorphisms-semigroups.lagda.md b/src/group-theory/homomorphisms-semigroups.lagda.md index 562bfe04a6..b00a30a3fa 100644 --- a/src/group-theory/homomorphisms-semigroups.lagda.md +++ b/src/group-theory/homomorphisms-semigroups.lagda.md @@ -1,12 +1,7 @@ # Homomorphisms of semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homomorphisms-semigroups - (funext : function-extensionality) - where +module group-theory.homomorphisms-semigroups where ```
Imports @@ -14,19 +9,19 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups ```
diff --git a/src/group-theory/homotopy-automorphism-groups.lagda.md b/src/group-theory/homotopy-automorphism-groups.lagda.md index 2cb60e575b..0e344923e4 100644 --- a/src/group-theory/homotopy-automorphism-groups.lagda.md +++ b/src/group-theory/homotopy-automorphism-groups.lagda.md @@ -1,25 +1,20 @@ # Homotopy automorphism groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.homotopy-automorphism-groups - (funext : function-extensionality) - where +module group-theory.homotopy-automorphism-groups where ```
Imports ```agda open import foundation.truncation-levels -open import foundation.truncations funext +open import foundation.truncations open import foundation.universe-levels -open import group-theory.automorphism-groups funext -open import group-theory.concrete-groups funext +open import group-theory.automorphism-groups +open import group-theory.concrete-groups -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types ``` diff --git a/src/group-theory/images-of-group-homomorphisms.lagda.md b/src/group-theory/images-of-group-homomorphisms.lagda.md index d45d2db35d..90366ef507 100644 --- a/src/group-theory/images-of-group-homomorphisms.lagda.md +++ b/src/group-theory/images-of-group-homomorphisms.lagda.md @@ -1,36 +1,31 @@ # Images of group homomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.images-of-group-homomorphisms - (funext : function-extensionality) - where +module group-theory.images-of-group-homomorphisms where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.images funext-subtypes -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext -open import foundation.universal-property-image funext +open import foundation.identity-types +open import foundation.images +open import foundation.images-subtypes +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.subtypes +open import foundation.universal-property-image open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.pullbacks-subgroups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.pullbacks-subgroups +open import group-theory.subgroups +open import group-theory.subsets-groups -open import order-theory.galois-connections-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.galois-connections-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders ```
diff --git a/src/group-theory/images-of-semigroup-homomorphisms.lagda.md b/src/group-theory/images-of-semigroup-homomorphisms.lagda.md index 7ab544ee1b..eced916451 100644 --- a/src/group-theory/images-of-semigroup-homomorphisms.lagda.md +++ b/src/group-theory/images-of-semigroup-homomorphisms.lagda.md @@ -1,35 +1,30 @@ # Images of semigroup homomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.images-of-semigroup-homomorphisms - (funext : function-extensionality) - where +module group-theory.images-of-semigroup-homomorphisms where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.images funext-subtypes -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.universal-property-image funext +open import foundation.identity-types +open import foundation.images +open import foundation.images-subtypes +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.universal-property-image open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups funext -open import group-theory.pullbacks-subsemigroups funext -open import group-theory.semigroups funext -open import group-theory.subsemigroups funext -open import group-theory.subsets-semigroups funext +open import group-theory.homomorphisms-semigroups +open import group-theory.pullbacks-subsemigroups +open import group-theory.semigroups +open import group-theory.subsemigroups +open import group-theory.subsets-semigroups -open import order-theory.galois-connections-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.galois-connections-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders ```
diff --git a/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md b/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md index a22caab59c..e592961eb4 100644 --- a/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md +++ b/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md @@ -1,32 +1,27 @@ # Integer multiples of elements in abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.integer-multiples-of-elements-abelian-groups - (funext : function-extensionality) - where +module group-theory.integer-multiples-of-elements-abelian-groups where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.integer-powers-of-elements-groups funext -open import group-theory.multiples-of-elements-abelian-groups funext +open import group-theory.abelian-groups +open import group-theory.homomorphisms-abelian-groups +open import group-theory.integer-powers-of-elements-groups +open import group-theory.multiples-of-elements-abelian-groups ```
diff --git a/src/group-theory/integer-powers-of-elements-groups.lagda.md b/src/group-theory/integer-powers-of-elements-groups.lagda.md index 3c9af34156..47de6edf13 100644 --- a/src/group-theory/integer-powers-of-elements-groups.lagda.md +++ b/src/group-theory/integer-powers-of-elements-groups.lagda.md @@ -1,36 +1,31 @@ # Integer powers of elements of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.integer-powers-of-elements-groups - (funext : function-extensionality) - where +module group-theory.integer-powers-of-elements-groups where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.iterating-automorphisms funext -open import foundation.propositions funext +open import foundation.coproduct-types +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.iterating-automorphisms +open import foundation.propositions open import foundation.universe-levels -open import group-theory.commuting-elements-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.powers-of-elements-groups funext +open import group-theory.commuting-elements-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.powers-of-elements-groups -open import structured-types.initial-pointed-type-equipped-with-automorphism funext +open import structured-types.initial-pointed-type-equipped-with-automorphism ```
diff --git a/src/group-theory/intersections-subgroups-abelian-groups.lagda.md b/src/group-theory/intersections-subgroups-abelian-groups.lagda.md index bc42c927cb..fe6d807e06 100644 --- a/src/group-theory/intersections-subgroups-abelian-groups.lagda.md +++ b/src/group-theory/intersections-subgroups-abelian-groups.lagda.md @@ -1,23 +1,18 @@ # Intersections of subgroups of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.intersections-subgroups-abelian-groups - (funext : function-extensionality) - where +module group-theory.intersections-subgroups-abelian-groups where ```
Imports ```agda -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.intersections-subgroups-groups funext -open import group-theory.subgroups-abelian-groups funext +open import group-theory.abelian-groups +open import group-theory.intersections-subgroups-groups +open import group-theory.subgroups-abelian-groups ```
diff --git a/src/group-theory/intersections-subgroups-groups.lagda.md b/src/group-theory/intersections-subgroups-groups.lagda.md index 3bf0d27920..485c7fe03b 100644 --- a/src/group-theory/intersections-subgroups-groups.lagda.md +++ b/src/group-theory/intersections-subgroups-groups.lagda.md @@ -1,27 +1,22 @@ # Intersections of subgroups of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.intersections-subgroups-groups - (funext : function-extensionality) - where +module group-theory.intersections-subgroups-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.intersections-subtypes funext -open import foundation.subtypes funext +open import foundation.intersections-subtypes +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.groups +open import group-theory.subgroups +open import group-theory.subsets-groups -open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets ```
diff --git a/src/group-theory/inverse-semigroups.lagda.md b/src/group-theory/inverse-semigroups.lagda.md index c75d2b828a..983cf5a04e 100644 --- a/src/group-theory/inverse-semigroups.lagda.md +++ b/src/group-theory/inverse-semigroups.lagda.md @@ -1,25 +1,20 @@ # Inverse semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.inverse-semigroups - (funext : function-extensionality) - where +module group-theory.inverse-semigroups where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups ```
diff --git a/src/group-theory/invertible-elements-monoids.lagda.md b/src/group-theory/invertible-elements-monoids.lagda.md index 5706614a84..c50cf77558 100644 --- a/src/group-theory/invertible-elements-monoids.lagda.md +++ b/src/group-theory/invertible-elements-monoids.lagda.md @@ -1,32 +1,27 @@ # Invertible elements in monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.invertible-elements-monoids - (funext : function-extensionality) - where +module group-theory.invertible-elements-monoids where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.monoids funext +open import group-theory.monoids ```
diff --git a/src/group-theory/isomorphisms-abelian-groups.lagda.md b/src/group-theory/isomorphisms-abelian-groups.lagda.md index eed2b52f43..9d7b07d36e 100644 --- a/src/group-theory/isomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/isomorphisms-abelian-groups.lagda.md @@ -1,34 +1,29 @@ # Isomorphisms of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.isomorphisms-abelian-groups - (funext : function-extensionality) - where +module group-theory.isomorphisms-abelian-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.isomorphisms-groups funext +open import group-theory.abelian-groups +open import group-theory.homomorphisms-abelian-groups +open import group-theory.isomorphisms-groups ```
diff --git a/src/group-theory/isomorphisms-concrete-groups.lagda.md b/src/group-theory/isomorphisms-concrete-groups.lagda.md index 7e1143d51b..0815e62ecb 100644 --- a/src/group-theory/isomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/isomorphisms-concrete-groups.lagda.md @@ -1,23 +1,18 @@ # Isomorphisms of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.isomorphisms-concrete-groups - (funext : function-extensionality) - where +module group-theory.isomorphisms-concrete-groups where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.precategory-of-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.precategory-of-concrete-groups ```
diff --git a/src/group-theory/isomorphisms-group-actions.lagda.md b/src/group-theory/isomorphisms-group-actions.lagda.md index 82f4801b94..49635eee09 100644 --- a/src/group-theory/isomorphisms-group-actions.lagda.md +++ b/src/group-theory/isomorphisms-group-actions.lagda.md @@ -1,39 +1,33 @@ # Isomorphisms of group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.isomorphisms-group-actions - (funext : function-extensionality) - where +module group-theory.isomorphisms-group-actions where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.equivalences-group-actions funext -open import group-theory.group-actions funext -open import group-theory.groups funext -open import group-theory.homomorphisms-group-actions funext -open import group-theory.precategory-of-group-actions funext +open import group-theory.equivalences-group-actions +open import group-theory.group-actions +open import group-theory.groups +open import group-theory.homomorphisms-group-actions +open import group-theory.precategory-of-group-actions ```
diff --git a/src/group-theory/isomorphisms-groups.lagda.md b/src/group-theory/isomorphisms-groups.lagda.md index 531aecb4c5..0ab46ae767 100644 --- a/src/group-theory/isomorphisms-groups.lagda.md +++ b/src/group-theory/isomorphisms-groups.lagda.md @@ -1,37 +1,32 @@ # Isomorphisms of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.isomorphisms-groups - (funext : function-extensionality) - where +module group-theory.isomorphisms-groups where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.category-of-semigroups funext -open import group-theory.equivalences-semigroups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.isomorphisms-semigroups funext -open import group-theory.precategory-of-groups funext +open import group-theory.category-of-semigroups +open import group-theory.equivalences-semigroups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.isomorphisms-semigroups +open import group-theory.precategory-of-groups ```
diff --git a/src/group-theory/isomorphisms-monoids.lagda.md b/src/group-theory/isomorphisms-monoids.lagda.md index acfa2dac4c..5ed4766a19 100644 --- a/src/group-theory/isomorphisms-monoids.lagda.md +++ b/src/group-theory/isomorphisms-monoids.lagda.md @@ -1,31 +1,26 @@ # Isomorphisms of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.isomorphisms-monoids - (funext : function-extensionality) - where +module group-theory.isomorphisms-monoids where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.homomorphisms-monoids funext -open import group-theory.invertible-elements-monoids funext -open import group-theory.monoids funext -open import group-theory.precategory-of-monoids funext +open import group-theory.homomorphisms-monoids +open import group-theory.invertible-elements-monoids +open import group-theory.monoids +open import group-theory.precategory-of-monoids ```
diff --git a/src/group-theory/isomorphisms-semigroups.lagda.md b/src/group-theory/isomorphisms-semigroups.lagda.md index c537d21d8d..c6f29143b3 100644 --- a/src/group-theory/isomorphisms-semigroups.lagda.md +++ b/src/group-theory/isomorphisms-semigroups.lagda.md @@ -1,37 +1,33 @@ # Isomorphisms of semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.isomorphisms-semigroups - (funext : function-extensionality) - where +module group-theory.isomorphisms-semigroups where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.equivalences-semigroups funext -open import group-theory.homomorphisms-semigroups funext -open import group-theory.precategory-of-semigroups funext -open import group-theory.semigroups funext +open import group-theory.equivalences-semigroups +open import group-theory.homomorphisms-semigroups +open import group-theory.precategory-of-semigroups +open import group-theory.semigroups ```
diff --git a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md index c530b22e44..d189124e89 100644 --- a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md +++ b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md @@ -1,12 +1,7 @@ # Iterated cartesian products of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.iterated-cartesian-products-concrete-groups - (funext : function-extensionality) - where +module group-theory.iterated-cartesian-products-concrete-groups where ```
Imports @@ -14,36 +9,36 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types funext -open import foundation.1-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.0-connected-types +open import foundation.1-types +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.iterated-cartesian-product-types funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sets funext -open import foundation.truncated-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.iterated-cartesian-product-types +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.sets +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.cartesian-products-concrete-groups funext -open import group-theory.concrete-groups funext -open import group-theory.groups funext -open import group-theory.trivial-concrete-groups funext +open import group-theory.cartesian-products-concrete-groups +open import group-theory.concrete-groups +open import group-theory.groups +open import group-theory.trivial-concrete-groups -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md b/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md index 79cd40d735..9772e78e5d 100644 --- a/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-abelian-groups.lagda.md @@ -1,12 +1,7 @@ # Kernels of homomorphisms between abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.kernels-homomorphisms-abelian-groups - (funext : function-extensionality) - where +module group-theory.kernels-homomorphisms-abelian-groups where ```
Imports @@ -14,12 +9,12 @@ module ```agda open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.embeddings-abelian-groups funext -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.kernels-homomorphisms-groups funext -open import group-theory.subgroups-abelian-groups funext -open import group-theory.subsets-abelian-groups funext +open import group-theory.abelian-groups +open import group-theory.embeddings-abelian-groups +open import group-theory.homomorphisms-abelian-groups +open import group-theory.kernels-homomorphisms-groups +open import group-theory.subgroups-abelian-groups +open import group-theory.subsets-abelian-groups ```
diff --git a/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md b/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md index f5fb11db12..fa5ce10e8c 100644 --- a/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-concrete-groups.lagda.md @@ -1,31 +1,26 @@ # Kernels of homomorphisms of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.kernels-homomorphisms-concrete-groups - (funext : function-extensionality) - where +module group-theory.kernels-homomorphisms-concrete-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.1-types funext -open import foundation.connected-components funext +open import foundation.0-connected-types +open import foundation.1-types +open import foundation.connected-components open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.sets funext -open import foundation.truncated-maps funext +open import foundation.fibers-of-maps +open import foundation.sets +open import foundation.truncated-maps open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.homomorphisms-concrete-groups -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types ``` diff --git a/src/group-theory/kernels-homomorphisms-groups.lagda.md b/src/group-theory/kernels-homomorphisms-groups.lagda.md index 6419141f21..ba177596f8 100644 --- a/src/group-theory/kernels-homomorphisms-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-groups.lagda.md @@ -1,12 +1,7 @@ # Kernels of homomorphisms of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.kernels-homomorphisms-groups - (funext : function-extensionality) - where +module group-theory.kernels-homomorphisms-groups where ```
Imports @@ -15,17 +10,17 @@ module open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.embeddings-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.normal-subgroups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.embeddings-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.normal-subgroups +open import group-theory.subgroups +open import group-theory.subsets-groups ```
diff --git a/src/group-theory/large-semigroups.lagda.md b/src/group-theory/large-semigroups.lagda.md index 73a82f7e53..b4d82ec9cb 100644 --- a/src/group-theory/large-semigroups.lagda.md +++ b/src/group-theory/large-semigroups.lagda.md @@ -1,23 +1,18 @@ # Large semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.large-semigroups - (funext : function-extensionality) - where +module group-theory.large-semigroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups ```
diff --git a/src/group-theory/loop-groups-sets.lagda.md b/src/group-theory/loop-groups-sets.lagda.md index d9d5e08354..15fdf92516 100644 --- a/src/group-theory/loop-groups-sets.lagda.md +++ b/src/group-theory/loop-groups-sets.lagda.md @@ -1,12 +1,7 @@ # Concrete automorphism groups on sets ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.loop-groups-sets - (funext : function-extensionality) - where +module group-theory.loop-groups-sets where ```
Imports @@ -14,30 +9,29 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.identity-truncated-types funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.truncated-types funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.identity-truncated-types +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.truncated-types open import foundation.truncation-levels -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import group-theory.automorphism-groups funext -open import group-theory.concrete-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-semigroups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext -open import group-theory.symmetric-groups funext +open import group-theory.automorphism-groups +open import group-theory.concrete-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-semigroups +open import group-theory.isomorphisms-groups +open import group-theory.monoids +open import group-theory.semigroups +open import group-theory.symmetric-groups ```
diff --git a/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md b/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md index 2ad2aa2bd4..5e895381eb 100644 --- a/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md +++ b/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md @@ -1,26 +1,21 @@ # Mere equivalences of concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.mere-equivalences-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.mere-equivalences-concrete-group-actions where ```
Imports ```agda -open import foundation.functoriality-propositional-truncation funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.functoriality-propositional-truncation +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext -open import group-theory.equivalences-concrete-group-actions funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups +open import group-theory.equivalences-concrete-group-actions ```
diff --git a/src/group-theory/mere-equivalences-group-actions.lagda.md b/src/group-theory/mere-equivalences-group-actions.lagda.md index 7436e2f743..72c1412d12 100644 --- a/src/group-theory/mere-equivalences-group-actions.lagda.md +++ b/src/group-theory/mere-equivalences-group-actions.lagda.md @@ -1,24 +1,19 @@ # Mere equivalences of group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.mere-equivalences-group-actions - (funext : function-extensionality) - where +module group-theory.mere-equivalences-group-actions where ```
Imports ```agda -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.universe-levels -open import group-theory.equivalences-group-actions funext -open import group-theory.group-actions funext -open import group-theory.groups funext +open import group-theory.equivalences-group-actions +open import group-theory.group-actions +open import group-theory.groups ```
diff --git a/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md b/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md index 6d31d54595..6433e5bbad 100644 --- a/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md +++ b/src/group-theory/minkowski-multiplication-commutative-monoids.lagda.md @@ -1,29 +1,24 @@ # Minkowski multiplication of subsets of a commutative monoid ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.minkowski-multiplication-commutative-monoids - (funext : function-extensionality) - where +module group-theory.minkowski-multiplication-commutative-monoids where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.inhabited-subtypes funext -open import foundation.powersets funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.inhabited-subtypes +open import foundation.powersets +open import foundation.subtypes open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.minkowski-multiplication-monoids funext -open import group-theory.subsets-commutative-monoids funext +open import group-theory.commutative-monoids +open import group-theory.minkowski-multiplication-monoids +open import group-theory.subsets-commutative-monoids ```
diff --git a/src/group-theory/minkowski-multiplication-monoids.lagda.md b/src/group-theory/minkowski-multiplication-monoids.lagda.md index ebbd8b00f3..8ce30adb8f 100644 --- a/src/group-theory/minkowski-multiplication-monoids.lagda.md +++ b/src/group-theory/minkowski-multiplication-monoids.lagda.md @@ -1,12 +1,7 @@ # Minkowski multiplication on subsets of a monoid ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.minkowski-multiplication-monoids - (funext : function-extensionality) - where +module group-theory.minkowski-multiplication-monoids where ```
Imports @@ -14,18 +9,18 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.inhabited-subtypes funext -open import foundation.powersets funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.inhabited-subtypes +open import foundation.powersets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.minkowski-multiplication-semigroups funext -open import group-theory.monoids funext -open import group-theory.subsets-monoids funext +open import group-theory.minkowski-multiplication-semigroups +open import group-theory.monoids +open import group-theory.subsets-monoids ```
diff --git a/src/group-theory/minkowski-multiplication-semigroups.lagda.md b/src/group-theory/minkowski-multiplication-semigroups.lagda.md index ab3cb551af..0fea876135 100644 --- a/src/group-theory/minkowski-multiplication-semigroups.lagda.md +++ b/src/group-theory/minkowski-multiplication-semigroups.lagda.md @@ -1,35 +1,30 @@ # Minkowski multiplication on subsets of a semigroup ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.minkowski-multiplication-semigroups - (funext : function-extensionality) - where +module group-theory.minkowski-multiplication-semigroups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext +open import foundation.cartesian-product-types +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.inhabited-subtypes funext -open import foundation.powersets funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.inhabited-subtypes +open import foundation.powersets +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.semigroups funext -open import group-theory.subsets-semigroups funext +open import group-theory.semigroups +open import group-theory.subsets-semigroups -open import logic.functoriality-existential-quantification funext +open import logic.functoriality-existential-quantification ```
diff --git a/src/group-theory/monoid-actions.lagda.md b/src/group-theory/monoid-actions.lagda.md index d504e9f202..e195c009af 100644 --- a/src/group-theory/monoid-actions.lagda.md +++ b/src/group-theory/monoid-actions.lagda.md @@ -1,12 +1,7 @@ # Monoid actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.monoid-actions - (funext : function-extensionality) - where +module group-theory.monoid-actions where ```
Imports @@ -14,13 +9,14 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.endomorphisms funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.endomorphisms +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.homomorphisms-monoids funext -open import group-theory.monoids funext +open import group-theory.homomorphisms-monoids +open import group-theory.monoids ```
diff --git a/src/group-theory/monoids.lagda.md b/src/group-theory/monoids.lagda.md index 50b0075ea2..6a0c542cfc 100644 --- a/src/group-theory/monoids.lagda.md +++ b/src/group-theory/monoids.lagda.md @@ -1,30 +1,25 @@ # Monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.monoids - (funext : function-extensionality) - where +module group-theory.monoids where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.unit-type open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups -open import structured-types.h-spaces funext -open import structured-types.wild-monoids funext +open import structured-types.h-spaces +open import structured-types.wild-monoids ```
diff --git a/src/group-theory/monomorphisms-concrete-groups.lagda.md b/src/group-theory/monomorphisms-concrete-groups.lagda.md index 1756c1ac04..243579c974 100644 --- a/src/group-theory/monomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/monomorphisms-concrete-groups.lagda.md @@ -1,24 +1,19 @@ # Monomorphisms of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.monomorphisms-concrete-groups - (funext : function-extensionality) - where +module group-theory.monomorphisms-concrete-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.propositions open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.homomorphisms-concrete-groups ```
diff --git a/src/group-theory/monomorphisms-groups.lagda.md b/src/group-theory/monomorphisms-groups.lagda.md index 14e478ba69..eeebe4fb6c 100644 --- a/src/group-theory/monomorphisms-groups.lagda.md +++ b/src/group-theory/monomorphisms-groups.lagda.md @@ -1,26 +1,21 @@ # Monomorphisms in the category of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.monomorphisms-groups - (funext : function-extensionality) - where +module group-theory.monomorphisms-groups where ```
Imports ```agda -open import category-theory.monomorphisms-in-large-precategories funext +open import category-theory.monomorphisms-in-large-precategories -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.precategory-of-groups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.isomorphisms-groups +open import group-theory.precategory-of-groups ```
diff --git a/src/group-theory/multiples-of-elements-abelian-groups.lagda.md b/src/group-theory/multiples-of-elements-abelian-groups.lagda.md index c155942fb6..475f609270 100644 --- a/src/group-theory/multiples-of-elements-abelian-groups.lagda.md +++ b/src/group-theory/multiples-of-elements-abelian-groups.lagda.md @@ -1,12 +1,7 @@ # Multiples of elements in abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.multiples-of-elements-abelian-groups - (funext : function-extensionality) - where +module group-theory.multiples-of-elements-abelian-groups where ```
Imports @@ -16,12 +11,12 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.powers-of-elements-groups funext +open import group-theory.abelian-groups +open import group-theory.powers-of-elements-groups ```
diff --git a/src/group-theory/nontrivial-groups.lagda.md b/src/group-theory/nontrivial-groups.lagda.md index 94edd22c3d..725296c895 100644 --- a/src/group-theory/nontrivial-groups.lagda.md +++ b/src/group-theory/nontrivial-groups.lagda.md @@ -1,39 +1,34 @@ # Nontrivial groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.nontrivial-groups - (funext : function-extensionality) - where +module group-theory.nontrivial-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.logical-equivalences funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.disjunction +open import foundation.embeddings +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.logical-equivalences +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-extensionality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.subgroups funext -open import group-theory.trivial-groups funext +open import group-theory.groups +open import group-theory.subgroups +open import group-theory.trivial-groups ```
diff --git a/src/group-theory/normal-closures-subgroups.lagda.md b/src/group-theory/normal-closures-subgroups.lagda.md index cbd8238c61..704d72a7b2 100644 --- a/src/group-theory/normal-closures-subgroups.lagda.md +++ b/src/group-theory/normal-closures-subgroups.lagda.md @@ -1,37 +1,32 @@ # Normal closures of subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.normal-closures-subgroups - (funext : function-extensionality) - where +module group-theory.normal-closures-subgroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.normal-subgroups funext -open import group-theory.subgroups funext -open import group-theory.subgroups funext-generated-by-subsets-groups -open import group-theory.subsets-groups funext +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.normal-subgroups +open import group-theory.subgroups +open import group-theory.subgroups-generated-by-subsets-groups +open import group-theory.subsets-groups -open import order-theory.galois-connections-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.galois-connections-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders ```
diff --git a/src/group-theory/normal-cores-subgroups.lagda.md b/src/group-theory/normal-cores-subgroups.lagda.md index 73dd8d195c..0e7447ffd7 100644 --- a/src/group-theory/normal-cores-subgroups.lagda.md +++ b/src/group-theory/normal-cores-subgroups.lagda.md @@ -1,12 +1,7 @@ # Normal cores of subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.normal-cores-subgroups - (funext : function-extensionality) - where +module group-theory.normal-cores-subgroups where ```
Imports @@ -14,24 +9,24 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.intersections-subtypes funext -open import foundation.logical-equivalences funext -open import foundation.propositional-maps funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.identity-types +open import foundation.intersections-subtypes +open import foundation.logical-equivalences +open import foundation.propositional-maps +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.normal-subgroups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.normal-subgroups +open import group-theory.subgroups +open import group-theory.subsets-groups -open import order-theory.galois-connections-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.galois-connections-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders ```
diff --git a/src/group-theory/normal-subgroups-concrete-groups.lagda.md b/src/group-theory/normal-subgroups-concrete-groups.lagda.md index 890bccc91d..5e095bd183 100644 --- a/src/group-theory/normal-subgroups-concrete-groups.lagda.md +++ b/src/group-theory/normal-subgroups-concrete-groups.lagda.md @@ -1,12 +1,7 @@ # Normal subgroups of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.normal-subgroups-concrete-groups - (funext : function-extensionality) - where +module group-theory.normal-subgroups-concrete-groups where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext -open import group-theory.subgroups-concrete-groups funext -open import group-theory.transitive-concrete-group-actions funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups +open import group-theory.subgroups-concrete-groups +open import group-theory.transitive-concrete-group-actions ```
diff --git a/src/group-theory/normal-subgroups.lagda.md b/src/group-theory/normal-subgroups.lagda.md index 9fd10db5e7..1691141439 100644 --- a/src/group-theory/normal-subgroups.lagda.md +++ b/src/group-theory/normal-subgroups.lagda.md @@ -1,45 +1,40 @@ # Normal subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.normal-subgroups - (funext : function-extensionality) - where +module group-theory.normal-subgroups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.congruence-relations-groups funext -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext - -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import group-theory.congruence-relations-groups +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.subgroups +open import group-theory.subsets-groups + +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/group-theory/normal-submonoids-commutative-monoids.lagda.md b/src/group-theory/normal-submonoids-commutative-monoids.lagda.md index 7734e0b99c..64d971f8b0 100644 --- a/src/group-theory/normal-submonoids-commutative-monoids.lagda.md +++ b/src/group-theory/normal-submonoids-commutative-monoids.lagda.md @@ -1,38 +1,33 @@ # Normal submonoids of commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.normal-submonoids-commutative-monoids - (funext : function-extensionality) - where +module group-theory.normal-submonoids-commutative-monoids where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.retracts-of-types funext -open import foundation.sets funext +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.retracts-of-types +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.congruence-relations-commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.saturated-congruence-relations-commutative-monoids funext -open import group-theory.semigroups funext -open import group-theory.submonoids-commutative-monoids funext -open import group-theory.subsets-commutative-monoids funext +open import group-theory.commutative-monoids +open import group-theory.congruence-relations-commutative-monoids +open import group-theory.monoids +open import group-theory.saturated-congruence-relations-commutative-monoids +open import group-theory.semigroups +open import group-theory.submonoids-commutative-monoids +open import group-theory.subsets-commutative-monoids ```
diff --git a/src/group-theory/normal-submonoids.lagda.md b/src/group-theory/normal-submonoids.lagda.md index 7f9c773cf0..45aaa58a2c 100644 --- a/src/group-theory/normal-submonoids.lagda.md +++ b/src/group-theory/normal-submonoids.lagda.md @@ -1,38 +1,33 @@ # Normal submonoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.normal-submonoids - (funext : function-extensionality) - where +module group-theory.normal-submonoids where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.retracts-of-types funext -open import foundation.sets funext +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.retracts-of-types +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.congruence-relations-monoids funext -open import group-theory.monoids funext -open import group-theory.saturated-congruence-relations-monoids funext -open import group-theory.semigroups funext -open import group-theory.submonoids funext -open import group-theory.subsets-monoids funext +open import group-theory.congruence-relations-monoids +open import group-theory.monoids +open import group-theory.saturated-congruence-relations-monoids +open import group-theory.semigroups +open import group-theory.submonoids +open import group-theory.subsets-monoids ```
diff --git a/src/group-theory/normalizer-subgroups.lagda.md b/src/group-theory/normalizer-subgroups.lagda.md index 9ffaea0c0e..dfdbbcae1a 100644 --- a/src/group-theory/normalizer-subgroups.lagda.md +++ b/src/group-theory/normalizer-subgroups.lagda.md @@ -1,31 +1,26 @@ # Normalizer subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.normalizer-subgroups - (funext : function-extensionality) - where +module group-theory.normalizer-subgroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.equality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.subgroups +open import group-theory.subsets-groups ```
diff --git a/src/group-theory/nullifying-group-homomorphisms.lagda.md b/src/group-theory/nullifying-group-homomorphisms.lagda.md index 0f324b0e80..92dfe9bbae 100644 --- a/src/group-theory/nullifying-group-homomorphisms.lagda.md +++ b/src/group-theory/nullifying-group-homomorphisms.lagda.md @@ -1,31 +1,26 @@ # Nullifying group homomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.nullifying-group-homomorphisms - (funext : function-extensionality) - where +module group-theory.nullifying-group-homomorphisms where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.reflecting-maps-equivalence-relations +open import foundation.subtypes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-groups funext-equipped-with-normal-subgroups -open import group-theory.kernels-homomorphisms-groups funext -open import group-theory.normal-subgroups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-groups-equipped-with-normal-subgroups +open import group-theory.kernels-homomorphisms-groups +open import group-theory.normal-subgroups ```
diff --git a/src/group-theory/opposite-groups.lagda.md b/src/group-theory/opposite-groups.lagda.md index 2b767bdc11..1b8b84aac2 100644 --- a/src/group-theory/opposite-groups.lagda.md +++ b/src/group-theory/opposite-groups.lagda.md @@ -1,12 +1,7 @@ # The opposite of a group ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.opposite-groups - (funext : function-extensionality) - where +module group-theory.opposite-groups where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.monoids funext -open import group-theory.opposite-semigroups funext +open import group-theory.groups +open import group-theory.isomorphisms-groups +open import group-theory.monoids +open import group-theory.opposite-semigroups ```
diff --git a/src/group-theory/opposite-semigroups.lagda.md b/src/group-theory/opposite-semigroups.lagda.md index 5ba26384b2..860ad6a7de 100644 --- a/src/group-theory/opposite-semigroups.lagda.md +++ b/src/group-theory/opposite-semigroups.lagda.md @@ -1,23 +1,18 @@ # The opposite of a semigroup ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.opposite-semigroups - (funext : function-extensionality) - where +module group-theory.opposite-semigroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups ```
diff --git a/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md b/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md index 9f94459dd5..d9cc6ffa5b 100644 --- a/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md +++ b/src/group-theory/orbit-stabilizer-theorem-concrete-groups.lagda.md @@ -1,12 +1,7 @@ # The orbit-stabilizer theorem for concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.orbit-stabilizer-theorem-concrete-groups - (funext : function-extensionality) - where +module group-theory.orbit-stabilizer-theorem-concrete-groups where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext -open import group-theory.mere-equivalences-concrete-group-actions funext -open import group-theory.stabilizer-groups-concrete-group-actions funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups +open import group-theory.mere-equivalences-concrete-group-actions +open import group-theory.stabilizer-groups-concrete-group-actions open import structured-types.pointed-types ``` diff --git a/src/group-theory/orbits-concrete-group-actions.lagda.md b/src/group-theory/orbits-concrete-group-actions.lagda.md index 7c3012abf1..1217af68ab 100644 --- a/src/group-theory/orbits-concrete-group-actions.lagda.md +++ b/src/group-theory/orbits-concrete-group-actions.lagda.md @@ -1,24 +1,19 @@ # Orbits of concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.orbits-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.orbits-concrete-group-actions where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups ```
diff --git a/src/group-theory/orbits-group-actions.lagda.md b/src/group-theory/orbits-group-actions.lagda.md index b3c0489c13..6cacd944fa 100644 --- a/src/group-theory/orbits-group-actions.lagda.md +++ b/src/group-theory/orbits-group-actions.lagda.md @@ -1,23 +1,18 @@ # Orbits of group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.orbits-group-actions - (funext : function-extensionality) - where +module group-theory.orbits-group-actions where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext +open import group-theory.group-actions +open import group-theory.groups ```
diff --git a/src/group-theory/orders-of-elements-groups.lagda.md b/src/group-theory/orders-of-elements-groups.lagda.md index 61462134f3..78115f630b 100644 --- a/src/group-theory/orders-of-elements-groups.lagda.md +++ b/src/group-theory/orders-of-elements-groups.lagda.md @@ -1,28 +1,23 @@ # The order of an element in a group ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.orders-of-elements-groups - (funext : function-extensionality) - where +module group-theory.orders-of-elements-groups where ```
Imports ```agda -open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.group-of-integers open import elementary-number-theory.integers open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator funext -open import group-theory.groups funext -open import group-theory.kernels-homomorphisms-groups funext -open import group-theory.normal-subgroups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.free-groups-with-one-generator +open import group-theory.groups +open import group-theory.kernels-homomorphisms-groups +open import group-theory.normal-subgroups +open import group-theory.subgroups +open import group-theory.subsets-groups ```
diff --git a/src/group-theory/perfect-cores.lagda.md b/src/group-theory/perfect-cores.lagda.md index f5eb7f729c..cb10247ebe 100644 --- a/src/group-theory/perfect-cores.lagda.md +++ b/src/group-theory/perfect-cores.lagda.md @@ -1,23 +1,18 @@ # Perfect cores ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.perfect-cores - (funext : function-extensionality) - where +module group-theory.perfect-cores where ```
Imports ```agda -open import foundation.logical-equivalences funext +open import foundation.logical-equivalences open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.perfect-subgroups funext -open import group-theory.subgroups funext +open import group-theory.groups +open import group-theory.perfect-subgroups +open import group-theory.subgroups ```
diff --git a/src/group-theory/perfect-groups.lagda.md b/src/group-theory/perfect-groups.lagda.md index 8494c47b8a..830d29efab 100644 --- a/src/group-theory/perfect-groups.lagda.md +++ b/src/group-theory/perfect-groups.lagda.md @@ -1,23 +1,18 @@ # Perfect groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.perfect-groups - (funext : function-extensionality) - where +module group-theory.perfect-groups where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import group-theory.commutator-subgroups funext -open import group-theory.full-subgroups funext -open import group-theory.groups funext +open import group-theory.commutator-subgroups +open import group-theory.full-subgroups +open import group-theory.groups ```
diff --git a/src/group-theory/perfect-subgroups.lagda.md b/src/group-theory/perfect-subgroups.lagda.md index e4d9c5c03a..9e4dac3fc1 100644 --- a/src/group-theory/perfect-subgroups.lagda.md +++ b/src/group-theory/perfect-subgroups.lagda.md @@ -1,23 +1,18 @@ # Perfect subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.perfect-subgroups - (funext : function-extensionality) - where +module group-theory.perfect-subgroups where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.perfect-groups funext -open import group-theory.subgroups funext +open import group-theory.groups +open import group-theory.perfect-groups +open import group-theory.subgroups ```
diff --git a/src/group-theory/powers-of-elements-commutative-monoids.lagda.md b/src/group-theory/powers-of-elements-commutative-monoids.lagda.md index 303bfe280a..344471dcb0 100644 --- a/src/group-theory/powers-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/powers-of-elements-commutative-monoids.lagda.md @@ -1,12 +1,7 @@ # Powers of elements in commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.powers-of-elements-commutative-monoids - (funext : function-extensionality) - where +module group-theory.powers-of-elements-commutative-monoids where ```
Imports @@ -16,13 +11,13 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.homomorphisms-commutative-monoids funext -open import group-theory.powers-of-elements-monoids funext +open import group-theory.commutative-monoids +open import group-theory.homomorphisms-commutative-monoids +open import group-theory.powers-of-elements-monoids ```
diff --git a/src/group-theory/powers-of-elements-groups.lagda.md b/src/group-theory/powers-of-elements-groups.lagda.md index 4085f7f059..745ee9159a 100644 --- a/src/group-theory/powers-of-elements-groups.lagda.md +++ b/src/group-theory/powers-of-elements-groups.lagda.md @@ -1,12 +1,7 @@ # Powers of elements in groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.powers-of-elements-groups - (funext : function-extensionality) - where +module group-theory.powers-of-elements-groups where ```
Imports @@ -16,14 +11,14 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.commuting-elements-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.powers-of-elements-monoids funext +open import group-theory.commuting-elements-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.powers-of-elements-monoids ```
diff --git a/src/group-theory/powers-of-elements-monoids.lagda.md b/src/group-theory/powers-of-elements-monoids.lagda.md index a9bc415e26..66c4e4f41b 100644 --- a/src/group-theory/powers-of-elements-monoids.lagda.md +++ b/src/group-theory/powers-of-elements-monoids.lagda.md @@ -1,12 +1,7 @@ # Powers of elements in monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.powers-of-elements-monoids - (funext : function-extensionality) - where +module group-theory.powers-of-elements-monoids where ```
Imports @@ -17,13 +12,13 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.homomorphisms-monoids funext -open import group-theory.monoids funext +open import group-theory.homomorphisms-monoids +open import group-theory.monoids ```
diff --git a/src/group-theory/precategory-of-commutative-monoids.lagda.md b/src/group-theory/precategory-of-commutative-monoids.lagda.md index b86a74eae7..f3d5757c93 100644 --- a/src/group-theory/precategory-of-commutative-monoids.lagda.md +++ b/src/group-theory/precategory-of-commutative-monoids.lagda.md @@ -1,25 +1,20 @@ # The precategory of commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.precategory-of-commutative-monoids - (funext : function-extensionality) - where +module group-theory.precategory-of-commutative-monoids where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.full-large-subprecategories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.precategory-of-monoids funext +open import group-theory.commutative-monoids +open import group-theory.precategory-of-monoids ```
diff --git a/src/group-theory/precategory-of-concrete-groups.lagda.md b/src/group-theory/precategory-of-concrete-groups.lagda.md index 5429bd563b..43b955bd5d 100644 --- a/src/group-theory/precategory-of-concrete-groups.lagda.md +++ b/src/group-theory/precategory-of-concrete-groups.lagda.md @@ -1,23 +1,18 @@ # The precategory of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.precategory-of-concrete-groups - (funext : function-extensionality) - where +module group-theory.precategory-of-concrete-groups where ```
Imports ```agda -open import category-theory.large-precategories funext +open import category-theory.large-precategories open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.homomorphisms-concrete-groups ```
diff --git a/src/group-theory/precategory-of-group-actions.lagda.md b/src/group-theory/precategory-of-group-actions.lagda.md index 7251001268..d8fc00a1c5 100644 --- a/src/group-theory/precategory-of-group-actions.lagda.md +++ b/src/group-theory/precategory-of-group-actions.lagda.md @@ -1,25 +1,20 @@ # The precategory of group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.precategory-of-group-actions - (funext : function-extensionality) - where +module group-theory.precategory-of-group-actions where ```
Imports ```agda -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext -open import group-theory.homomorphisms-group-actions funext +open import group-theory.group-actions +open import group-theory.groups +open import group-theory.homomorphisms-group-actions ```
diff --git a/src/group-theory/precategory-of-groups.lagda.md b/src/group-theory/precategory-of-groups.lagda.md index 58987a13e0..10f8be5a09 100644 --- a/src/group-theory/precategory-of-groups.lagda.md +++ b/src/group-theory/precategory-of-groups.lagda.md @@ -1,25 +1,20 @@ # The precategory of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.precategory-of-groups - (funext : function-extensionality) - where +module group-theory.precategory-of-groups where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.full-large-subprecategories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.precategory-of-semigroups funext +open import group-theory.groups +open import group-theory.precategory-of-semigroups ```
diff --git a/src/group-theory/precategory-of-monoids.lagda.md b/src/group-theory/precategory-of-monoids.lagda.md index 9ca444fa42..a16650574c 100644 --- a/src/group-theory/precategory-of-monoids.lagda.md +++ b/src/group-theory/precategory-of-monoids.lagda.md @@ -1,27 +1,22 @@ # The precategory of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.precategory-of-monoids - (funext : function-extensionality) - where +module group-theory.precategory-of-monoids where ```
Imports ```agda -open import category-theory.large-precategories funext -open import category-theory.large-subprecategories funext -open import category-theory.precategories funext +open import category-theory.large-precategories +open import category-theory.large-subprecategories +open import category-theory.precategories open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.homomorphisms-monoids funext -open import group-theory.monoids funext -open import group-theory.precategory-of-semigroups funext +open import group-theory.homomorphisms-monoids +open import group-theory.monoids +open import group-theory.precategory-of-semigroups ```
diff --git a/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md b/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md index 0645388abf..5a51488a0e 100644 --- a/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md +++ b/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md @@ -1,32 +1,27 @@ # The precategory of orbits of a monoid action ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.precategory-of-orbits-monoid-actions - (funext : function-extensionality) - where +module group-theory.precategory-of-orbits-monoid-actions where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.monoid-actions funext -open import group-theory.monoids funext +open import group-theory.monoid-actions +open import group-theory.monoids ```
diff --git a/src/group-theory/precategory-of-semigroups.lagda.md b/src/group-theory/precategory-of-semigroups.lagda.md index 25507ba6d1..264d32e6b7 100644 --- a/src/group-theory/precategory-of-semigroups.lagda.md +++ b/src/group-theory/precategory-of-semigroups.lagda.md @@ -1,23 +1,18 @@ # The precategory of semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.precategory-of-semigroups - (funext : function-extensionality) - where +module group-theory.precategory-of-semigroups where ```
Imports ```agda -open import category-theory.large-precategories funext +open import category-theory.large-precategories open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups funext -open import group-theory.semigroups funext +open import group-theory.homomorphisms-semigroups +open import group-theory.semigroups ```
diff --git a/src/group-theory/principal-group-actions.lagda.md b/src/group-theory/principal-group-actions.lagda.md index 4d19a8506a..18aaf88ca9 100644 --- a/src/group-theory/principal-group-actions.lagda.md +++ b/src/group-theory/principal-group-actions.lagda.md @@ -1,23 +1,18 @@ # Principal group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.principal-group-actions - (funext : function-extensionality) - where +module group-theory.principal-group-actions where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext +open import foundation.equivalence-extensionality open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext +open import group-theory.group-actions +open import group-theory.groups ```
diff --git a/src/group-theory/principal-torsors-concrete-groups.lagda.md b/src/group-theory/principal-torsors-concrete-groups.lagda.md index 30c416d128..d90716ffd3 100644 --- a/src/group-theory/principal-torsors-concrete-groups.lagda.md +++ b/src/group-theory/principal-torsors-concrete-groups.lagda.md @@ -1,12 +1,7 @@ # Principal torsors of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.principal-torsors-concrete-groups - (funext : function-extensionality) - where +module group-theory.principal-torsors-concrete-groups where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups ```
diff --git a/src/group-theory/products-of-elements-monoids.lagda.md b/src/group-theory/products-of-elements-monoids.lagda.md index aaf2cafbad..a4712a4f13 100644 --- a/src/group-theory/products-of-elements-monoids.lagda.md +++ b/src/group-theory/products-of-elements-monoids.lagda.md @@ -1,24 +1,19 @@ # Products of elements in a monoid ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.products-of-elements-monoids - (funext : function-extensionality) - where +module group-theory.products-of-elements-monoids where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.monoids funext +open import group-theory.monoids -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists ``` diff --git a/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md b/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md index b3cdcaeddb..120ca6b54c 100644 --- a/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/products-of-tuples-of-elements-commutative-monoids.lagda.md @@ -1,12 +1,7 @@ # Products of tuples of elements in commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.products-of-tuples-of-elements-commutative-monoids - (funext : function-extensionality) - where +module group-theory.products-of-tuples-of-elements-commutative-monoids where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext -open import foundation.function-types funext +open import foundation.coproduct-types +open import foundation.function-types open import foundation.unit-type open import foundation.universe-levels -open import group-theory.commutative-monoids funext +open import group-theory.commutative-monoids -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/group-theory/pullbacks-subgroups.lagda.md b/src/group-theory/pullbacks-subgroups.lagda.md index 123a31645f..8ac1c10168 100644 --- a/src/group-theory/pullbacks-subgroups.lagda.md +++ b/src/group-theory/pullbacks-subgroups.lagda.md @@ -1,36 +1,31 @@ # Pullbacks of subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.pullbacks-subgroups - (funext : function-extensionality) - where +module group-theory.pullbacks-subgroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.powersets funext -open import foundation.pullbacks-subtypes funext +open import foundation.identity-types +open import foundation.powersets +open import foundation.pullbacks-subtypes open import foundation.universe-levels -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.normal-subgroups funext -open import group-theory.pullbacks-subsemigroups funext -open import group-theory.subgroups funext -open import group-theory.subsemigroups funext -open import group-theory.subsets-groups funext - -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.similarity-of-order-preserving-maps-large-posets funext +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.normal-subgroups +open import group-theory.pullbacks-subsemigroups +open import group-theory.subgroups +open import group-theory.subsemigroups +open import group-theory.subsets-groups + +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.similarity-of-order-preserving-maps-large-posets ```
diff --git a/src/group-theory/pullbacks-subsemigroups.lagda.md b/src/group-theory/pullbacks-subsemigroups.lagda.md index 1013c64069..cfefc2061d 100644 --- a/src/group-theory/pullbacks-subsemigroups.lagda.md +++ b/src/group-theory/pullbacks-subsemigroups.lagda.md @@ -1,33 +1,28 @@ # Pullbacks of subsemigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.pullbacks-subsemigroups - (funext : function-extensionality) - where +module group-theory.pullbacks-subsemigroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.powersets funext -open import foundation.pullbacks-subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.powersets +open import foundation.pullbacks-subtypes open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups funext -open import group-theory.semigroups funext -open import group-theory.subsemigroups funext -open import group-theory.subsets-semigroups funext +open import group-theory.homomorphisms-semigroups +open import group-theory.semigroups +open import group-theory.subsemigroups +open import group-theory.subsets-semigroups -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.similarity-of-order-preserving-maps-large-posets funext +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.similarity-of-order-preserving-maps-large-posets ```
diff --git a/src/group-theory/quotient-groups-concrete-groups.lagda.md b/src/group-theory/quotient-groups-concrete-groups.lagda.md index 4f8afde78f..f23e72c900 100644 --- a/src/group-theory/quotient-groups-concrete-groups.lagda.md +++ b/src/group-theory/quotient-groups-concrete-groups.lagda.md @@ -1,41 +1,36 @@ # Quotient groups of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.quotient-groups-concrete-groups - (funext : function-extensionality) - where +module group-theory.quotient-groups-concrete-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.0-images-of-maps funext -open import foundation.1-types funext +open import foundation.0-connected-types +open import foundation.0-images-of-maps +open import foundation.1-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.equivalences-concrete-group-actions funext -open import group-theory.mere-equivalences-concrete-group-actions funext -open import group-theory.normal-subgroups-concrete-groups funext -open import group-theory.transitive-concrete-group-actions funext +open import group-theory.concrete-groups +open import group-theory.equivalences-concrete-group-actions +open import group-theory.mere-equivalences-concrete-group-actions +open import group-theory.normal-subgroups-concrete-groups +open import group-theory.transitive-concrete-group-actions -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/group-theory/quotient-groups.lagda.md b/src/group-theory/quotient-groups.lagda.md index 272a8392ca..d109a8292d 100644 --- a/src/group-theory/quotient-groups.lagda.md +++ b/src/group-theory/quotient-groups.lagda.md @@ -1,45 +1,40 @@ # Quotient groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.quotient-groups - (funext : function-extensionality) - where +module group-theory.quotient-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-functoriality-set-quotients funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.binary-functoriality-set-quotients +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-set-quotients funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.set-quotients funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext -open import foundation.universal-property-set-quotients funext +open import foundation.effective-maps-equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-set-quotients +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.reflecting-maps-equivalence-relations +open import foundation.set-quotients +open import foundation.sets +open import foundation.subtypes +open import foundation.surjective-maps +open import foundation.universal-property-set-quotients open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.kernels-homomorphisms-groups funext -open import group-theory.normal-subgroups funext -open import group-theory.nullifying-group-homomorphisms funext -open import group-theory.semigroups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.kernels-homomorphisms-groups +open import group-theory.normal-subgroups +open import group-theory.nullifying-group-homomorphisms +open import group-theory.semigroups ```
diff --git a/src/group-theory/quotients-abelian-groups.lagda.md b/src/group-theory/quotients-abelian-groups.lagda.md index 65f86ed3f1..51ce7f9b4a 100644 --- a/src/group-theory/quotients-abelian-groups.lagda.md +++ b/src/group-theory/quotients-abelian-groups.lagda.md @@ -3,39 +3,34 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - group-theory.quotients-abelian-groups - (funext : function-extensionality) - where +module group-theory.quotients-abelian-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-functoriality-set-quotients funext +open import foundation.binary-functoriality-set-quotients open import foundation.dependent-pair-types -open import foundation.effective-maps-equivalence-relations funext -open import foundation.equivalences funext -open import foundation.functoriality-set-quotients funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.set-quotients funext -open import foundation.sets funext -open import foundation.surjective-maps funext -open import foundation.universal-property-set-quotients funext +open import foundation.effective-maps-equivalence-relations +open import foundation.equivalences +open import foundation.functoriality-set-quotients +open import foundation.identity-types +open import foundation.propositions +open import foundation.reflecting-maps-equivalence-relations +open import foundation.set-quotients +open import foundation.sets +open import foundation.surjective-maps +open import foundation.universal-property-set-quotients open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.nullifying-group-homomorphisms funext -open import group-theory.quotient-groups funext -open import group-theory.semigroups funext -open import group-theory.subgroups-abelian-groups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.homomorphisms-abelian-groups +open import group-theory.nullifying-group-homomorphisms +open import group-theory.quotient-groups +open import group-theory.semigroups +open import group-theory.subgroups-abelian-groups ```
diff --git a/src/group-theory/rational-commutative-monoids.lagda.md b/src/group-theory/rational-commutative-monoids.lagda.md index 1785c5a04e..2c036f47fe 100644 --- a/src/group-theory/rational-commutative-monoids.lagda.md +++ b/src/group-theory/rational-commutative-monoids.lagda.md @@ -1,12 +1,7 @@ # Rational commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.rational-commutative-monoids - (funext : function-extensionality) - where +module group-theory.rational-commutative-monoids where ```
Imports @@ -15,14 +10,14 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.powers-of-elements-commutative-monoids funext +open import group-theory.commutative-monoids +open import group-theory.monoids +open import group-theory.powers-of-elements-commutative-monoids ```
diff --git a/src/group-theory/representations-monoids-precategories.lagda.md b/src/group-theory/representations-monoids-precategories.lagda.md index 086c4099f1..934a1e2362 100644 --- a/src/group-theory/representations-monoids-precategories.lagda.md +++ b/src/group-theory/representations-monoids-precategories.lagda.md @@ -1,28 +1,23 @@ # Representations of monoids in precategories ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.representations-monoids-precategories - (funext : function-extensionality) - where +module group-theory.representations-monoids-precategories where ```
Imports ```agda -open import category-theory.endomorphisms-in-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.one-object-precategories funext -open import category-theory.precategories funext +open import category-theory.endomorphisms-in-precategories +open import category-theory.functors-precategories +open import category-theory.one-object-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels -open import group-theory.monoids funext +open import group-theory.monoids ```
diff --git a/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md b/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md index 3a2f48b02f..52a270e3cb 100644 --- a/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md +++ b/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md @@ -1,31 +1,26 @@ # Saturated congruence relations on commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.saturated-congruence-relations-commutative-monoids - (funext : function-extensionality) - where +module group-theory.saturated-congruence-relations-commutative-monoids where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext +open import foundation.equivalence-relations +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.congruence-relations-commutative-monoids funext +open import group-theory.commutative-monoids +open import group-theory.congruence-relations-commutative-monoids ```
diff --git a/src/group-theory/saturated-congruence-relations-monoids.lagda.md b/src/group-theory/saturated-congruence-relations-monoids.lagda.md index 4e3d71eeb4..fe77217ff6 100644 --- a/src/group-theory/saturated-congruence-relations-monoids.lagda.md +++ b/src/group-theory/saturated-congruence-relations-monoids.lagda.md @@ -1,31 +1,26 @@ # Saturated congruence relations on monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.saturated-congruence-relations-monoids - (funext : function-extensionality) - where +module group-theory.saturated-congruence-relations-monoids where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext +open import foundation.equivalence-relations +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.congruence-relations-monoids funext -open import group-theory.monoids funext +open import group-theory.congruence-relations-monoids +open import group-theory.monoids ```
diff --git a/src/group-theory/semigroups.lagda.md b/src/group-theory/semigroups.lagda.md index a078dfb8f2..4709573fcf 100644 --- a/src/group-theory/semigroups.lagda.md +++ b/src/group-theory/semigroups.lagda.md @@ -1,12 +1,7 @@ # Semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.semigroups - (funext : function-extensionality) - where +module group-theory.semigroups where ```
Imports @@ -15,8 +10,8 @@ module open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/group-theory/sheargroups.lagda.md b/src/group-theory/sheargroups.lagda.md index 0c48f9f41c..42becd5b2b 100644 --- a/src/group-theory/sheargroups.lagda.md +++ b/src/group-theory/sheargroups.lagda.md @@ -1,21 +1,16 @@ # Sheargroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.sheargroups - (funext : function-extensionality) - where +module group-theory.sheargroups where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/group-theory/shriek-concrete-group-actions.lagda.md b/src/group-theory/shriek-concrete-group-actions.lagda.md index 077d3dbd4d..6e5364e97f 100644 --- a/src/group-theory/shriek-concrete-group-actions.lagda.md +++ b/src/group-theory/shriek-concrete-group-actions.lagda.md @@ -1,27 +1,22 @@ # Shriek of concrete group homomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.shriek-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.shriek-concrete-group-actions where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.set-truncations +open import foundation.sets open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext -open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups +open import group-theory.homomorphisms-concrete-groups ```
diff --git a/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md b/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md index 8531ba783d..fccff9b2a3 100644 --- a/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md +++ b/src/group-theory/stabilizer-groups-concrete-group-actions.lagda.md @@ -1,31 +1,26 @@ # Stabilizers of concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.stabilizer-groups-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.stabilizer-groups-concrete-group-actions where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.sets +open import foundation.subtypes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext -open import group-theory.subgroups-concrete-groups funext -open import group-theory.transitive-concrete-group-actions funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups +open import group-theory.subgroups-concrete-groups +open import group-theory.transitive-concrete-group-actions ```
diff --git a/src/group-theory/stabilizer-groups.lagda.md b/src/group-theory/stabilizer-groups.lagda.md index ac0a6b7282..6786bf463a 100644 --- a/src/group-theory/stabilizer-groups.lagda.md +++ b/src/group-theory/stabilizer-groups.lagda.md @@ -1,23 +1,18 @@ # Stabilizer groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.stabilizer-groups - (funext : function-extensionality) - where +module group-theory.stabilizer-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext +open import group-theory.group-actions +open import group-theory.groups ```
diff --git a/src/group-theory/subgroups-abelian-groups.lagda.md b/src/group-theory/subgroups-abelian-groups.lagda.md index 2729ca79d1..61238aa5c7 100644 --- a/src/group-theory/subgroups-abelian-groups.lagda.md +++ b/src/group-theory/subgroups-abelian-groups.lagda.md @@ -1,42 +1,37 @@ # Subgroups of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subgroups-abelian-groups - (funext : function-extensionality) - where +module group-theory.subgroups-abelian-groups where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.congruence-relations-abelian-groups funext -open import group-theory.congruence-relations-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.normal-subgroups funext -open import group-theory.semigroups funext -open import group-theory.subgroups funext -open import group-theory.subsets-abelian-groups funext - -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import group-theory.abelian-groups +open import group-theory.congruence-relations-abelian-groups +open import group-theory.congruence-relations-groups +open import group-theory.groups +open import group-theory.homomorphisms-abelian-groups +open import group-theory.normal-subgroups +open import group-theory.semigroups +open import group-theory.subgroups +open import group-theory.subsets-abelian-groups + +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/group-theory/subgroups-concrete-groups.lagda.md b/src/group-theory/subgroups-concrete-groups.lagda.md index 275e88ba57..eb86e36730 100644 --- a/src/group-theory/subgroups-concrete-groups.lagda.md +++ b/src/group-theory/subgroups-concrete-groups.lagda.md @@ -1,42 +1,37 @@ # Subgroups of concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subgroups-concrete-groups - (funext : function-extensionality) - where +module group-theory.subgroups-concrete-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.0-maps funext +open import foundation.0-connected-types +open import foundation.0-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.faithful-maps funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.faithful-maps +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.structure-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext -open import group-theory.equivalences-concrete-group-actions funext -open import group-theory.homomorphisms-concrete-groups funext -open import group-theory.orbits-concrete-group-actions funext -open import group-theory.transitive-concrete-group-actions funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups +open import group-theory.equivalences-concrete-group-actions +open import group-theory.homomorphisms-concrete-groups +open import group-theory.orbits-concrete-group-actions +open import group-theory.transitive-concrete-group-actions -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces funext -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/group-theory/subgroups-generated-by-elements-groups.lagda.md b/src/group-theory/subgroups-generated-by-elements-groups.lagda.md index 76613f3386..fe9afdb421 100644 --- a/src/group-theory/subgroups-generated-by-elements-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-elements-groups.lagda.md @@ -1,38 +1,33 @@ # Subgroups generated by elements of a group ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subgroups-generated-by-elements-groups - (funext : function-extensionality) - where +module group-theory.subgroups-generated-by-elements-groups where ```
Imports ```agda -open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.group-of-integers open import elementary-number-theory.integers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.images-subtypes funext -open import foundation.logical-equivalences funext -open import foundation.singleton-subtypes funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.images-subtypes +open import foundation.logical-equivalences +open import foundation.singleton-subtypes +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.free-groups-with-one-generator funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.images-of-group-homomorphisms funext -open import group-theory.integer-powers-of-elements-groups funext -open import group-theory.subgroups funext -open import group-theory.subgroups funext-generated-by-subsets-groups -open import group-theory.subsets-groups funext -open import group-theory.trivial-subgroups funext +open import group-theory.free-groups-with-one-generator +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.images-of-group-homomorphisms +open import group-theory.integer-powers-of-elements-groups +open import group-theory.subgroups +open import group-theory.subgroups-generated-by-subsets-groups +open import group-theory.subsets-groups +open import group-theory.trivial-subgroups ```
diff --git a/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md b/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md index 997a2cb12f..34c8ab61bf 100644 --- a/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-families-of-elements-groups.lagda.md @@ -1,35 +1,30 @@ # Subgroups generated by families of elements ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subgroups-generated-by-families-of-elements-groups - (funext : function-extensionality) - where +module group-theory.subgroups-generated-by-families-of-elements-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.images funext-subtypes -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext -open import foundation.universal-property-image funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.images +open import foundation.images-subtypes +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.subtypes +open import foundation.universal-property-image open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.images-of-group-homomorphisms funext -open import group-theory.subgroups funext -open import group-theory.subgroups funext-generated-by-subsets-groups -open import group-theory.subsets-groups funext -open import group-theory.trivial-subgroups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.images-of-group-homomorphisms +open import group-theory.subgroups +open import group-theory.subgroups-generated-by-subsets-groups +open import group-theory.subsets-groups +open import group-theory.trivial-subgroups ```
diff --git a/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md b/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md index 25aab31f29..bdcb3c854f 100644 --- a/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md @@ -1,57 +1,52 @@ # Subgroups generated by subsets of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subgroups-generated-by-subsets-groups - (funext : function-extensionality) - where +module group-theory.subgroups-generated-by-subsets-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.images-subtypes funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.pullbacks-subtypes funext -open import foundation.singleton-subtypes funext -open import foundation.subtypes funext +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.identity-types +open import foundation.images-subtypes +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.pullbacks-subtypes +open import foundation.singleton-subtypes +open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels -open import group-theory.conjugation funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.images-of-group-homomorphisms funext -open import group-theory.normal-subgroups funext -open import group-theory.pullbacks-subgroups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext -open import group-theory.trivial-subgroups funext - -open import lists.concatenation-lists funext +open import group-theory.conjugation +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.images-of-group-homomorphisms +open import group-theory.normal-subgroups +open import group-theory.pullbacks-subgroups +open import group-theory.subgroups +open import group-theory.subsets-groups +open import group-theory.trivial-subgroups + +open import lists.concatenation-lists open import lists.lists -open import order-theory.commuting-squares-of-galois-connections-large-posets funext -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext -open import order-theory.galois-connections-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.similarity-of-elements-large-posets funext -open import order-theory.similarity-of-order-preserving-maps-large-posets funext +open import order-theory.commuting-squares-of-galois-connections-large-posets +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets +open import order-theory.galois-connections-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.similarity-of-elements-large-posets +open import order-theory.similarity-of-order-preserving-maps-large-posets -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/group-theory/subgroups.lagda.md b/src/group-theory/subgroups.lagda.md index 071aad55eb..98631e94e6 100644 --- a/src/group-theory/subgroups.lagda.md +++ b/src/group-theory/subgroups.lagda.md @@ -1,12 +1,7 @@ # Subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subgroups - (funext : function-extensionality) - where +module group-theory.subgroups where ```
Imports @@ -15,41 +10,41 @@ module open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import foundation.binary-relations funext -open import foundation.coproduct-types funext +open import foundation.binary-relations +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.embeddings funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.large-binary-relations funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.disjunction +open import foundation.embeddings +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.large-binary-relations +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.integer-powers-of-elements-groups funext -open import group-theory.semigroups funext -open import group-theory.subsemigroups funext -open import group-theory.subsets-groups funext - -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.similarity-of-elements-large-posets funext +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.integer-powers-of-elements-groups +open import group-theory.semigroups +open import group-theory.subsemigroups +open import group-theory.subsets-groups + +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.posets +open import order-theory.preorders +open import order-theory.similarity-of-elements-large-posets ```
diff --git a/src/group-theory/submonoids-commutative-monoids.lagda.md b/src/group-theory/submonoids-commutative-monoids.lagda.md index 2bc32fe8cf..1b93a31af2 100644 --- a/src/group-theory/submonoids-commutative-monoids.lagda.md +++ b/src/group-theory/submonoids-commutative-monoids.lagda.md @@ -1,31 +1,26 @@ # Submonoids of commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.submonoids-commutative-monoids - (funext : function-extensionality) - where +module group-theory.submonoids-commutative-monoids where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.homomorphisms-commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext -open import group-theory.submonoids funext -open import group-theory.subsets-commutative-monoids funext +open import group-theory.commutative-monoids +open import group-theory.homomorphisms-commutative-monoids +open import group-theory.monoids +open import group-theory.semigroups +open import group-theory.submonoids +open import group-theory.subsets-commutative-monoids ```
diff --git a/src/group-theory/submonoids.lagda.md b/src/group-theory/submonoids.lagda.md index 6da7d43b49..4245b22e10 100644 --- a/src/group-theory/submonoids.lagda.md +++ b/src/group-theory/submonoids.lagda.md @@ -1,31 +1,26 @@ # Submonoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.submonoids - (funext : function-extensionality) - where +module group-theory.submonoids where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.homomorphisms-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext -open import group-theory.subsets-monoids funext +open import group-theory.homomorphisms-monoids +open import group-theory.monoids +open import group-theory.semigroups +open import group-theory.subsets-monoids ```
diff --git a/src/group-theory/subsemigroups.lagda.md b/src/group-theory/subsemigroups.lagda.md index 78903abd03..f283a68db3 100644 --- a/src/group-theory/subsemigroups.lagda.md +++ b/src/group-theory/subsemigroups.lagda.md @@ -1,39 +1,34 @@ # Subsemigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subsemigroups - (funext : function-extensionality) - where +module group-theory.subsemigroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.powersets funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.powersets +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups funext -open import group-theory.semigroups funext -open import group-theory.subsets-semigroups funext +open import group-theory.homomorphisms-semigroups +open import group-theory.semigroups +open import group-theory.subsets-semigroups -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/group-theory/subsets-abelian-groups.lagda.md b/src/group-theory/subsets-abelian-groups.lagda.md index 0802611e6c..98fe503199 100644 --- a/src/group-theory/subsets-abelian-groups.lagda.md +++ b/src/group-theory/subsets-abelian-groups.lagda.md @@ -1,27 +1,22 @@ # Subsets of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subsets-abelian-groups - (funext : function-extensionality) - where +module group-theory.subsets-abelian-groups where ```
Imports ```agda -open import foundation.large-locale-of-subtypes funext -open import foundation.powersets funext -open import foundation.sets funext +open import foundation.large-locale-of-subtypes +open import foundation.powersets +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.subsets-groups funext +open import group-theory.abelian-groups +open import group-theory.subsets-groups -open import order-theory.large-locales funext -open import order-theory.large-posets funext +open import order-theory.large-locales +open import order-theory.large-posets ```
diff --git a/src/group-theory/subsets-commutative-monoids.lagda.md b/src/group-theory/subsets-commutative-monoids.lagda.md index ab7a48756b..be1275afe2 100644 --- a/src/group-theory/subsets-commutative-monoids.lagda.md +++ b/src/group-theory/subsets-commutative-monoids.lagda.md @@ -1,24 +1,19 @@ # Subsets of commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subsets-commutative-monoids - (funext : function-extensionality) - where +module group-theory.subsets-commutative-monoids where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.subsets-monoids funext +open import group-theory.commutative-monoids +open import group-theory.subsets-monoids ```
diff --git a/src/group-theory/subsets-groups.lagda.md b/src/group-theory/subsets-groups.lagda.md index 617a4b4edc..7eab7bced3 100644 --- a/src/group-theory/subsets-groups.lagda.md +++ b/src/group-theory/subsets-groups.lagda.md @@ -1,25 +1,20 @@ # Subsets of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subsets-groups - (funext : function-extensionality) - where +module group-theory.subsets-groups where ```
Imports ```agda -open import foundation.large-locale-of-subtypes funext -open import foundation.sets funext +open import foundation.large-locale-of-subtypes +open import foundation.sets open import foundation.universe-levels -open import group-theory.groups funext +open import group-theory.groups -open import order-theory.large-locales funext -open import order-theory.large-posets funext +open import order-theory.large-locales +open import order-theory.large-posets ```
diff --git a/src/group-theory/subsets-monoids.lagda.md b/src/group-theory/subsets-monoids.lagda.md index 8312af5e92..97bb8b9059 100644 --- a/src/group-theory/subsets-monoids.lagda.md +++ b/src/group-theory/subsets-monoids.lagda.md @@ -1,24 +1,19 @@ # Subsets of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subsets-monoids - (funext : function-extensionality) - where +module group-theory.subsets-monoids where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.monoids funext +open import group-theory.monoids ```
diff --git a/src/group-theory/subsets-semigroups.lagda.md b/src/group-theory/subsets-semigroups.lagda.md index af75cb9b55..ddfdf50d40 100644 --- a/src/group-theory/subsets-semigroups.lagda.md +++ b/src/group-theory/subsets-semigroups.lagda.md @@ -1,29 +1,24 @@ # Subsets of semigroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.subsets-semigroups - (funext : function-extensionality) - where +module group-theory.subsets-semigroups where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.large-locale-of-subtypes funext -open import foundation.powersets funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.large-locale-of-subtypes +open import foundation.powersets +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups -open import order-theory.large-locales funext -open import order-theory.large-posets funext +open import order-theory.large-locales +open import order-theory.large-posets ```
diff --git a/src/group-theory/substitution-functor-concrete-group-actions.lagda.md b/src/group-theory/substitution-functor-concrete-group-actions.lagda.md index 7469055db2..80b294ad6c 100644 --- a/src/group-theory/substitution-functor-concrete-group-actions.lagda.md +++ b/src/group-theory/substitution-functor-concrete-group-actions.lagda.md @@ -1,12 +1,7 @@ # The substitution functor of concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.substitution-functor-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.substitution-functor-concrete-group-actions where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext -open import group-theory.homomorphisms-concrete-groups funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups +open import group-theory.homomorphisms-concrete-groups ```
diff --git a/src/group-theory/substitution-functor-group-actions.lagda.md b/src/group-theory/substitution-functor-group-actions.lagda.md index e744fab386..d8d73e7e03 100644 --- a/src/group-theory/substitution-functor-group-actions.lagda.md +++ b/src/group-theory/substitution-functor-group-actions.lagda.md @@ -1,36 +1,31 @@ # The substitution functor of group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.substitution-functor-group-actions - (funext : function-extensionality) - where +module group-theory.substitution-functor-group-actions where ```
Imports ```agda -open import category-theory.functors-large-precategories funext +open import category-theory.functors-large-precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalence-classes funext -open import foundation.equivalence-relations funext -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.equivalence-classes +open import foundation.equivalence-relations +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.sets open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext -open import group-theory.homomorphisms-group-actions funext -open import group-theory.homomorphisms-groups funext -open import group-theory.precategory-of-group-actions funext -open import group-theory.symmetric-groups funext +open import group-theory.group-actions +open import group-theory.groups +open import group-theory.homomorphisms-group-actions +open import group-theory.homomorphisms-groups +open import group-theory.precategory-of-group-actions +open import group-theory.symmetric-groups ```
diff --git a/src/group-theory/surjective-group-homomorphisms.lagda.md b/src/group-theory/surjective-group-homomorphisms.lagda.md index 5e9dd1691c..c482bc5e50 100644 --- a/src/group-theory/surjective-group-homomorphisms.lagda.md +++ b/src/group-theory/surjective-group-homomorphisms.lagda.md @@ -1,26 +1,21 @@ # Surjective group homomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.surjective-group-homomorphisms - (funext : function-extensionality) - where +module group-theory.surjective-group-homomorphisms where ```
Imports ```agda -open import foundation.propositions funext -open import foundation.surjective-maps funext +open import foundation.propositions +open import foundation.surjective-maps open import foundation.universe-levels -open import group-theory.full-subgroups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.images-of-group-homomorphisms funext -open import group-theory.surjective-semigroup-homomorphisms funext +open import group-theory.full-subgroups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.images-of-group-homomorphisms +open import group-theory.surjective-semigroup-homomorphisms ```
diff --git a/src/group-theory/surjective-semigroup-homomorphisms.lagda.md b/src/group-theory/surjective-semigroup-homomorphisms.lagda.md index 131c05bf24..e112844df8 100644 --- a/src/group-theory/surjective-semigroup-homomorphisms.lagda.md +++ b/src/group-theory/surjective-semigroup-homomorphisms.lagda.md @@ -1,25 +1,20 @@ # Surjective semigroup homomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.surjective-semigroup-homomorphisms - (funext : function-extensionality) - where +module group-theory.surjective-semigroup-homomorphisms where ```
Imports ```agda -open import foundation.propositions funext -open import foundation.surjective-maps funext +open import foundation.propositions +open import foundation.surjective-maps open import foundation.universe-levels -open import group-theory.full-subsemigroups funext -open import group-theory.homomorphisms-semigroups funext -open import group-theory.images-of-semigroup-homomorphisms funext -open import group-theory.semigroups funext +open import group-theory.full-subsemigroups +open import group-theory.homomorphisms-semigroups +open import group-theory.images-of-semigroup-homomorphisms +open import group-theory.semigroups ```
diff --git a/src/group-theory/symmetric-concrete-groups.lagda.md b/src/group-theory/symmetric-concrete-groups.lagda.md index aa4d03f779..006ef44e03 100644 --- a/src/group-theory/symmetric-concrete-groups.lagda.md +++ b/src/group-theory/symmetric-concrete-groups.lagda.md @@ -1,27 +1,22 @@ # Symmetric concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.symmetric-concrete-groups - (funext : function-extensionality) - where +module group-theory.symmetric-concrete-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.sets open import foundation.subtype-identity-principle open import foundation.universe-levels -open import group-theory.automorphism-groups funext -open import group-theory.concrete-groups funext +open import group-theory.automorphism-groups +open import group-theory.concrete-groups ```
diff --git a/src/group-theory/symmetric-groups.lagda.md b/src/group-theory/symmetric-groups.lagda.md index d0dbabcfb6..bb5b38be9e 100644 --- a/src/group-theory/symmetric-groups.lagda.md +++ b/src/group-theory/symmetric-groups.lagda.md @@ -1,37 +1,31 @@ # Symmetric groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.symmetric-groups - (funext : function-extensionality) - where +module group-theory.symmetric-groups where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.automorphisms funext +open import foundation.automorphisms open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-semigroups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.monoids funext -open import group-theory.opposite-groups funext -open import group-theory.semigroups funext -open import group-theory.symmetric-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-semigroups +open import group-theory.isomorphisms-groups +open import group-theory.monoids +open import group-theory.opposite-groups +open import group-theory.semigroups +open import group-theory.symmetric-concrete-groups ```
diff --git a/src/group-theory/torsion-elements-groups.lagda.md b/src/group-theory/torsion-elements-groups.lagda.md index 45e2e658ba..9b7a129185 100644 --- a/src/group-theory/torsion-elements-groups.lagda.md +++ b/src/group-theory/torsion-elements-groups.lagda.md @@ -1,29 +1,24 @@ # Torsion elements of groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.torsion-elements-groups - (funext : function-extensionality) - where +module group-theory.torsion-elements-groups where ```
Imports ```agda open import elementary-number-theory.integers -open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.nonzero-integers open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.integer-powers-of-elements-groups funext +open import group-theory.groups +open import group-theory.integer-powers-of-elements-groups ```
diff --git a/src/group-theory/torsion-free-groups.lagda.md b/src/group-theory/torsion-free-groups.lagda.md index 01a8150b3d..d7e4ed6170 100644 --- a/src/group-theory/torsion-free-groups.lagda.md +++ b/src/group-theory/torsion-free-groups.lagda.md @@ -1,39 +1,34 @@ # Torsion-free groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.torsion-free-groups - (funext : function-extensionality) - where +module group-theory.torsion-free-groups where ```
Imports ```agda -open import elementary-number-theory.group-of-integers funext -open import elementary-number-theory.nonzero-integers funext +open import elementary-number-theory.group-of-integers +open import elementary-number-theory.nonzero-integers open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.existential-quantification funext +open import foundation.equivalences +open import foundation.existential-quantification open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.singleton-subtypes funext -open import foundation.standard-pullbacks funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.singleton-subtypes +open import foundation.standard-pullbacks open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.integer-powers-of-elements-groups funext -open import group-theory.orders-of-elements-groups funext -open import group-theory.subgroups funext -open import group-theory.torsion-elements-groups funext +open import group-theory.groups +open import group-theory.integer-powers-of-elements-groups +open import group-theory.orders-of-elements-groups +open import group-theory.subgroups +open import group-theory.torsion-elements-groups ```
diff --git a/src/group-theory/torsors.lagda.md b/src/group-theory/torsors.lagda.md index feb12a47c6..0e1b1d1375 100644 --- a/src/group-theory/torsors.lagda.md +++ b/src/group-theory/torsors.lagda.md @@ -1,47 +1,42 @@ # Torsors of abstract groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.torsors - (funext : function-extensionality) - where +module group-theory.torsors where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.equivalences-group-actions funext -open import group-theory.group-actions funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.isomorphisms-groups funext -open import group-theory.mere-equivalences-group-actions funext -open import group-theory.principal-group-actions funext -open import group-theory.symmetric-groups funext - -open import higher-group-theory.higher-groups funext +open import group-theory.concrete-groups +open import group-theory.equivalences-group-actions +open import group-theory.group-actions +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.isomorphisms-groups +open import group-theory.mere-equivalences-group-actions +open import group-theory.principal-group-actions +open import group-theory.symmetric-groups + +open import higher-group-theory.higher-groups ```
diff --git a/src/group-theory/transitive-concrete-group-actions.lagda.md b/src/group-theory/transitive-concrete-group-actions.lagda.md index ff360cb51c..f6af5d47b3 100644 --- a/src/group-theory/transitive-concrete-group-actions.lagda.md +++ b/src/group-theory/transitive-concrete-group-actions.lagda.md @@ -1,37 +1,32 @@ # Transitive concrete group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.transitive-concrete-group-actions - (funext : function-extensionality) - where +module group-theory.transitive-concrete-group-actions where ```
Imports ```agda -open import foundation.1-types funext +open import foundation.1-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.universe-levels -open import group-theory.concrete-group-actions funext -open import group-theory.concrete-groups funext -open import group-theory.equivalences-concrete-group-actions funext +open import group-theory.concrete-group-actions +open import group-theory.concrete-groups +open import group-theory.equivalences-concrete-group-actions -open import higher-group-theory.transitive-higher-group-actions funext +open import higher-group-theory.transitive-higher-group-actions ```
diff --git a/src/group-theory/transitive-group-actions.lagda.md b/src/group-theory/transitive-group-actions.lagda.md index 662c6efd2d..c8513a1bf5 100644 --- a/src/group-theory/transitive-group-actions.lagda.md +++ b/src/group-theory/transitive-group-actions.lagda.md @@ -1,25 +1,20 @@ # Transitive group actions ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.transitive-group-actions - (funext : function-extensionality) - where +module group-theory.transitive-group-actions where ```
Imports ```agda -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.surjective-maps funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositions +open import foundation.surjective-maps open import foundation.universe-levels -open import group-theory.group-actions funext -open import group-theory.groups funext +open import group-theory.group-actions +open import group-theory.groups ```
diff --git a/src/group-theory/trivial-concrete-groups.lagda.md b/src/group-theory/trivial-concrete-groups.lagda.md index b138f2f6ca..5c20a531f4 100644 --- a/src/group-theory/trivial-concrete-groups.lagda.md +++ b/src/group-theory/trivial-concrete-groups.lagda.md @@ -1,28 +1,23 @@ # Trivial concrete groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.trivial-concrete-groups - (funext : function-extensionality) - where +module group-theory.trivial-concrete-groups where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import group-theory.concrete-groups funext +open import group-theory.concrete-groups -open import higher-group-theory.trivial-higher-groups funext +open import higher-group-theory.trivial-higher-groups ```
diff --git a/src/group-theory/trivial-group-homomorphisms.lagda.md b/src/group-theory/trivial-group-homomorphisms.lagda.md index 40ce202e9a..3cc3b50278 100644 --- a/src/group-theory/trivial-group-homomorphisms.lagda.md +++ b/src/group-theory/trivial-group-homomorphisms.lagda.md @@ -1,25 +1,20 @@ # Trivial group homomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.trivial-group-homomorphisms - (funext : function-extensionality) - where +module group-theory.trivial-group-homomorphisms where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext +open import group-theory.groups +open import group-theory.homomorphisms-groups ```
diff --git a/src/group-theory/trivial-groups.lagda.md b/src/group-theory/trivial-groups.lagda.md index c1170859b4..a018e83b69 100644 --- a/src/group-theory/trivial-groups.lagda.md +++ b/src/group-theory/trivial-groups.lagda.md @@ -1,33 +1,28 @@ # Trivial groups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.trivial-groups - (funext : function-extensionality) - where +module group-theory.trivial-groups where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.raising-universe-levels open import foundation.structure-identity-principle open import foundation.unit-type open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.full-subgroups funext -open import group-theory.groups funext -open import group-theory.subgroups funext -open import group-theory.trivial-subgroups funext +open import group-theory.abelian-groups +open import group-theory.full-subgroups +open import group-theory.groups +open import group-theory.subgroups +open import group-theory.trivial-subgroups ```
diff --git a/src/group-theory/trivial-subgroups.lagda.md b/src/group-theory/trivial-subgroups.lagda.md index 035cfcf327..e26bfde47b 100644 --- a/src/group-theory/trivial-subgroups.lagda.md +++ b/src/group-theory/trivial-subgroups.lagda.md @@ -1,23 +1,18 @@ # Trivial subgroups ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.trivial-subgroups - (funext : function-extensionality) - where +module group-theory.trivial-subgroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.subgroups funext +open import group-theory.groups +open import group-theory.subgroups ```
diff --git a/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md b/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md index 76e345d173..55ccfa28c6 100644 --- a/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/unordered-tuples-of-elements-commutative-monoids.lagda.md @@ -1,12 +1,7 @@ # Unordered tuples of elements in commutative monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.unordered-tuples-of-elements-commutative-monoids - (funext : function-extensionality) - where +module group-theory.unordered-tuples-of-elements-commutative-monoids where ```
Imports @@ -15,9 +10,9 @@ module open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import foundation.unordered-tuples funext +open import foundation.unordered-tuples -open import group-theory.commutative-monoids funext +open import group-theory.commutative-monoids ```
diff --git a/src/group-theory/wild-representations-monoids.lagda.md b/src/group-theory/wild-representations-monoids.lagda.md index e61a3803d0..153d5c80a5 100644 --- a/src/group-theory/wild-representations-monoids.lagda.md +++ b/src/group-theory/wild-representations-monoids.lagda.md @@ -1,26 +1,21 @@ # Wild representations of monoids ```agda -open import foundation.function-extensionality-axiom - -module - group-theory.wild-representations-monoids - (funext : function-extensionality) - where +module group-theory.wild-representations-monoids where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.endomorphisms funext -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.endomorphisms +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.monoids funext +open import group-theory.monoids -open import structured-types.morphisms-wild-monoids funext +open import structured-types.morphisms-wild-monoids ```
diff --git a/src/higher-group-theory.lagda.md b/src/higher-group-theory.lagda.md index 23d3cb9fdc..14d69b791a 100644 --- a/src/higher-group-theory.lagda.md +++ b/src/higher-group-theory.lagda.md @@ -3,36 +3,31 @@ ## Modules in the higher group theory namespace ```agda -open import foundation.function-extensionality-axiom +module higher-group-theory where -module - higher-group-theory - (funext : function-extensionality) - where - -open import higher-group-theory.abelian-higher-groups funext public -open import higher-group-theory.automorphism-groups funext public -open import higher-group-theory.cartesian-products-higher-groups funext public -open import higher-group-theory.conjugation funext public -open import higher-group-theory.cyclic-higher-groups funext public -open import higher-group-theory.deloopable-groups funext public -open import higher-group-theory.deloopable-h-spaces funext public -open import higher-group-theory.deloopable-types funext public -open import higher-group-theory.eilenberg-mac-lane-spaces funext public -open import higher-group-theory.equivalences-higher-groups funext public -open import higher-group-theory.fixed-points-higher-group-actions funext public -open import higher-group-theory.free-higher-group-actions funext public -open import higher-group-theory.higher-group-actions funext public -open import higher-group-theory.higher-groups funext public -open import higher-group-theory.homomorphisms-higher-group-actions funext public -open import higher-group-theory.homomorphisms-higher-groups funext public -open import higher-group-theory.integers-higher-group funext public -open import higher-group-theory.iterated-cartesian-products-higher-groups funext public -open import higher-group-theory.iterated-deloopings-of-pointed-types funext public -open import higher-group-theory.orbits-higher-group-actions funext public -open import higher-group-theory.small-higher-groups funext public -open import higher-group-theory.subgroups-higher-groups funext public -open import higher-group-theory.symmetric-higher-groups funext public -open import higher-group-theory.transitive-higher-group-actions funext public -open import higher-group-theory.trivial-higher-groups funext public +open import higher-group-theory.abelian-higher-groups public +open import higher-group-theory.automorphism-groups public +open import higher-group-theory.cartesian-products-higher-groups public +open import higher-group-theory.conjugation public +open import higher-group-theory.cyclic-higher-groups public +open import higher-group-theory.deloopable-groups public +open import higher-group-theory.deloopable-h-spaces public +open import higher-group-theory.deloopable-types public +open import higher-group-theory.eilenberg-mac-lane-spaces public +open import higher-group-theory.equivalences-higher-groups public +open import higher-group-theory.fixed-points-higher-group-actions public +open import higher-group-theory.free-higher-group-actions public +open import higher-group-theory.higher-group-actions public +open import higher-group-theory.higher-groups public +open import higher-group-theory.homomorphisms-higher-group-actions public +open import higher-group-theory.homomorphisms-higher-groups public +open import higher-group-theory.integers-higher-group public +open import higher-group-theory.iterated-cartesian-products-higher-groups public +open import higher-group-theory.iterated-deloopings-of-pointed-types public +open import higher-group-theory.orbits-higher-group-actions public +open import higher-group-theory.small-higher-groups public +open import higher-group-theory.subgroups-higher-groups public +open import higher-group-theory.symmetric-higher-groups public +open import higher-group-theory.transitive-higher-group-actions public +open import higher-group-theory.trivial-higher-groups public ``` diff --git a/src/higher-group-theory/abelian-higher-groups.lagda.md b/src/higher-group-theory/abelian-higher-groups.lagda.md index 78a688d1fc..cdfe3e08ba 100644 --- a/src/higher-group-theory/abelian-higher-groups.lagda.md +++ b/src/higher-group-theory/abelian-higher-groups.lagda.md @@ -1,31 +1,26 @@ # Abelian higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.abelian-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.abelian-higher-groups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.small-types funext +open import foundation.equivalences +open import foundation.small-types open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups funext -open import higher-group-theory.higher-groups funext -open import higher-group-theory.small-higher-groups funext +open import higher-group-theory.equivalences-higher-groups +open import higher-group-theory.higher-groups +open import higher-group-theory.small-higher-groups -open import structured-types.pointed-equivalences funext +open import structured-types.pointed-equivalences open import structured-types.pointed-types -open import structured-types.small-pointed-types funext +open import structured-types.small-pointed-types -open import synthetic-homotopy-theory.connective-spectra funext +open import synthetic-homotopy-theory.connective-spectra ```
diff --git a/src/higher-group-theory/automorphism-groups.lagda.md b/src/higher-group-theory/automorphism-groups.lagda.md index c94fe7ae18..3c2e64a205 100644 --- a/src/higher-group-theory/automorphism-groups.lagda.md +++ b/src/higher-group-theory/automorphism-groups.lagda.md @@ -1,31 +1,26 @@ # Automorphism groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.automorphism-groups - (funext : function-extensionality) - where +module higher-group-theory.automorphism-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.connected-components funext -open import foundation.contractible-types funext +open import foundation.0-connected-types +open import foundation.connected-components +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups funext -open import higher-group-theory.higher-groups funext +open import higher-group-theory.equivalences-higher-groups +open import higher-group-theory.higher-groups open import structured-types.pointed-types ``` diff --git a/src/higher-group-theory/cartesian-products-higher-groups.lagda.md b/src/higher-group-theory/cartesian-products-higher-groups.lagda.md index 9903fc84a6..2183bb2862 100644 --- a/src/higher-group-theory/cartesian-products-higher-groups.lagda.md +++ b/src/higher-group-theory/cartesian-products-higher-groups.lagda.md @@ -1,33 +1,28 @@ # Cartesian products of higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.cartesian-products-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.cartesian-products-higher-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.cartesian-product-types funext +open import foundation.0-connected-types +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.propositions open import foundation.universe-levels -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups -open import structured-types.pointed-cartesian-product-types funext +open import structured-types.pointed-cartesian-product-types open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/higher-group-theory/conjugation.lagda.md b/src/higher-group-theory/conjugation.lagda.md index 00540064f2..66e53af615 100644 --- a/src/higher-group-theory/conjugation.lagda.md +++ b/src/higher-group-theory/conjugation.lagda.md @@ -1,27 +1,22 @@ # Conjugation in higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.conjugation - (funext : function-extensionality) - where +module higher-group-theory.conjugation where ```
Imports ```agda -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import higher-group-theory.higher-groups funext -open import higher-group-theory.homomorphisms-higher-groups funext +open import higher-group-theory.higher-groups +open import higher-group-theory.homomorphisms-higher-groups -open import structured-types.conjugation-pointed-types funext +open import structured-types.conjugation-pointed-types -open import synthetic-homotopy-theory.conjugation-loops funext +open import synthetic-homotopy-theory.conjugation-loops ```
diff --git a/src/higher-group-theory/cyclic-higher-groups.lagda.md b/src/higher-group-theory/cyclic-higher-groups.lagda.md index 4a3dfc4861..d9067fb971 100644 --- a/src/higher-group-theory/cyclic-higher-groups.lagda.md +++ b/src/higher-group-theory/cyclic-higher-groups.lagda.md @@ -1,24 +1,19 @@ # Cyclic higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.cyclic-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.cyclic-higher-groups where ```
Imports ```agda -open import foundation.embeddings funext -open import foundation.existential-quantification funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.existential-quantification +open import foundation.propositions open import foundation.universe-levels -open import higher-group-theory.higher-groups funext -open import higher-group-theory.homomorphisms-higher-groups funext +open import higher-group-theory.higher-groups +open import higher-group-theory.homomorphisms-higher-groups ```
diff --git a/src/higher-group-theory/deloopable-groups.lagda.md b/src/higher-group-theory/deloopable-groups.lagda.md index 65447fd5ac..45c31edf78 100644 --- a/src/higher-group-theory/deloopable-groups.lagda.md +++ b/src/higher-group-theory/deloopable-groups.lagda.md @@ -1,12 +1,7 @@ # Deloopable groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.deloopable-groups - (funext : function-extensionality) - where +module higher-group-theory.deloopable-groups where ```
Imports @@ -15,9 +10,9 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import group-theory.groups funext +open import group-theory.groups -open import higher-group-theory.deloopable-h-spaces funext +open import higher-group-theory.deloopable-h-spaces ```
diff --git a/src/higher-group-theory/deloopable-h-spaces.lagda.md b/src/higher-group-theory/deloopable-h-spaces.lagda.md index 24138fd502..90b0d90e0c 100644 --- a/src/higher-group-theory/deloopable-h-spaces.lagda.md +++ b/src/higher-group-theory/deloopable-h-spaces.lagda.md @@ -1,12 +1,7 @@ # Deloopable H-spaces ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.deloopable-h-spaces - (funext : function-extensionality) - where +module higher-group-theory.deloopable-h-spaces where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups -open import structured-types.equivalences-h-spaces funext -open import structured-types.h-spaces funext +open import structured-types.equivalences-h-spaces +open import structured-types.h-spaces ```
diff --git a/src/higher-group-theory/deloopable-types.lagda.md b/src/higher-group-theory/deloopable-types.lagda.md index 5b090c33f6..23e7bac773 100644 --- a/src/higher-group-theory/deloopable-types.lagda.md +++ b/src/higher-group-theory/deloopable-types.lagda.md @@ -1,29 +1,24 @@ # Deloopable types ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.deloopable-types - (funext : function-extensionality) - where +module higher-group-theory.deloopable-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.small-types funext +open import foundation.equivalences +open import foundation.small-types open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups funext -open import higher-group-theory.higher-groups funext -open import higher-group-theory.small-higher-groups funext +open import higher-group-theory.equivalences-higher-groups +open import higher-group-theory.higher-groups +open import higher-group-theory.small-higher-groups -open import structured-types.pointed-equivalences funext +open import structured-types.pointed-equivalences open import structured-types.pointed-types -open import structured-types.small-pointed-types funext +open import structured-types.small-pointed-types ```
diff --git a/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md b/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md index 574ce2d003..13a8cf9fab 100644 --- a/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md +++ b/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md @@ -1,12 +1,7 @@ # Eilenberg-Mac Lane spaces ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.eilenberg-mac-lane-spaces - (funext : function-extensionality) - where +module higher-group-theory.eilenberg-mac-lane-spaces where ```
Imports @@ -14,22 +9,22 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types funext -open import foundation.cartesian-product-types funext -open import foundation.connected-types funext -open import foundation.truncated-types funext +open import foundation.0-connected-types +open import foundation.cartesian-product-types +open import foundation.connected-types +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext +open import group-theory.abelian-groups +open import group-theory.groups -open import structured-types.equivalences-h-spaces funext -open import structured-types.pointed-equivalences funext +open import structured-types.equivalences-h-spaces +open import structured-types.pointed-equivalences open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-loop-spaces funext -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.iterated-loop-spaces +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/higher-group-theory/equivalences-higher-groups.lagda.md b/src/higher-group-theory/equivalences-higher-groups.lagda.md index cc73889557..c494c345cf 100644 --- a/src/higher-group-theory/equivalences-higher-groups.lagda.md +++ b/src/higher-group-theory/equivalences-higher-groups.lagda.md @@ -1,35 +1,30 @@ # Equivalences of higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.equivalences-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.equivalences-higher-groups where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import higher-group-theory.higher-groups funext -open import higher-group-theory.homomorphisms-higher-groups funext +open import higher-group-theory.higher-groups +open import higher-group-theory.homomorphisms-higher-groups -open import structured-types.pointed-equivalences funext -open import structured-types.pointed-isomorphisms funext +open import structured-types.pointed-equivalences +open import structured-types.pointed-isomorphisms open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.functoriality-loop-spaces ```
diff --git a/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md b/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md index befb47ba5b..4dfdc5fb40 100644 --- a/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md +++ b/src/higher-group-theory/fixed-points-higher-group-actions.lagda.md @@ -1,12 +1,7 @@ # Fixed points of higher group actions ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.fixed-points-higher-group-actions - (funext : function-extensionality) - where +module higher-group-theory.fixed-points-higher-group-actions where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import higher-group-theory.higher-group-actions funext -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-group-actions +open import higher-group-theory.higher-groups ```
diff --git a/src/higher-group-theory/free-higher-group-actions.lagda.md b/src/higher-group-theory/free-higher-group-actions.lagda.md index b0bae655f6..ea43e3e1b2 100644 --- a/src/higher-group-theory/free-higher-group-actions.lagda.md +++ b/src/higher-group-theory/free-higher-group-actions.lagda.md @@ -1,32 +1,27 @@ # Free higher group actions ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.free-higher-group-actions - (funext : function-extensionality) - where +module higher-group-theory.free-higher-group-actions where ```
Imports ```agda -open import foundation.embeddings funext -open import foundation.identity-types funext -open import foundation.propositional-maps funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.regensburg-extension-fundamental-theorem-of-identity-types funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.identity-types +open import foundation.propositional-maps +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.regensburg-extension-fundamental-theorem-of-identity-types +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.truncation-levels open import foundation.universe-levels -open import higher-group-theory.higher-group-actions funext -open import higher-group-theory.higher-groups funext -open import higher-group-theory.orbits-higher-group-actions funext +open import higher-group-theory.higher-group-actions +open import higher-group-theory.higher-groups +open import higher-group-theory.orbits-higher-group-actions ```
diff --git a/src/higher-group-theory/higher-group-actions.lagda.md b/src/higher-group-theory/higher-group-actions.lagda.md index a08fbae8eb..67119d09c0 100644 --- a/src/higher-group-theory/higher-group-actions.lagda.md +++ b/src/higher-group-theory/higher-group-actions.lagda.md @@ -1,22 +1,17 @@ # Higher group actions ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.higher-group-actions - (funext : function-extensionality) - where +module higher-group-theory.higher-group-actions where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups ```
diff --git a/src/higher-group-theory/higher-groups.lagda.md b/src/higher-group-theory/higher-groups.lagda.md index c2f464f64e..6102d85536 100644 --- a/src/higher-group-theory/higher-groups.lagda.md +++ b/src/higher-group-theory/higher-groups.lagda.md @@ -1,33 +1,28 @@ # Higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.higher-groups - (funext : function-extensionality) - where +module higher-group-theory.higher-groups where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.full-subtypes funext -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.full-subtypes +open import foundation.identity-types +open import foundation.images +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import structured-types.h-spaces funext +open import structured-types.h-spaces open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md b/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md index d522aa80ca..5929ab0dbc 100644 --- a/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md +++ b/src/higher-group-theory/homomorphisms-higher-group-actions.lagda.md @@ -1,28 +1,22 @@ # Homomorphisms of higher group actions ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.homomorphisms-higher-group-actions - (funext : function-extensionality) - where +module higher-group-theory.homomorphisms-higher-group-actions where ```
Imports ```agda -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.homotopies +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.higher-group-actions funext -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-group-actions +open import higher-group-theory.higher-groups ```
diff --git a/src/higher-group-theory/homomorphisms-higher-groups.lagda.md b/src/higher-group-theory/homomorphisms-higher-groups.lagda.md index 2b2aae3694..cd94013ef2 100644 --- a/src/higher-group-theory/homomorphisms-higher-groups.lagda.md +++ b/src/higher-group-theory/homomorphisms-higher-groups.lagda.md @@ -1,27 +1,22 @@ # Homomorphisms of higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.homomorphisms-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.homomorphisms-higher-groups where ```
Imports ```agda -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps -open import synthetic-homotopy-theory.functoriality-loop-spaces funext +open import synthetic-homotopy-theory.functoriality-loop-spaces ```
diff --git a/src/higher-group-theory/integers-higher-group.lagda.md b/src/higher-group-theory/integers-higher-group.lagda.md index 15af00e242..7220677f16 100644 --- a/src/higher-group-theory/integers-higher-group.lagda.md +++ b/src/higher-group-theory/integers-higher-group.lagda.md @@ -1,12 +1,7 @@ # The higher group of integers ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.integers-higher-group - (funext : function-extensionality) - where +module higher-group-theory.integers-higher-group where ```
Imports @@ -15,11 +10,11 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types -open import synthetic-homotopy-theory.circle funext +open import synthetic-homotopy-theory.circle ```
diff --git a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md index 261d2a7c94..d8ae507260 100644 --- a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md +++ b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md @@ -1,12 +1,7 @@ # Iterated cartesian products of higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.iterated-cartesian-products-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.iterated-cartesian-products-higher-groups where ```
Imports @@ -14,31 +9,31 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.0-connected-types +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.iterated-cartesian-product-types funext -open import foundation.mere-equality funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.iterated-cartesian-product-types +open import foundation.mere-equality +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import higher-group-theory.cartesian-products-higher-groups funext -open import higher-group-theory.higher-groups funext -open import higher-group-theory.trivial-higher-groups funext +open import higher-group-theory.cartesian-products-higher-groups +open import higher-group-theory.higher-groups +open import higher-group-theory.trivial-higher-groups open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md b/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md index b854b63b88..d5f051b7fd 100644 --- a/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md +++ b/src/higher-group-theory/iterated-deloopings-of-pointed-types.lagda.md @@ -1,12 +1,7 @@ # Iterated deloopings of pointed types ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.iterated-deloopings-of-pointed-types - (funext : function-extensionality) - where +module higher-group-theory.iterated-deloopings-of-pointed-types where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.connected-types funext +open import foundation.cartesian-product-types +open import foundation.connected-types open import foundation.dependent-pair-types open import foundation.truncation-levels open import foundation.universe-levels -open import structured-types.pointed-equivalences funext +open import structured-types.pointed-equivalences open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-loop-spaces funext +open import synthetic-homotopy-theory.iterated-loop-spaces ```
diff --git a/src/higher-group-theory/orbits-higher-group-actions.lagda.md b/src/higher-group-theory/orbits-higher-group-actions.lagda.md index 68e9932188..69003ac59b 100644 --- a/src/higher-group-theory/orbits-higher-group-actions.lagda.md +++ b/src/higher-group-theory/orbits-higher-group-actions.lagda.md @@ -1,12 +1,7 @@ # Orbits of higher group actions ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.orbits-higher-group-actions - (funext : function-extensionality) - where +module higher-group-theory.orbits-higher-group-actions where ```
Imports @@ -15,8 +10,8 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import higher-group-theory.higher-group-actions funext -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-group-actions +open import higher-group-theory.higher-groups ```
diff --git a/src/higher-group-theory/small-higher-groups.lagda.md b/src/higher-group-theory/small-higher-groups.lagda.md index 9443afbd5f..0252d1093d 100644 --- a/src/higher-group-theory/small-higher-groups.lagda.md +++ b/src/higher-group-theory/small-higher-groups.lagda.md @@ -1,37 +1,32 @@ # Small ∞-groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.small-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.small-higher-groups where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.locally-small-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.replacement funext -open import foundation.small-types funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.images +open import foundation.locally-small-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.replacement +open import foundation.small-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels -open import higher-group-theory.equivalences-higher-groups funext -open import higher-group-theory.higher-groups funext +open import higher-group-theory.equivalences-higher-groups +open import higher-group-theory.higher-groups -open import structured-types.pointed-equivalences funext +open import structured-types.pointed-equivalences open import structured-types.pointed-types -open import structured-types.small-pointed-types funext +open import structured-types.small-pointed-types ```
diff --git a/src/higher-group-theory/subgroups-higher-groups.lagda.md b/src/higher-group-theory/subgroups-higher-groups.lagda.md index f0a3239346..14e6b1ebce 100644 --- a/src/higher-group-theory/subgroups-higher-groups.lagda.md +++ b/src/higher-group-theory/subgroups-higher-groups.lagda.md @@ -1,25 +1,20 @@ # Subgroups of higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.subgroups-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.subgroups-higher-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.cartesian-product-types funext +open import foundation.0-connected-types +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.sets open import foundation.universe-levels -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types ``` diff --git a/src/higher-group-theory/symmetric-higher-groups.lagda.md b/src/higher-group-theory/symmetric-higher-groups.lagda.md index 0dcec903bf..9af7adc4fe 100644 --- a/src/higher-group-theory/symmetric-higher-groups.lagda.md +++ b/src/higher-group-theory/symmetric-higher-groups.lagda.md @@ -1,24 +1,19 @@ # Symmetric higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.symmetric-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.symmetric-higher-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.connected-components-universes funext +open import foundation.0-connected-types +open import foundation.connected-components-universes open import foundation.dependent-pair-types -open import foundation.mere-equivalences funext +open import foundation.mere-equivalences open import foundation.universe-levels -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types ``` diff --git a/src/higher-group-theory/transitive-higher-group-actions.lagda.md b/src/higher-group-theory/transitive-higher-group-actions.lagda.md index 9592ad6059..a6a4b3f711 100644 --- a/src/higher-group-theory/transitive-higher-group-actions.lagda.md +++ b/src/higher-group-theory/transitive-higher-group-actions.lagda.md @@ -1,31 +1,26 @@ # Transitive higher group actions ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.transitive-higher-group-actions - (funext : function-extensionality) - where +module higher-group-theory.transitive-higher-group-actions where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.regensburg-extension-fundamental-theorem-of-identity-types funext -open import foundation.surjective-maps funext +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.regensburg-extension-fundamental-theorem-of-identity-types +open import foundation.surjective-maps open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.higher-group-actions funext -open import higher-group-theory.higher-groups funext -open import higher-group-theory.orbits-higher-group-actions funext +open import higher-group-theory.higher-group-actions +open import higher-group-theory.higher-groups +open import higher-group-theory.orbits-higher-group-actions ```
diff --git a/src/higher-group-theory/trivial-higher-groups.lagda.md b/src/higher-group-theory/trivial-higher-groups.lagda.md index 7ec887a0f5..32e453fac8 100644 --- a/src/higher-group-theory/trivial-higher-groups.lagda.md +++ b/src/higher-group-theory/trivial-higher-groups.lagda.md @@ -1,26 +1,21 @@ # Trivial higher groups ```agda -open import foundation.function-extensionality-axiom - -module - higher-group-theory.trivial-higher-groups - (funext : function-extensionality) - where +module higher-group-theory.trivial-higher-groups where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.contractible-types funext +open import foundation.0-connected-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups ```
diff --git a/src/linear-algebra.lagda.md b/src/linear-algebra.lagda.md index 55f66bbd51..883be1c3fa 100644 --- a/src/linear-algebra.lagda.md +++ b/src/linear-algebra.lagda.md @@ -3,29 +3,24 @@ ## Modules in the linear algebra namespace ```agda -open import foundation.function-extensionality-axiom +module linear-algebra where -module - linear-algebra - (funext : function-extensionality) - where - -open import linear-algebra.constant-matrices funext public -open import linear-algebra.constant-vectors funext public -open import linear-algebra.diagonal-matrices-on-rings funext public -open import linear-algebra.functoriality-matrices funext public -open import linear-algebra.functoriality-vectors funext public -open import linear-algebra.matrices funext public -open import linear-algebra.matrices-on-rings funext public +open import linear-algebra.constant-matrices public +open import linear-algebra.constant-vectors public +open import linear-algebra.diagonal-matrices-on-rings public +open import linear-algebra.functoriality-matrices public +open import linear-algebra.functoriality-vectors public +open import linear-algebra.matrices public +open import linear-algebra.matrices-on-rings public open import linear-algebra.multiplication-matrices public -open import linear-algebra.scalar-multiplication-matrices funext public -open import linear-algebra.scalar-multiplication-vectors funext public -open import linear-algebra.scalar-multiplication-vectors-on-rings funext public -open import linear-algebra.transposition-matrices funext public -open import linear-algebra.vectors funext public -open import linear-algebra.vectors-on-commutative-rings funext public -open import linear-algebra.vectors-on-commutative-semirings funext public -open import linear-algebra.vectors-on-euclidean-domains funext public -open import linear-algebra.vectors-on-rings funext public -open import linear-algebra.vectors-on-semirings funext public +open import linear-algebra.scalar-multiplication-matrices public +open import linear-algebra.scalar-multiplication-vectors public +open import linear-algebra.scalar-multiplication-vectors-on-rings public +open import linear-algebra.transposition-matrices public +open import linear-algebra.vectors public +open import linear-algebra.vectors-on-commutative-rings public +open import linear-algebra.vectors-on-commutative-semirings public +open import linear-algebra.vectors-on-euclidean-domains public +open import linear-algebra.vectors-on-rings public +open import linear-algebra.vectors-on-semirings public ``` diff --git a/src/linear-algebra/constant-matrices.lagda.md b/src/linear-algebra/constant-matrices.lagda.md index 0025604aa4..03b95489d8 100644 --- a/src/linear-algebra/constant-matrices.lagda.md +++ b/src/linear-algebra/constant-matrices.lagda.md @@ -1,12 +1,7 @@ # Constant matrices ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.constant-matrices - (funext : function-extensionality) - where +module linear-algebra.constant-matrices where ```
Imports @@ -16,8 +11,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.constant-vectors funext -open import linear-algebra.matrices funext +open import linear-algebra.constant-vectors +open import linear-algebra.matrices ```
diff --git a/src/linear-algebra/constant-vectors.lagda.md b/src/linear-algebra/constant-vectors.lagda.md index e55194a3f4..11b8372bc9 100644 --- a/src/linear-algebra/constant-vectors.lagda.md +++ b/src/linear-algebra/constant-vectors.lagda.md @@ -1,12 +1,7 @@ # Diagonal vectors ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.constant-vectors - (funext : function-extensionality) - where +module linear-algebra.constant-vectors where ```
Imports @@ -16,7 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors ```
diff --git a/src/linear-algebra/diagonal-matrices-on-rings.lagda.md b/src/linear-algebra/diagonal-matrices-on-rings.lagda.md index 5983c684dd..c15d89761a 100644 --- a/src/linear-algebra/diagonal-matrices-on-rings.lagda.md +++ b/src/linear-algebra/diagonal-matrices-on-rings.lagda.md @@ -1,12 +1,7 @@ # Diagonal matrices on rings ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.diagonal-matrices-on-rings - (funext : function-extensionality) - where +module linear-algebra.diagonal-matrices-on-rings where ```
Imports @@ -16,13 +11,13 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.constant-vectors funext -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.matrices-on-rings funext -open import linear-algebra.vectors funext -open import linear-algebra.vectors funext-on-rings +open import linear-algebra.constant-vectors +open import linear-algebra.functoriality-vectors +open import linear-algebra.matrices-on-rings +open import linear-algebra.vectors +open import linear-algebra.vectors-on-rings -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/linear-algebra/functoriality-matrices.lagda.md b/src/linear-algebra/functoriality-matrices.lagda.md index 88f49cc229..1c0b419bd0 100644 --- a/src/linear-algebra/functoriality-matrices.lagda.md +++ b/src/linear-algebra/functoriality-matrices.lagda.md @@ -1,12 +1,7 @@ # Functoriality of the type of matrices ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.functoriality-matrices - (funext : function-extensionality) - where +module linear-algebra.functoriality-matrices where ```
Imports @@ -16,8 +11,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.matrices funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.matrices ```
diff --git a/src/linear-algebra/functoriality-vectors.lagda.md b/src/linear-algebra/functoriality-vectors.lagda.md index 1c89cf7c4f..021cff9837 100644 --- a/src/linear-algebra/functoriality-vectors.lagda.md +++ b/src/linear-algebra/functoriality-vectors.lagda.md @@ -1,12 +1,7 @@ # Functoriality of the type of vectors ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.functoriality-vectors - (funext : function-extensionality) - where +module linear-algebra.functoriality-vectors where ```
Imports @@ -16,15 +11,15 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.postcomposition-functions open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/linear-algebra/matrices-on-rings.lagda.md b/src/linear-algebra/matrices-on-rings.lagda.md index 606dc31e5e..e14bfa5210 100644 --- a/src/linear-algebra/matrices-on-rings.lagda.md +++ b/src/linear-algebra/matrices-on-rings.lagda.md @@ -1,12 +1,7 @@ # Matrices on rings ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.matrices-on-rings - (funext : function-extensionality) - where +module linear-algebra.matrices-on-rings where ```
Imports @@ -15,16 +10,16 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.constant-matrices funext -open import linear-algebra.functoriality-matrices funext -open import linear-algebra.matrices funext -open import linear-algebra.vectors funext -open import linear-algebra.vectors funext-on-rings +open import linear-algebra.constant-matrices +open import linear-algebra.functoriality-matrices +open import linear-algebra.matrices +open import linear-algebra.vectors +open import linear-algebra.vectors-on-rings -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/linear-algebra/matrices.lagda.md b/src/linear-algebra/matrices.lagda.md index 48e1ccd5a7..f95efc19d8 100644 --- a/src/linear-algebra/matrices.lagda.md +++ b/src/linear-algebra/matrices.lagda.md @@ -1,12 +1,7 @@ # Matrices ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.matrices - (funext : function-extensionality) - where +module linear-algebra.matrices where ```
Imports @@ -15,13 +10,13 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors ```
diff --git a/src/linear-algebra/scalar-multiplication-matrices.lagda.md b/src/linear-algebra/scalar-multiplication-matrices.lagda.md index ffc8eaa057..460f312973 100644 --- a/src/linear-algebra/scalar-multiplication-matrices.lagda.md +++ b/src/linear-algebra/scalar-multiplication-matrices.lagda.md @@ -1,12 +1,7 @@ # Scalar multiplication on matrices ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.scalar-multiplication-matrices - (funext : function-extensionality) - where +module linear-algebra.scalar-multiplication-matrices where ```
Imports @@ -16,8 +11,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.matrices funext -open import linear-algebra.scalar-multiplication-vectors funext +open import linear-algebra.matrices +open import linear-algebra.scalar-multiplication-vectors ```
diff --git a/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md b/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md index 795bd5e2a7..b4d616f839 100644 --- a/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md +++ b/src/linear-algebra/scalar-multiplication-vectors-on-rings.lagda.md @@ -1,12 +1,7 @@ # Scalar multiplication of vectors on rings ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.scalar-multiplication-vectors-on-rings - (funext : function-extensionality) - where +module linear-algebra.scalar-multiplication-vectors-on-rings where ```
Imports @@ -16,18 +11,18 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.endomorphism-rings-abelian-groups funext -open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.endomorphism-rings-abelian-groups +open import group-theory.homomorphisms-abelian-groups -open import linear-algebra.vectors funext -open import linear-algebra.vectors funext-on-rings +open import linear-algebra.vectors +open import linear-algebra.vectors-on-rings -open import ring-theory.homomorphisms-rings funext -open import ring-theory.modules-rings funext -open import ring-theory.rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.modules-rings +open import ring-theory.rings ```
diff --git a/src/linear-algebra/scalar-multiplication-vectors.lagda.md b/src/linear-algebra/scalar-multiplication-vectors.lagda.md index e86ec48a77..b6f55dd1cd 100644 --- a/src/linear-algebra/scalar-multiplication-vectors.lagda.md +++ b/src/linear-algebra/scalar-multiplication-vectors.lagda.md @@ -1,12 +1,7 @@ # Scalar multiplication of vectors ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.scalar-multiplication-vectors - (funext : function-extensionality) - where +module linear-algebra.scalar-multiplication-vectors where ```
Imports @@ -16,8 +11,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors ```
diff --git a/src/linear-algebra/transposition-matrices.lagda.md b/src/linear-algebra/transposition-matrices.lagda.md index c391e5f214..c46fe91ff2 100644 --- a/src/linear-algebra/transposition-matrices.lagda.md +++ b/src/linear-algebra/transposition-matrices.lagda.md @@ -1,12 +1,7 @@ # Transposition of matrices ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.transposition-matrices - (funext : function-extensionality) - where +module linear-algebra.transposition-matrices where ```
Imports @@ -16,12 +11,12 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.matrices funext -open import linear-algebra.vectors funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.matrices +open import linear-algebra.vectors ```
diff --git a/src/linear-algebra/vectors-on-commutative-rings.lagda.md b/src/linear-algebra/vectors-on-commutative-rings.lagda.md index 1c3e1e2eee..83724fd171 100644 --- a/src/linear-algebra/vectors-on-commutative-rings.lagda.md +++ b/src/linear-algebra/vectors-on-commutative-rings.lagda.md @@ -1,30 +1,25 @@ # Vectors on commutative rings ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.vectors-on-commutative-rings - (funext : function-extensionality) - where +module linear-algebra.vectors-on-commutative-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.commutative-monoids +open import group-theory.monoids +open import group-theory.semigroups -open import linear-algebra.constant-vectors funext -open import linear-algebra.vectors-on-rings funext +open import linear-algebra.constant-vectors +open import linear-algebra.vectors-on-rings ```
diff --git a/src/linear-algebra/vectors-on-commutative-semirings.lagda.md b/src/linear-algebra/vectors-on-commutative-semirings.lagda.md index 63053b91d4..37cfe9c5b2 100644 --- a/src/linear-algebra/vectors-on-commutative-semirings.lagda.md +++ b/src/linear-algebra/vectors-on-commutative-semirings.lagda.md @@ -1,30 +1,25 @@ # Vectors on commutative semirings ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.vectors-on-commutative-semirings - (funext : function-extensionality) - where +module linear-algebra.vectors-on-commutative-semirings where ```
Imports ```agda -open import commutative-algebra.commutative-semirings funext +open import commutative-algebra.commutative-semirings open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.commutative-monoids +open import group-theory.monoids +open import group-theory.semigroups -open import linear-algebra.constant-vectors funext -open import linear-algebra.vectors-on-semirings funext +open import linear-algebra.constant-vectors +open import linear-algebra.vectors-on-semirings ```
diff --git a/src/linear-algebra/vectors-on-euclidean-domains.lagda.md b/src/linear-algebra/vectors-on-euclidean-domains.lagda.md index 39fad1bf18..63019ac835 100644 --- a/src/linear-algebra/vectors-on-euclidean-domains.lagda.md +++ b/src/linear-algebra/vectors-on-euclidean-domains.lagda.md @@ -1,38 +1,32 @@ # Vectors on euclidean domains ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.vectors-on-euclidean-domains - (funext : function-extensionality) - where +module linear-algebra.vectors-on-euclidean-domains where ```
Imports ```agda -open import commutative-algebra.euclidean-domains funext +open import commutative-algebra.euclidean-domains open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext +open import foundation.function-extensionality +open import foundation.identity-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import linear-algebra.constant-vectors funext -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.constant-vectors +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors ```
diff --git a/src/linear-algebra/vectors-on-rings.lagda.md b/src/linear-algebra/vectors-on-rings.lagda.md index 1cd2806ae8..fbeb4ee829 100644 --- a/src/linear-algebra/vectors-on-rings.lagda.md +++ b/src/linear-algebra/vectors-on-rings.lagda.md @@ -1,12 +1,7 @@ # Vectors on rings ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.vectors-on-rings - (funext : function-extensionality) - where +module linear-algebra.vectors-on-rings where ```
Imports @@ -16,23 +11,22 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext +open import foundation.function-extensionality +open import foundation.identity-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import linear-algebra.constant-vectors funext -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.constant-vectors +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/linear-algebra/vectors-on-semirings.lagda.md b/src/linear-algebra/vectors-on-semirings.lagda.md index 9736c97e98..c66387088a 100644 --- a/src/linear-algebra/vectors-on-semirings.lagda.md +++ b/src/linear-algebra/vectors-on-semirings.lagda.md @@ -1,12 +1,7 @@ # Vectors on semirings ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.vectors-on-semirings - (funext : function-extensionality) - where +module linear-algebra.vectors-on-semirings where ```
Imports @@ -16,20 +11,19 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext +open import foundation.function-extensionality +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.commutative-monoids +open import group-theory.monoids +open import group-theory.semigroups -open import linear-algebra.constant-vectors funext -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.constant-vectors +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/linear-algebra/vectors.lagda.md b/src/linear-algebra/vectors.lagda.md index 4d7ecc8350..4a6be035b9 100644 --- a/src/linear-algebra/vectors.lagda.md +++ b/src/linear-algebra/vectors.lagda.md @@ -1,12 +1,7 @@ # Vectors ```agda -open import foundation.function-extensionality-axiom - -module - linear-algebra.vectors - (funext : function-extensionality) - where +module linear-algebra.vectors where ```
Imports @@ -15,30 +10,30 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type -open import foundation.sets funext +open import foundation.dependent-products-truncated-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type +open import foundation.sets open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import univalent-combinatorics.involution-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.involution-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/lists.lagda.md b/src/lists.lagda.md index 14cd2e5402..612d0e6270 100644 --- a/src/lists.lagda.md +++ b/src/lists.lagda.md @@ -3,30 +3,25 @@ ## Modules in the lists namespace ```agda -open import foundation.function-extensionality-axiom +module lists where -module - lists - (funext : function-extensionality) - where - -open import lists.arrays funext public -open import lists.concatenation-lists funext public -open import lists.equality-lists funext public -open import lists.flattening-lists funext public -open import lists.functoriality-lists funext public +open import lists.arrays public +open import lists.concatenation-lists public +open import lists.equality-lists public +open import lists.flattening-lists public +open import lists.functoriality-lists public open import lists.lists public -open import lists.lists-discrete-types funext public -open import lists.permutation-lists funext public -open import lists.permutation-vectors funext public -open import lists.predicates-on-lists funext public -open import lists.quicksort-lists funext public -open import lists.reversing-lists funext public -open import lists.sort-by-insertion-lists funext public -open import lists.sort-by-insertion-vectors funext public -open import lists.sorted-lists funext public -open import lists.sorted-vectors funext public -open import lists.sorting-algorithms-lists funext public -open import lists.sorting-algorithms-vectors funext public -open import lists.universal-property-lists-wild-monoids funext public +open import lists.lists-discrete-types public +open import lists.permutation-lists public +open import lists.permutation-vectors public +open import lists.predicates-on-lists public +open import lists.quicksort-lists public +open import lists.reversing-lists public +open import lists.sort-by-insertion-lists public +open import lists.sort-by-insertion-vectors public +open import lists.sorted-lists public +open import lists.sorted-vectors public +open import lists.sorting-algorithms-lists public +open import lists.sorting-algorithms-vectors public +open import lists.universal-property-lists-wild-monoids public ``` diff --git a/src/lists/arrays.lagda.md b/src/lists/arrays.lagda.md index 573d6784f1..054ea39af4 100644 --- a/src/lists/arrays.lagda.md +++ b/src/lists/arrays.lagda.md @@ -1,12 +1,7 @@ # Arrays ```agda -open import foundation.function-extensionality-axiom - -module - lists.arrays - (funext : function-extensionality) - where +module lists.arrays where ```
Imports @@ -15,24 +10,24 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors open import lists.lists -open import univalent-combinatorics.involution-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.involution-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/lists/concatenation-lists.lagda.md b/src/lists/concatenation-lists.lagda.md index a093dd4793..3471f3bcc5 100644 --- a/src/lists/concatenation-lists.lagda.md +++ b/src/lists/concatenation-lists.lagda.md @@ -1,12 +1,7 @@ # Concatenation of lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.concatenation-lists - (funext : function-extensionality) - where +module lists.concatenation-lists where ```
Imports @@ -17,14 +12,14 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.monoids funext +open import group-theory.monoids -open import lists.equality-lists funext +open import lists.equality-lists open import lists.lists ``` diff --git a/src/lists/equality-lists.lagda.md b/src/lists/equality-lists.lagda.md index ff2997e650..b2345f4801 100644 --- a/src/lists/equality-lists.lagda.md +++ b/src/lists/equality-lists.lagda.md @@ -1,12 +1,7 @@ # Equality of lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.equality-lists - (funext : function-extensionality) - where +module lists.equality-lists where ```
Imports @@ -14,23 +9,23 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.negation funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type -open import foundation.sets funext -open import foundation.torsorial-type-families funext -open import foundation.truncated-types funext +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.negation +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type +open import foundation.sets +open import foundation.torsorial-type-families +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels diff --git a/src/lists/flattening-lists.lagda.md b/src/lists/flattening-lists.lagda.md index 2e28302871..3534e0b657 100644 --- a/src/lists/flattening-lists.lagda.md +++ b/src/lists/flattening-lists.lagda.md @@ -1,26 +1,21 @@ # Flattening of lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.flattening-lists - (funext : function-extensionality) - where +module lists.flattening-lists where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.sums-of-natural-numbers funext +open import elementary-number-theory.sums-of-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import lists.concatenation-lists funext -open import lists.functoriality-lists funext +open import lists.concatenation-lists +open import lists.functoriality-lists open import lists.lists ``` diff --git a/src/lists/functoriality-lists.lagda.md b/src/lists/functoriality-lists.lagda.md index a4e7f0ee73..233992c6a0 100644 --- a/src/lists/functoriality-lists.lagda.md +++ b/src/lists/functoriality-lists.lagda.md @@ -1,36 +1,31 @@ # Functoriality of the list operation ```agda -open import foundation.function-extensionality-axiom - -module - lists.functoriality-lists - (funext : function-extensionality) - where +module lists.functoriality-lists where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equality-dependent-pair-types +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors -open import lists.arrays funext -open import lists.concatenation-lists funext -open import lists.equality-lists funext +open import lists.arrays +open import lists.concatenation-lists +open import lists.equality-lists open import lists.lists ``` diff --git a/src/lists/lists-discrete-types.lagda.md b/src/lists/lists-discrete-types.lagda.md index ca6bc9d44e..64cecc520a 100644 --- a/src/lists/lists-discrete-types.lagda.md +++ b/src/lists/lists-discrete-types.lagda.md @@ -1,32 +1,27 @@ # Lists of elements in discrete types ```agda -open import foundation.function-extensionality-axiom - -module - lists.lists-discrete-types - (funext : function-extensionality) - where +module lists.lists-discrete-types where ```
Imports ```agda -open import foundation.booleans funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.booleans +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import lists.equality-lists funext +open import lists.equality-lists open import lists.lists ``` diff --git a/src/lists/permutation-lists.lagda.md b/src/lists/permutation-lists.lagda.md index f9ed68f56f..26ca630086 100644 --- a/src/lists/permutation-lists.lagda.md +++ b/src/lists/permutation-lists.lagda.md @@ -1,37 +1,32 @@ # Permutations of lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.permutation-lists - (funext : function-extensionality) - where +module lists.permutation-lists where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors -open import lists.arrays funext -open import lists.functoriality-lists funext +open import lists.arrays +open import lists.functoriality-lists open import lists.lists -open import lists.permutation-vectors funext +open import lists.permutation-vectors ```
diff --git a/src/lists/permutation-vectors.lagda.md b/src/lists/permutation-vectors.lagda.md index ab3e646a0c..4099f1bfe0 100644 --- a/src/lists/permutation-vectors.lagda.md +++ b/src/lists/permutation-vectors.lagda.md @@ -1,12 +1,7 @@ # Permutations of vectors ```agda -open import foundation.function-extensionality-axiom - -module - lists.permutation-vectors - (funext : function-extensionality) - where +module lists.permutation-vectors where ```
Imports @@ -14,29 +9,29 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext -open import finite-group-theory.transpositions-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.transpositions-standard-finite-types open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.negated-equality open import foundation.transport-along-identifications open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors -open import lists.arrays funext +open import lists.arrays open import lists.lists -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/lists/predicates-on-lists.lagda.md b/src/lists/predicates-on-lists.lagda.md index 9b30b6df8f..69fb45c9a5 100644 --- a/src/lists/predicates-on-lists.lagda.md +++ b/src/lists/predicates-on-lists.lagda.md @@ -1,19 +1,14 @@ # Predicates on lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.predicates-on-lists - (funext : function-extensionality) - where +module lists.predicates-on-lists where ```
Imports ```agda -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels diff --git a/src/lists/quicksort-lists.lagda.md b/src/lists/quicksort-lists.lagda.md index 55b3c13ade..0acbdc4224 100644 --- a/src/lists/quicksort-lists.lagda.md +++ b/src/lists/quicksort-lists.lagda.md @@ -1,30 +1,25 @@ # Quicksort for lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.quicksort-lists - (funext : function-extensionality) - where +module lists.quicksort-lists where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strong-induction-natural-numbers funext +open import elementary-number-theory.strong-induction-natural-numbers -open import foundation.coproduct-types funext -open import foundation.identity-types funext +open import foundation.coproduct-types +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import order-theory.decidable-total-orders funext +open import order-theory.decidable-total-orders ```
diff --git a/src/lists/reversing-lists.lagda.md b/src/lists/reversing-lists.lagda.md index cd09f824b3..551bed29c5 100644 --- a/src/lists/reversing-lists.lagda.md +++ b/src/lists/reversing-lists.lagda.md @@ -1,12 +1,7 @@ # Reversing lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.reversing-lists - (funext : function-extensionality) - where +module lists.reversing-lists where ```
Imports @@ -15,13 +10,13 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import lists.concatenation-lists funext -open import lists.flattening-lists funext -open import lists.functoriality-lists funext +open import lists.concatenation-lists +open import lists.flattening-lists +open import lists.functoriality-lists open import lists.lists ``` diff --git a/src/lists/sort-by-insertion-lists.lagda.md b/src/lists/sort-by-insertion-lists.lagda.md index 2882f9f99a..c14433df58 100644 --- a/src/lists/sort-by-insertion-lists.lagda.md +++ b/src/lists/sort-by-insertion-lists.lagda.md @@ -1,31 +1,26 @@ # Sort by insertion for lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.sort-by-insertion-lists - (funext : function-extensionality) - where +module lists.sort-by-insertion-lists where ```
Imports ```agda -open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import lists.arrays funext +open import lists.arrays open import lists.lists -open import lists.permutation-lists funext -open import lists.sort-by-insertion-vectors funext -open import lists.sorted-lists funext -open import lists.sorting-algorithms-lists funext +open import lists.permutation-lists +open import lists.sort-by-insertion-vectors +open import lists.sorted-lists +open import lists.sorting-algorithms-lists -open import order-theory.decidable-total-orders funext +open import order-theory.decidable-total-orders ```
diff --git a/src/lists/sort-by-insertion-vectors.lagda.md b/src/lists/sort-by-insertion-vectors.lagda.md index 968c5cfc0c..0624942846 100644 --- a/src/lists/sort-by-insertion-vectors.lagda.md +++ b/src/lists/sort-by-insertion-vectors.lagda.md @@ -1,12 +1,7 @@ # Sort by insertion for vectors ```agda -open import foundation.function-extensionality-axiom - -module - lists.sort-by-insertion-vectors - (funext : function-extensionality) - where +module lists.sort-by-insertion-vectors where ```
Imports @@ -14,27 +9,27 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext -open import finite-group-theory.transpositions-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types +open import finite-group-theory.transpositions-standard-finite-types open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.equivalences +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import lists.permutation-vectors funext -open import lists.sorted-vectors funext -open import lists.sorting-algorithms-vectors funext +open import lists.permutation-vectors +open import lists.sorted-vectors +open import lists.sorting-algorithms-vectors -open import order-theory.decidable-total-orders funext +open import order-theory.decidable-total-orders ```
diff --git a/src/lists/sorted-lists.lagda.md b/src/lists/sorted-lists.lagda.md index 9b78e228d3..fb82aebedd 100644 --- a/src/lists/sorted-lists.lagda.md +++ b/src/lists/sorted-lists.lagda.md @@ -1,12 +1,7 @@ # Sorted lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.sorted-lists - (funext : function-extensionality) - where +module lists.sorted-lists where ```
Imports @@ -15,18 +10,18 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import lists.arrays funext +open import lists.arrays open import lists.lists -open import lists.sorted-vectors funext +open import lists.sorted-vectors -open import order-theory.decidable-total-orders funext +open import order-theory.decidable-total-orders ```
diff --git a/src/lists/sorted-vectors.lagda.md b/src/lists/sorted-vectors.lagda.md index 50783db037..0aeb41d303 100644 --- a/src/lists/sorted-vectors.lagda.md +++ b/src/lists/sorted-vectors.lagda.md @@ -1,12 +1,7 @@ # Sorted vectors ```agda -open import foundation.function-extensionality-axiom - -module - lists.sorted-vectors - (funext : function-extensionality) - where +module lists.sorted-vectors where ```
Imports @@ -14,24 +9,24 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import lists.permutation-vectors funext +open import lists.permutation-vectors -open import order-theory.decidable-total-orders funext +open import order-theory.decidable-total-orders -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/lists/sorting-algorithms-lists.lagda.md b/src/lists/sorting-algorithms-lists.lagda.md index 72c6fb4ecc..14b5f6541e 100644 --- a/src/lists/sorting-algorithms-lists.lagda.md +++ b/src/lists/sorting-algorithms-lists.lagda.md @@ -1,12 +1,7 @@ # Sorting algorithms for lists ```agda -open import foundation.function-extensionality-axiom - -module - lists.sorting-algorithms-lists - (funext : function-extensionality) - where +module lists.sorting-algorithms-lists where ```
Imports @@ -14,22 +9,22 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import lists.arrays funext +open import lists.arrays open import lists.lists -open import lists.permutation-lists funext -open import lists.sorted-lists funext -open import lists.sorting-algorithms-vectors funext +open import lists.permutation-lists +open import lists.sorted-lists +open import lists.sorting-algorithms-vectors -open import order-theory.decidable-total-orders funext +open import order-theory.decidable-total-orders ```
diff --git a/src/lists/sorting-algorithms-vectors.lagda.md b/src/lists/sorting-algorithms-vectors.lagda.md index 2126ed7c65..029591d5fb 100644 --- a/src/lists/sorting-algorithms-vectors.lagda.md +++ b/src/lists/sorting-algorithms-vectors.lagda.md @@ -1,12 +1,7 @@ # Sorting algorithms for vectors ```agda -open import foundation.function-extensionality-axiom - -module - lists.sorting-algorithms-vectors - (funext : function-extensionality) - where +module lists.sorting-algorithms-vectors where ```
Imports @@ -14,19 +9,19 @@ module ```agda open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import lists.permutation-vectors funext -open import lists.sorted-vectors funext +open import lists.permutation-vectors +open import lists.sorted-vectors -open import order-theory.decidable-total-orders funext +open import order-theory.decidable-total-orders ```
diff --git a/src/lists/universal-property-lists-wild-monoids.lagda.md b/src/lists/universal-property-lists-wild-monoids.lagda.md index 37cd520af5..67c4735fec 100644 --- a/src/lists/universal-property-lists-wild-monoids.lagda.md +++ b/src/lists/universal-property-lists-wild-monoids.lagda.md @@ -1,12 +1,7 @@ # The universal property of lists with respect to wild monoids ```agda -open import foundation.function-extensionality-axiom - -module - lists.universal-property-lists-wild-monoids - (funext : function-extensionality) - where +module lists.universal-property-lists-wild-monoids where ```
Imports @@ -14,22 +9,22 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition -open import group-theory.homomorphisms-semigroups funext +open import group-theory.homomorphisms-semigroups -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import structured-types.h-spaces funext -open import structured-types.morphisms-h-spaces funext -open import structured-types.morphisms-wild-monoids funext -open import structured-types.pointed-maps funext +open import structured-types.h-spaces +open import structured-types.morphisms-h-spaces +open import structured-types.morphisms-wild-monoids +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.wild-monoids funext +open import structured-types.wild-monoids ```
diff --git a/src/literature.lagda.md b/src/literature.lagda.md index 3d35112637..97fa876ae4 100644 --- a/src/literature.lagda.md +++ b/src/literature.lagda.md @@ -7,19 +7,14 @@ ## Modules in the literature namespace ```agda -open import foundation.function-extensionality-axiom +module literature where -module - literature - (funext : function-extensionality) - where - -open import literature.100-theorems funext public -open import literature.1000plus-theorems funext public -open import literature.idempotents-in-intensional-type-theory funext public -open import literature.introduction-to-homotopy-type-theory funext public -open import literature.oeis funext public -open import literature.sequential-colimits-in-homotopy-type-theory funext public +open import literature.100-theorems public +open import literature.1000plus-theorems public +open import literature.idempotents-in-intensional-type-theory public +open import literature.introduction-to-homotopy-type-theory public +open import literature.oeis public +open import literature.sequential-colimits-in-homotopy-type-theory public ``` ## References diff --git a/src/literature/100-theorems.lagda.md b/src/literature/100-theorems.lagda.md index e7bf258f14..a7891c065f 100644 --- a/src/literature/100-theorems.lagda.md +++ b/src/literature/100-theorems.lagda.md @@ -6,12 +6,7 @@ This file records formalized results from {{#cite 100theorems}} ```agda -open import foundation.function-extensionality-axiom - -module - literature.100-theorems - (funext : function-extensionality) - where +module literature.100-theorems where ``` ## The list @@ -21,7 +16,7 @@ module **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import elementary-number-theory.rational-numbers funext using +open import elementary-number-theory.rational-numbers using ( is-countable-ℚ) ``` @@ -30,7 +25,7 @@ open import elementary-number-theory.rational-numbers funext using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import elementary-number-theory.infinitude-of-primes funext using +open import elementary-number-theory.infinitude-of-primes using ( infinitude-of-primes-ℕ) ``` @@ -45,7 +40,7 @@ hence we refer to the generalization as the Cantor-Schröder-Bernstein-Escardó theorem. ```agda -open import foundation.cantor-schroder-bernstein-escardo funext using +open import foundation.cantor-schroder-bernstein-escardo using ( Cantor-Schröder-Bernstein-Escardó ; Cantor-Schröder-Bernstein) ``` @@ -55,17 +50,17 @@ open import foundation.cantor-schroder-bernstein-escardo funext using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import commutative-algebra.binomial-theorem-commutative-rings funext using +open import commutative-algebra.binomial-theorem-commutative-rings using ( binomial-theorem-Commutative-Ring) -open import commutative-algebra.binomial-theorem-commutative-semirings funext using +open import commutative-algebra.binomial-theorem-commutative-semirings using ( binomial-theorem-Commutative-Semiring) -open import ring-theory.binomial-theorem-rings funext using +open import ring-theory.binomial-theorem-rings using ( binomial-theorem-Ring) -open import ring-theory.binomial-theorem-semirings funext using +open import ring-theory.binomial-theorem-semirings using ( binomial-theorem-Semiring) -open import elementary-number-theory.binomial-theorem-integers funext using +open import elementary-number-theory.binomial-theorem-integers using ( binomial-theorem-ℤ) -open import elementary-number-theory.binomial-theorem-natural-numbers funext using +open import elementary-number-theory.binomial-theorem-natural-numbers using ( binomial-theorem-ℕ) ``` @@ -74,7 +69,7 @@ open import elementary-number-theory.binomial-theorem-natural-numbers funext usi **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import univalent-combinatorics.decidable-subtypes funext using +open import univalent-combinatorics.decidable-subtypes using ( number-of-elements-decidable-subtype-is-finite) ``` @@ -83,7 +78,7 @@ open import univalent-combinatorics.decidable-subtypes funext using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import univalent-combinatorics.binomial-types funext using +open import univalent-combinatorics.binomial-types using ( has-cardinality-binomial-type) ``` @@ -96,9 +91,9 @@ while the linked theorems are formalizations of Bezout's lemma, even though these are different statements. ```agda -open import elementary-number-theory.bezouts-lemma-integers funext using +open import elementary-number-theory.bezouts-lemma-integers using ( bezouts-lemma-ℤ) -open import elementary-number-theory.bezouts-lemma-natural-numbers funext using +open import elementary-number-theory.bezouts-lemma-natural-numbers using ( bezouts-lemma-ℕ) ``` @@ -107,7 +102,7 @@ open import elementary-number-theory.bezouts-lemma-natural-numbers funext using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.cantors-theorem funext using +open import foundation.cantors-theorem using ( theorem-Cantor) ``` @@ -117,7 +112,7 @@ open import foundation.cantors-theorem funext using ```agda open import - elementary-number-theory.greatest-common-divisor-natural-numbers funext using + elementary-number-theory.greatest-common-divisor-natural-numbers using ( GCD-ℕ) ``` @@ -135,7 +130,7 @@ open import elementary-number-theory.natural-numbers using **Author:** [Victor Blanchi](https://github.com/VictorBlanchi) ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic funext using +open import elementary-number-theory.fundamental-theorem-of-arithmetic using ( fundamental-theorem-arithmetic-list-ℕ) ``` @@ -144,7 +139,7 @@ open import elementary-number-theory.fundamental-theorem-of-arithmetic funext us **Author:** [malarbol](https://github.com/malarbol) ```agda -open import real-numbers.metric-space-of-real-numbers funext using +open import real-numbers.metric-space-of-real-numbers using ( is-triangular-premetric-leq-ℝ) ``` diff --git a/src/literature/1000plus-theorems.lagda.md b/src/literature/1000plus-theorems.lagda.md index a8d7e1e978..2257a9effc 100644 --- a/src/literature/1000plus-theorems.lagda.md +++ b/src/literature/1000plus-theorems.lagda.md @@ -9,12 +9,7 @@ theorems in mathematics that have their own Wikipedia entry. We welcome any contribution to this list! ```agda -open import foundation.function-extensionality-axiom - -module - literature.1000plus-theorems - (funext : function-extensionality) - where +module literature.1000plus-theorems where ``` ## Formalized theorems @@ -26,9 +21,9 @@ The theorems are ordered alphabetically, omitting definite articles ("the"). **Author:** [Bryan Lu](https://blu-bird.github.io) ```agda -open import elementary-number-theory.bezouts-lemma-integers funext using +open import elementary-number-theory.bezouts-lemma-integers using ( bezouts-lemma-ℤ) -open import elementary-number-theory.bezouts-lemma-natural-numbers funext using +open import elementary-number-theory.bezouts-lemma-natural-numbers using ( bezouts-lemma-ℕ) ``` @@ -37,17 +32,17 @@ open import elementary-number-theory.bezouts-lemma-natural-numbers funext using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import commutative-algebra.binomial-theorem-commutative-rings funext using +open import commutative-algebra.binomial-theorem-commutative-rings using ( binomial-theorem-Commutative-Ring) -open import commutative-algebra.binomial-theorem-commutative-semirings funext using +open import commutative-algebra.binomial-theorem-commutative-semirings using ( binomial-theorem-Commutative-Semiring) -open import ring-theory.binomial-theorem-rings funext using +open import ring-theory.binomial-theorem-rings using ( binomial-theorem-Ring) -open import ring-theory.binomial-theorem-semirings funext using +open import ring-theory.binomial-theorem-semirings using ( binomial-theorem-Semiring) -open import elementary-number-theory.binomial-theorem-integers funext using +open import elementary-number-theory.binomial-theorem-integers using ( binomial-theorem-ℤ) -open import elementary-number-theory.binomial-theorem-natural-numbers funext using +open import elementary-number-theory.binomial-theorem-natural-numbers using ( binomial-theorem-ℕ) ``` @@ -62,7 +57,7 @@ hence we refer to the generalization as the Cantor-Schröder-Bernstein-Escardó theorem. ```agda -open import foundation.cantor-schroder-bernstein-escardo funext using +open import foundation.cantor-schroder-bernstein-escardo using ( Cantor-Schröder-Bernstein-Escardó ; Cantor-Schröder-Bernstein) ``` @@ -72,7 +67,7 @@ open import foundation.cantor-schroder-bernstein-escardo funext using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.cantors-theorem funext using +open import foundation.cantors-theorem using ( theorem-Cantor) ``` @@ -81,7 +76,7 @@ open import foundation.cantors-theorem funext using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import group-theory.cayleys-theorem funext using +open import group-theory.cayleys-theorem using ( Cayleys-theorem) ``` @@ -90,7 +85,7 @@ open import group-theory.cayleys-theorem funext using **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import foundation.diaconescus-theorem funext using +open import foundation.diaconescus-theorem using ( theorem-Diaconescu) ``` @@ -99,7 +94,7 @@ open import foundation.diaconescus-theorem funext using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import elementary-number-theory.infinitude-of-primes funext using +open import elementary-number-theory.infinitude-of-primes using ( infinitude-of-primes-ℕ) ``` @@ -108,7 +103,7 @@ open import elementary-number-theory.infinitude-of-primes funext using **Author:** [Victor Blanchi](https://github.com/VictorBlanchi) ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic funext using +open import elementary-number-theory.fundamental-theorem-of-arithmetic using ( fundamental-theorem-arithmetic-list-ℕ) ``` @@ -117,7 +112,7 @@ open import elementary-number-theory.fundamental-theorem-of-arithmetic funext us **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.fundamental-theorem-of-equivalence-relations funext using +open import foundation.fundamental-theorem-of-equivalence-relations using ( equiv-equivalence-relation-partition) ``` @@ -126,10 +121,10 @@ open import foundation.fundamental-theorem-of-equivalence-relations funext using **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import domain-theory.kleenes-fixed-point-theorem-posets funext using +open import domain-theory.kleenes-fixed-point-theorem-posets using ( is-least-fixed-point-theorem-kleene-hom-Poset ; is-least-fixed-point-theorem-kleene-Poset) -open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets funext using +open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets using ( is-least-fixed-point-theorem-kleene-hom-ω-Complete-Poset ; is-least-fixed-point-theorem-kleene-ω-Complete-Poset) ``` @@ -139,7 +134,7 @@ open import domain-theory.kleenes-fixed-point-theorem-omega-complete-posets fune **Author:** [Fredrik Bakke](https://www.ntnu.edu/employees/fredrik.bakke) ```agda -open import order-theory.knaster-tarski-fixed-point-theorem funext using +open import order-theory.knaster-tarski-fixed-point-theorem using ( least-fixed-point-knaster-tarski-Inflattice ; greatest-fixed-point-knaster-tarski-Suplattice) ``` @@ -149,7 +144,7 @@ open import order-theory.knaster-tarski-fixed-point-theorem funext using **Author:** [Egbert Rijke](https://egbertrijke.github.io) ```agda -open import foundation.lawveres-fixed-point-theorem funext using +open import foundation.lawveres-fixed-point-theorem using ( fixed-point-theorem-Lawvere) ``` @@ -158,9 +153,9 @@ open import foundation.lawveres-fixed-point-theorem funext using **Author:** [Emily Riehl](https://emilyriehl.github.io/) ```agda -open import category-theory.yoneda-lemma-categories funext using +open import category-theory.yoneda-lemma-categories using ( lemma-yoneda-Category) -open import category-theory.yoneda-lemma-precategories funext using +open import category-theory.yoneda-lemma-precategories using ( lemma-yoneda-Precategory) ``` diff --git a/src/literature/idempotents-in-intensional-type-theory.lagda.md b/src/literature/idempotents-in-intensional-type-theory.lagda.md index fe8f2d81d7..448cd6e695 100644 --- a/src/literature/idempotents-in-intensional-type-theory.lagda.md +++ b/src/literature/idempotents-in-intensional-type-theory.lagda.md @@ -4,12 +4,7 @@ This file collects references to formalization of constructions and theorems from {{#cite Shu17}}. ```agda -open import foundation.function-extensionality-axiom - -module - literature.idempotents-in-intensional-type-theory - (funext : function-extensionality) - where +module literature.idempotents-in-intensional-type-theory where ``` ## 1 Introduction @@ -18,11 +13,11 @@ The introduction section gives an introduction to the problem at hand and motivates its study in univalent foundations. ```agda -open import group-theory.groups funext using +open import group-theory.groups using ( Group ) -open import higher-group-theory.higher-groups funext using +open import higher-group-theory.higher-groups using ( ∞-Group ) ``` @@ -32,11 +27,11 @@ open import higher-group-theory.higher-groups funext using The second section introduces basic notions from homotopy type theory. ```agda -open import foundation.dependent-function-types funext -- "dependent products" +open import foundation.dependent-function-types -- "dependent products" open import foundation.dependent-pair-types -- "dependent sums" -open import foundation.identity-types funext using +open import foundation.identity-types using ( _＝_ -- "identity type, its elements are paths" ; refl -- "the canonical elements of the identity types" ; concat -- "transitivity of paths" @@ -72,7 +67,7 @@ open import foundation-core.sets using ; is-set -- all identity types are propositions ) -open import foundation.homotopies funext using +open import foundation.homotopies using ( _~_ -- "homotopy" ; nat-htpy -- "naturality of homotopies" ) @@ -83,33 +78,32 @@ given in the article: an equivalence is a function equipped with a left inverse and a right inverse. ```agda -open import foundation.equivalences funext using +open import foundation.equivalences using ( is-equiv -- "type of equivalence proofs" ; equiv -- "type of equivalences" ; is-property-is-equiv -- "the type of equivalence proofs is a mere proposition" ) -open import foundation.function-extensionality funext - using +open import foundation.function-extensionality using ( funext -- "the function extensionality axiom" ) -open import foundation.univalence funext using +open import foundation.univalence using ( equiv-eq -- "the canonical map `(A ＝ B) → (A ≃ B)`" ; univalence -- "the univalence axiom" ) -open import foundation.propositional-truncations funext using +open import foundation.propositional-truncations using ( ║_║₋₁ -- "propositional truncation" ; unit-trunc-Prop -- "the map `A → ║ A ║₋₁`" ; universal-property-trunc-Prop -- "the universal property of propositional truncation" ) -open import foundation.mere-equivalences funext using +open import foundation.mere-equivalences using ( mere-equiv -- "merely equivalent" ) -open import foundation.univalence-implies-function-extensionality funext using +open import foundation.univalence-implies-function-extensionality using ( funext-univalence -- "univalence implies function extensionality" ) @@ -133,11 +127,11 @@ We reserve the terminology "a coherent idempotent" for what in the article is referred to as "a (fully coherent) idempotent". ```agda -open import foundation.endomorphisms funext using +open import foundation.endomorphisms using ( endo -- "endofunction" ) -open import foundation.idempotent-maps funext using +open import foundation.idempotent-maps using ( is-idempotent -- "idempotency witness" ; idempotent-map -- "pre-idempotent (map)" ) @@ -146,27 +140,29 @@ open import foundation.idempotent-maps funext using **Definition 3.2.** Retracts and splittings. ```agda -open import foundation.retracts-of-types funext using +open import foundation.retracts-of-types using ( retracts -- "retracts of a type" ; retract -- "type of retracts between two types" ) -open import foundation.split-idempotent-maps funext using +open import foundation.split-idempotent-maps using ( is-split-idempotent -- "splitting of an endofunction" ) ``` **Lemma 3.3.** If $f$ has a splitting, then it is pre-idempotent. -`open import foundation.split-idempotent-maps funext using - using +```agda +open import foundation.split-idempotent-maps using ( is-idempotent-is-split-idempotent ) ``` **Lemma 3.4.** The type associated to a splitting of a map is unique up to -equivaleopen import foundation.split-idempotent-maps funext using -nt-maps using +equivalence. + +```agda +open import foundation.split-idempotent-maps using ( essentially-unique-splitting-type-is-split-idempotent ) ``` @@ -177,20 +173,25 @@ The library's preferred terminology for "a quasi-idempotent" is "a quasicoherent idempotent". ```agda -open import foundation.quasicoherently-idempotent-maps funext using +open import foundation.quasicoherently-idempotent-maps using ( is-quasicoherently-idempotent -- "the type of witnesses of quasi-idempotence" ; quasicoherently-idempotent-map -- "the type of quasi-idempotents" ) ``` -**Lemma 3.6.** If $f$ has a splitting, then it is a quasi-open import foundation.split-idempotent-maps funext using -dempotent-maps using +**Lemma 3.6.** If $f$ has a splitting, then it is a quasi-idempotent. + +```agda +open import foundation.split-idempotent-maps using ( is-quasicoherently-idempotent-is-split-idempotent ) ``` -**Theorem 3.7.** If $X$ is a set, then any pre-idempotent on $Xopen import foundation.split-idempotent-maps funext using -split-idempotent-maps using +**Theorem 3.7.** If $X$ is a set, then any pre-idempotent on $X$ has a +splitting. + +```agda +open import foundation.split-idempotent-maps using ( is-split-idempotent-is-idempotent-is-set ) ``` @@ -203,10 +204,12 @@ split-idempotent-maps using splitting. ```agda -open import foundation.weakly-constant-maps funext using +open import foundation.weakly-constant-maps using ( is-weakly-constant -- "the type of witnesses that a map is weakly constant" - ; weakly-constant-map -- "the open import foundation.split-idempotent-maps funext using -dation.split-idempotent-maps using + ; weakly-constant-map -- "the type of weakly constant maps" + ) + +open import foundation.split-idempotent-maps using ( is-split-idempotent-is-weakly-constant-is-idempotent ) ``` @@ -216,12 +219,12 @@ is an embedding if and only if it is pre-idempotent and the type $f(x) = x$ admits a weakly constant endofunction for all $x$. ```agda -open import foundation.sections funext using +open import foundation.sections using ( is-section -- "the type of witnesses that a map is a section to a map" ; section -- "the type of sections of a map" ) -open import foundation.embeddings funext using +open import foundation.embeddings using ( is-emb -- "the type of witnesses that a map is an embedding" ; _↪_ -- "the type of embeddings between two types" ) @@ -251,7 +254,7 @@ a coherent system of idempotence data. **Definition 4.2.** The Cantor space. ```agda -open import set-theory.cantor-space funext using +open import set-theory.cantor-space using ( cantor-space -- "C" ) ``` @@ -265,7 +268,7 @@ open import set-theory.cantor-space funext using **Definition 4.5.** $B\operatorname{Aut}({-})$. ```agda -open import foundation.connected-components-universes funext using +open import foundation.connected-components-universes using ( component-UU -- "BAut(-)" ) ``` @@ -297,11 +300,11 @@ quasi-idempotent map splits. Sequential colimits of types. ```agda -open import synthetic-homotopy-theory.sequential-diagrams funext using +open import synthetic-homotopy-theory.sequential-diagrams using ( sequential-diagram ) -open import synthetic-homotopy-theory.sequential-colimits funext using +open import synthetic-homotopy-theory.sequential-colimits using ( standard-sequential-colimit ) ``` @@ -309,11 +312,11 @@ open import synthetic-homotopy-theory.sequential-colimits funext using Sequential limits of types. ```agda -open import foundation.inverse-sequential-diagrams funext using +open import foundation.inverse-sequential-diagrams using ( inverse-sequential-diagram ) -open import foundation.sequential-limits funext using +open import foundation.sequential-limits using ( standard-sequential-limit ) ``` @@ -325,21 +328,25 @@ The formalization generalizes the result of the paper by considering general inverse sequential diagrams rather than those that are constantly $f$. Also note that compared to the paper, the coherences in the formalization are transposed. -`open import foundation.sequential-limits funext using - using +```agda +open import foundation.sequential-limits using ( Eq-standard-sequential-limit -- observational equality on standard sequential limits ; extensionality-standard-sequential-limit ) ``` -**Theorem 5.3.** Assuming function extensionaliopen import foundation.split-idempotent-maps funext using -rt foundation.split-idempotent-maps using +**Theorem 5.3.** Assuming function extensionality, any quasi-idempotent splits. + +```agda +open import foundation.split-idempotent-maps using ( is-split-idempotent-is-quasicoherently-idempotent ) ``` -**Remarkopen import foundation.split-idempotent-maps funext using -en import foundation.split-idempotent-maps using +**Remark 5.4.** Components of the construction. + +```agda +open import foundation.split-idempotent-maps using ( inverse-sequential-diagram-splitting-type-is-quasicoherently-idempotent' ; splitting-type-is-quasicoherently-idempotent' ; inclusion-splitting-type-is-quasicoherently-idempotent' @@ -359,8 +366,8 @@ quasi-idempotence. **Lemma 6.3.** Characterization of the identity types of retract formation. -`open import foundation.retracts-of-types funext using - using +```agda +open import foundation.retracts-of-types using ( equiv-retracts -- observational equality on retracts ; extensionality-retracts ) @@ -391,7 +398,7 @@ definition of coherently idempotent maps is given. **Definition 9.1.** (Fully coherent) idempotents. ```agda -open import foundation.coherently-idempotent-maps funext using +open import foundation.coherently-idempotent-maps using ( is-coherently-idempotent -- "type of (fully coherent) idempotence witnesses" ) ``` diff --git a/src/literature/introduction-to-homotopy-type-theory.lagda.md b/src/literature/introduction-to-homotopy-type-theory.lagda.md index b12f99d148..73694d20ac 100644 --- a/src/literature/introduction-to-homotopy-type-theory.lagda.md +++ b/src/literature/introduction-to-homotopy-type-theory.lagda.md @@ -4,12 +4,7 @@ This file collects references to formalization of constructions, propositions, theorems and exercises from {{#cite Rij22}}. ```agda -open import foundation.function-extensionality-axiom - -module - literature.introduction-to-homotopy-type-theory - (funext : function-extensionality) - where +module literature.introduction-to-homotopy-type-theory where open import foundation.universe-levels ``` @@ -42,7 +37,7 @@ open import elementary-number-theory.addition-natural-numbers using ### 3.3 Pattern matching ```agda -open import elementary-number-theory.fibonacci-sequence funext using +open import elementary-number-theory.fibonacci-sequence using ( Fibonacci-ℕ) ``` @@ -56,16 +51,16 @@ open import elementary-number-theory.multiplication-natural-numbers using ( mul-ℕ ; _*ℕ_) -- (b) -open import elementary-number-theory.exponentiation-natural-numbers funext using +open import elementary-number-theory.exponentiation-natural-numbers using ( exp-ℕ) ``` **Exercise 3.2.** Minimum and maximum. ```agda -open import elementary-number-theory.minimum-natural-numbers funext using +open import elementary-number-theory.minimum-natural-numbers using ( min-ℕ) -open import elementary-number-theory.maximum-natural-numbers funext using +open import elementary-number-theory.maximum-natural-numbers using ( max-ℕ) ``` @@ -77,14 +72,14 @@ open import elementary-number-theory.triangular-numbers using ( triangular-number-ℕ) -- (b) -open import elementary-number-theory.factorials funext using +open import elementary-number-theory.factorials using ( factorial-ℕ) ``` **Exercise 3.4.** Binomial coefficients. ```agda -open import elementary-number-theory.binomial-coefficients funext using +open import elementary-number-theory.binomial-coefficients using ( binomial-coefficient-ℕ ; is-zero-binomial-coefficient-ℕ) ``` @@ -92,8 +87,8 @@ open import elementary-number-theory.binomial-coefficients funext using **Exercise 3.5.** Fibonacci sequence using the induction principle of natural numbers. -`open import elementary-number-theory.fibonacci-sequence funext using - using +```agda +open import elementary-number-theory.fibonacci-sequence using ( Fibo) ``` @@ -108,8 +103,10 @@ div-two-pattern-match (succ-ℕ (succ-ℕ n)) = succ-ℕ (div-two-pattern-match For the definition using the induction principle, we think of iterating the swapping operation `(m, 0) ↦ (m, 1) ; (m, 1) ↦ (m + 1, 0)`, using the same -encoding of pairs with functions as the definition of the Fibonacci sequeopen import elementary-number-theory.fibonacci-sequence funext using -equence using +encoding of pairs with functions as the definition of the Fibonacci sequence. + +```agda +open import elementary-number-theory.fibonacci-sequence using ( shift-one ; shift-two) div-two-induction-step : (ℕ → ℕ) → (ℕ → ℕ) @@ -157,7 +154,7 @@ open import foundation.unit-type using **Definition 4.3.1.** The empty type. ```agda -open import foundation.empty-types funext using +open import foundation.empty-types using ( empty -- ∅ ; ind-empty ; ex-falso) @@ -166,16 +163,16 @@ open import foundation.empty-types funext using **Definition 4.3.2.** Negation of types. ```agda -open import foundation.negation funext using - open import foundation.empty-types funext using - using +open import foundation.negation using + ( ¬_) +open import foundation.empty-types using ( is-empty) ``` **Proposition 4.3.4** Contrapositives. -`open import foundation.negation funext using - using +```agda +open import foundation.negation using ( map-neg) ``` @@ -184,7 +181,7 @@ open import foundation.negation funext using **Definition 4.4.1.** Coproducts of types. ```agda -open import foundation.coproduct-types funext using +open import foundation.coproduct-types using ( _+_ ; inl ; inr @@ -195,7 +192,7 @@ open import foundation.coproduct-types funext using **Remark 4.4.2.** Coproducts of functions. ```agda -open import foundation.functoriality-coproduct-types funext using +open import foundation.functoriality-coproduct-types using ( map-coproduct -- f + g : A + B → A' + B' ) ``` @@ -203,7 +200,7 @@ open import foundation.functoriality-coproduct-types funext using **Proposition 4.4.3.** Projections from coproducts with an empty type. ```agda -open import foundation.type-arithmetic-empty-type funext using +open import foundation.type-arithmetic-empty-type using ( map-right-unit-law-coproduct-is-empty -- is-empty B → (A + B) → A ) ``` @@ -269,7 +266,7 @@ open import foundation.dependent-pair-types using **Definition 4.6.4.** The cartesian product. ```agda -open import foundation.cartesian-product-types funext using +open import foundation.cartesian-product-types using ( _×_ ; ind-product) ``` @@ -285,31 +282,35 @@ open import elementary-number-theory.integers using ( pred-ℤ) -- (b) -open import elementary-number-theory.addition-integers funext using +open import elementary-number-theory.addition-integers using ( add-ℤ) open import elementary-number-theory.integers using ( neg-ℤ) -- (c) -open import elementary-number-theory.multiplication-integers funext using +open import elementary-number-theory.multiplication-integers using ( mul-ℤ) ``` **Exercise 4.2.** Boolean negation, conjunction and disjunction. ```agda -open import foundation.booleans funext using +open import foundation.booleans using ( bool ; false ; true ; ind-bool) -open import foundation.booleans funext using - using - ( neg-open import foundation.booleans funext using -ooleans using - ( conjuopen import foundation.booleans funext using -ation.booleans using +-- (a) +open import foundation.booleans using + ( neg-bool) + +-- (b) +open import foundation.booleans using + ( conjunction-bool) + +-- (c) +open import foundation.booleans using ( disjunction-bool) ``` @@ -320,36 +321,36 @@ Note that we call bi-implications _logical equivalences_ in the library. A type `X` for which we can show `¬¬X` is called _irrefutable_. ```agda -open import foundation.logical-equivalences funext using +open import foundation.logical-equivalences using ( _↔_) -- (a) _ : {l : Level} (P : UU l) → ¬ (P × ¬ P) -_ = λ P (popen import foundation.negation funext using -egation using +_ = λ P (p , np) → np p +open import foundation.negation using ( no-fixed-points-neg -- ¬(P ↔ ¬P) ) -- (b) -open import foundation.double-negation funext using +open import foundation.double-negation using ( ¬¬_ ; intro-double-negation -- P → ¬¬P ; map-double-negation -- (P → Q) → (¬¬P → ¬¬Q) ; double-negation-extend -- (P → ¬¬Q) → (¬¬P → ¬¬Q) ) -open import foundation.double-negation funext using - using +-- (c) +open import foundation.double-negation using ( double-negation-double-negation-elim -- ¬¬(¬¬P → P) ; double-negation-Peirces-law -- ¬¬(((P → Q) → P) → P) ; double-negation-linearity-implication -- ¬¬((P → Q) + (Q → P)) ) -open import foundation.irrefutable-propositions funext using +open import foundation.irrefutable-propositions using ( is-irrefutable-is-decidable -- ¬¬(P + ¬P) ) -- (d) -open import foundation.decidable-types funext using +open import foundation.decidable-types using ( double-negation-elim-is-decidable -- (P + ¬P) → (¬¬P → P) ) @@ -365,7 +366,7 @@ _ = ( λ (p : P) → nqp (λ _ → p)) -- (e) -open import logic.double-negation-elimination funext using +open import logic.double-negation-elimination using ( double-negation-elim-neg -- ¬¬(¬ P) → P ; double-negation-elim-exp-neg-neg -- ¬¬(P → ¬¬Q) → (P → ¬¬Q) ; double-negation-elim-product @@ -380,8 +381,8 @@ _ = ( double-negation-elim-neg (¬ P)) ( double-negation-elim-neg (¬ Q)) -open import foundation.irrefutable-propositions funext using - using +-- (f) +open import foundation.irrefutable-propositions using ( is-irrefutable-product -- ¬¬A → ¬¬B → ¬¬(A × B) ) @@ -426,7 +427,7 @@ open import lists.lists using ( fold-list) -- (c) -open import lists.functoriality-lists funext using +open import lists.functoriality-lists using ( map-list) -- (d) @@ -434,21 +435,21 @@ open import lists.lists using ( length-list) -- (e) -open import elementary-number-theory.sums-of-natural-numbers funext using +open import elementary-number-theory.sums-of-natural-numbers using ( sum-list-ℕ) -open import elementary-number-theory.products-of-natural-numbers funext using +open import elementary-number-theory.products-of-natural-numbers using ( product-list-ℕ) -- (f) -open import lists.concatenation-lists funext using +open import lists.concatenation-lists using ( concat-list) -- (g) -open import lists.flattening-lists funext using +open import lists.flattening-lists using ( flatten-list) -- (h) -open import lists.reversing-lists funext using +open import lists.reversing-lists using ( reverse-list) ``` @@ -459,7 +460,7 @@ open import lists.reversing-lists funext using **Definition 5.1.1.** The identity type. ```agda -open import foundation.identity-types funext using +open import foundation.identity-types using ( _＝_ ; Id ; refl ; ind-Id) @@ -469,31 +470,39 @@ open import foundation.identity-types funext using **Definition 5.2.1.** Concatenation of identifications. -`open import foundation.identity-types funext using - using +```agda +open import foundation.identity-types using ( concat ; _∙_) ``` -**Definition 5.2.2.** Inverse operatopen import foundation.identity-types funext using -y-types using +**Definition 5.2.2.** Inverse operation. + +```agda +open import foundation.identity-types using ( inv) ``` -**Definition 5.2.4.** open import foundation.identity-types funext using -identity-types using +**Definition 5.2.4.** Associator. + +```agda +open import foundation.identity-types using ( assoc -- (p ∙ q) ∙ r = p ∙ (q ∙ r) ) ``` -**Definition 5.2.5.** Unopen import foundation.identity-types funext using -dation.identity-types using +**Definition 5.2.5.** Unit law operations. + +```agda +open import foundation.identity-types using ( left-unit -- refl ∙ p = p ; right-unit -- p ∙ refl = p ) ``` -**Definition 5.2.5.*open import foundation.identity-types funext using -rt foundation.identity-types using +**Definition 5.2.5.** Inverse law operations. + +```agda +open import foundation.identity-types using ( left-inv -- inv p ∙ p = refl ; right-inv -- p ∙ inv p = refl ) @@ -545,9 +554,9 @@ open import foundation.action-on-identifications-dependent-functions using **Proposition 5.5.1.** Contractibility of singletons. ```agda -open import foundation.torsorial-type-families funext using +open import foundation.torsorial-type-families using ( is-torsorial-Id) -open import foundation.contractible-types funext using +open import foundation.contractible-types using ( eq-is-contr') _ : {l : Level} {A : UU l} (a : A) (y : Σ A (λ x → a ＝ x)) → (a , refl) ＝ y @@ -592,15 +601,18 @@ open import elementary-number-theory.addition-natural-numbers using ### Exercises -**Exercise 5.1.** Distributivity open import foundation.identity-types funext using -en import foundation.identity-types using +**Exercise 5.1.** Distributivity of inversion over concatenation. + +```agda +open import foundation.identity-types using ( distributive-inv-concat -- inv (p ∙ q) = inv q ∙ inv p ) ``` -**Exeopen import foundation.identity-types funext using -agda -open import foundation.identity-types funext using +**Exercise 5.2.** Transposing concatenation. + +```agda +open import foundation.identity-types using ( left-transpose-eq-concat -- (p ∙ q = r) → (q = inv p ∙ r) ; right-transpose-eq-concat -- (p ∙ q = r) → (p = r ∙ inv q) ) @@ -609,12 +621,14 @@ open import foundation.identity-types funext using **Exercise 5.3.** Path lifting. ```agda -open import foundation.equality-dependent-pair-types funext using - ( eq-pair-eq-bopen import foundation.identity-types funext using -n. +open import foundation.equality-dependent-pair-types using + ( eq-pair-eq-base) +``` + +**Exercise 5.4.** Mac Lane pentagon. -`open import foundation.identity-types funext using - using +```agda +open import foundation.identity-types using ( mac-lane-pentagon) ``` @@ -662,19 +676,28 @@ open import elementary-number-theory.integers using **Exercise 5.7.** Abelian group laws for addition of integers. ```agda -open import elementary-number-theory.addition-integers funext using - using +-- (a) +open import elementary-number-theory.addition-integers using ( left-unit-law-add-ℤ -- 0 + x = x - ; right-unit-law-add-ℤ -- x + 0 = open import elementary-number-theory.addition-integers funext using -ntegers using + ; right-unit-law-add-ℤ -- x + 0 = x + ) + +-- (b) +open import elementary-number-theory.addition-integers using ( left-predecessor-law-add-ℤ -- pred x + y = pred (x + y) ; right-predecessor-law-add-ℤ -- x + pred y = pred (x + y) ; left-successor-law-add-ℤ -- succ x + y = succ (x + y) - ; right-successor-law-add-ℤ -- x + succ y = succopen import elementary-number-theory.addition-integers funext using -ition-integers using + ; right-successor-law-add-ℤ -- x + succ y = succ (x + y) + ) + +-- (c) +open import elementary-number-theory.addition-integers using ( associative-add-ℤ -- (x + y) + z = x + (y + z) - ; commutative-add-ℤ -open import elementary-number-theory.addition-integers funext using -ory.addition-integers using + ; commutative-add-ℤ -- x + y = y + x + ) + +-- (d) +open import elementary-number-theory.addition-integers using ( left-inverse-law-add-ℤ -- (-x) + x = 0 ; right-inverse-law-add-ℤ -- x + (-x) = 0 ) @@ -683,21 +706,30 @@ ory.addition-integers using **Exercise 5.8.** Ring laws for multiplication of integers. ```agda -open import elementary-number-theory.multiplication-integers funext using - using +-- (a) +open import elementary-number-theory.multiplication-integers using ( left-zero-law-mul-ℤ -- 0 * x = x ; right-zero-law-mul-ℤ -- x * 0 = x ; left-unit-law-mul-ℤ -- 1 * x = x - ; right-unit-law-mul-ℤ -- x * 1 = open import elementary-number-theory.multiplication-integers funext using -ntegers using + ; right-unit-law-mul-ℤ -- x * 1 = x + ) + +-- (b) +open import elementary-number-theory.multiplication-integers using ( left-predecessor-law-mul-ℤ' -- pred x * y = x * y - y ; right-predecessor-law-mul-ℤ' -- x * pred y = x * y - x ; left-successor-law-mul-ℤ' -- succ x * y = x * y + y - ; right-successor-law-mul-ℤ' -- x * succ y = xopen import elementary-number-theory.multiplication-integers funext using -ation-integers using + ; right-successor-law-mul-ℤ' -- x * succ y = x * y + x + ) + +-- (c) +open import elementary-number-theory.multiplication-integers using ( left-distributive-mul-add-ℤ -- x * (y + z) = x * y + x * z - ; right-distributive-mul-add-ℤ -- (x + y) * z open import elementary-number-theory.multiplication-integers funext using -ltiplication-integers using + ; right-distributive-mul-add-ℤ -- (x + y) * z = x * z + y * z + ) + +-- (d) +open import elementary-number-theory.multiplication-integers using ( associative-mul-ℤ -- (x * y) * z = x * (y * z) ; commutative-mul-ℤ -- x * y = y * x ) @@ -754,7 +786,7 @@ open import foundation.universe-levels using **Remark 6.2.4.** Inclusions into the successor universe. ```agda -open import foundation.raising-universe-levels funext using +open import foundation.raising-universe-levels using ( raise) _ : (l : Level) → UU l → UU (lsuc l) @@ -779,20 +811,22 @@ unrelated, Agda considers them equal. Other universe equalities may be found in **Definition 6.3.1.** Observational equality of ℕ. ```agda -open import elementary-number-theory.equality-natural-numbers funext using +open import elementary-number-theory.equality-natural-numbers using ( Eq-ℕ) ``` **Lemma 6.3.2.** Observational equality of ℕ is reflexive. -`open import elementary-number-theory.equality-natural-numbers funext using - using +```agda +open import elementary-number-theory.equality-natural-numbers using ( refl-Eq-ℕ) ``` **Proposition 6.3.3.** Logical equivalence of observational equality of ℕ and -identificatiopen import elementary-number-theory.equality-natural-numbers funext using -numbers using +identifications. + +```agda +open import elementary-number-theory.equality-natural-numbers using ( Eq-eq-ℕ ; eq-Eq-ℕ) @@ -885,16 +919,23 @@ open import elementary-number-theory.multiplication-natural-numbers using ) ``` -**Exercise 6.2.** Observational equality oopen import foundation.booleans funext using -t foundation.bopen import foundation.booleans funext using -n import foundation.booleans using +**Exercise 6.2.** Observational equality of booleans. + +```agda +-- (a) +open import foundation.booleans using + ( Eq-bool) + +-- (b) +open import foundation.booleans using ( Eq-eq-bool ; eq-Eq-bool) _ : (x y : bool) → (x ＝ y) ↔ Eq-bool x y -_ = open import foundation.booleans funext using -(c) -open import foundation.booleans funext using +_ = λ x y → (Eq-eq-bool , eq-Eq-bool) + +-- (c) +open import foundation.booleans using ( neq-neg-bool -- b ≠ neg-bool b ) _ : ¬ (false ＝ true) @@ -904,24 +945,31 @@ _ = neq-neg-bool false **Exercise 6.3.** Standard linear order on ℕ. ```agda -open import elementary-number-theory.inequality-natural-numbers funext using +open import elementary-number-theory.inequality-natural-numbers using ( _≤-ℕ_) -open import elementary-number-theory.inequality-natural-numbers funext using - using +-- (a) +open import elementary-number-theory.inequality-natural-numbers using ( refl-leq-ℕ ; antisymmetric-leq-ℕ - ; transitive-lopen import elementary-number-theory.inequality-natural-numbers funext using -numbers using - ( linear-leq-ℕ -- (m ≤ n) +open import elementary-number-theory.inequality-natural-numbers funext using -atural-numbers using + ; transitive-leq-ℕ) + +-- (b) +open import elementary-number-theory.inequality-natural-numbers using + ( linear-leq-ℕ -- (m ≤ n) + (n ≤ m) + ) + +-- (c) +open import elementary-number-theory.inequality-natural-numbers using ( preserves-leq-left-add-ℕ ; reflects-leq-left-add-ℕ) _ : (m n k : ℕ) → (m ≤-ℕ n) ↔ (m +ℕ k ≤-ℕ n +ℕ k) _ = - λ m n k → (preserves-leq-left-add-ℕ k m n , reflects-leopen import elementary-number-theory.inequality-natural-numbers funext using -ality-natural-numbers using + λ m n k → (preserves-leq-left-add-ℕ k m n , reflects-leq-left-add-ℕ k m n) + +-- (d) +open import elementary-number-theory.inequality-natural-numbers using ( preserves-leq-left-mul-ℕ ; reflects-order-mul-ℕ) @@ -930,10 +978,11 @@ _ = λ m n k → (preserves-leq-left-mul-ℕ (succ-ℕ k) m n , reflects-order-mul-ℕ k m n) -open import elementary-number-theory.minimum-natural-numbers funext using - using - ( is-greatest-lower-bound-min-ℕ -- (k ≤ min m n) ↔ (k ≤ m) × (k ≤ open import elementary-number-theory.maximum-natural-numbers funext using - using +-- (e) +open import elementary-number-theory.minimum-natural-numbers using + ( is-greatest-lower-bound-min-ℕ -- (k ≤ min m n) ↔ (k ≤ m) × (k ≤ n) + ) +open import elementary-number-theory.maximum-natural-numbers using ( is-least-upper-bound-max-ℕ -- (max m n ≤ k) ↔ (m ≤ k) × (n ≤ k) ) ``` @@ -941,18 +990,23 @@ open import elementary-number-theory.minimum-natural-numbers funext using **Exercise 6.4.** Standard strict order on ℕ. ```agda -open import elementary-number-theory.strict-inequality-natural-numbers funext using +open import elementary-number-theory.strict-inequality-natural-numbers using ( _<-ℕ_) -open import elementary-number-theory.strict-inequality-natural-numbers funext using - using +-- (a) +open import elementary-number-theory.strict-inequality-natural-numbers using ( anti-reflexive-le-ℕ ; antisymmetric-le-ℕ - ; transitive-open import elementary-number-theory.strict-inequality-natural-numbers funext using -numbers using + ; transitive-le-ℕ) + +-- (b) +open import elementary-number-theory.strict-inequality-natural-numbers using ( succ-le-ℕ -- n < n + 1 - ; preserves-le-succ-ℕ -- m < n → mopen import elementary-number-theory.strict-inequality-natural-numbers funext using -atural-numbers using + ; preserves-le-succ-ℕ -- m < n → m < n + 1 + ) + +-- (c) +open import elementary-number-theory.strict-inequality-natural-numbers using ( leq-succ-le-ℕ ; le-leq-succ-ℕ ; contradiction-le-ℕ @@ -968,11 +1022,11 @@ _ = λ m n → contradiction-le-ℕ m n , le-not-leq-ℕ m n **Exercise 6.5.** Distance function on ℕ. ```agda -open import elementary-number-theory.distance-natural-numbers funext using +open import elementary-number-theory.distance-natural-numbers using ( dist-ℕ) -open import elementary-number-theory.distance-natural-numbers funext using - using +-- (a) +open import elementary-number-theory.distance-natural-numbers using ( dist-eq-ℕ ; eq-dist-ℕ ; symmetric-dist-ℕ -- dist m n = dist n m @@ -982,11 +1036,16 @@ open import elementary-number-theory.distance-natural-numbers funext using _ : (m n : ℕ) → (m ＝ n) ↔ (dist-ℕ m n ＝ 0) _ = λ m n → (dist-eq-ℕ m n , eq-dist-ℕ m n) --- TOopen import elementary-number-theory.distance-natural-numbers funext using -numbers using +-- TODO: b + +-- (c) +open import elementary-number-theory.distance-natural-numbers using ( translation-invariant-dist-ℕ -- dist (a + m) (a + n) = dist m n - ; left-distributive-mul-dist-ℕ' -- dist (k * m) (k * n) = k * (dopen import elementary-number-theory.distance-natural-numbers funext using -atural-numbers using + ; left-distributive-mul-dist-ℕ' -- dist (k * m) (k * n) = k * (dist m n) + ) + +-- (d) +open import elementary-number-theory.distance-natural-numbers using ( is-additive-right-inverse-dist-ℕ -- x + dist x y = y for x ≤ y ) ``` @@ -994,7 +1053,7 @@ atural-numbers using **Exercise 6.6.** The absolute value function. ```agda -open import elementary-number-theory.absolute-value-integers funext using +open import elementary-number-theory.absolute-value-integers using ( abs-ℤ ; eq-abs-ℤ ; abs-eq-ℤ @@ -1016,21 +1075,23 @@ Note that the library's division relation uses the property `k * d = n`, as opposed to the book's `d * k = n`. ```agda -open import elementary-number-theory.divisibility-natural-numbers funext using +open import elementary-number-theory.divisibility-natural-numbers using ( div-ℕ) ``` **Example 7.1.4.** Divisibility by one. -`open import elementary-number-theory.divisibility-natural-numbers funext using - using +```agda +open import elementary-number-theory.divisibility-natural-numbers using ( div-one-ℕ -- 1 | x ) ``` **Proposition 7.1.5.** A 3-for-2 property of division. -open import elementary-number-theory.divisibility-natural-numbers funext using -numbers using + + +```agda +open import elementary-number-theory.divisibility-natural-numbers using ( div-add-ℕ -- d | x → d | y → d | (x + y) ) ``` @@ -1042,7 +1103,7 @@ The other other two claims are shown in Exercise [7.1](#exercise-7.1). **Definition 7.2.1.** Typal binary relations. ```agda -open import foundation.binary-relations funext using +open import foundation.binary-relations using ( Relation ; is-reflexive ; is-symmetric @@ -1053,20 +1114,22 @@ open import foundation.binary-relations funext using **Definition 7.2.2.** Congruence relations on ℕ. ```agda -open import elementary-number-theory.congruence-natural-numbers funext using +open import elementary-number-theory.congruence-natural-numbers using ( _≡_mod_) ``` **Example 7.2.3.** The modulus is congruent to zero. -`open import elementary-number-theory.congruence-natural-numbers funext using - using +```agda +open import elementary-number-theory.congruence-natural-numbers using ( cong-zero-ℕ -- k ≡ 0 mod k ) ``` -**Proposition 7.2.4.** Congruence modulo `k` is an equivalence relatopen import elementary-number-theory.congruence-natural-numbers funext using -numbers using +**Proposition 7.2.4.** Congruence modulo `k` is an equivalence relation. + +```agda +open import elementary-number-theory.congruence-natural-numbers using ( refl-cong-ℕ ; symmetric-cong-ℕ ; transitive-cong-ℕ) @@ -1080,7 +1143,7 @@ The point `⋆` is called `neg-one-Fin` because it represents the element `k - 1 under the inclusion into ℕ. ```agda -open import univalent-combinatorics.standard-finite-types funext using +open import univalent-combinatorics.standard-finite-types using ( Fin ; inl-Fin -- inclusion Fin k → Fin (k + 1) ; neg-one-Fin -- point Fin (k + 1) @@ -1089,19 +1152,23 @@ open import univalent-combinatorics.standard-finite-types funext using **Definition 7.3.4.** Inclusion into ℕ. -`open import univalent-combinatorics.standard-finite-types funext using - using +```agda +open import univalent-combinatorics.standard-finite-types using ( nat-Fin) ``` -**Lemma 7.3.5.** The inclusion into ℕ is bounopen import univalent-combinatorics.standard-finite-types funext using -e-types using +**Lemma 7.3.5.** The inclusion into ℕ is bounded. + +```agda +open import univalent-combinatorics.standard-finite-types using ( strict-upper-bound-nat-Fin -- ι x < k ) ``` -**Proposition 7.3.6.** The inclusion into ℕ isopen import univalent-combinatorics.standard-finite-types funext using -d-finite-types using +**Proposition 7.3.6.** The inclusion into ℕ is injective. + +```agda +open import univalent-combinatorics.standard-finite-types using ( is-injective-nat-Fin) ``` @@ -1114,8 +1181,10 @@ open import foundation.split-surjective-maps using ( is-split-surjective) ``` -**Definition 7.4.2.** Zero and successor on stanopen import univalent-combinatorics.standard-finite-types funext using -standard-finite-types using +**Definition 7.4.2.** Zero and successor on standard finite types. + +```agda +open import univalent-combinatorics.standard-finite-types using ( zero-Fin ; skip-zero-Fin ; succ-Fin) @@ -1124,34 +1193,42 @@ standard-finite-types using **Definition 7.4.3.** The surjection from ℕ into standard finite types. ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext using +open import elementary-number-theory.modular-arithmetic-standard-finite-types using ( mod-succ-ℕ -- [-]ₖ₊₁ ) ``` -**Lemma 7.4.4.** Preservation of zeopen import univalent-combinatorics.standard-finite-types funext using -torics.standard-finite-types using +**Lemma 7.4.4.** Preservation of zero and successor `mod k`. + +```agda +open import univalent-combinatorics.standard-finite-types using ( is-zero-nat-zero-Fin -- ι(zero) = 0 - ; nat-skip-zero-Fin -- ι(skip-zero x) = ι(x) +open import elementary-number-theory.modular-arithmetic-standard-finite-types funext using - using + ; nat-skip-zero-Fin -- ι(skip-zero x) = ι(x) + 1 + ) +open import elementary-number-theory.modular-arithmetic-standard-finite-types using ( cong-nat-succ-Fin -- ι(succ x) ≡ ι(x) + 1 mod k ) ``` -**Proposition 7.4.open import elementary-number-theory.modular-arithmetic-standard-finite-types funext using -e-types using +**Proposition 7.4.5.** + +```agda +open import elementary-number-theory.modular-arithmetic-standard-finite-types using ( cong-nat-mod-succ-ℕ -- ι[x]ₖ₊₁ ≡ x mod (k + 1) ) ``` -**Propositiopen import elementary-number-theory.divisibility-natural-numbers funext using -atural-numbers using +**Proposition 7.4.6.** + +```agda +open import elementary-number-theory.divisibility-natural-numbers using ( is-zero-div-ℕ ; div-is-zero-ℕ) _ : (d x : ℕ) → x <-ℕ d → div-ℕ d x ↔ (x ＝ 0) -_ = λ d x x + +```agda +open import elementary-number-theory.divisibility-natural-numbers using ( div-right-summand-ℕ -- d | x → d | x + y → d | y ; div-left-summand-ℕ -- d | y → d | x + y → d | x ) ``` -**Exercise 7.2.** Divisibopen import elementary-number-theory.divisibility-natural-numbers funext using -divisibility-natural-numbers using +**Exercise 7.2.** Divisibility is a partial order. + +```agda +open import elementary-number-theory.divisibility-natural-numbers using ( refl-div-ℕ ; antisymmetric-div-ℕ ; transitive-div-ℕ) @@ -1241,37 +1333,49 @@ divisibility-natural-numbers using **Exercise 7.3.** `n!` is divisible by all `0 < x ≤ n` -`open import elementary-number-theory.factorials funext using - using +```agda +open import elementary-number-theory.factorials using ( div-factorial-ℕ) ``` -**Exercise 7.4.** Topen import elementary-number-theory.modular-arithmetic-standard-finite-types funext using -y.modular-arithmetic-standard-finite-types using +**Exercise 7.4.** The successor on `Fin (k + 1)` adds one. + +```agda +open import elementary-number-theory.modular-arithmetic-standard-finite-types using ( is-add-one-succ-Fin') ``` **Exercise 7.5.** Observational equality of `Fin k`. ```agda -open import univalent-combinatorics.equality-standard-finite-types funext using +open import univalent-combinatorics.equality-standard-finite-types using ( Eq-Fin) -open import univalent-combinatorics.equality-standard-finite-types funext using - using +-- (a) +open import univalent-combinatorics.equality-standard-finite-types using ( Eq-Fin-eq ; eq-Eq-Fin) _ : (k : ℕ) → {x y : Fin k} → (x ＝ y) ↔ Eq-Fin k x y -_ = open import univalent-combinatorics.standard-finite-types funext using -combinatorics.standard-finiopen import univalent-combinatorics.standard-finite-types funext using -valent-combinatorics.staopen import univalent-combinatorics.standard-finite-types funext using -ort univalent-combinatorics.standard-finite-types using +_ = λ k → (Eq-Fin-eq k , eq-Eq-Fin k) + +-- (b) +open import univalent-combinatorics.standard-finite-types using + ( is-injective-inl-Fin) + +-- (c) +open import univalent-combinatorics.standard-finite-types using + ( neq-zero-succ-Fin) + +-- (d) +open import univalent-combinatorics.standard-finite-types using ( is-injective-succ-Fin) ``` -*open import univalent-combinatorics.standard-finite-types funext using -pen import univalent-combinatorics.standard-finite-types using +**Exercise 7.6.** The predecessor function on `Fin k`. + +```agda +open import univalent-combinatorics.standard-finite-types using ( neg-two-Fin ; skip-neg-two-Fin ; pred-Fin @@ -1283,18 +1387,20 @@ pen import univalent-combinatorics.standard-finite-types using **Exercise 7.7.** Classical finite types. ```agda -open import univalent-combinatorics.classical-finite-types funext using +open import univalent-combinatorics.classical-finite-types using ( classical-Fin) -open import univalent-combinatorics.classical-finite-types funext using - using +-- (a) +open import univalent-combinatorics.classical-finite-types using ( Eq-classical-Fin ; Eq-eq-classical-Fin ; eq-Eq-classical-Fin) _ : (k : ℕ) → (x y : classical-Fin k) → (x ＝ y) ↔ Eq-classical-Fin k x y -_ = λ k x y → (Eq-eq-classical-Fin k x y , eq-Eq-classical-Fin kopen import univalent-combinatorics.classical-finite-types funext using -e-types using +_ = λ k x y → (Eq-eq-classical-Fin k x y , eq-Eq-classical-Fin k x y) + +-- (b) +open import univalent-combinatorics.classical-finite-types using ( classical-standard-Fin -- ι ; standard-classical-Fin -- α ; is-section-classical-standard-Fin -- α (ι x) = x @@ -1302,13 +1408,24 @@ e-types using ) ``` -**open import elementary-number-theory.modular-arithmetic-standard-finite-types funext using -r-theory.modulopen import elementary-number-theory.modular-arithmetic-standard-finite-types funext using -y-number-theory.modular-arithmetic-standard-finite-types using - ( cong-mul-Fin -- ι(x * y) ≡open import elementary-number-theory.congruence-natural-numbers funext using -y.congruence-natural-numbers using - ( open import elementary-number-theory.modular-arithmetic-standard-finite-types funext using -ementary-number-theory.modular-arithmetic-standard-finite-types using +**Exercise 7.8.** Multiplication on `ℤ/(k + 1)`. + +```agda +open import elementary-number-theory.modular-arithmetic-standard-finite-types using + ( mul-Fin) + +-- (a) +open import elementary-number-theory.modular-arithmetic-standard-finite-types using + ( cong-mul-Fin -- ι(x * y) ≡ ι x * ι y mod (k + 1) + ) + +-- (b) +open import elementary-number-theory.congruence-natural-numbers using + ( congruence-mul-ℕ -- x ≡ x' → y ≡ y' → (x * y) ≡ (x' * y') + ) + +-- (c) +open import elementary-number-theory.modular-arithmetic-standard-finite-types using ( associative-mul-Fin -- (x * y) * z = x * (y * z) ; commutative-mul-Fin -- x * y = y * x ; left-unit-law-mul-Fin -- 1 * x = x @@ -1322,7 +1439,7 @@ ementary-number-theory.modular-arithmetic-standard-finite-types using ```agda -- (a) -open import elementary-number-theory.euclidean-division-natural-numbers funext using +open import elementary-number-theory.euclidean-division-natural-numbers using ( euclidean-division-ℕ) -- TODO: b @@ -1331,17 +1448,21 @@ open import elementary-number-theory.euclidean-division-natural-numbers funext u **Exercise 7.10.** `k`-ary natural numbers. ```agda -open import elementary-number-theory.finitary-natural-numbers funext using +open import elementary-number-theory.finitary-natural-numbers using ( based-ℕ -- ℕₖ ; convert-based-ℕ -- fₖ ) -open import elementary-number-theory.finitary-natural-numbers funext using - using - ( is-empty-based-zeopen import elementary-number-theory.finitary-natural-numbers funext using -numbers using - ( is-injective-convopen import elementary-number-theory.finitary-natural-numbers funext using -atural-numbers using +-- (a) +open import elementary-number-theory.finitary-natural-numbers using + ( is-empty-based-zero-ℕ) + +-- (b) +open import elementary-number-theory.finitary-natural-numbers using + ( is-injective-convert-based-ℕ) + +-- (c) +open import elementary-number-theory.finitary-natural-numbers using ( inv-convert-based-ℕ -- gₖ ; is-section-inv-convert-based-ℕ -- fₖ₊₁ (gₖ n) = n ; is-retraction-inv-convert-based-ℕ -- gₖ (fₖ₊₁ x) = x @@ -1354,19 +1475,23 @@ atural-numbers using **Definition 8.1.1.** Decidable types. -`open import foundation.decidable-types funext using - using +```agda +open import foundation.decidable-types using ( is-decidable) ``` -**Example 8.1.2.** The unit type and the empty type are decidopen import foundation.decidable-types funext using -e-types using +**Example 8.1.2.** The unit type and the empty type are decidable + +```agda +open import foundation.decidable-types using ( is-decidable-unit ; is-decidable-empty) ``` -**Example 8.1.3.** Decidability of coproducts, products andopen import foundation.decidable-types funext using -ecidable-types using +**Example 8.1.3.** Decidability of coproducts, products and functions. + +```agda +open import foundation.decidable-types using ( is-decidable-coproduct -- if A and B are decidable, then A + B is decidable ; is-decidable-product -- if A and B are decidable, then A × B is decidable ; is-decidable-function-type -- if A and B are decidable, then A → B is decidable @@ -1374,35 +1499,51 @@ ecidable-types using ) ``` -**Example 8.1.4.** Decidability of observational equality and inequopen import elementary-number-theory.equality-natural-numbers funext using -atural-nuopen import elementary-number-theory.inequality-natural-numbers funext using -y.inequality-natural-numbers usopen import elementary-number-theory.strict-inequality-natural-numbers funext using -ality-natural-numbers using +**Example 8.1.4.** Decidability of observational equality and inequality on ℕ. + +```agda +open import elementary-number-theory.equality-natural-numbers using + ( is-decidable-Eq-ℕ) +open import elementary-number-theory.inequality-natural-numbers using + ( is-decidable-leq-ℕ) +open import elementary-number-theory.strict-inequality-natural-numbers using ( is-decidable-le-ℕ) ``` **Definition 8.1.5.** Decidable equality. ```agda -open import foundation.decidable-equality funext using +open import foundation.decidable-equality using ( has-decidable-equality) ``` -**Lemma 8.1.6.** Decidability of logically equivalent types is logopen import foundation.decidable-types funext using -ation.decidable-types using +**Lemma 8.1.6.** Decidability of logically equivalent types is logically +equivalent. + +```agda +open import foundation.decidable-types using ( is-decidable-iff') ``` -**Proposition 8.1.7.** Equality open import elementary-number-theory.equality-natural-numbers funext using -ality-natural-numbers using +**Proposition 8.1.7.** Equality on ℕ is decidable. + +```agda +open import elementary-number-theory.equality-natural-numbers using ( has-decidable-equality-ℕ) ``` -**Proposition 8.1.8.** Equality on `Fin k` is decidaopen import univalent-combinatorics.equality-standard-finite-types funext using -e-types using +**Proposition 8.1.8.** Equality on `Fin k` is decidable. + +```agda +open import univalent-combinatorics.equality-standard-finite-types using ( is-decidable-Eq-Fin - ; has-decidabopen import elementary-number-theory.modular-arithmetic-standard-finite-types funext using -port elementary-number-theory.modular-arithmetic-standard-finite-types using + ; has-decidable-equality-Fin) +``` + +**Theorem 8.1.9.** Divisibility is decidable. + +```agda +open import elementary-number-theory.modular-arithmetic-standard-finite-types using ( is-decidable-div-ℕ) ``` @@ -1415,12 +1556,15 @@ Instead we use Agda's `with` abstraction to do case analysis on the result of `is-decidable-div-ℕ 2 n`, as explained in Remark 8.2.2. ```agda -open import elementary-number-theory.collatz-conjecture funext using +open import elementary-number-theory.collatz-conjecture using ( collatz) ``` -**Proposition 8.2.3.** Decidability of products and function typesopen import foundation.decidable-types funext using -t foundation.decidable-types using +**Proposition 8.2.3.** Decidability of products and function types with weaker +assumptions. + +```agda +open import foundation.decidable-types using ( is-decidable-product' ; is-decidable-function-type') ``` @@ -1428,14 +1572,14 @@ t foundation.decidable-types using **Proposition 8.2.4.** ```agda -open import elementary-number-theory.decidable-types funext using +open import elementary-number-theory.decidable-types using ( is-decidable-Π-ℕ) ``` **Corollary 8.2.5.** -`open import elementary-number-theory.decidable-types funext using - using +```agda +open import elementary-number-theory.decidable-types using ( is-decidable-bounded-Π-ℕ) ``` @@ -1444,18 +1588,18 @@ open import elementary-number-theory.decidable-types funext using **Definition 8.3.1.** Bounds for families over ℕ. ```agda -open import elementary-number-theory.lower-bounds-natural-numbers funext using +open import elementary-number-theory.lower-bounds-natural-numbers using ( is-lower-bound-ℕ) -open import elementary-number-theory.upper-bounds-natural-numbers funext using +open import elementary-number-theory.upper-bounds-natural-numbers using ( is-upper-bound-ℕ) -open import elementary-number-theory.well-ordering-principle-natural-numbers funext using +open import elementary-number-theory.well-ordering-principle-natural-numbers using ( minimal-element-ℕ) ``` **Theorem 8.3.2.** Well-ordering principle of ℕ. -`open import elementary-number-theory.well-ordering-principle-natural-numbers funext using - using +```agda +open import elementary-number-theory.well-ordering-principle-natural-numbers using ( well-ordering-principle-ℕ) ``` @@ -1464,39 +1608,49 @@ open import elementary-number-theory.well-ordering-principle-natural-numbers fun **Definition 8.4.1.** The type of greatest common divisors. ```agda -open import elementary-number-theory.greatest-common-divisor-natural-numbers funext using +open import elementary-number-theory.greatest-common-divisor-natural-numbers using ( is-gcd-ℕ) ``` **Proposition 8.4.2.** Uniqueness of the greatest common divisor. -`open import elementary-number-theory.greatest-common-divisor-natural-numbers funext using - using +```agda +open import elementary-number-theory.greatest-common-divisor-natural-numbers using ( uniqueness-is-gcd-ℕ) ``` -**Definition 8.4.3.** Multiples of the greatest common diviopen import elementary-number-theory.greatest-common-divisor-natural-numbers funext using -numbers using +**Definition 8.4.3.** Multiples of the greatest common divisor. + +```agda +open import elementary-number-theory.greatest-common-divisor-natural-numbers using ( is-multiple-of-gcd-ℕ) ``` -**Proposition 8.4.4.** Decidability of multiples of the greatest commopen import elementary-number-theory.greatest-common-divisor-natural-numbers funext using -atural-numbers using +**Proposition 8.4.4.** Decidability of multiples of the greatest common divisor. + +```agda +open import elementary-number-theory.greatest-common-divisor-natural-numbers using ( is-decidable-is-multiple-of-gcd-ℕ) ``` -**Lemma 8.4.5.** `a + b` is a multipopen import elementary-number-theory.greatest-common-divisor-natural-numbers funext using -visor-natural-numbers using +**Lemma 8.4.5.** `a + b` is a multiple of `gcd(a, b)`. + +```agda +open import elementary-number-theory.greatest-common-divisor-natural-numbers using ( sum-is-multiple-of-gcd-ℕ) ``` -**Definition 8.4.6.** Theopen import elementary-number-theory.greatest-common-divisor-natural-numbers funext using -mmon-divisor-natural-numbers using +**Definition 8.4.6.** The greatest common divisor. + +```agda +open import elementary-number-theory.greatest-common-divisor-natural-numbers using ( gcd-ℕ) ``` -**Lemma 8.4.7.** `gcd(a, b)` is open import elementary-number-theory.greatest-common-divisor-natural-numbers funext using -test-common-divisor-natural-numbers using +**Lemma 8.4.7.** `gcd(a, b)` is zero if and only if `a + b` = 0. + +```agda +open import elementary-number-theory.greatest-common-divisor-natural-numbers using ( is-zero-gcd-ℕ ; is-zero-add-is-zero-gcd-ℕ) @@ -1504,8 +1658,10 @@ _ : (a b : ℕ) → (gcd-ℕ a b ＝ 0) ↔ (add-ℕ a b ＝ 0) _ = λ a b → (is-zero-add-is-zero-gcd-ℕ a b , is-zero-gcd-ℕ a b) ``` -**Theorem 8.4.8.** `gopen import elementary-number-theory.greatest-common-divisor-natural-numbers funext using -ry.greatest-common-divisor-natural-numbers using +**Theorem 8.4.8.** `gcd(a, b)` is a greatest common divisor. + +```agda +open import elementary-number-theory.greatest-common-divisor-natural-numbers using ( is-gcd-gcd-ℕ) ``` @@ -1514,42 +1670,44 @@ ry.greatest-common-divisor-natural-numbers using **Definition 8.5.1.** Proper divisors and primes. ```agda -open import elementary-number-theory.proper-divisors-natural-numbers funext using +open import elementary-number-theory.proper-divisors-natural-numbers using ( is-proper-divisor-ℕ) -open import elementary-number-theory.prime-numbers funext using +open import elementary-number-theory.prime-numbers using ( is-prime-ℕ) ``` **Proposition 8.5.2.** Being a prime is decidable. -`open import elementary-number-theory.prime-numbers funext using - using +```agda +open import elementary-number-theory.prime-numbers using ( is-decidable-is-prime-ℕ) ``` **Definition 8.5.3.** Sieve of Erathostenes. ```agda -open import elementary-number-theory.sieve-of-eratosthenes funext using +open import elementary-number-theory.sieve-of-eratosthenes using ( in-sieve-of-eratosthenes-ℕ) ``` **Lemma 8.5.4.** Being in the sieve of Erathostenes is decidable. -`open import elementary-number-theory.sieve-of-eratosthenes funext using - using +```agda +open import elementary-number-theory.sieve-of-eratosthenes using ( is-decidable-in-sieve-of-eratosthenes-ℕ) ``` -**Lemma 8.5.5.** `n! + 1` is above `n` in the siopen import elementary-number-theory.sieve-of-eratosthenes funext using -sthenes using +**Lemma 8.5.5.** `n! + 1` is above `n` in the sieve. + +```agda +open import elementary-number-theory.sieve-of-eratosthenes using ( in-sieve-of-eratosthenes-succ-factorial-ℕ) ``` **Theorem 8.5.6.** Infinitude of primes. ```agda -open import elementary-number-theory.infinitude-of-primes funext using +open import elementary-number-theory.infinitude-of-primes using ( infinitude-of-primes-ℕ) ``` @@ -1558,14 +1716,14 @@ open import elementary-number-theory.infinitude-of-primes funext using **Definition 8.6.1.** Booleanization. ```agda -open import reflection.boolean-reflection funext using +open import reflection.boolean-reflection using ( booleanization) ``` **Theorem 8.6.2.** Boolean reflection principle. -`open import reflection.boolean-reflection funext using - using +```agda +open import reflection.boolean-reflection using ( boolean-reflection -- reflect ) @@ -1579,20 +1737,22 @@ _ = boolean-reflection (is-decidable-is-prime-ℕ 37) refl ```agda -- (a) -open import elementary-number-theory.goldbach-conjecture funext using +open import elementary-number-theory.goldbach-conjecture using ( Goldbach-conjecture) -- (b) -open import elementary-number-theory.twin-prime-conjecture funext using +open import elementary-number-theory.twin-prime-conjecture using ( twin-prime-conjecture) -open import elementary-number-theory.collatz-conjecture funext using - using +-- (c) +open import elementary-number-theory.collatz-conjecture using ( Collatz-conjecture) ``` -**Exercise 8.2.open import foundation.decidable-types funext using -n import foundation.decidable-types using +**Exercise 8.2.** `is-decidable` is idempotent. + +```agda +open import foundation.decidable-types using ( idempotent-is-decidable -- is-decidable (is-decidable P) → is-decidable P ) ``` @@ -1600,15 +1760,15 @@ n import foundation.decidable-types using **Exercise 8.3.** Markov's principle over finite types. ```agda -open import elementary-number-theory.well-ordering-principle-standard-finite-types funext using +open import elementary-number-theory.well-ordering-principle-standard-finite-types using ( exists-not-not-for-all-Fin -- ¬((x : Fin k) → P x) → Σ (x : Fin k) ¬(P x) ) ``` **Exercise 8.4.** Prime functions. -`open import elementary-number-theory.infinitude-of-primes funext using - using +```agda +open import elementary-number-theory.infinitude-of-primes using ( prime-ℕ -- n-th prime ; prime-counting-ℕ -- number of primes less than or equal `n` ) @@ -1621,8 +1781,8 @@ TODO **Exercise 8.6.** Products have decidable equality if and only if factors have decidable equality, assuming the other factor is pointed. -`open import foundation.decidable-equality funext using - using +```agda +open import foundation.decidable-equality using ( has-decidable-equality-product' ; has-decidable-equality-left-factor ; has-decidable-equality-right-factor) @@ -1635,8 +1795,9 @@ _ = ( λ (eqA , eqB) → has-decidable-equality-product' eqA eqB) , ( λ eqAB → has-decidable-equality-left-factor eqAB , - has-decidable-equality-right-open import foundation.decidable-equality funext using -quality using + has-decidable-equality-right-factor eqAB) + +open import foundation.decidable-equality using ( has-decidable-equality-product) ``` @@ -1648,19 +1809,21 @@ and `B : 𝒱` aren't assumed to be in the same universe, then we need to raise identity type of `A`, the identity type of `B`, and the empty type to `𝒰 ⊔ 𝒱`. ```agda -open import foundation.equality-coproduct-types funext using +open import foundation.equality-coproduct-types using ( Eq-coproduct) -open import foundation.equality-coproduct-types funext using - using +-- (a) +open import foundation.equality-coproduct-types using ( Eq-eq-coproduct ; eq-Eq-coproduct) _ : {l1 l2 : Level} {A : UU l1} {B : UU l2} → (x y : A + B) → (x ＝ y) ↔ Eq-coproduct x y -_ = λ x y → (Eq-eq-coproduct x y , eq-Eq-coopen import foundation.decidable-equality funext using -dable-equality using +_ = λ x y → (Eq-eq-coproduct x y , eq-Eq-coproduct x y) + +-- (b) +open import foundation.decidable-equality using ( has-decidable-equality-coproduct ; has-decidable-equality-left-summand ; has-decidable-equality-right-summand) @@ -1675,12 +1838,14 @@ _ = has-decidable-equality-left-summand eqAB , has-decidable-equality-right-summand eqAB) -open import elementary-number-theory.equality-integers funext using +open import elementary-number-theory.equality-integers using ( has-decidable-equality-ℤ) ``` -**Exercise 8.8.** Decidable equality in depopen import foundation.decidable-equality funext using -on.decidable-equality using +**Exercise 8.8.** Decidable equality in dependent pair types. + +```agda +open import foundation.decidable-equality using ( has-decidable-equality-Σ ; has-decidable-equality-fiber-has-decidable-equality-Σ) @@ -1691,8 +1856,9 @@ _ : _ = λ eqA → has-decidable-equality-Σ eqA , - has-decidable-equality-fopen import foundation.decidable-equality funext using -oundation.decidable-equality using + has-decidable-equality-fiber-has-decidable-equality-Σ eqA + +open import foundation.decidable-equality using ( has-decidable-equality-base-has-decidable-equality-Σ) ``` @@ -1700,7 +1866,7 @@ oundation.decidable-equality using of `Fin k` ```agda -open import univalent-combinatorics.decidable-dependent-function-types funext using +open import univalent-combinatorics.decidable-dependent-function-types using ( is-decidable-Π-Fin) -- TODO: b @@ -1714,7 +1880,7 @@ TODO **Exercise 8.11.** Bézout's identity. ```agda -open import elementary-number-theory.bezouts-lemma-natural-numbers funext using +open import elementary-number-theory.bezouts-lemma-natural-numbers using ( is-decidable-is-distance-between-multiples-ℕ --^ Σ (k : ℕ) Σ (l : ℕ) dist(k*x, l*x) = z is decidable ; minimal-positive-distance-x-coeff @@ -1735,16 +1901,18 @@ _ = **Exercise 8.12.** Prime factor decomposition. ```agda -open import elementary-number-theory.fundamental-theorem-of-arithmetic funext using +open import elementary-number-theory.fundamental-theorem-of-arithmetic using ( nat-least-nontrivial-divisor-ℕ -- for every 1 < n a number... ; is-prime-least-nontrivial-divisor-ℕ -- which is a prime... - ; div-least-nontrivial-divisor-ℕ -- and dividesopen import elementary-number-theory.fundamental-theorem-of-arithmetic funext using - using + ; div-least-nontrivial-divisor-ℕ -- and divides n + ) +open import elementary-number-theory.fundamental-theorem-of-arithmetic using ( list-fundamental-theorem-arithmetic-ℕ -- for every 1 < n a list of numbers... ; is-sorted-list-fundamental-theorem-arithmetic-ℕ -- which is sorted... ; is-prime-list-fundamental-theorem-arithmetic-ℕ -- only contains primes... - ; is-decomposition-list-fundamental-theorem-arithmetic-ℕ -- and multiplieopen import elementary-number-theory.fundamental-theorem-of-arithmetic funext using -thmetic using + ; is-decomposition-list-fundamental-theorem-arithmetic-ℕ -- and multiplies up to n + ) +open import elementary-number-theory.fundamental-theorem-of-arithmetic using ( eq-prime-decomposition-list-ℕ -- prime decompositions of a fixed number are equal ) ``` @@ -1760,7 +1928,7 @@ TODO. **Exercise 8.15.** The cofibonacci sequenece. ```agda -open import elementary-number-theory.cofibonacci funext using +open import elementary-number-theory.cofibonacci using ( cofibonacci ; forward-is-left-adjoint-cofibonacci) diff --git a/src/literature/oeis.lagda.md b/src/literature/oeis.lagda.md index 6ef96205b5..9ecf4af942 100644 --- a/src/literature/oeis.lagda.md +++ b/src/literature/oeis.lagda.md @@ -4,21 +4,16 @@ This file records formalized sequences of the [Online Encyclopedia of Integer Sequences](https://oeis.org) {{#cite oeis}}. ```agda -open import foundation.function-extensionality-axiom - -module - literature.oeis - (funext : function-extensionality) - where +module literature.oeis where ```
Imports ```agda -open import elementary-number-theory.exponentiation-natural-numbers funext +open import elementary-number-theory.exponentiation-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types funext +open import foundation.function-types ```
@@ -28,14 +23,14 @@ open import foundation.function-types funext ### [A000001](https://oeis.org/A000001) The number of groups of order `n` ```agda -open import finite-group-theory.finite-groups funext using +open import finite-group-theory.finite-groups using ( number-of-groups-of-order) ``` ### [A000002](https://oeis.org/A000002) The Kolakoski sequence ```agda -open import elementary-number-theory.kolakoski-sequence funext using +open import elementary-number-theory.kolakoski-sequence using ( kolakoski) ``` @@ -57,7 +52,7 @@ A000007 (succ-ℕ _) = 0 ### [A000010](https://oeis.org/A000010) Euler's totient function ```agda -open import elementary-number-theory.eulers-totient-function funext using +open import elementary-number-theory.eulers-totient-function using ( eulers-totient-function-relatively-prime) ``` @@ -78,21 +73,21 @@ A000027 = succ-ℕ ### [A000040](https://oeis.org/A000040) The prime numbers ```agda -open import elementary-number-theory.infinitude-of-primes funext using +open import elementary-number-theory.infinitude-of-primes using ( prime-ℕ) ``` ### [A000045](https://oeis.org/A000045) The Fibonacci sequence ```agda -open import elementary-number-theory.fibonacci-sequence funext using +open import elementary-number-theory.fibonacci-sequence using ( Fibonacci-ℕ) ``` ### [A000058](https://oeis.org/A000058) Sylvester's sequence ```agda -open import elementary-number-theory.sylvesters-sequence funext using +open import elementary-number-theory.sylvesters-sequence using ( sylvesters-sequence-ℕ) ``` @@ -106,28 +101,28 @@ A000079 = exp-ℕ 2 ### [A000108](https://oeis.org/A000108) The Catalan numbers ```agda -open import elementary-number-theory.catalan-numbers funext using +open import elementary-number-theory.catalan-numbers using ( catalan-numbers) ``` ### [A000110](https://oeis.org/A000110) The Bell numbers ```agda -open import elementary-number-theory.bell-numbers funext using +open import elementary-number-theory.bell-numbers using ( bell-number-ℕ) ``` ### [A000142](https://oeis.org/A000142) Factorials ```agda -open import elementary-number-theory.factorials funext using +open import elementary-number-theory.factorials using ( factorial-ℕ) ``` ### [A000215](https://oeis.org/A000215) The Fermat numbers ```agda -open import elementary-number-theory.fermat-numbers funext using +open import elementary-number-theory.fermat-numbers using ( fermat-number-ℕ) ``` @@ -140,29 +135,29 @@ A000244 = exp-ℕ 3 ### [A000720](https://oeis.org/A000720) The prime counting function -`open import elementary-number-theory.infinitude-of-primes funext using - using +```agda +open import elementary-number-theory.infinitude-of-primes using ( prime-counting-ℕ) ``` ### [A000945](https://oeis.org/A000945) The Euclid–Mullin sequence ```agda -open import elementary-number-theory.euclid-mullin-sequence funext using +open import elementary-number-theory.euclid-mullin-sequence using ( euclid-mullin-ℕ) ``` ### [A001175](https://oeis.org/A001175) Pisano periods ```agda -open import elementary-number-theory.pisano-periods funext using +open import elementary-number-theory.pisano-periods using ( pisano-period) ``` ### [A001177](https://oeis.org/A001177) The cofibonacci sequence ```agda -open import elementary-number-theory.cofibonacci funext using +open import elementary-number-theory.cofibonacci using ( cofibonacci) ``` @@ -176,21 +171,21 @@ A001477 = id ### [A003090](https://oeis.org/A003090) The number of main classes of Latin squares of order `n` ```agda -open import univalent-combinatorics.main-classes-of-latin-squares funext using +open import univalent-combinatorics.main-classes-of-latin-squares using ( number-of-main-classes-of-Latin-squares-of-order) ``` ### [A006369](https://oeis.org/A006369) Collatz' bijection ```agda -open import elementary-number-theory.collatz-bijection funext using +open import elementary-number-theory.collatz-bijection using ( map-collatz-bijection) ``` ### [A027851](https://oeis.org/A027851) The number of semigroups of order `n` up to isomorphism ```agda -open import finite-group-theory.finite-semigroups funext using +open import finite-group-theory.finite-semigroups using ( number-of-semigroups-of-order) ``` @@ -204,7 +199,7 @@ open import elementary-number-theory.ackermann-function using ### [A058129](https://oeis.org/A058129) The number of monoids of order `n` up to isomorphism ```agda -open import finite-group-theory.finite-monoids funext using +open import finite-group-theory.finite-monoids using ( number-of-monoids-of-order) ``` diff --git a/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md b/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md index fa47ad683d..34e5e2e86f 100644 --- a/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md +++ b/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md @@ -4,12 +4,7 @@ This file collects references to formalization of constructions and theorems from {{#cite SvDR20}}. ```agda -open import foundation.function-extensionality-axiom - -module - literature.sequential-colimits-in-homotopy-type-theory - (funext : function-extensionality) - where +module literature.sequential-colimits-in-homotopy-type-theory where ``` ## 2 Homotopy Type Theory @@ -21,7 +16,7 @@ import below for completeness. open import foundation.universe-levels using ( UU ) -open import foundation.identity-types funext using +open import foundation.identity-types using ( Id -- "path" ; refl -- "constant path" ; inv -- "inverse path" @@ -31,21 +26,20 @@ open import foundation.identity-types funext using open import foundation.action-on-identifications-functions using ( ap -- "functions respect paths" ) -open import foundation.homotopies funext using +open import foundation.homotopies using ( _~_ -- "homotopy" ) -open import foundation.equivalences funext using +open import foundation.equivalences using ( equiv -- "equivalence" ) -open import foundation.univalence funext using +open import foundation.univalence using ( univalence -- "the univalence axiom" ; map-eq -- "function p̅ associated to a path" ) -open import foundation.function-extensionality funext - using +open import foundation.function-extensionality using ( funext -- "the function extensionality axiom" ) -open import foundation.fibers-of-maps funext using +open import foundation.fibers-of-maps using ( fiber -- "the homotopy fiber of a function" ) open import foundation.transport-along-identifications using @@ -54,21 +48,21 @@ open import foundation.transport-along-identifications using open import foundation.action-on-identifications-dependent-functions using ( apd -- "dependent functions respect paths" ) -open import foundation.truncated-types funext using +open import foundation.truncated-types using ( is-trunc -- "`n`-truncated types" ) -open import foundation.truncations funext using +open import foundation.truncations using ( trunc -- "the `n`-truncation of a type" ; unit-trunc -- "the unit map into a type's `n`-truncation" ; is-truncation-trunc -- "precomposing by the unit is an equivalence" ) -open import foundation.connected-types funext using +open import foundation.connected-types using ( is-connected -- "`n`-connected types" ) -open import foundation.truncated-maps funext using +open import foundation.truncated-maps using ( is-trunc-map -- "`n`-truncated functions" ) -open import foundation.connected-maps funext using +open import foundation.connected-maps using ( is-connected-map -- "`n`-connected functions" ) ``` @@ -83,7 +77,7 @@ sequential colimits, and defines lifts of elements in a sequential diagram. **Definition 3.1.** Sequences. ```agda -open import synthetic-homotopy-theory.sequential-diagrams funext using +open import synthetic-homotopy-theory.sequential-diagrams using ( sequential-diagram ) ``` @@ -102,7 +96,7 @@ universal property, and results about the standard construction of colimits are obtained by specialization to the canonical cocone. ```agda -open import synthetic-homotopy-theory.sequential-colimits funext using +open import synthetic-homotopy-theory.sequential-colimits using ( standard-sequential-colimit -- the canonical colimit type ; map-cocone-standard-sequential-colimit -- "the canonical injection" ; coherence-cocone-standard-sequential-colimit -- "the glue" @@ -117,8 +111,8 @@ The data of a homotopy between two functions out of the standard sequential colimit is specified by the type `htpy-out-of-standard-sequential-colimit`, which we can then turn into a proper homotopy. -`open import synthetic-homotopy-theory.sequential-colimits funext using - using +```agda +open import synthetic-homotopy-theory.sequential-colimits using ( htpy-out-of-standard-sequential-colimit -- data of a homotopy ; htpy-htpy-out-of-standard-sequential-colimit -- "data of a homotopy induces a homotopy" ) @@ -131,12 +125,12 @@ We call natural transformations _morphisms of sequential diagrams_, and natural equivalences _equivalences of sequential diagrams_. ```agda -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext using +open import synthetic-homotopy-theory.morphisms-sequential-diagrams using ( hom-sequential-diagram -- "natural transformation" ; id-hom-sequential-diagram -- "identity natural transformation" ; comp-hom-sequential-diagram -- "composition of natural transformations" ) -open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext using +open import synthetic-homotopy-theory.equivalences-sequential-diagrams using ( equiv-sequential-diagram -- "natural equivalence" ) ``` @@ -144,7 +138,7 @@ open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext us **Lemma 3.5.** Functoriality of the Sequential Colimit. ```agda -open import synthetic-homotopy-theory.functoriality-sequential-colimits funext using +open import synthetic-homotopy-theory.functoriality-sequential-colimits using ( map-hom-standard-sequential-colimit -- "a natural transformation induces a map" ; preserves-id-map-hom-standard-sequential-colimit -- "1∞ ~ id(A∞)" ; preserves-comp-map-hom-standard-sequential-colimit -- "(σ ∘ τ)∞ ~ σ∞ ∘ τ∞" @@ -166,7 +160,7 @@ property of a colimit of `A`. Specializing to the standard sequential colimit, we get and equivalence `A[k]∞ ≃ A∞`. ```agda -open import synthetic-homotopy-theory.shifts-sequential-diagrams funext using +open import synthetic-homotopy-theory.shifts-sequential-diagrams using ( compute-sequential-colimit-shift-sequential-diagram -- "A[k]∞ ≃ A∞" ) compute-sequential-colimit-shift-sequential-diagram-once = @@ -187,7 +181,7 @@ The paper defines fibered sequences as a family over the total space **Definition 4.1.** Fibered sequences. Equifibered sequences. ```agda -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext using +open import synthetic-homotopy-theory.dependent-sequential-diagrams using ( dependent-sequential-diagram -- "A sequence (B, b) fibered over (A, a)" ) ``` @@ -205,7 +199,7 @@ because it characterizes families over a sequential colimit. **Definition 4.3.** Σ of a fibered sequence. ```agda -open import synthetic-homotopy-theory.total-sequential-diagrams funext using +open import synthetic-homotopy-theory.total-sequential-diagrams using ( total-sequential-diagram -- "Σ (A, a) (B, b)" ; pr1-total-sequential-diagram -- "the canonical projection" ) diff --git a/src/logic.lagda.md b/src/logic.lagda.md index 0edf5d2f34..840556f77d 100644 --- a/src/logic.lagda.md +++ b/src/logic.lagda.md @@ -3,27 +3,22 @@ ## Modules in the logic namespace ```agda -open import foundation.function-extensionality-axiom +module logic where -module - logic - (funext : function-extensionality) - where - -open import logic.complements-de-morgan-subtypes funext public -open import logic.complements-decidable-subtypes funext public -open import logic.complements-double-negation-stable-subtypes funext public -open import logic.de-morgan-embeddings funext public -open import logic.de-morgan-maps funext public -open import logic.de-morgan-propositions funext public -open import logic.de-morgan-subtypes funext public -open import logic.de-morgan-types funext public -open import logic.de-morgans-law funext public -open import logic.double-negation-eliminating-maps funext public -open import logic.double-negation-elimination funext public -open import logic.double-negation-stable-embeddings funext public -open import logic.double-negation-stable-subtypes funext public -open import logic.functoriality-existential-quantification funext public -open import logic.markovian-types funext public -open import logic.markovs-principle funext public +open import logic.complements-de-morgan-subtypes public +open import logic.complements-decidable-subtypes public +open import logic.complements-double-negation-stable-subtypes public +open import logic.de-morgan-embeddings public +open import logic.de-morgan-maps public +open import logic.de-morgan-propositions public +open import logic.de-morgan-subtypes public +open import logic.de-morgan-types public +open import logic.de-morgans-law public +open import logic.double-negation-eliminating-maps public +open import logic.double-negation-elimination public +open import logic.double-negation-stable-embeddings public +open import logic.double-negation-stable-subtypes public +open import logic.functoriality-existential-quantification public +open import logic.markovian-types public +open import logic.markovs-principle public ``` diff --git a/src/logic/complements-de-morgan-subtypes.lagda.md b/src/logic/complements-de-morgan-subtypes.lagda.md index 6978a82369..fbfe0b0e4a 100644 --- a/src/logic/complements-de-morgan-subtypes.lagda.md +++ b/src/logic/complements-de-morgan-subtypes.lagda.md @@ -1,36 +1,31 @@ # Complements of De Morgan subtypes ```agda -open import foundation.function-extensionality-axiom - -module - logic.complements-de-morgan-subtypes - (funext : function-extensionality) - where +module logic.complements-de-morgan-subtypes where ```
Imports ```agda -open import foundation.complements-subtypes funext -open import foundation.decidable-subtypes funext +open import foundation.complements-subtypes +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.full-subtypes funext -open import foundation.involutions funext -open import foundation.negation funext -open import foundation.postcomposition-functions funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext -open import foundation.unions-subtypes funext +open import foundation.double-negation +open import foundation.full-subtypes +open import foundation.involutions +open import foundation.negation +open import foundation.postcomposition-functions +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.subtypes +open import foundation.unions-subtypes open import foundation.universe-levels open import foundation-core.function-types -open import logic.complements-decidable-subtypes funext -open import logic.de-morgan-propositions funext -open import logic.de-morgan-subtypes funext +open import logic.complements-decidable-subtypes +open import logic.de-morgan-propositions +open import logic.de-morgan-subtypes ```
diff --git a/src/logic/complements-decidable-subtypes.lagda.md b/src/logic/complements-decidable-subtypes.lagda.md index 59a094daab..ae2a775f33 100644 --- a/src/logic/complements-decidable-subtypes.lagda.md +++ b/src/logic/complements-decidable-subtypes.lagda.md @@ -1,38 +1,33 @@ # Complements of decidable subtypes ```agda -open import foundation.function-extensionality-axiom - -module - logic.complements-decidable-subtypes - (funext : function-extensionality) - where +module logic.complements-decidable-subtypes where ```
Imports ```agda -open import foundation.complements-subtypes funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.complements-subtypes +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions funext +open import foundation.double-negation-stable-propositions open import foundation.evaluation-functions -open import foundation.full-subtypes funext -open import foundation.involutions funext -open import foundation.negation funext -open import foundation.postcomposition-functions funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.unions-subtypes funext +open import foundation.full-subtypes +open import foundation.involutions +open import foundation.negation +open import foundation.postcomposition-functions +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.unions-subtypes open import foundation.universe-levels open import foundation-core.function-types -open import foundation-core.subtypes funext +open import foundation-core.subtypes -open import logic.double-negation-stable-subtypes funext +open import logic.double-negation-stable-subtypes ```
diff --git a/src/logic/complements-double-negation-stable-subtypes.lagda.md b/src/logic/complements-double-negation-stable-subtypes.lagda.md index 2b574ab615..e4ba546190 100644 --- a/src/logic/complements-double-negation-stable-subtypes.lagda.md +++ b/src/logic/complements-double-negation-stable-subtypes.lagda.md @@ -1,33 +1,28 @@ # Complements of double negation stable subtypes ```agda -open import foundation.function-extensionality-axiom - -module - logic.complements-double-negation-stable-subtypes - (funext : function-extensionality) - where +module logic.complements-double-negation-stable-subtypes where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.double-negation funext-stable-propositions -open import foundation.full-subtypes funext -open import foundation.involutions funext -open import foundation.negation funext -open import foundation.postcomposition-functions funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext -open import foundation.unions-subtypes funext +open import foundation.double-negation +open import foundation.double-negation-stable-propositions +open import foundation.full-subtypes +open import foundation.involutions +open import foundation.negation +open import foundation.postcomposition-functions +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.subtypes +open import foundation.unions-subtypes open import foundation.universe-levels open import foundation-core.function-types -open import logic.double-negation-stable-subtypes funext +open import logic.double-negation-stable-subtypes ```
diff --git a/src/logic/de-morgan-embeddings.lagda.md b/src/logic/de-morgan-embeddings.lagda.md index 0a24ef774b..3391dea43b 100644 --- a/src/logic/de-morgan-embeddings.lagda.md +++ b/src/logic/de-morgan-embeddings.lagda.md @@ -1,40 +1,35 @@ # De Morgan embeddings ```agda -open import foundation.function-extensionality-axiom - -module - logic.de-morgan-embeddings - (funext : function-extensionality) - where +module logic.de-morgan-embeddings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows funext -open import foundation.decidable-embeddings funext -open import foundation.decidable-maps funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.cartesian-morphisms-arrows +open import foundation.decidable-embeddings +open import foundation.decidable-maps +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.fibers-of-maps funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext +open import foundation.embeddings +open import foundation.fibers-of-maps +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-maps funext -open import foundation.propositions funext -open import foundation.retracts-of-maps funext +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-maps +open import foundation.propositions +open import foundation.retracts-of-maps open import foundation.subtype-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -47,11 +42,11 @@ open import foundation-core.homotopies open import foundation-core.injective-maps open import foundation-core.torsorial-type-families -open import logic.de-morgan-maps funext -open import logic.de-morgan-propositions funext -open import logic.de-morgan-types funext -open import logic.double-negation-eliminating-maps funext -open import logic.double-negation-elimination funext +open import logic.de-morgan-maps +open import logic.de-morgan-propositions +open import logic.de-morgan-types +open import logic.double-negation-eliminating-maps +open import logic.double-negation-elimination ```
diff --git a/src/logic/de-morgan-maps.lagda.md b/src/logic/de-morgan-maps.lagda.md index 9850f05d95..17b5a68d6e 100644 --- a/src/logic/de-morgan-maps.lagda.md +++ b/src/logic/de-morgan-maps.lagda.md @@ -1,12 +1,7 @@ # De Morgan maps ```agda -open import foundation.function-extensionality-axiom - -module - logic.de-morgan-maps - (funext : function-extensionality) - where +module logic.de-morgan-maps where ```
Imports @@ -15,28 +10,28 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows funext -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-maps funext -open import foundation.decidable-types funext +open import foundation.cartesian-morphisms-arrows +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-maps +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.retracts-of-maps funext -open import foundation.retracts-of-types funext +open import foundation.double-negation +open import foundation.embeddings +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negation +open import foundation.propositions +open import foundation.retractions +open import foundation.retracts-of-maps +open import foundation.retracts-of-types open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.contractible-maps @@ -46,10 +41,10 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import logic.de-morgan-types funext -open import logic.de-morgans-law funext -open import logic.double-negation-eliminating-maps funext -open import logic.double-negation-elimination funext +open import logic.de-morgan-types +open import logic.de-morgans-law +open import logic.double-negation-eliminating-maps +open import logic.double-negation-elimination ```
diff --git a/src/logic/de-morgan-propositions.lagda.md b/src/logic/de-morgan-propositions.lagda.md index c779611211..5ca81ba117 100644 --- a/src/logic/de-morgan-propositions.lagda.md +++ b/src/logic/de-morgan-propositions.lagda.md @@ -1,48 +1,43 @@ # De Morgan propositions ```agda -open import foundation.function-extensionality-axiom - -module - logic.de-morgan-propositions - (funext : function-extensionality) - where +module logic.de-morgan-propositions where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.conjunction +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.double-negation funext -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equivalences funext +open import foundation.disjunction +open import foundation.double-negation +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equivalences open import foundation.evaluation-functions -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.irrefutable-propositions funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.retracts-of-types funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.irrefutable-propositions +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-extensionality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.retracts-of-types +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions -open import logic.de-morgan-types funext -open import logic.de-morgans-law funext +open import logic.de-morgan-types +open import logic.de-morgans-law ```
diff --git a/src/logic/de-morgan-subtypes.lagda.md b/src/logic/de-morgan-subtypes.lagda.md index 1fd8ac5b63..b01a79ab1f 100644 --- a/src/logic/de-morgan-subtypes.lagda.md +++ b/src/logic/de-morgan-subtypes.lagda.md @@ -1,30 +1,25 @@ # De Morgan subtypes ```agda -open import foundation.function-extensionality-axiom - -module - logic.de-morgan-subtypes - (funext : function-extensionality) - where +module logic.de-morgan-subtypes where ```
Imports ```agda -open import foundation.1-types funext -open import foundation.coproduct-types funext +open import foundation.1-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.equality-dependent-function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-maps funext -open import foundation.sets funext -open import foundation.structured-type-duality funext -open import foundation.subtypes funext -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.dependent-products-propositions +open import foundation.equality-dependent-function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.logical-equivalences +open import foundation.propositional-maps +open import foundation.sets +open import foundation.structured-type-duality +open import foundation.subtypes +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels open import foundation-core.embeddings @@ -37,10 +32,10 @@ open import foundation-core.propositions open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import logic.de-morgan-embeddings funext -open import logic.de-morgan-maps funext -open import logic.de-morgan-propositions funext -open import logic.de-morgan-types funext +open import logic.de-morgan-embeddings +open import logic.de-morgan-maps +open import logic.de-morgan-propositions +open import logic.de-morgan-types ```
diff --git a/src/logic/de-morgan-types.lagda.md b/src/logic/de-morgan-types.lagda.md index 108a756610..749e83645f 100644 --- a/src/logic/de-morgan-types.lagda.md +++ b/src/logic/de-morgan-types.lagda.md @@ -1,46 +1,41 @@ # De Morgan types ```agda -open import foundation.function-extensionality-axiom - -module - logic.de-morgan-types - (funext : function-extensionality) - where +module logic.de-morgan-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.conjunction +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.disjunction funext -open import foundation.double-negation funext -open import foundation.empty-types funext +open import foundation.dependent-products-propositions +open import foundation.disjunction +open import foundation.double-negation +open import foundation.empty-types open import foundation.evaluation-functions -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.irrefutable-propositions funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.precomposition-functions funext -open import foundation.propositional-truncations funext -open import foundation.retracts-of-types funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.irrefutable-propositions +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.precomposition-functions +open import foundation.propositional-truncations +open import foundation.retracts-of-types open import foundation.truncation-levels -open import foundation.truncations funext +open import foundation.truncations open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.equivalences open import foundation-core.propositions -open import logic.de-morgans-law funext +open import logic.de-morgans-law ```
diff --git a/src/logic/de-morgans-law.lagda.md b/src/logic/de-morgans-law.lagda.md index ea1a05566f..670b532a88 100644 --- a/src/logic/de-morgans-law.lagda.md +++ b/src/logic/de-morgans-law.lagda.md @@ -1,36 +1,31 @@ # De Morgan's law ```agda -open import foundation.function-extensionality-axiom - -module - logic.de-morgans-law - (funext : function-extensionality) - where +module logic.de-morgans-law where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.conjunction +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.disjunction funext -open import foundation.double-negation funext -open import foundation.empty-types funext +open import foundation.dependent-products-propositions +open import foundation.disjunction +open import foundation.double-negation +open import foundation.empty-types open import foundation.evaluation-functions -open import foundation.function-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext +open import foundation.function-types +open import foundation.logical-equivalences +open import foundation.negation open import foundation.universe-levels -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.propositions -open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.2-element-types ```
diff --git a/src/logic/double-negation-eliminating-maps.lagda.md b/src/logic/double-negation-eliminating-maps.lagda.md index c4c043f1ce..836e3191e1 100644 --- a/src/logic/double-negation-eliminating-maps.lagda.md +++ b/src/logic/double-negation-eliminating-maps.lagda.md @@ -1,33 +1,28 @@ # Double negation eliminating maps ```agda -open import foundation.function-extensionality-axiom - -module - logic.double-negation-eliminating-maps - (funext : function-extensionality) - where +module logic.double-negation-eliminating-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows funext -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-maps funext -open import foundation.decidable-types funext +open import foundation.cartesian-morphisms-arrows +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-maps +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.empty-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.retractions funext -open import foundation.retracts-of-maps funext -open import foundation.retracts-of-types funext +open import foundation.double-negation +open import foundation.empty-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.retractions +open import foundation.retracts-of-maps +open import foundation.retracts-of-types open import foundation.transport-along-identifications open import foundation.universe-levels @@ -38,7 +33,7 @@ open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies -open import logic.double-negation-elimination funext +open import logic.double-negation-elimination ```
diff --git a/src/logic/double-negation-elimination.lagda.md b/src/logic/double-negation-elimination.lagda.md index 37fefe6cad..cdc299f056 100644 --- a/src/logic/double-negation-elimination.lagda.md +++ b/src/logic/double-negation-elimination.lagda.md @@ -1,33 +1,28 @@ # Double negation elimination ```agda -open import foundation.function-extensionality-axiom - -module - logic.double-negation-elimination - (funext : function-extensionality) - where +module logic.double-negation-elimination where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.double-negation funext +open import foundation.dependent-products-propositions +open import foundation.double-negation open import foundation.evaluation-functions -open import foundation.hilberts-epsilon-operators funext -open import foundation.logical-equivalences funext -open import foundation.retracts-of-types funext +open import foundation.hilberts-epsilon-operators +open import foundation.logical-equivalences +open import foundation.retracts-of-types open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels open import foundation-core.contractible-types -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.function-types diff --git a/src/logic/double-negation-stable-embeddings.lagda.md b/src/logic/double-negation-stable-embeddings.lagda.md index 7686f9eb4d..4e6a207085 100644 --- a/src/logic/double-negation-stable-embeddings.lagda.md +++ b/src/logic/double-negation-stable-embeddings.lagda.md @@ -1,41 +1,36 @@ # Double negation stable embeddings ```agda -open import foundation.function-extensionality-axiom - -module - logic.double-negation-stable-embeddings - (funext : function-extensionality) - where +module logic.double-negation-stable-embeddings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows funext -open import foundation.decidable-embeddings funext -open import foundation.decidable-maps funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.cartesian-morphisms-arrows +open import foundation.decidable-embeddings +open import foundation.decidable-maps +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.double-negation-stable-propositions funext -open import foundation.embeddings funext -open import foundation.fibers-of-maps funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext +open import foundation.double-negation-stable-propositions +open import foundation.embeddings +open import foundation.fibers-of-maps +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-maps funext -open import foundation.propositions funext -open import foundation.retracts-of-maps funext +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-maps +open import foundation.propositions +open import foundation.retracts-of-maps open import foundation.subtype-identity-principle open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.cartesian-product-types @@ -48,8 +43,8 @@ open import foundation-core.homotopies open import foundation-core.injective-maps open import foundation-core.torsorial-type-families -open import logic.double-negation-eliminating-maps funext -open import logic.double-negation-elimination funext +open import logic.double-negation-eliminating-maps +open import logic.double-negation-elimination ```
diff --git a/src/logic/double-negation-stable-subtypes.lagda.md b/src/logic/double-negation-stable-subtypes.lagda.md index 4833b34673..5780836046 100644 --- a/src/logic/double-negation-stable-subtypes.lagda.md +++ b/src/logic/double-negation-stable-subtypes.lagda.md @@ -1,32 +1,27 @@ # Double negation stable subtypes ```agda -open import foundation.function-extensionality-axiom - -module - logic.double-negation-stable-subtypes - (funext : function-extensionality) - where +module logic.double-negation-stable-subtypes where ```
Imports ```agda -open import foundation.1-types funext -open import foundation.coproduct-types funext +open import foundation.1-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.double-negation-stable-propositions funext -open import foundation.equality-dependent-function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-maps funext -open import foundation.sets funext -open import foundation.structured-type-duality funext -open import foundation.subtypes funext -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.dependent-products-propositions +open import foundation.double-negation-stable-propositions +open import foundation.equality-dependent-function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.logical-equivalences +open import foundation.propositional-maps +open import foundation.sets +open import foundation.structured-type-duality +open import foundation.subtypes +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels open import foundation-core.embeddings @@ -40,9 +35,9 @@ open import foundation-core.transport-along-identifications open import foundation-core.truncated-types open import foundation-core.truncation-levels -open import logic.double-negation-eliminating-maps funext -open import logic.double-negation-elimination funext -open import logic.double-negation-stable-embeddings funext +open import logic.double-negation-eliminating-maps +open import logic.double-negation-elimination +open import logic.double-negation-stable-embeddings ```
diff --git a/src/logic/functoriality-existential-quantification.lagda.md b/src/logic/functoriality-existential-quantification.lagda.md index baf5f5ac62..30953b6729 100644 --- a/src/logic/functoriality-existential-quantification.lagda.md +++ b/src/logic/functoriality-existential-quantification.lagda.md @@ -1,18 +1,13 @@ # Functoriality of existential quantification ```agda -open import foundation.function-extensionality-axiom - -module - logic.functoriality-existential-quantification - (funext : function-extensionality) - where +module logic.functoriality-existential-quantification where ```
Imports ```agda -open import foundation.existential-quantification funext +open import foundation.existential-quantification open import foundation.universe-levels open import foundation-core.function-types diff --git a/src/logic/markovian-types.lagda.md b/src/logic/markovian-types.lagda.md index 0327bc37f4..4add56697f 100644 --- a/src/logic/markovian-types.lagda.md +++ b/src/logic/markovian-types.lagda.md @@ -1,12 +1,7 @@ # Markovian types ```agda -open import foundation.function-extensionality-axiom - -module - logic.markovian-types - (funext : function-extensionality) - where +module logic.markovian-types where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-subtypes funext +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.disjunction funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.inhabited-types funext -open import foundation.negation funext -open import foundation.universal-quantification funext +open import foundation.dependent-products-propositions +open import foundation.disjunction +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.inhabited-types +open import foundation.negation +open import foundation.universal-quantification open import foundation.universe-levels open import foundation-core.booleans @@ -30,7 +25,7 @@ open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/logic/markovs-principle.lagda.md b/src/logic/markovs-principle.lagda.md index 64312c7b02..66eeefbf91 100644 --- a/src/logic/markovs-principle.lagda.md +++ b/src/logic/markovs-principle.lagda.md @@ -1,12 +1,7 @@ # Markov's principle ```agda -open import foundation.function-extensionality-axiom - -module - logic.markovs-principle - (funext : function-extensionality) - where +module logic.markovs-principle where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-subtypes funext +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.inhabited-types funext -open import foundation.negation funext -open import foundation.universal-quantification funext +open import foundation.disjunction +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.inhabited-types +open import foundation.negation +open import foundation.universal-quantification open import foundation.universe-levels open import foundation-core.booleans @@ -29,9 +24,9 @@ open import foundation-core.identity-types open import foundation-core.propositions open import foundation-core.sets -open import logic.markovian-types funext +open import logic.markovian-types -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/metric-spaces.lagda.md b/src/metric-spaces.lagda.md index bbfdcf4620..24e7a77fbe 100644 --- a/src/metric-spaces.lagda.md +++ b/src/metric-spaces.lagda.md @@ -43,55 +43,50 @@ property of **indistinguishability of identicals** ## Modules in the metric spaces namespace ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces - (funext : function-extensionality) - where - -open import metric-spaces.category-of-metric-spaces-and-isometries funext public -open import metric-spaces.category-of-metric-spaces-and-short-functions funext public -open import metric-spaces.cauchy-approximations-metric-spaces funext public -open import metric-spaces.cauchy-approximations-premetric-spaces funext public -open import metric-spaces.closed-premetric-structures funext public -open import metric-spaces.complete-metric-spaces funext public -open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext public -open import metric-spaces.dependent-products-metric-spaces funext public -open import metric-spaces.discrete-premetric-structures funext public -open import metric-spaces.equality-of-metric-spaces funext public -open import metric-spaces.equality-of-premetric-spaces funext public -open import metric-spaces.extensional-premetric-structures funext public -open import metric-spaces.functions-metric-spaces funext public -open import metric-spaces.functor-category-set-functions-isometry-metric-spaces funext public -open import metric-spaces.functor-category-short-isometry-metric-spaces funext public -open import metric-spaces.induced-premetric-structures-on-preimages funext public -open import metric-spaces.isometric-equivalences-premetric-spaces funext public -open import metric-spaces.isometries-metric-spaces funext public -open import metric-spaces.isometries-premetric-spaces funext public -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext public -open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space funext public -open import metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space funext public -open import metric-spaces.metric-space-of-rational-numbers funext public -open import metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods funext public -open import metric-spaces.metric-spaces funext public -open import metric-spaces.metric-structures funext public -open import metric-spaces.monotonic-premetric-structures funext public -open import metric-spaces.ordering-premetric-structures funext public -open import metric-spaces.precategory-of-metric-spaces-and-functions funext public -open import metric-spaces.precategory-of-metric-spaces-and-isometries funext public -open import metric-spaces.precategory-of-metric-spaces-and-short-functions funext public -open import metric-spaces.premetric-spaces funext public -open import metric-spaces.premetric-structures funext public -open import metric-spaces.pseudometric-spaces funext public -open import metric-spaces.pseudometric-structures funext public -open import metric-spaces.reflexive-premetric-structures funext public -open import metric-spaces.saturated-metric-spaces funext public -open import metric-spaces.short-functions-metric-spaces funext public -open import metric-spaces.short-functions-premetric-spaces funext public -open import metric-spaces.subspaces-metric-spaces funext public -open import metric-spaces.symmetric-premetric-structures funext public -open import metric-spaces.triangular-premetric-structures funext public +module metric-spaces where + +open import metric-spaces.category-of-metric-spaces-and-isometries public +open import metric-spaces.category-of-metric-spaces-and-short-functions public +open import metric-spaces.cauchy-approximations-metric-spaces public +open import metric-spaces.cauchy-approximations-premetric-spaces public +open import metric-spaces.closed-premetric-structures public +open import metric-spaces.complete-metric-spaces public +open import metric-spaces.convergent-cauchy-approximations-metric-spaces public +open import metric-spaces.dependent-products-metric-spaces public +open import metric-spaces.discrete-premetric-structures public +open import metric-spaces.equality-of-metric-spaces public +open import metric-spaces.equality-of-premetric-spaces public +open import metric-spaces.extensional-premetric-structures public +open import metric-spaces.functions-metric-spaces public +open import metric-spaces.functor-category-set-functions-isometry-metric-spaces public +open import metric-spaces.functor-category-short-isometry-metric-spaces public +open import metric-spaces.induced-premetric-structures-on-preimages public +open import metric-spaces.isometric-equivalences-premetric-spaces public +open import metric-spaces.isometries-metric-spaces public +open import metric-spaces.isometries-premetric-spaces public +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces public +open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space public +open import metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space public +open import metric-spaces.metric-space-of-rational-numbers public +open import metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods public +open import metric-spaces.metric-spaces public +open import metric-spaces.metric-structures public +open import metric-spaces.monotonic-premetric-structures public +open import metric-spaces.ordering-premetric-structures public +open import metric-spaces.precategory-of-metric-spaces-and-functions public +open import metric-spaces.precategory-of-metric-spaces-and-isometries public +open import metric-spaces.precategory-of-metric-spaces-and-short-functions public +open import metric-spaces.premetric-spaces public +open import metric-spaces.premetric-structures public +open import metric-spaces.pseudometric-spaces public +open import metric-spaces.pseudometric-structures public +open import metric-spaces.reflexive-premetric-structures public +open import metric-spaces.saturated-metric-spaces public +open import metric-spaces.short-functions-metric-spaces public +open import metric-spaces.short-functions-premetric-spaces public +open import metric-spaces.subspaces-metric-spaces public +open import metric-spaces.symmetric-premetric-structures public +open import metric-spaces.triangular-premetric-structures public ``` ## References diff --git a/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md index 3d5ba921b6..33740c7c95 100644 --- a/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md @@ -1,30 +1,25 @@ # The category of metric spaces and isometries ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.category-of-metric-spaces-and-isometries - (funext : function-extensionality) - where +module metric-spaces.category-of-metric-spaces-and-isometries where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-precategories funext +open import category-theory.categories +open import category-theory.isomorphisms-in-precategories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.precategory-of-metric-spaces-and-isometries funext +open import metric-spaces.equality-of-metric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.precategory-of-metric-spaces-and-isometries ```
diff --git a/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md index e3646ffe3e..64d510500c 100644 --- a/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md @@ -1,30 +1,25 @@ # The category of metric spaces and short maps ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.category-of-metric-spaces-and-short-functions - (funext : function-extensionality) - where +module metric-spaces.category-of-metric-spaces-and-short-functions where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-precategories funext +open import category-theory.categories +open import category-theory.isomorphisms-in-precategories -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.precategory-of-metric-spaces-and-short-functions funext +open import metric-spaces.equality-of-metric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.precategory-of-metric-spaces-and-short-functions ```
diff --git a/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md index b530112c5f..1b5a1f41c2 100644 --- a/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md @@ -1,31 +1,26 @@ # Cauchy approximations in metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.cauchy-approximations-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.cauchy-approximations-metric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-premetric-spaces funext -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext -open import metric-spaces.metric-spaces funext +open import metric-spaces.cauchy-approximations-premetric-spaces +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces +open import metric-spaces.metric-spaces ```
diff --git a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md index 07df9fb1c1..55627ce6e3 100644 --- a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md @@ -1,28 +1,23 @@ # Cauchy approximations in premetric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.cauchy-approximations-premetric-spaces - (funext : function-extensionality) - where +module metric-spaces.cauchy-approximations-premetric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.premetric-spaces funext -open import metric-spaces.short-functions-premetric-spaces funext +open import metric-spaces.premetric-spaces +open import metric-spaces.short-functions-premetric-spaces ```
diff --git a/src/metric-spaces/closed-premetric-structures.lagda.md b/src/metric-spaces/closed-premetric-structures.lagda.md index 877ecb766d..8bf46dea34 100644 --- a/src/metric-spaces/closed-premetric-structures.lagda.md +++ b/src/metric-spaces/closed-premetric-structures.lagda.md @@ -1,47 +1,41 @@ # Closed premetric structures ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.closed-premetric-structures - (funext : function-extensionality) - where +module metric-spaces.closed-premetric-structures where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-extensionality funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositional-extensionality +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.ordering-premetric-structures funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.ordering-premetric-structures +open import metric-spaces.premetric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/complete-metric-spaces.lagda.md b/src/metric-spaces/complete-metric-spaces.lagda.md index 66ed58c7df..1cb1c38a3a 100644 --- a/src/metric-spaces/complete-metric-spaces.lagda.md +++ b/src/metric-spaces/complete-metric-spaces.lagda.md @@ -1,27 +1,22 @@ # Complete metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.complete-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.complete-metric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces funext -open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext -open import metric-spaces.metric-spaces funext +open import metric-spaces.cauchy-approximations-metric-spaces +open import metric-spaces.convergent-cauchy-approximations-metric-spaces +open import metric-spaces.metric-spaces ```
diff --git a/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md b/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md index a6748e121a..f8ade7ad4b 100644 --- a/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md +++ b/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md @@ -1,27 +1,22 @@ # Convergent Cauchy approximations in metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.convergent-cauchy-approximations-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.convergent-cauchy-approximations-metric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces funext -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext -open import metric-spaces.metric-spaces funext +open import metric-spaces.cauchy-approximations-metric-spaces +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces +open import metric-spaces.metric-spaces ```
diff --git a/src/metric-spaces/dependent-products-metric-spaces.lagda.md b/src/metric-spaces/dependent-products-metric-spaces.lagda.md index ff0cc56e35..9114877759 100644 --- a/src/metric-spaces/dependent-products-metric-spaces.lagda.md +++ b/src/metric-spaces/dependent-products-metric-spaces.lagda.md @@ -1,34 +1,28 @@ # Dependent products of metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.dependent-products-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.dependent-products-metric-spaces where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.metric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.pseudometric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.short-functions-metric-spaces funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.metric-spaces +open import metric-spaces.metric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-structures +open import metric-spaces.pseudometric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.short-functions-metric-spaces +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/discrete-premetric-structures.lagda.md b/src/metric-spaces/discrete-premetric-structures.lagda.md index 3bf776ea51..7dfae22799 100644 --- a/src/metric-spaces/discrete-premetric-structures.lagda.md +++ b/src/metric-spaces/discrete-premetric-structures.lagda.md @@ -1,34 +1,29 @@ # Discrete premetric structures ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.discrete-premetric-structures - (funext : function-extensionality) - where +module metric-spaces.discrete-premetric-structures where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.premetric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/equality-of-metric-spaces.lagda.md b/src/metric-spaces/equality-of-metric-spaces.lagda.md index 472ffa7569..9e6b49a73c 100644 --- a/src/metric-spaces/equality-of-metric-spaces.lagda.md +++ b/src/metric-spaces/equality-of-metric-spaces.lagda.md @@ -1,32 +1,27 @@ # Equality of metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.equality-of-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.equality-of-metric-spaces where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import metric-spaces.equality-of-premetric-spaces funext -open import metric-spaces.isometric-equivalences-premetric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.premetric-spaces funext +open import metric-spaces.equality-of-premetric-spaces +open import metric-spaces.isometric-equivalences-premetric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.premetric-spaces ```
diff --git a/src/metric-spaces/equality-of-premetric-spaces.lagda.md b/src/metric-spaces/equality-of-premetric-spaces.lagda.md index 55888aa93f..bf75c6dad0 100644 --- a/src/metric-spaces/equality-of-premetric-spaces.lagda.md +++ b/src/metric-spaces/equality-of-premetric-spaces.lagda.md @@ -1,12 +1,7 @@ # Equality of premetric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.equality-of-premetric-spaces - (funext : function-extensionality) - where +module metric-spaces.equality-of-premetric-spaces where ```
Imports @@ -14,23 +9,23 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import metric-spaces.isometries-premetric-spaces funext -open import metric-spaces.premetric-spaces funext -open import metric-spaces.premetric-structures funext +open import metric-spaces.isometries-premetric-spaces +open import metric-spaces.premetric-spaces +open import metric-spaces.premetric-structures ```
diff --git a/src/metric-spaces/extensional-premetric-structures.lagda.md b/src/metric-spaces/extensional-premetric-structures.lagda.md index 52f1bf0412..0e614ca440 100644 --- a/src/metric-spaces/extensional-premetric-structures.lagda.md +++ b/src/metric-spaces/extensional-premetric-structures.lagda.md @@ -1,33 +1,28 @@ # Extensional premetric structures on types ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.extensional-premetric-structures - (funext : function-extensionality) - where +module metric-spaces.extensional-premetric-structures where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.premetric-structures funext -open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.premetric-structures +open import metric-spaces.reflexive-premetric-structures ```
diff --git a/src/metric-spaces/functions-metric-spaces.lagda.md b/src/metric-spaces/functions-metric-spaces.lagda.md index fc758b51e0..2c95ab35af 100644 --- a/src/metric-spaces/functions-metric-spaces.lagda.md +++ b/src/metric-spaces/functions-metric-spaces.lagda.md @@ -1,24 +1,19 @@ # Functions between metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.functions-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.functions-metric-spaces where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.sets open import foundation.universe-levels -open import metric-spaces.metric-spaces funext -open import metric-spaces.premetric-spaces funext +open import metric-spaces.metric-spaces +open import metric-spaces.premetric-spaces ```
diff --git a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md index e7938e25bf..e825f25eff 100644 --- a/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-set-functions-isometry-metric-spaces.lagda.md @@ -1,32 +1,27 @@ # The functor from the precategory of metric spaces and isometries to the precategory of sets ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.functor-category-set-functions-isometry-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.functor-category-set-functions-isometry-metric-spaces where ```
Imports ```agda -open import category-theory.conservative-functors-precategories funext -open import category-theory.faithful-functors-precategories funext -open import category-theory.functors-precategories funext +open import category-theory.conservative-functors-precategories +open import category-theory.faithful-functors-precategories +open import category-theory.functors-precategories -open import foundation.category-of-sets funext +open import foundation.category-of-sets open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.isomorphisms-of-sets funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.isomorphisms-of-sets +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.isometries-metric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.precategory-of-metric-spaces-and-isometries funext +open import metric-spaces.isometries-metric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.precategory-of-metric-spaces-and-isometries ```
diff --git a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md index 89d9412938..9e55f22584 100644 --- a/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md +++ b/src/metric-spaces/functor-category-short-isometry-metric-spaces.lagda.md @@ -1,29 +1,24 @@ # The inclusion of isometries into the category of metric spaces and short maps ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.functor-category-short-isometry-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.functor-category-short-isometry-metric-spaces where ```
Imports ```agda -open import category-theory.conservative-functors-precategories funext -open import category-theory.faithful-functors-precategories funext -open import category-theory.functors-precategories funext +open import category-theory.conservative-functors-precategories +open import category-theory.faithful-functors-precategories +open import category-theory.functors-precategories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import metric-spaces.precategory-of-metric-spaces-and-isometries funext -open import metric-spaces.precategory-of-metric-spaces-and-short-functions funext -open import metric-spaces.short-functions-metric-spaces funext +open import metric-spaces.precategory-of-metric-spaces-and-isometries +open import metric-spaces.precategory-of-metric-spaces-and-short-functions +open import metric-spaces.short-functions-metric-spaces ```
diff --git a/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md b/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md index cd57a57411..880bd2efd8 100644 --- a/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md +++ b/src/metric-spaces/induced-premetric-structures-on-preimages.lagda.md @@ -1,30 +1,25 @@ # Induced premetric structures on preimages ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.induced-premetric-structures-on-preimages - (funext : function-extensionality) - where +module metric-spaces.induced-premetric-structures-on-preimages where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md b/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md index 2e9b722b02..34c143ce20 100644 --- a/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md +++ b/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md @@ -1,37 +1,31 @@ # Isometric equivalences between premetric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.isometric-equivalences-premetric-spaces - (funext : function-extensionality) - where +module metric-spaces.isometric-equivalences-premetric-spaces where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import metric-spaces.equality-of-premetric-spaces funext -open import metric-spaces.isometries-premetric-spaces funext -open import metric-spaces.premetric-spaces funext +open import metric-spaces.equality-of-premetric-spaces +open import metric-spaces.isometries-premetric-spaces +open import metric-spaces.premetric-spaces ```
diff --git a/src/metric-spaces/isometries-metric-spaces.lagda.md b/src/metric-spaces/isometries-metric-spaces.lagda.md index 7bdd0581d1..5078244b1f 100644 --- a/src/metric-spaces/isometries-metric-spaces.lagda.md +++ b/src/metric-spaces/isometries-metric-spaces.lagda.md @@ -1,41 +1,35 @@ # Isometries between metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.isometries-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.isometries-metric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.sequences -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.univalence funext +open import foundation.sets +open import foundation.subtypes +open import foundation.univalence open import foundation.universe-levels -open import metric-spaces.functions-metric-spaces funext -open import metric-spaces.isometries-premetric-spaces funext -open import metric-spaces.metric-spaces funext +open import metric-spaces.functions-metric-spaces +open import metric-spaces.isometries-premetric-spaces +open import metric-spaces.metric-spaces ```
diff --git a/src/metric-spaces/isometries-premetric-spaces.lagda.md b/src/metric-spaces/isometries-premetric-spaces.lagda.md index 96b0f1beb8..6b3812351b 100644 --- a/src/metric-spaces/isometries-premetric-spaces.lagda.md +++ b/src/metric-spaces/isometries-premetric-spaces.lagda.md @@ -1,36 +1,30 @@ # Isometries between premetric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.isometries-premetric-spaces - (funext : function-extensionality) - where +module metric-spaces.isometries-premetric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.premetric-spaces funext +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.premetric-spaces ```
diff --git a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md index 370b61f10b..a3390d3a52 100644 --- a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md +++ b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md @@ -1,29 +1,24 @@ # Limits of Cauchy approximations in premetric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces - (funext : function-extensionality) - where +module metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-premetric-spaces funext -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.premetric-spaces funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.cauchy-approximations-premetric-spaces +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.premetric-spaces +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md b/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md index d5b8b6abaf..dc0c9c9e53 100644 --- a/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md +++ b/src/metric-spaces/metric-space-of-cauchy-approximations-in-a-metric-space.lagda.md @@ -1,25 +1,20 @@ # The metric space of cauchy approximations in a metric space ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space - (funext : function-extensionality) - where +module metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces funext -open import metric-spaces.dependent-products-metric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.subspaces-metric-spaces funext +open import metric-spaces.cauchy-approximations-metric-spaces +open import metric-spaces.dependent-products-metric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.subspaces-metric-spaces ```
diff --git a/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md b/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md index 5782851d81..07c23b1fdf 100644 --- a/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md +++ b/src/metric-spaces/metric-space-of-convergent-cauchy-approximations-in-a-metric-space.lagda.md @@ -1,12 +1,7 @@ # The metric space of convergent cauchy approximations in a metric space ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space - (funext : function-extensionality) - where +module metric-spaces.metric-space-of-convergent-cauchy-approximations-in-a-metric-space where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.universe-levels -open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext -open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.subspaces-metric-spaces funext +open import metric-spaces.convergent-cauchy-approximations-metric-spaces +open import metric-spaces.metric-space-of-cauchy-approximations-in-a-metric-space +open import metric-spaces.metric-spaces +open import metric-spaces.subspaces-metric-spaces ```
diff --git a/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md b/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md index 0046388c48..5f2525fef2 100644 --- a/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md +++ b/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md @@ -3,45 +3,40 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods - (funext : function-extensionality) - where +module metric-spaces.metric-space-of-rational-numbers-with-open-neighborhoods where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.difference-rational-numbers funext -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.difference-rational-numbers +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.metric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-spaces funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.pseudometric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.metric-spaces +open import metric-spaces.metric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-spaces +open import metric-spaces.premetric-structures +open import metric-spaces.pseudometric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/metric-space-of-rational-numbers.lagda.md b/src/metric-spaces/metric-space-of-rational-numbers.lagda.md index c643b02bac..8ad75841c4 100644 --- a/src/metric-spaces/metric-space-of-rational-numbers.lagda.md +++ b/src/metric-spaces/metric-space-of-rational-numbers.lagda.md @@ -3,54 +3,49 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - metric-spaces.metric-space-of-rational-numbers - (funext : function-extensionality) - where +module metric-spaces.metric-space-of-rational-numbers where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.difference-rational-numbers funext -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.difference-rational-numbers +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.diagonal-maps-cartesian-products-of-types funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.diagonal-maps-cartesian-products-of-types +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.cauchy-approximations-metric-spaces funext -open import metric-spaces.convergent-cauchy-approximations-metric-spaces funext -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.isometries-metric-spaces funext -open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.metric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-spaces funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.pseudometric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.saturated-metric-spaces funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.cauchy-approximations-metric-spaces +open import metric-spaces.convergent-cauchy-approximations-metric-spaces +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.isometries-metric-spaces +open import metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.metric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-spaces +open import metric-spaces.premetric-structures +open import metric-spaces.pseudometric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.saturated-metric-spaces +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/metric-spaces.lagda.md b/src/metric-spaces/metric-spaces.lagda.md index ab46d4e6a9..27701dbe35 100644 --- a/src/metric-spaces/metric-spaces.lagda.md +++ b/src/metric-spaces/metric-spaces.lagda.md @@ -1,41 +1,36 @@ # Metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.metric-spaces - (funext : function-extensionality) - where +module metric-spaces.metric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.metric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-spaces funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.pseudometric-spaces funext -open import metric-spaces.pseudometric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.metric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-spaces +open import metric-spaces.premetric-structures +open import metric-spaces.pseudometric-spaces +open import metric-spaces.pseudometric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/metric-structures.lagda.md b/src/metric-spaces/metric-structures.lagda.md index a67b035f6b..0839f2efae 100644 --- a/src/metric-spaces/metric-structures.lagda.md +++ b/src/metric-spaces/metric-structures.lagda.md @@ -1,32 +1,27 @@ # Metric structures ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.metric-structures - (funext : function-extensionality) - where +module metric-spaces.metric-structures where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.universe-levels -open import metric-spaces.closed-premetric-structures funext -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.ordering-premetric-structures funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.pseudometric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.closed-premetric-structures +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.ordering-premetric-structures +open import metric-spaces.premetric-structures +open import metric-spaces.pseudometric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/monotonic-premetric-structures.lagda.md b/src/metric-spaces/monotonic-premetric-structures.lagda.md index c7caede9ab..d495f3087d 100644 --- a/src/metric-spaces/monotonic-premetric-structures.lagda.md +++ b/src/metric-spaces/monotonic-premetric-structures.lagda.md @@ -1,23 +1,18 @@ # Monotonic premetric structures on types ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.monotonic-premetric-structures - (funext : function-extensionality) - where +module metric-spaces.monotonic-premetric-structures where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import metric-spaces.premetric-structures funext +open import metric-spaces.premetric-structures ```
diff --git a/src/metric-spaces/ordering-premetric-structures.lagda.md b/src/metric-spaces/ordering-premetric-structures.lagda.md index 646ebe12c8..9d31996995 100644 --- a/src/metric-spaces/ordering-premetric-structures.lagda.md +++ b/src/metric-spaces/ordering-premetric-structures.lagda.md @@ -1,30 +1,25 @@ # The poset of premetric structures on a type ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.ordering-premetric-structures - (funext : function-extensionality) - where +module metric-spaces.ordering-premetric-structures where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import metric-spaces.premetric-structures funext +open import metric-spaces.premetric-structures -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md index b959e04df2..0ad621c3a1 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-functions.lagda.md @@ -1,25 +1,20 @@ # The precategory of metric spaces and functions ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.precategory-of-metric-spaces-and-functions - (funext : function-extensionality) - where +module metric-spaces.precategory-of-metric-spaces-and-functions where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import metric-spaces.functions-metric-spaces funext -open import metric-spaces.metric-spaces funext +open import metric-spaces.functions-metric-spaces +open import metric-spaces.metric-spaces ```
diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md index 8ec36ffd11..aceb047872 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-isometries.lagda.md @@ -1,34 +1,30 @@ # The precategory of metric spaces and isometries ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.precategory-of-metric-spaces-and-isometries - (funext : function-extensionality) - where +module metric-spaces.precategory-of-metric-spaces-and-isometries where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.logical-equivalences funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.logical-equivalences open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces funext -open import metric-spaces.functions-metric-spaces funext -open import metric-spaces.isometries-metric-spaces funext -open import metric-spaces.metric-spaces funext +open import metric-spaces.equality-of-metric-spaces +open import metric-spaces.functions-metric-spaces +open import metric-spaces.isometries-metric-spaces +open import metric-spaces.metric-spaces ```
diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md index ba40e55f4f..bc3ca88ffe 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md @@ -1,36 +1,32 @@ # The precategory of metric spaces and short functions ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.precategory-of-metric-spaces-and-short-functions - (funext : function-extensionality) - where +module metric-spaces.precategory-of-metric-spaces-and-short-functions where ```
Imports ```agda -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.functoriality-dependent-pair-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import metric-spaces.equality-of-metric-spaces funext -open import metric-spaces.functions-metric-spaces funext -open import metric-spaces.isometric-equivalences-premetric-spaces funext -open import metric-spaces.isometries-metric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.short-functions-metric-spaces funext +open import metric-spaces.equality-of-metric-spaces +open import metric-spaces.functions-metric-spaces +open import metric-spaces.isometric-equivalences-premetric-spaces +open import metric-spaces.isometries-metric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.short-functions-metric-spaces ```
diff --git a/src/metric-spaces/premetric-spaces.lagda.md b/src/metric-spaces/premetric-spaces.lagda.md index 9ee09c5365..edc68f4a20 100644 --- a/src/metric-spaces/premetric-spaces.lagda.md +++ b/src/metric-spaces/premetric-spaces.lagda.md @@ -1,31 +1,26 @@ # Premetric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.premetric-spaces - (funext : function-extensionality) - where +module metric-spaces.premetric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.propositions open import foundation.universe-levels -open import metric-spaces.discrete-premetric-structures funext -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.discrete-premetric-structures +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/premetric-structures.lagda.md b/src/metric-spaces/premetric-structures.lagda.md index 8b0066b45a..1efac73fa8 100644 --- a/src/metric-spaces/premetric-structures.lagda.md +++ b/src/metric-spaces/premetric-structures.lagda.md @@ -1,38 +1,32 @@ # Premetric structures on types ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.premetric-structures - (funext : function-extensionality) - where +module metric-spaces.premetric-structures where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-extensionality +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-extensionality funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-extensionality +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels ``` diff --git a/src/metric-spaces/pseudometric-spaces.lagda.md b/src/metric-spaces/pseudometric-spaces.lagda.md index 7537bab100..1504bef0ae 100644 --- a/src/metric-spaces/pseudometric-spaces.lagda.md +++ b/src/metric-spaces/pseudometric-spaces.lagda.md @@ -1,35 +1,30 @@ # Pseudometric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.pseudometric-spaces - (funext : function-extensionality) - where +module metric-spaces.pseudometric-spaces where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalence-relations +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.discrete-premetric-structures funext -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-spaces funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.pseudometric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.discrete-premetric-structures +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-spaces +open import metric-spaces.premetric-structures +open import metric-spaces.pseudometric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/pseudometric-structures.lagda.md b/src/metric-spaces/pseudometric-structures.lagda.md index a7ee1b258c..fb0476457b 100644 --- a/src/metric-spaces/pseudometric-structures.lagda.md +++ b/src/metric-spaces/pseudometric-structures.lagda.md @@ -1,30 +1,25 @@ # Pseudometric structures on a type ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.pseudometric-structures - (funext : function-extensionality) - where +module metric-spaces.pseudometric-structures where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import metric-spaces.closed-premetric-structures funext -open import metric-spaces.discrete-premetric-structures funext -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.closed-premetric-structures +open import metric-spaces.discrete-premetric-structures +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/reflexive-premetric-structures.lagda.md b/src/metric-spaces/reflexive-premetric-structures.lagda.md index 26a2f94f85..5bb77664f7 100644 --- a/src/metric-spaces/reflexive-premetric-structures.lagda.md +++ b/src/metric-spaces/reflexive-premetric-structures.lagda.md @@ -1,33 +1,28 @@ # Reflexive premetric structures on types ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.reflexive-premetric-structures - (funext : function-extensionality) - where +module metric-spaces.reflexive-premetric-structures where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.premetric-structures funext +open import metric-spaces.premetric-structures ```
diff --git a/src/metric-spaces/saturated-metric-spaces.lagda.md b/src/metric-spaces/saturated-metric-spaces.lagda.md index b0101f8cd1..f4d759453b 100644 --- a/src/metric-spaces/saturated-metric-spaces.lagda.md +++ b/src/metric-spaces/saturated-metric-spaces.lagda.md @@ -1,38 +1,33 @@ # Saturated metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.saturated-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.saturated-metric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.closed-premetric-structures funext -open import metric-spaces.functions-metric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.metric-structures funext -open import metric-spaces.premetric-spaces funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.short-functions-metric-spaces funext +open import metric-spaces.closed-premetric-structures +open import metric-spaces.functions-metric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.metric-structures +open import metric-spaces.premetric-spaces +open import metric-spaces.premetric-structures +open import metric-spaces.short-functions-metric-spaces ```
diff --git a/src/metric-spaces/short-functions-metric-spaces.lagda.md b/src/metric-spaces/short-functions-metric-spaces.lagda.md index 37f418dfb9..bab344ebbb 100644 --- a/src/metric-spaces/short-functions-metric-spaces.lagda.md +++ b/src/metric-spaces/short-functions-metric-spaces.lagda.md @@ -1,38 +1,32 @@ # Short functions between metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.short-functions-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.short-functions-metric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.sequences -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.functions-metric-spaces funext -open import metric-spaces.isometries-metric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.short-functions-premetric-spaces funext +open import metric-spaces.functions-metric-spaces +open import metric-spaces.isometries-metric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.short-functions-premetric-spaces ```
diff --git a/src/metric-spaces/short-functions-premetric-spaces.lagda.md b/src/metric-spaces/short-functions-premetric-spaces.lagda.md index 6afcde009f..f719e1acfc 100644 --- a/src/metric-spaces/short-functions-premetric-spaces.lagda.md +++ b/src/metric-spaces/short-functions-premetric-spaces.lagda.md @@ -1,37 +1,31 @@ # Short functions between premetric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.short-functions-premetric-spaces - (funext : function-extensionality) - where +module metric-spaces.short-functions-premetric-spaces where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.sequences -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.isometries-premetric-spaces funext -open import metric-spaces.premetric-spaces funext +open import metric-spaces.isometries-premetric-spaces +open import metric-spaces.premetric-spaces ```
diff --git a/src/metric-spaces/subspaces-metric-spaces.lagda.md b/src/metric-spaces/subspaces-metric-spaces.lagda.md index 3753d76e4f..0b5765b507 100644 --- a/src/metric-spaces/subspaces-metric-spaces.lagda.md +++ b/src/metric-spaces/subspaces-metric-spaces.lagda.md @@ -1,33 +1,28 @@ # Subspaces of metric spaces ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.subspaces-metric-spaces - (funext : function-extensionality) - where +module metric-spaces.subspaces-metric-spaces where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.logical-equivalences funext -open import foundation.subtypes funext +open import foundation.logical-equivalences +open import foundation.subtypes open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.functions-metric-spaces funext -open import metric-spaces.isometries-metric-spaces funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.metric-structures funext -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.pseudometric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.functions-metric-spaces +open import metric-spaces.isometries-metric-spaces +open import metric-spaces.metric-spaces +open import metric-spaces.metric-structures +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-structures +open import metric-spaces.pseudometric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures ```
diff --git a/src/metric-spaces/symmetric-premetric-structures.lagda.md b/src/metric-spaces/symmetric-premetric-structures.lagda.md index b4df549191..86d360e6a2 100644 --- a/src/metric-spaces/symmetric-premetric-structures.lagda.md +++ b/src/metric-spaces/symmetric-premetric-structures.lagda.md @@ -1,27 +1,22 @@ # Symmetric premetric structures on types ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.symmetric-premetric-structures - (funext : function-extensionality) - where +module metric-spaces.symmetric-premetric-structures where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.binary-relations funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.binary-relations +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import metric-spaces.premetric-structures funext +open import metric-spaces.premetric-structures ```
diff --git a/src/metric-spaces/triangular-premetric-structures.lagda.md b/src/metric-spaces/triangular-premetric-structures.lagda.md index de181e5683..98b2b7c42a 100644 --- a/src/metric-spaces/triangular-premetric-structures.lagda.md +++ b/src/metric-spaces/triangular-premetric-structures.lagda.md @@ -1,29 +1,24 @@ # Triangular premetric structures on types ```agda -open import foundation.function-extensionality-axiom - -module - metric-spaces.triangular-premetric-structures - (funext : function-extensionality) - where +module metric-spaces.triangular-premetric-structures where ```
Imports ```agda -open import elementary-number-theory.positive-rational-numbers funext +open import elementary-number-theory.positive-rational-numbers -open import foundation.binary-relations funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.binary-relations +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.monotonic-premetric-structures funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.reflexive-premetric-structures funext +open import metric-spaces.monotonic-premetric-structures +open import metric-spaces.premetric-structures +open import metric-spaces.reflexive-premetric-structures ```
diff --git a/src/modal-type-theory.lagda.md b/src/modal-type-theory.lagda.md index e278c1e9b9..e9f60ad038 100644 --- a/src/modal-type-theory.lagda.md +++ b/src/modal-type-theory.lagda.md @@ -20,34 +20,29 @@ _cohesive_ structure. ## Modules in the modal type theory namespace ```agda -open import foundation.function-extensionality-axiom - -module - modal-type-theory - (funext : function-extensionality) - where - -open import modal-type-theory.action-on-homotopies-flat-modality funext public -open import modal-type-theory.action-on-identifications-crisp-functions funext public -open import modal-type-theory.action-on-identifications-flat-modality funext public -open import modal-type-theory.crisp-cartesian-product-types funext public -open import modal-type-theory.crisp-coproduct-types funext public -open import modal-type-theory.crisp-dependent-function-types funext public -open import modal-type-theory.crisp-dependent-pair-types funext public -open import modal-type-theory.crisp-function-types funext public -open import modal-type-theory.crisp-identity-types funext public -open import modal-type-theory.crisp-law-of-excluded-middle funext public -open import modal-type-theory.crisp-pullbacks funext public +module modal-type-theory where + +open import modal-type-theory.action-on-homotopies-flat-modality public +open import modal-type-theory.action-on-identifications-crisp-functions public +open import modal-type-theory.action-on-identifications-flat-modality public +open import modal-type-theory.crisp-cartesian-product-types public +open import modal-type-theory.crisp-coproduct-types public +open import modal-type-theory.crisp-dependent-function-types public +open import modal-type-theory.crisp-dependent-pair-types public +open import modal-type-theory.crisp-function-types public +open import modal-type-theory.crisp-identity-types public +open import modal-type-theory.crisp-law-of-excluded-middle public +open import modal-type-theory.crisp-pullbacks public open import modal-type-theory.crisp-types public -open import modal-type-theory.dependent-universal-property-flat-discrete-crisp-types funext public -open import modal-type-theory.flat-discrete-crisp-types funext public -open import modal-type-theory.flat-modality funext public -open import modal-type-theory.flat-sharp-adjunction funext public -open import modal-type-theory.functoriality-flat-modality funext public -open import modal-type-theory.functoriality-sharp-modality funext public -open import modal-type-theory.sharp-codiscrete-maps funext public -open import modal-type-theory.sharp-codiscrete-types funext public -open import modal-type-theory.sharp-modality funext public -open import modal-type-theory.transport-along-crisp-identifications funext public -open import modal-type-theory.universal-property-flat-discrete-crisp-types funext public +open import modal-type-theory.dependent-universal-property-flat-discrete-crisp-types public +open import modal-type-theory.flat-discrete-crisp-types public +open import modal-type-theory.flat-modality public +open import modal-type-theory.flat-sharp-adjunction public +open import modal-type-theory.functoriality-flat-modality public +open import modal-type-theory.functoriality-sharp-modality public +open import modal-type-theory.sharp-codiscrete-maps public +open import modal-type-theory.sharp-codiscrete-types public +open import modal-type-theory.sharp-modality public +open import modal-type-theory.transport-along-crisp-identifications public +open import modal-type-theory.universal-property-flat-discrete-crisp-types public ``` diff --git a/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md b/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md index f9768264b9..248652177b 100644 --- a/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md +++ b/src/modal-type-theory/action-on-homotopies-flat-modality.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.action-on-homotopies-flat-modality - (funext : function-extensionality) - where +module modal-type-theory.action-on-homotopies-flat-modality where ```
Imports ```agda -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality funext -open import modal-type-theory.flat-modality funext -open import modal-type-theory.functoriality-flat-modality funext +open import modal-type-theory.action-on-identifications-flat-modality +open import modal-type-theory.flat-modality +open import modal-type-theory.functoriality-flat-modality ```
diff --git a/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md b/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md index f1824ee303..085fda16e2 100644 --- a/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md +++ b/src/modal-type-theory/action-on-identifications-crisp-functions.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.action-on-identifications-crisp-functions - (funext : function-extensionality) - where +module modal-type-theory.action-on-identifications-crisp-functions where ```
Imports @@ -18,7 +13,7 @@ open import foundation.universe-levels open import foundation-core.identity-types -open import modal-type-theory.crisp-identity-types funext +open import modal-type-theory.crisp-identity-types ```
diff --git a/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md b/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md index ef1612fb19..4f878208a8 100644 --- a/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md +++ b/src/modal-type-theory/action-on-identifications-flat-modality.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.action-on-identifications-flat-modality - (funext : function-extensionality) - where +module modal-type-theory.action-on-identifications-flat-modality where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-crisp-functions funext -open import modal-type-theory.crisp-identity-types funext -open import modal-type-theory.flat-modality funext +open import modal-type-theory.action-on-identifications-crisp-functions +open import modal-type-theory.crisp-identity-types +open import modal-type-theory.flat-modality ```
diff --git a/src/modal-type-theory/crisp-cartesian-product-types.lagda.md b/src/modal-type-theory/crisp-cartesian-product-types.lagda.md index 01a8bc6fd2..000d78c746 100644 --- a/src/modal-type-theory/crisp-cartesian-product-types.lagda.md +++ b/src/modal-type-theory/crisp-cartesian-product-types.lagda.md @@ -3,32 +3,27 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.crisp-cartesian-product-types - (funext : function-extensionality) - where +module modal-type-theory.crisp-cartesian-product-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.propositional-truncations +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels -open import modal-type-theory.flat-discrete-crisp-types funext -open import modal-type-theory.flat-modality funext +open import modal-type-theory.flat-discrete-crisp-types +open import modal-type-theory.flat-modality ```
diff --git a/src/modal-type-theory/crisp-coproduct-types.lagda.md b/src/modal-type-theory/crisp-coproduct-types.lagda.md index 41bc6c326b..1fc84587d7 100644 --- a/src/modal-type-theory/crisp-coproduct-types.lagda.md +++ b/src/modal-type-theory/crisp-coproduct-types.lagda.md @@ -3,30 +3,25 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.crisp-coproduct-types - (funext : function-extensionality) - where +module modal-type-theory.crisp-coproduct-types where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels -open import modal-type-theory.flat-discrete-crisp-types funext -open import modal-type-theory.flat-modality funext +open import modal-type-theory.flat-discrete-crisp-types +open import modal-type-theory.flat-modality ```
diff --git a/src/modal-type-theory/crisp-dependent-function-types.lagda.md b/src/modal-type-theory/crisp-dependent-function-types.lagda.md index 3f438c2db7..a5034fb664 100644 --- a/src/modal-type-theory/crisp-dependent-function-types.lagda.md +++ b/src/modal-type-theory/crisp-dependent-function-types.lagda.md @@ -3,29 +3,23 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.crisp-dependent-function-types - (funext : function-extensionality) - where +module modal-type-theory.crisp-dependent-function-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality funext -open import modal-type-theory.flat-modality funext -open import modal-type-theory.functoriality-flat-modality funext +open import modal-type-theory.action-on-identifications-flat-modality +open import modal-type-theory.flat-modality +open import modal-type-theory.functoriality-flat-modality ```
diff --git a/src/modal-type-theory/crisp-dependent-pair-types.lagda.md b/src/modal-type-theory/crisp-dependent-pair-types.lagda.md index c1c0612e10..962a9f0762 100644 --- a/src/modal-type-theory/crisp-dependent-pair-types.lagda.md +++ b/src/modal-type-theory/crisp-dependent-pair-types.lagda.md @@ -3,30 +3,25 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.crisp-dependent-pair-types - (funext : function-extensionality) - where +module modal-type-theory.crisp-dependent-pair-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels -open import modal-type-theory.flat-discrete-crisp-types funext -open import modal-type-theory.flat-modality funext -open import modal-type-theory.functoriality-flat-modality funext +open import modal-type-theory.flat-discrete-crisp-types +open import modal-type-theory.flat-modality +open import modal-type-theory.functoriality-flat-modality ```
diff --git a/src/modal-type-theory/crisp-function-types.lagda.md b/src/modal-type-theory/crisp-function-types.lagda.md index 78b625299f..57b0ed3e46 100644 --- a/src/modal-type-theory/crisp-function-types.lagda.md +++ b/src/modal-type-theory/crisp-function-types.lagda.md @@ -3,31 +3,25 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.crisp-function-types - (funext : function-extensionality) - where +module modal-type-theory.crisp-function-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.postcomposition-functions +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality funext -open import modal-type-theory.crisp-dependent-function-types funext -open import modal-type-theory.flat-modality funext -open import modal-type-theory.functoriality-flat-modality funext +open import modal-type-theory.action-on-identifications-flat-modality +open import modal-type-theory.crisp-dependent-function-types +open import modal-type-theory.flat-modality +open import modal-type-theory.functoriality-flat-modality ```
diff --git a/src/modal-type-theory/crisp-identity-types.lagda.md b/src/modal-type-theory/crisp-identity-types.lagda.md index a17e0ba7a4..adffea8d96 100644 --- a/src/modal-type-theory/crisp-identity-types.lagda.md +++ b/src/modal-type-theory/crisp-identity-types.lagda.md @@ -3,27 +3,22 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.crisp-identity-types - (funext : function-extensionality) - where +module modal-type-theory.crisp-identity-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.retractions funext -open import foundation.retracts-of-types funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.retractions +open import foundation.retracts-of-types +open import foundation.sections open import foundation.universe-levels -open import modal-type-theory.flat-modality funext +open import modal-type-theory.flat-modality ```
diff --git a/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md b/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md index 3651c68d44..52f9b9c10f 100644 --- a/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md +++ b/src/modal-type-theory/crisp-law-of-excluded-middle.lagda.md @@ -3,22 +3,17 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.crisp-law-of-excluded-middle - (funext : function-extensionality) - where +module modal-type-theory.crisp-law-of-excluded-middle where ```
Imports ```agda -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions open import foundation-core.propositions ``` diff --git a/src/modal-type-theory/crisp-pullbacks.lagda.md b/src/modal-type-theory/crisp-pullbacks.lagda.md index 30a578b33a..d0e87ca486 100644 --- a/src/modal-type-theory/crisp-pullbacks.lagda.md +++ b/src/modal-type-theory/crisp-pullbacks.lagda.md @@ -3,38 +3,33 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.crisp-pullbacks - (funext : function-extensionality) - where +module modal-type-theory.crisp-pullbacks where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-pullbacks funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-pullbacks +open import foundation.homotopies +open import foundation.identity-types open import foundation.morphisms-cospan-diagrams -open import foundation.pullbacks funext -open import foundation.standard-pullbacks funext +open import foundation.pullbacks +open import foundation.standard-pullbacks open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-crisp-functions funext -open import modal-type-theory.action-on-identifications-flat-modality funext -open import modal-type-theory.crisp-dependent-pair-types funext -open import modal-type-theory.crisp-identity-types funext -open import modal-type-theory.flat-discrete-crisp-types funext -open import modal-type-theory.flat-modality funext -open import modal-type-theory.functoriality-flat-modality funext +open import modal-type-theory.action-on-identifications-crisp-functions +open import modal-type-theory.action-on-identifications-flat-modality +open import modal-type-theory.crisp-dependent-pair-types +open import modal-type-theory.crisp-identity-types +open import modal-type-theory.flat-discrete-crisp-types +open import modal-type-theory.flat-modality +open import modal-type-theory.functoriality-flat-modality ```
diff --git a/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md index 1e107b20da..1754d487ba 100644 --- a/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/dependent-universal-property-flat-discrete-crisp-types.lagda.md @@ -3,21 +3,16 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.dependent-universal-property-flat-discrete-crisp-types - (funext : function-extensionality) - where +module modal-type-theory.dependent-universal-property-flat-discrete-crisp-types where ```
Imports ```agda -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import modal-type-theory.flat-modality funext +open import modal-type-theory.flat-modality ```
diff --git a/src/modal-type-theory/flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/flat-discrete-crisp-types.lagda.md index d587bee7bc..5bf37687fc 100644 --- a/src/modal-type-theory/flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/flat-discrete-crisp-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.flat-discrete-crisp-types - (funext : function-extensionality) - where +module modal-type-theory.flat-discrete-crisp-types where ```
Imports @@ -17,24 +12,24 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.booleans funext +open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.retractions +open import foundation.sections open import foundation.unit-type open import foundation.universe-levels -open import modal-type-theory.action-on-homotopies-flat-modality funext -open import modal-type-theory.crisp-identity-types funext -open import modal-type-theory.flat-modality funext -open import modal-type-theory.functoriality-flat-modality funext +open import modal-type-theory.action-on-homotopies-flat-modality +open import modal-type-theory.crisp-identity-types +open import modal-type-theory.flat-modality +open import modal-type-theory.functoriality-flat-modality ```
diff --git a/src/modal-type-theory/flat-modality.lagda.md b/src/modal-type-theory/flat-modality.lagda.md index d3e917659d..10318f9d11 100644 --- a/src/modal-type-theory/flat-modality.lagda.md +++ b/src/modal-type-theory/flat-modality.lagda.md @@ -3,22 +3,17 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.flat-modality - (funext : function-extensionality) - where +module modal-type-theory.flat-modality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels ``` diff --git a/src/modal-type-theory/flat-sharp-adjunction.lagda.md b/src/modal-type-theory/flat-sharp-adjunction.lagda.md index be552aa494..f3cd07d5ef 100644 --- a/src/modal-type-theory/flat-sharp-adjunction.lagda.md +++ b/src/modal-type-theory/flat-sharp-adjunction.lagda.md @@ -3,31 +3,26 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.flat-sharp-adjunction - (funext : function-extensionality) - where +module modal-type-theory.flat-sharp-adjunction where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections open import foundation.transport-along-identifications open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality funext -open import modal-type-theory.flat-modality funext -open import modal-type-theory.functoriality-flat-modality funext -open import modal-type-theory.sharp-codiscrete-types funext -open import modal-type-theory.sharp-modality funext +open import modal-type-theory.action-on-identifications-flat-modality +open import modal-type-theory.flat-modality +open import modal-type-theory.functoriality-flat-modality +open import modal-type-theory.sharp-codiscrete-types +open import modal-type-theory.sharp-modality ```
diff --git a/src/modal-type-theory/functoriality-flat-modality.lagda.md b/src/modal-type-theory/functoriality-flat-modality.lagda.md index 9e238b8219..150a1c469e 100644 --- a/src/modal-type-theory/functoriality-flat-modality.lagda.md +++ b/src/modal-type-theory/functoriality-flat-modality.lagda.md @@ -3,29 +3,24 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.functoriality-flat-modality - (funext : function-extensionality) - where +module modal-type-theory.functoriality-flat-modality where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.retracts-of-types funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.retractions +open import foundation.retracts-of-types +open import foundation.sections open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-flat-modality funext -open import modal-type-theory.flat-modality funext +open import modal-type-theory.action-on-identifications-flat-modality +open import modal-type-theory.flat-modality ```
diff --git a/src/modal-type-theory/functoriality-sharp-modality.lagda.md b/src/modal-type-theory/functoriality-sharp-modality.lagda.md index 14a7e2c95a..673562dad9 100644 --- a/src/modal-type-theory/functoriality-sharp-modality.lagda.md +++ b/src/modal-type-theory/functoriality-sharp-modality.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.functoriality-sharp-modality - (funext : function-extensionality) - where +module modal-type-theory.functoriality-sharp-modality where ```
Imports @@ -16,17 +11,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.locally-small-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.locally-small-types open import foundation.universe-levels -open import modal-type-theory.sharp-modality funext +open import modal-type-theory.sharp-modality -open import orthogonal-factorization-systems.locally-small-modal-operators funext -open import orthogonal-factorization-systems.modal-induction funext -open import orthogonal-factorization-systems.modal-subuniverse-induction funext +open import orthogonal-factorization-systems.locally-small-modal-operators +open import orthogonal-factorization-systems.modal-induction +open import orthogonal-factorization-systems.modal-subuniverse-induction ```
diff --git a/src/modal-type-theory/sharp-codiscrete-maps.lagda.md b/src/modal-type-theory/sharp-codiscrete-maps.lagda.md index bed39825a8..b6f62e6748 100644 --- a/src/modal-type-theory/sharp-codiscrete-maps.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-maps.lagda.md @@ -3,22 +3,17 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.sharp-codiscrete-maps - (funext : function-extensionality) - where +module modal-type-theory.sharp-codiscrete-maps where ```
Imports ```agda -open import foundation.fibers-of-maps funext -open import foundation.propositions funext +open import foundation.fibers-of-maps +open import foundation.propositions open import foundation.universe-levels -open import modal-type-theory.sharp-codiscrete-types funext +open import modal-type-theory.sharp-codiscrete-types ```
diff --git a/src/modal-type-theory/sharp-codiscrete-types.lagda.md b/src/modal-type-theory/sharp-codiscrete-types.lagda.md index 94caf20a69..7b570a8aa2 100644 --- a/src/modal-type-theory/sharp-codiscrete-types.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.sharp-codiscrete-types - (funext : function-extensionality) - where +module modal-type-theory.sharp-codiscrete-types where ```
Imports @@ -16,18 +11,19 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.transport-along-equivalences funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.transport-along-equivalences open import foundation.universe-levels -open import modal-type-theory.sharp-modality funext +open import modal-type-theory.sharp-modality -open import orthogonal-factorization-systems.higher-modalities funext -open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.higher-modalities +open import orthogonal-factorization-systems.modal-operators ```
diff --git a/src/modal-type-theory/sharp-modality.lagda.md b/src/modal-type-theory/sharp-modality.lagda.md index 779b136c63..3dba911431 100644 --- a/src/modal-type-theory/sharp-modality.lagda.md +++ b/src/modal-type-theory/sharp-modality.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.sharp-modality - (funext : function-extensionality) - where +module modal-type-theory.sharp-modality where ```
Imports @@ -16,15 +11,15 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.locally-small-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.locally-small-types open import foundation.universe-levels -open import orthogonal-factorization-systems.locally-small-modal-operators funext -open import orthogonal-factorization-systems.modal-induction funext -open import orthogonal-factorization-systems.modal-subuniverse-induction funext +open import orthogonal-factorization-systems.locally-small-modal-operators +open import orthogonal-factorization-systems.modal-induction +open import orthogonal-factorization-systems.modal-subuniverse-induction ```
diff --git a/src/modal-type-theory/transport-along-crisp-identifications.lagda.md b/src/modal-type-theory/transport-along-crisp-identifications.lagda.md index 233d03b939..3405430500 100644 --- a/src/modal-type-theory/transport-along-crisp-identifications.lagda.md +++ b/src/modal-type-theory/transport-along-crisp-identifications.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.transport-along-crisp-identifications - (funext : function-extensionality) - where +module modal-type-theory.transport-along-crisp-identifications where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import modal-type-theory.crisp-identity-types funext +open import modal-type-theory.crisp-identity-types ```
diff --git a/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md index 759461fb7e..63e293c714 100644 --- a/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/universal-property-flat-discrete-crisp-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --cohesion --flat-split #-} -open import foundation.function-extensionality-axiom - -module - modal-type-theory.universal-property-flat-discrete-crisp-types - (funext : function-extensionality) - where +module modal-type-theory.universal-property-flat-discrete-crisp-types where ```
Imports @@ -16,20 +11,19 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext -open import foundation.universal-property-equivalences funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.identity-types +open import foundation.postcomposition-functions +open import foundation.universal-property-equivalences open import foundation.universe-levels -open import modal-type-theory.action-on-identifications-crisp-functions funext -open import modal-type-theory.crisp-function-types funext -open import modal-type-theory.flat-discrete-crisp-types funext -open import modal-type-theory.flat-modality funext -open import modal-type-theory.functoriality-flat-modality funext +open import modal-type-theory.action-on-identifications-crisp-functions +open import modal-type-theory.crisp-function-types +open import modal-type-theory.flat-discrete-crisp-types +open import modal-type-theory.flat-modality +open import modal-type-theory.functoriality-flat-modality ```
diff --git a/src/order-theory.lagda.md b/src/order-theory.lagda.md index c38720517a..349f62993a 100644 --- a/src/order-theory.lagda.md +++ b/src/order-theory.lagda.md @@ -3,144 +3,139 @@ ## Modules in the order theory namespace ```agda -open import foundation.function-extensionality-axiom +module order-theory where -module - order-theory - (funext : function-extensionality) - where - -open import order-theory.accessible-elements-relations funext public -open import order-theory.bottom-elements-large-posets funext public -open import order-theory.bottom-elements-posets funext public -open import order-theory.bottom-elements-preorders funext public -open import order-theory.chains-posets funext public -open import order-theory.chains-preorders funext public -open import order-theory.closure-operators-large-locales funext public -open import order-theory.closure-operators-large-posets funext public -open import order-theory.commuting-squares-of-galois-connections-large-posets funext public -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext public -open import order-theory.coverings-locales funext public -open import order-theory.decidable-posets funext public -open import order-theory.decidable-preorders funext public -open import order-theory.decidable-subposets funext public -open import order-theory.decidable-subpreorders funext public -open import order-theory.decidable-total-orders funext public -open import order-theory.decidable-total-preorders funext public -open import order-theory.deflationary-maps-posets funext public -open import order-theory.deflationary-maps-preorders funext public -open import order-theory.dependent-products-large-frames funext public -open import order-theory.dependent-products-large-inflattices funext public -open import order-theory.dependent-products-large-locales funext public -open import order-theory.dependent-products-large-meet-semilattices funext public -open import order-theory.dependent-products-large-posets funext public -open import order-theory.dependent-products-large-preorders funext public -open import order-theory.dependent-products-large-suplattices funext public -open import order-theory.distributive-lattices funext public -open import order-theory.finite-coverings-locales funext public -open import order-theory.finite-posets funext public -open import order-theory.finite-preorders funext public -open import order-theory.finite-total-orders funext public -open import order-theory.finitely-graded-posets funext public -open import order-theory.frames funext public -open import order-theory.galois-connections funext public -open import order-theory.galois-connections-large-posets funext public -open import order-theory.greatest-lower-bounds-large-posets funext public -open import order-theory.greatest-lower-bounds-posets funext public -open import order-theory.homomorphisms-frames funext public -open import order-theory.homomorphisms-large-frames funext public -open import order-theory.homomorphisms-large-locales funext public -open import order-theory.homomorphisms-large-meet-semilattices funext public -open import order-theory.homomorphisms-large-suplattices funext public -open import order-theory.homomorphisms-meet-semilattices funext public -open import order-theory.homomorphisms-meet-suplattices funext public -open import order-theory.homomorphisms-suplattices funext public -open import order-theory.ideals-preorders funext public -open import order-theory.incidence-algebras funext public -open import order-theory.inflationary-maps-posets funext public -open import order-theory.inflationary-maps-preorders funext public -open import order-theory.inflattices funext public -open import order-theory.inhabited-chains-posets funext public -open import order-theory.inhabited-chains-preorders funext public -open import order-theory.inhabited-finite-total-orders funext public -open import order-theory.interval-subposets funext public -open import order-theory.join-preserving-maps-posets funext public -open import order-theory.join-semilattices funext public -open import order-theory.knaster-tarski-fixed-point-theorem funext public -open import order-theory.large-frames funext public -open import order-theory.large-inflattices funext public -open import order-theory.large-join-semilattices funext public -open import order-theory.large-locales funext public -open import order-theory.large-meet-semilattices funext public -open import order-theory.large-meet-subsemilattices funext public -open import order-theory.large-posets funext public -open import order-theory.large-preorders funext public -open import order-theory.large-quotient-locales funext public -open import order-theory.large-subframes funext public -open import order-theory.large-subposets funext public -open import order-theory.large-subpreorders funext public -open import order-theory.large-subsuplattices funext public -open import order-theory.large-suplattices funext public -open import order-theory.lattices funext public -open import order-theory.least-upper-bounds-large-posets funext public -open import order-theory.least-upper-bounds-posets funext public -open import order-theory.locales funext public -open import order-theory.locally-finite-posets funext public -open import order-theory.lower-bounds-large-posets funext public -open import order-theory.lower-bounds-posets funext public -open import order-theory.lower-sets-large-posets funext public -open import order-theory.lower-types-preorders funext public -open import order-theory.maximal-chains-posets funext public -open import order-theory.maximal-chains-preorders funext public -open import order-theory.meet-semilattices funext public -open import order-theory.meet-suplattices funext public -open import order-theory.nuclei-large-locales funext public -open import order-theory.opposite-large-posets funext public -open import order-theory.opposite-large-preorders funext public -open import order-theory.opposite-posets funext public -open import order-theory.opposite-preorders funext public -open import order-theory.order-preserving-maps-large-posets funext public -open import order-theory.order-preserving-maps-large-preorders funext public -open import order-theory.order-preserving-maps-posets funext public -open import order-theory.order-preserving-maps-preorders funext public -open import order-theory.ordinals funext public -open import order-theory.posets funext public -open import order-theory.powers-of-large-locales funext public -open import order-theory.precategory-of-decidable-total-orders funext public -open import order-theory.precategory-of-finite-posets funext public -open import order-theory.precategory-of-finite-total-orders funext public -open import order-theory.precategory-of-inhabited-finite-total-orders funext public -open import order-theory.precategory-of-posets funext public -open import order-theory.precategory-of-total-orders funext public -open import order-theory.preorders funext public -open import order-theory.principal-lower-sets-large-posets funext public -open import order-theory.principal-upper-sets-large-posets funext public -open import order-theory.reflective-galois-connections-large-posets funext public -open import order-theory.resizing-posets funext public -open import order-theory.resizing-preorders funext public -open import order-theory.resizing-suplattices funext public -open import order-theory.similarity-of-elements-large-posets funext public -open import order-theory.similarity-of-elements-large-preorders funext public -open import order-theory.similarity-of-order-preserving-maps-large-posets funext public -open import order-theory.similarity-of-order-preserving-maps-large-preorders funext public -open import order-theory.strict-order-preserving-maps funext public -open import order-theory.strict-preorders funext public -open import order-theory.strictly-inflationary-maps-strict-preorders funext public -open import order-theory.strictly-preordered-sets funext public -open import order-theory.subposets funext public -open import order-theory.subpreorders funext public -open import order-theory.suplattices funext public -open import order-theory.supremum-preserving-maps-posets funext public -open import order-theory.top-elements-large-posets funext public -open import order-theory.top-elements-posets funext public -open import order-theory.top-elements-preorders funext public -open import order-theory.total-orders funext public -open import order-theory.total-preorders funext public -open import order-theory.transitive-well-founded-relations funext public -open import order-theory.upper-bounds-chains-posets funext public -open import order-theory.upper-bounds-large-posets funext public -open import order-theory.upper-bounds-posets funext public -open import order-theory.upper-sets-large-posets funext public -open import order-theory.well-founded-relations funext public -open import order-theory.zorns-lemma funext public +open import order-theory.accessible-elements-relations public +open import order-theory.bottom-elements-large-posets public +open import order-theory.bottom-elements-posets public +open import order-theory.bottom-elements-preorders public +open import order-theory.chains-posets public +open import order-theory.chains-preorders public +open import order-theory.closure-operators-large-locales public +open import order-theory.closure-operators-large-posets public +open import order-theory.commuting-squares-of-galois-connections-large-posets public +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets public +open import order-theory.coverings-locales public +open import order-theory.decidable-posets public +open import order-theory.decidable-preorders public +open import order-theory.decidable-subposets public +open import order-theory.decidable-subpreorders public +open import order-theory.decidable-total-orders public +open import order-theory.decidable-total-preorders public +open import order-theory.deflationary-maps-posets public +open import order-theory.deflationary-maps-preorders public +open import order-theory.dependent-products-large-frames public +open import order-theory.dependent-products-large-inflattices public +open import order-theory.dependent-products-large-locales public +open import order-theory.dependent-products-large-meet-semilattices public +open import order-theory.dependent-products-large-posets public +open import order-theory.dependent-products-large-preorders public +open import order-theory.dependent-products-large-suplattices public +open import order-theory.distributive-lattices public +open import order-theory.finite-coverings-locales public +open import order-theory.finite-posets public +open import order-theory.finite-preorders public +open import order-theory.finite-total-orders public +open import order-theory.finitely-graded-posets public +open import order-theory.frames public +open import order-theory.galois-connections public +open import order-theory.galois-connections-large-posets public +open import order-theory.greatest-lower-bounds-large-posets public +open import order-theory.greatest-lower-bounds-posets public +open import order-theory.homomorphisms-frames public +open import order-theory.homomorphisms-large-frames public +open import order-theory.homomorphisms-large-locales public +open import order-theory.homomorphisms-large-meet-semilattices public +open import order-theory.homomorphisms-large-suplattices public +open import order-theory.homomorphisms-meet-semilattices public +open import order-theory.homomorphisms-meet-suplattices public +open import order-theory.homomorphisms-suplattices public +open import order-theory.ideals-preorders public +open import order-theory.incidence-algebras public +open import order-theory.inflationary-maps-posets public +open import order-theory.inflationary-maps-preorders public +open import order-theory.inflattices public +open import order-theory.inhabited-chains-posets public +open import order-theory.inhabited-chains-preorders public +open import order-theory.inhabited-finite-total-orders public +open import order-theory.interval-subposets public +open import order-theory.join-preserving-maps-posets public +open import order-theory.join-semilattices public +open import order-theory.knaster-tarski-fixed-point-theorem public +open import order-theory.large-frames public +open import order-theory.large-inflattices public +open import order-theory.large-join-semilattices public +open import order-theory.large-locales public +open import order-theory.large-meet-semilattices public +open import order-theory.large-meet-subsemilattices public +open import order-theory.large-posets public +open import order-theory.large-preorders public +open import order-theory.large-quotient-locales public +open import order-theory.large-subframes public +open import order-theory.large-subposets public +open import order-theory.large-subpreorders public +open import order-theory.large-subsuplattices public +open import order-theory.large-suplattices public +open import order-theory.lattices public +open import order-theory.least-upper-bounds-large-posets public +open import order-theory.least-upper-bounds-posets public +open import order-theory.locales public +open import order-theory.locally-finite-posets public +open import order-theory.lower-bounds-large-posets public +open import order-theory.lower-bounds-posets public +open import order-theory.lower-sets-large-posets public +open import order-theory.lower-types-preorders public +open import order-theory.maximal-chains-posets public +open import order-theory.maximal-chains-preorders public +open import order-theory.meet-semilattices public +open import order-theory.meet-suplattices public +open import order-theory.nuclei-large-locales public +open import order-theory.opposite-large-posets public +open import order-theory.opposite-large-preorders public +open import order-theory.opposite-posets public +open import order-theory.opposite-preorders public +open import order-theory.order-preserving-maps-large-posets public +open import order-theory.order-preserving-maps-large-preorders public +open import order-theory.order-preserving-maps-posets public +open import order-theory.order-preserving-maps-preorders public +open import order-theory.ordinals public +open import order-theory.posets public +open import order-theory.powers-of-large-locales public +open import order-theory.precategory-of-decidable-total-orders public +open import order-theory.precategory-of-finite-posets public +open import order-theory.precategory-of-finite-total-orders public +open import order-theory.precategory-of-inhabited-finite-total-orders public +open import order-theory.precategory-of-posets public +open import order-theory.precategory-of-total-orders public +open import order-theory.preorders public +open import order-theory.principal-lower-sets-large-posets public +open import order-theory.principal-upper-sets-large-posets public +open import order-theory.reflective-galois-connections-large-posets public +open import order-theory.resizing-posets public +open import order-theory.resizing-preorders public +open import order-theory.resizing-suplattices public +open import order-theory.similarity-of-elements-large-posets public +open import order-theory.similarity-of-elements-large-preorders public +open import order-theory.similarity-of-order-preserving-maps-large-posets public +open import order-theory.similarity-of-order-preserving-maps-large-preorders public +open import order-theory.strict-order-preserving-maps public +open import order-theory.strict-preorders public +open import order-theory.strictly-inflationary-maps-strict-preorders public +open import order-theory.strictly-preordered-sets public +open import order-theory.subposets public +open import order-theory.subpreorders public +open import order-theory.suplattices public +open import order-theory.supremum-preserving-maps-posets public +open import order-theory.top-elements-large-posets public +open import order-theory.top-elements-posets public +open import order-theory.top-elements-preorders public +open import order-theory.total-orders public +open import order-theory.total-preorders public +open import order-theory.transitive-well-founded-relations public +open import order-theory.upper-bounds-chains-posets public +open import order-theory.upper-bounds-large-posets public +open import order-theory.upper-bounds-posets public +open import order-theory.upper-sets-large-posets public +open import order-theory.well-founded-relations public +open import order-theory.zorns-lemma public ``` diff --git a/src/order-theory/accessible-elements-relations.lagda.md b/src/order-theory/accessible-elements-relations.lagda.md index 523ff37fd9..a6b6863dca 100644 --- a/src/order-theory/accessible-elements-relations.lagda.md +++ b/src/order-theory/accessible-elements-relations.lagda.md @@ -1,22 +1,16 @@ # Accessible elements with respect to relations ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.accessible-elements-relations - (funext : function-extensionality) - where +module order-theory.accessible-elements-relations where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.universe-levels open import foundation-core.negation diff --git a/src/order-theory/bottom-elements-large-posets.lagda.md b/src/order-theory/bottom-elements-large-posets.lagda.md index 2906b54ffc..76262a6702 100644 --- a/src/order-theory/bottom-elements-large-posets.lagda.md +++ b/src/order-theory/bottom-elements-large-posets.lagda.md @@ -1,12 +1,7 @@ # Bottom elements in large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.bottom-elements-large-posets - (funext : function-extensionality) - where +module order-theory.bottom-elements-large-posets where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import order-theory.dependent-products-large-posets funext -open import order-theory.large-posets funext +open import order-theory.dependent-products-large-posets +open import order-theory.large-posets ```
diff --git a/src/order-theory/bottom-elements-posets.lagda.md b/src/order-theory/bottom-elements-posets.lagda.md index 60fa8dae52..19f835b65c 100644 --- a/src/order-theory/bottom-elements-posets.lagda.md +++ b/src/order-theory/bottom-elements-posets.lagda.md @@ -1,24 +1,19 @@ # Bottom elements in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.bottom-elements-posets - (funext : function-extensionality) - where +module order-theory.bottom-elements-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.bottom-elements-preorders funext -open import order-theory.posets funext +open import order-theory.bottom-elements-preorders +open import order-theory.posets ```
diff --git a/src/order-theory/bottom-elements-preorders.lagda.md b/src/order-theory/bottom-elements-preorders.lagda.md index 04c1dfb0d0..5d5c0f1b8b 100644 --- a/src/order-theory/bottom-elements-preorders.lagda.md +++ b/src/order-theory/bottom-elements-preorders.lagda.md @@ -1,22 +1,17 @@ # Bottom elements in preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.bottom-elements-preorders - (funext : function-extensionality) - where +module order-theory.bottom-elements-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import order-theory.preorders funext +open import order-theory.preorders ```
diff --git a/src/order-theory/chains-posets.lagda.md b/src/order-theory/chains-posets.lagda.md index 48b47da535..404b506ee9 100644 --- a/src/order-theory/chains-posets.lagda.md +++ b/src/order-theory/chains-posets.lagda.md @@ -1,34 +1,29 @@ # Chains in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.chains-posets - (funext : function-extensionality) - where +module order-theory.chains-posets where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.images funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.disjunction +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.images +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.chains-preorders funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext -open import order-theory.subposets funext -open import order-theory.total-orders funext +open import order-theory.chains-preorders +open import order-theory.order-preserving-maps-posets +open import order-theory.posets +open import order-theory.subposets +open import order-theory.total-orders ```
diff --git a/src/order-theory/chains-preorders.lagda.md b/src/order-theory/chains-preorders.lagda.md index 13ef627d97..65c1ad4c19 100644 --- a/src/order-theory/chains-preorders.lagda.md +++ b/src/order-theory/chains-preorders.lagda.md @@ -1,25 +1,20 @@ # Chains in preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.chains-preorders - (funext : function-extensionality) - where +module order-theory.chains-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.preorders funext -open import order-theory.subpreorders funext -open import order-theory.total-preorders funext +open import order-theory.preorders +open import order-theory.subpreorders +open import order-theory.total-preorders ```
diff --git a/src/order-theory/closure-operators-large-locales.lagda.md b/src/order-theory/closure-operators-large-locales.lagda.md index 9e8b6172e8..3bc839becd 100644 --- a/src/order-theory/closure-operators-large-locales.lagda.md +++ b/src/order-theory/closure-operators-large-locales.lagda.md @@ -1,12 +1,7 @@ # Closure operators on large locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.closure-operators-large-locales - (funext : function-extensionality) - where +module order-theory.closure-operators-large-locales where ```
Imports @@ -14,26 +9,26 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.closure-operators-large-posets funext -open import order-theory.large-frames funext -open import order-theory.large-locales funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-meet-subsemilattices funext -open import order-theory.large-posets funext -open import order-theory.large-subposets funext -open import order-theory.large-subpreorders funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.closure-operators-large-posets +open import order-theory.large-frames +open import order-theory.large-locales +open import order-theory.large-meet-semilattices +open import order-theory.large-meet-subsemilattices +open import order-theory.large-posets +open import order-theory.large-subposets +open import order-theory.large-subpreorders +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.order-preserving-maps-large-posets ```
diff --git a/src/order-theory/closure-operators-large-posets.lagda.md b/src/order-theory/closure-operators-large-posets.lagda.md index 0b0359c810..edc0a558e9 100644 --- a/src/order-theory/closure-operators-large-posets.lagda.md +++ b/src/order-theory/closure-operators-large-posets.lagda.md @@ -1,27 +1,22 @@ # Closure operators on large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.closure-operators-large-posets - (funext : function-extensionality) - where +module order-theory.closure-operators-large-posets where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-subposets funext -open import order-theory.large-subpreorders funext -open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.large-posets +open import order-theory.large-subposets +open import order-theory.large-subpreorders +open import order-theory.order-preserving-maps-large-posets ```
diff --git a/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md b/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md index 68101ec457..ff9bfb86c1 100644 --- a/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md +++ b/src/order-theory/commuting-squares-of-galois-connections-large-posets.lagda.md @@ -1,12 +1,7 @@ # Commuting squares of Galois connections between large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.commuting-squares-of-galois-connections-large-posets - (funext : function-extensionality) - where +module order-theory.commuting-squares-of-galois-connections-large-posets where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.universe-levels -open import order-theory.commuting-squares-of-order-preserving-maps-large-posets funext -open import order-theory.galois-connections-large-posets funext -open import order-theory.large-posets funext +open import order-theory.commuting-squares-of-order-preserving-maps-large-posets +open import order-theory.galois-connections-large-posets +open import order-theory.large-posets ```
diff --git a/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md b/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md index a233ea711b..42b32bdb2f 100644 --- a/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md +++ b/src/order-theory/commuting-squares-of-order-preserving-maps-large-posets.lagda.md @@ -11,11 +11,11 @@ module ```agda open import foundation.universe-levels -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps -open import order-theory.large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.similarity-of-order-preserving-maps-large-posets funext +open import order-theory.large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.similarity-of-order-preserving-maps-large-posets ```
@@ -51,12 +51,7 @@ words, we say that the square above commutes if the composites `j ∘ f` and ## Definitions ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {αP αQ αU αV γi γf γg γj : Level → Level} {βP βQ βU βV : Level → Level → Level} (P : Large-Poset αP βP) diff --git a/src/order-theory/coverings-locales.lagda.md b/src/order-theory/coverings-locales.lagda.md index bc63072dfc..70165cf95e 100644 --- a/src/order-theory/coverings-locales.lagda.md +++ b/src/order-theory/coverings-locales.lagda.md @@ -1,22 +1,17 @@ # Coverings in locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.coverings-locales - (funext : function-extensionality) - where +module order-theory.coverings-locales where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import order-theory.locales funext +open import order-theory.locales ```
diff --git a/src/order-theory/decidable-posets.lagda.md b/src/order-theory/decidable-posets.lagda.md index a6697faaa9..b02c21afbf 100644 --- a/src/order-theory/decidable-posets.lagda.md +++ b/src/order-theory/decidable-posets.lagda.md @@ -1,28 +1,23 @@ # Decidable posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.decidable-posets - (funext : function-extensionality) - where +module order-theory.decidable-posets where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.decidable-propositions funext +open import foundation.binary-relations +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.decidable-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.decidable-preorders +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/order-theory/decidable-preorders.lagda.md b/src/order-theory/decidable-preorders.lagda.md index 02adf9422b..b752e33a13 100644 --- a/src/order-theory/decidable-preorders.lagda.md +++ b/src/order-theory/decidable-preorders.lagda.md @@ -1,24 +1,19 @@ # Decidable preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.decidable-preorders - (funext : function-extensionality) - where +module order-theory.decidable-preorders where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.decidable-propositions funext +open import foundation.binary-relations +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import order-theory.preorders funext +open import order-theory.preorders ```
diff --git a/src/order-theory/decidable-subposets.lagda.md b/src/order-theory/decidable-subposets.lagda.md index 2216b42708..d57463aa0b 100644 --- a/src/order-theory/decidable-subposets.lagda.md +++ b/src/order-theory/decidable-subposets.lagda.md @@ -1,26 +1,21 @@ # Decidable subposets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.decidable-subposets - (funext : function-extensionality) - where +module order-theory.decidable-subposets where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.decidable-subtypes funext +open import foundation.binary-relations +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.subposets funext +open import order-theory.posets +open import order-theory.subposets ```
diff --git a/src/order-theory/decidable-subpreorders.lagda.md b/src/order-theory/decidable-subpreorders.lagda.md index 720d13a3fc..57e290edc2 100644 --- a/src/order-theory/decidable-subpreorders.lagda.md +++ b/src/order-theory/decidable-subpreorders.lagda.md @@ -1,26 +1,21 @@ # Decidable subpreorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.decidable-subpreorders - (funext : function-extensionality) - where +module order-theory.decidable-subpreorders where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.decidable-subtypes funext +open import foundation.binary-relations +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import order-theory.preorders funext -open import order-theory.subpreorders funext +open import order-theory.preorders +open import order-theory.subpreorders ```
diff --git a/src/order-theory/decidable-total-orders.lagda.md b/src/order-theory/decidable-total-orders.lagda.md index 8725952740..1b3086e12d 100644 --- a/src/order-theory/decidable-total-orders.lagda.md +++ b/src/order-theory/decidable-total-orders.lagda.md @@ -1,36 +1,31 @@ # Decidable total orders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.decidable-total-orders - (funext : function-extensionality) - where +module order-theory.decidable-total-orders where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext +open import foundation.binary-relations +open import foundation.coproduct-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.decidable-posets funext -open import order-theory.decidable-total-preorders funext -open import order-theory.greatest-lower-bounds-posets funext -open import order-theory.join-semilattices funext -open import order-theory.least-upper-bounds-posets funext -open import order-theory.meet-semilattices funext -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.total-orders funext +open import order-theory.decidable-posets +open import order-theory.decidable-total-preorders +open import order-theory.greatest-lower-bounds-posets +open import order-theory.join-semilattices +open import order-theory.least-upper-bounds-posets +open import order-theory.meet-semilattices +open import order-theory.posets +open import order-theory.preorders +open import order-theory.total-orders ```
diff --git a/src/order-theory/decidable-total-preorders.lagda.md b/src/order-theory/decidable-total-preorders.lagda.md index f0e25d8bdb..c3385ce7ae 100644 --- a/src/order-theory/decidable-total-preorders.lagda.md +++ b/src/order-theory/decidable-total-preorders.lagda.md @@ -1,33 +1,28 @@ # Decidable total preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.decidable-total-preorders - (funext : function-extensionality) - where +module order-theory.decidable-total-preorders where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.universe-levels -open import order-theory.decidable-preorders funext -open import order-theory.preorders funext -open import order-theory.total-preorders funext +open import order-theory.decidable-preorders +open import order-theory.preorders +open import order-theory.total-preorders ```
diff --git a/src/order-theory/deflationary-maps-posets.lagda.md b/src/order-theory/deflationary-maps-posets.lagda.md index 555331ec25..ffeb8f4da5 100644 --- a/src/order-theory/deflationary-maps-posets.lagda.md +++ b/src/order-theory/deflationary-maps-posets.lagda.md @@ -1,25 +1,20 @@ # Deflationary maps on a poset ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.deflationary-maps-posets - (funext : function-extensionality) - where +module order-theory.deflationary-maps-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.deflationary-maps-preorders funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.deflationary-maps-preorders +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/order-theory/deflationary-maps-preorders.lagda.md b/src/order-theory/deflationary-maps-preorders.lagda.md index 3206a6d1a3..508b702878 100644 --- a/src/order-theory/deflationary-maps-preorders.lagda.md +++ b/src/order-theory/deflationary-maps-preorders.lagda.md @@ -1,24 +1,19 @@ # Deflationary maps on a preorder ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.deflationary-maps-preorders - (funext : function-extensionality) - where +module order-theory.deflationary-maps-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders funext -open import order-theory.preorders funext +open import order-theory.order-preserving-maps-preorders +open import order-theory.preorders ```
diff --git a/src/order-theory/dependent-products-large-frames.lagda.md b/src/order-theory/dependent-products-large-frames.lagda.md index 3002829f36..8766e231c0 100644 --- a/src/order-theory/dependent-products-large-frames.lagda.md +++ b/src/order-theory/dependent-products-large-frames.lagda.md @@ -1,34 +1,28 @@ # Dependent products of large frames ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.dependent-products-large-frames - (funext : function-extensionality) - where +module order-theory.dependent-products-large-frames where ```
Imports ```agda -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.dependent-products-large-meet-semilattices funext -open import order-theory.dependent-products-large-posets funext -open import order-theory.dependent-products-large-suplattices funext -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-frames funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.top-elements-large-posets funext +open import order-theory.dependent-products-large-meet-semilattices +open import order-theory.dependent-products-large-posets +open import order-theory.dependent-products-large-suplattices +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-frames +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.top-elements-large-posets ```
diff --git a/src/order-theory/dependent-products-large-inflattices.lagda.md b/src/order-theory/dependent-products-large-inflattices.lagda.md index 1672173eb0..7078f31b85 100644 --- a/src/order-theory/dependent-products-large-inflattices.lagda.md +++ b/src/order-theory/dependent-products-large-inflattices.lagda.md @@ -1,25 +1,20 @@ # Dependent products of large inflattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.dependent-products-large-inflattices - (funext : function-extensionality) - where +module order-theory.dependent-products-large-inflattices where ```
Imports ```agda -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.dependent-products-large-posets funext -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-inflattices funext -open import order-theory.large-posets funext +open import order-theory.dependent-products-large-posets +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-inflattices +open import order-theory.large-posets ```
diff --git a/src/order-theory/dependent-products-large-locales.lagda.md b/src/order-theory/dependent-products-large-locales.lagda.md index 0c5a8eaab1..07f9743e81 100644 --- a/src/order-theory/dependent-products-large-locales.lagda.md +++ b/src/order-theory/dependent-products-large-locales.lagda.md @@ -1,30 +1,25 @@ # Dependent products of large locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.dependent-products-large-locales - (funext : function-extensionality) - where +module order-theory.dependent-products-large-locales where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.dependent-products-large-frames funext -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-locales funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.top-elements-large-posets funext +open import order-theory.dependent-products-large-frames +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-locales +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.top-elements-large-posets ```
diff --git a/src/order-theory/dependent-products-large-meet-semilattices.lagda.md b/src/order-theory/dependent-products-large-meet-semilattices.lagda.md index a2c44bf15c..5d235a6767 100644 --- a/src/order-theory/dependent-products-large-meet-semilattices.lagda.md +++ b/src/order-theory/dependent-products-large-meet-semilattices.lagda.md @@ -1,26 +1,21 @@ # Dependent products of large meet-semilattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.dependent-products-large-meet-semilattices - (funext : function-extensionality) - where +module order-theory.dependent-products-large-meet-semilattices where ```
Imports ```agda -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.dependent-products-large-posets funext -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.top-elements-large-posets funext +open import order-theory.dependent-products-large-posets +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.top-elements-large-posets ```
diff --git a/src/order-theory/dependent-products-large-posets.lagda.md b/src/order-theory/dependent-products-large-posets.lagda.md index c73e4e4c69..f445638b89 100644 --- a/src/order-theory/dependent-products-large-posets.lagda.md +++ b/src/order-theory/dependent-products-large-posets.lagda.md @@ -1,25 +1,19 @@ # Dependent products of large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.dependent-products-large-posets - (funext : function-extensionality) - where +module order-theory.dependent-products-large-posets where ```
Imports ```agda -open import foundation.function-extensionality funext - -open import foundation.large-binary-relations funext +open import foundation.function-extensionality +open import foundation.large-binary-relations open import foundation.universe-levels -open import order-theory.dependent-products-large-preorders funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext +open import order-theory.dependent-products-large-preorders +open import order-theory.large-posets +open import order-theory.large-preorders ```
diff --git a/src/order-theory/dependent-products-large-preorders.lagda.md b/src/order-theory/dependent-products-large-preorders.lagda.md index e6956c6c21..fa7fafa61e 100644 --- a/src/order-theory/dependent-products-large-preorders.lagda.md +++ b/src/order-theory/dependent-products-large-preorders.lagda.md @@ -1,22 +1,17 @@ # Dependent products of large preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.dependent-products-large-preorders - (funext : function-extensionality) - where +module order-theory.dependent-products-large-preorders where ```
Imports ```agda -open import foundation.large-binary-relations funext -open import foundation.propositions funext +open import foundation.large-binary-relations +open import foundation.propositions open import foundation.universe-levels -open import order-theory.large-preorders funext +open import order-theory.large-preorders ```
diff --git a/src/order-theory/dependent-products-large-suplattices.lagda.md b/src/order-theory/dependent-products-large-suplattices.lagda.md index b18ea1d500..41fbf2ead1 100644 --- a/src/order-theory/dependent-products-large-suplattices.lagda.md +++ b/src/order-theory/dependent-products-large-suplattices.lagda.md @@ -1,25 +1,20 @@ # Dependent products of large suplattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.dependent-products-large-suplattices - (funext : function-extensionality) - where +module order-theory.dependent-products-large-suplattices where ```
Imports ```agda -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.dependent-products-large-posets funext -open import order-theory.large-posets funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.dependent-products-large-posets +open import order-theory.large-posets +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets ```
diff --git a/src/order-theory/distributive-lattices.lagda.md b/src/order-theory/distributive-lattices.lagda.md index 9b864b2b0b..e2dff425a0 100644 --- a/src/order-theory/distributive-lattices.lagda.md +++ b/src/order-theory/distributive-lattices.lagda.md @@ -1,28 +1,23 @@ # Distributive lattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.distributive-lattices - (funext : function-extensionality) - where +module order-theory.distributive-lattices where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.join-semilattices funext -open import order-theory.lattices funext -open import order-theory.meet-semilattices funext -open import order-theory.posets funext +open import order-theory.join-semilattices +open import order-theory.lattices +open import order-theory.meet-semilattices +open import order-theory.posets ```
diff --git a/src/order-theory/finite-coverings-locales.lagda.md b/src/order-theory/finite-coverings-locales.lagda.md index fffe499e6e..94b7b34648 100644 --- a/src/order-theory/finite-coverings-locales.lagda.md +++ b/src/order-theory/finite-coverings-locales.lagda.md @@ -1,12 +1,7 @@ # Finite coverings in locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.finite-coverings-locales - (funext : function-extensionality) - where +module order-theory.finite-coverings-locales where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import order-theory.coverings-locales funext -open import order-theory.locales funext +open import order-theory.coverings-locales +open import order-theory.locales -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/order-theory/finite-posets.lagda.md b/src/order-theory/finite-posets.lagda.md index 7fa14856f5..597af98d12 100644 --- a/src/order-theory/finite-posets.lagda.md +++ b/src/order-theory/finite-posets.lagda.md @@ -1,28 +1,23 @@ # Finite posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.finite-posets - (funext : function-extensionality) - where +module order-theory.finite-posets where ```
Imports ```agda -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.propositions open import foundation.universe-levels -open import order-theory.finite-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.finite-preorders +open import order-theory.posets +open import order-theory.preorders -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/order-theory/finite-preorders.lagda.md b/src/order-theory/finite-preorders.lagda.md index 2905166f62..b7a2511b49 100644 --- a/src/order-theory/finite-preorders.lagda.md +++ b/src/order-theory/finite-preorders.lagda.md @@ -1,12 +1,7 @@ # Finite preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.finite-preorders - (funext : function-extensionality) - where +module order-theory.finite-preorders where ```
Imports @@ -14,26 +9,26 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types +open import foundation.decidable-equality +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.mere-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.mere-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.decidable-preorders funext -open import order-theory.decidable-subpreorders funext -open import order-theory.preorders funext +open import order-theory.decidable-preorders +open import order-theory.decidable-subpreorders +open import order-theory.preorders -open import univalent-combinatorics.decidable-subtypes funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.decidable-subtypes +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/order-theory/finite-total-orders.lagda.md b/src/order-theory/finite-total-orders.lagda.md index 7b734d440c..4bfb6edcd4 100644 --- a/src/order-theory/finite-total-orders.lagda.md +++ b/src/order-theory/finite-total-orders.lagda.md @@ -1,28 +1,23 @@ # Finite total orders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.finite-total-orders - (funext : function-extensionality) - where +module order-theory.finite-total-orders where ```
Imports ```agda -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.propositions open import foundation.universe-levels -open import order-theory.finite-posets funext -open import order-theory.posets funext -open import order-theory.total-orders funext +open import order-theory.finite-posets +open import order-theory.posets +open import order-theory.total-orders -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/order-theory/finitely-graded-posets.lagda.md b/src/order-theory/finitely-graded-posets.lagda.md index 332e3a237a..b4fb4a404b 100644 --- a/src/order-theory/finitely-graded-posets.lagda.md +++ b/src/order-theory/finitely-graded-posets.lagda.md @@ -1,45 +1,40 @@ # Finitely graded posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.finitely-graded-posets - (funext : function-extensionality) - where +module order-theory.finitely-graded-posets where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types funext -open import elementary-number-theory.modular-arithmetic funext +open import elementary-number-theory.inequality-standard-finite-types +open import elementary-number-theory.modular-arithmetic open import elementary-number-theory.natural-numbers -open import foundation.binary-relations funext -open import foundation.coproduct-types funext +open import foundation.binary-relations +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import order-theory.bottom-elements-posets funext -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.top-elements-posets funext -open import order-theory.total-orders funext +open import order-theory.bottom-elements-posets +open import order-theory.posets +open import order-theory.preorders +open import order-theory.top-elements-posets +open import order-theory.total-orders -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/order-theory/frames.lagda.md b/src/order-theory/frames.lagda.md index 034be27e22..96d2f47cec 100644 --- a/src/order-theory/frames.lagda.md +++ b/src/order-theory/frames.lagda.md @@ -1,30 +1,25 @@ # Frames ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.frames - (funext : function-extensionality) - where +module order-theory.frames where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-posets funext -open import order-theory.least-upper-bounds-posets funext -open import order-theory.meet-semilattices funext -open import order-theory.meet-suplattices funext -open import order-theory.posets funext -open import order-theory.suplattices funext +open import order-theory.greatest-lower-bounds-posets +open import order-theory.least-upper-bounds-posets +open import order-theory.meet-semilattices +open import order-theory.meet-suplattices +open import order-theory.posets +open import order-theory.suplattices ```
diff --git a/src/order-theory/galois-connections-large-posets.lagda.md b/src/order-theory/galois-connections-large-posets.lagda.md index 8c05372f9e..eee2b9a4da 100644 --- a/src/order-theory/galois-connections-large-posets.lagda.md +++ b/src/order-theory/galois-connections-large-posets.lagda.md @@ -1,12 +1,7 @@ # Galois connections between large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.galois-connections-large-posets - (funext : function-extensionality) - where +module order-theory.galois-connections-large-posets where ```
Imports @@ -14,18 +9,18 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.logical-equivalences funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.logical-equivalences open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.principal-lower-sets-large-posets funext -open import order-theory.principal-upper-sets-large-posets funext -open import order-theory.similarity-of-elements-large-posets funext -open import order-theory.similarity-of-order-preserving-maps-large-posets funext +open import order-theory.large-posets +open import order-theory.least-upper-bounds-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.principal-lower-sets-large-posets +open import order-theory.principal-upper-sets-large-posets +open import order-theory.similarity-of-elements-large-posets +open import order-theory.similarity-of-order-preserving-maps-large-posets ```
diff --git a/src/order-theory/galois-connections.lagda.md b/src/order-theory/galois-connections.lagda.md index 3657f75826..e0ac6170c7 100644 --- a/src/order-theory/galois-connections.lagda.md +++ b/src/order-theory/galois-connections.lagda.md @@ -1,12 +1,7 @@ # Galois connections ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.galois-connections - (funext : function-extensionality) - where +module order-theory.galois-connections where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/order-theory/greatest-lower-bounds-large-posets.lagda.md b/src/order-theory/greatest-lower-bounds-large-posets.lagda.md index f44de6e120..c7a54580f2 100644 --- a/src/order-theory/greatest-lower-bounds-large-posets.lagda.md +++ b/src/order-theory/greatest-lower-bounds-large-posets.lagda.md @@ -1,23 +1,18 @@ # Greatest lower bounds in large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.greatest-lower-bounds-large-posets - (funext : function-extensionality) - where +module order-theory.greatest-lower-bounds-large-posets where ```
Imports ```agda -open import foundation.logical-equivalences funext +open import foundation.logical-equivalences open import foundation.universe-levels -open import order-theory.dependent-products-large-posets funext -open import order-theory.large-posets funext -open import order-theory.lower-bounds-large-posets funext +open import order-theory.dependent-products-large-posets +open import order-theory.large-posets +open import order-theory.lower-bounds-large-posets ```
diff --git a/src/order-theory/greatest-lower-bounds-posets.lagda.md b/src/order-theory/greatest-lower-bounds-posets.lagda.md index dc1c5f0142..9a1430a0c4 100644 --- a/src/order-theory/greatest-lower-bounds-posets.lagda.md +++ b/src/order-theory/greatest-lower-bounds-posets.lagda.md @@ -1,12 +1,7 @@ # Greatest lower bounds in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.greatest-lower-bounds-posets - (funext : function-extensionality) - where +module order-theory.greatest-lower-bounds-posets where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.lower-bounds-posets funext -open import order-theory.posets funext +open import order-theory.lower-bounds-posets +open import order-theory.posets ```
diff --git a/src/order-theory/homomorphisms-frames.lagda.md b/src/order-theory/homomorphisms-frames.lagda.md index 78864fb775..2af1ac44de 100644 --- a/src/order-theory/homomorphisms-frames.lagda.md +++ b/src/order-theory/homomorphisms-frames.lagda.md @@ -1,27 +1,22 @@ # Homomorphisms of frames ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.homomorphisms-frames - (funext : function-extensionality) - where +module order-theory.homomorphisms-frames where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext +open import foundation.function-types open import foundation.universe-levels -open import order-theory.frames funext -open import order-theory.homomorphisms-meet-semilattices funext -open import order-theory.homomorphisms-meet-suplattices funext -open import order-theory.homomorphisms-suplattices funext -open import order-theory.order-preserving-maps-posets funext +open import order-theory.frames +open import order-theory.homomorphisms-meet-semilattices +open import order-theory.homomorphisms-meet-suplattices +open import order-theory.homomorphisms-suplattices +open import order-theory.order-preserving-maps-posets ```
diff --git a/src/order-theory/homomorphisms-large-frames.lagda.md b/src/order-theory/homomorphisms-large-frames.lagda.md index 6f223802fe..80de9de25d 100644 --- a/src/order-theory/homomorphisms-large-frames.lagda.md +++ b/src/order-theory/homomorphisms-large-frames.lagda.md @@ -1,23 +1,18 @@ # Homomorphisms of large frames ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.homomorphisms-large-frames - (funext : function-extensionality) - where +module order-theory.homomorphisms-large-frames where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import order-theory.homomorphisms-large-meet-semilattices funext -open import order-theory.homomorphisms-large-suplattices funext -open import order-theory.large-frames funext +open import order-theory.homomorphisms-large-meet-semilattices +open import order-theory.homomorphisms-large-suplattices +open import order-theory.large-frames ```
diff --git a/src/order-theory/homomorphisms-large-locales.lagda.md b/src/order-theory/homomorphisms-large-locales.lagda.md index f1331e5338..ae621fd45d 100644 --- a/src/order-theory/homomorphisms-large-locales.lagda.md +++ b/src/order-theory/homomorphisms-large-locales.lagda.md @@ -1,22 +1,17 @@ # Homomorphisms of large locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.homomorphisms-large-locales - (funext : function-extensionality) - where +module order-theory.homomorphisms-large-locales where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import order-theory.homomorphisms-large-frames funext -open import order-theory.large-locales funext +open import order-theory.homomorphisms-large-frames +open import order-theory.large-locales ```
diff --git a/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md b/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md index 37d17a88f2..c209e7d907 100644 --- a/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md +++ b/src/order-theory/homomorphisms-large-meet-semilattices.lagda.md @@ -1,22 +1,17 @@ # Homomorphisms of large meet-semilattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.homomorphisms-large-meet-semilattices - (funext : function-extensionality) - where +module order-theory.homomorphisms-large-meet-semilattices where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import order-theory.large-meet-semilattices funext -open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.large-meet-semilattices +open import order-theory.order-preserving-maps-large-posets ```
diff --git a/src/order-theory/homomorphisms-large-suplattices.lagda.md b/src/order-theory/homomorphisms-large-suplattices.lagda.md index 7ff77c91a7..181c422651 100644 --- a/src/order-theory/homomorphisms-large-suplattices.lagda.md +++ b/src/order-theory/homomorphisms-large-suplattices.lagda.md @@ -1,22 +1,17 @@ # Homomorphisms of large suplattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.homomorphisms-large-suplattices - (funext : function-extensionality) - where +module order-theory.homomorphisms-large-suplattices where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import order-theory.large-suplattices funext -open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.large-suplattices +open import order-theory.order-preserving-maps-large-posets ```
diff --git a/src/order-theory/homomorphisms-meet-semilattices.lagda.md b/src/order-theory/homomorphisms-meet-semilattices.lagda.md index 6051dd310b..d22b55a690 100644 --- a/src/order-theory/homomorphisms-meet-semilattices.lagda.md +++ b/src/order-theory/homomorphisms-meet-semilattices.lagda.md @@ -1,12 +1,7 @@ # Homomorphisms of meet-semilattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.homomorphisms-meet-semilattices - (funext : function-extensionality) - where +module order-theory.homomorphisms-meet-semilattices where ```
Imports @@ -14,17 +9,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups funext +open import group-theory.homomorphisms-semigroups -open import order-theory.greatest-lower-bounds-posets funext -open import order-theory.meet-semilattices funext -open import order-theory.order-preserving-maps-posets funext +open import order-theory.greatest-lower-bounds-posets +open import order-theory.meet-semilattices +open import order-theory.order-preserving-maps-posets ```
diff --git a/src/order-theory/homomorphisms-meet-suplattices.lagda.md b/src/order-theory/homomorphisms-meet-suplattices.lagda.md index 54d3e0b5bd..ea4c27b234 100644 --- a/src/order-theory/homomorphisms-meet-suplattices.lagda.md +++ b/src/order-theory/homomorphisms-meet-suplattices.lagda.md @@ -1,26 +1,21 @@ # Homomorphisms of meet-suplattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.homomorphisms-meet-suplattices - (funext : function-extensionality) - where +module order-theory.homomorphisms-meet-suplattices where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext +open import foundation.function-types open import foundation.universe-levels -open import order-theory.homomorphisms-meet-semilattices funext -open import order-theory.homomorphisms-suplattices funext -open import order-theory.meet-suplattices funext -open import order-theory.order-preserving-maps-posets funext +open import order-theory.homomorphisms-meet-semilattices +open import order-theory.homomorphisms-suplattices +open import order-theory.meet-suplattices +open import order-theory.order-preserving-maps-posets ```
diff --git a/src/order-theory/homomorphisms-suplattices.lagda.md b/src/order-theory/homomorphisms-suplattices.lagda.md index b4437e0082..081cd8f204 100644 --- a/src/order-theory/homomorphisms-suplattices.lagda.md +++ b/src/order-theory/homomorphisms-suplattices.lagda.md @@ -1,25 +1,20 @@ # Homomorphisms of suplattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.homomorphisms-suplattices - (funext : function-extensionality) - where +module order-theory.homomorphisms-suplattices where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext +open import foundation.function-types open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.suplattices funext +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.suplattices ```
diff --git a/src/order-theory/ideals-preorders.lagda.md b/src/order-theory/ideals-preorders.lagda.md index 8bb6460c0d..2994939994 100644 --- a/src/order-theory/ideals-preorders.lagda.md +++ b/src/order-theory/ideals-preorders.lagda.md @@ -1,24 +1,19 @@ # Ideals in preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.ideals-preorders - (funext : function-extensionality) - where +module order-theory.ideals-preorders where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.inhabited-types funext +open import foundation.inhabited-types open import foundation.universe-levels -open import order-theory.lower-types-preorders funext -open import order-theory.preorders funext +open import order-theory.lower-types-preorders +open import order-theory.preorders ```
diff --git a/src/order-theory/incidence-algebras.lagda.md b/src/order-theory/incidence-algebras.lagda.md index 66047c38f9..f96b061659 100644 --- a/src/order-theory/incidence-algebras.lagda.md +++ b/src/order-theory/incidence-algebras.lagda.md @@ -1,28 +1,23 @@ # Incidence algebras ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.incidence-algebras - (funext : function-extensionality) - where +module order-theory.incidence-algebras where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import foundation.dependent-pair-types -open import foundation.inhabited-types funext +open import foundation.inhabited-types open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import order-theory.interval-subposets funext -open import order-theory.locally-finite-posets funext -open import order-theory.posets funext +open import order-theory.interval-subposets +open import order-theory.locally-finite-posets +open import order-theory.posets ```
diff --git a/src/order-theory/inflationary-maps-posets.lagda.md b/src/order-theory/inflationary-maps-posets.lagda.md index 0985a10151..00c3374a3b 100644 --- a/src/order-theory/inflationary-maps-posets.lagda.md +++ b/src/order-theory/inflationary-maps-posets.lagda.md @@ -1,25 +1,20 @@ # Inflationary maps on a poset ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.inflationary-maps-posets - (funext : function-extensionality) - where +module order-theory.inflationary-maps-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.inflationary-maps-preorders funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.inflationary-maps-preorders +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/order-theory/inflationary-maps-preorders.lagda.md b/src/order-theory/inflationary-maps-preorders.lagda.md index 35d6ee1697..aa2d482b97 100644 --- a/src/order-theory/inflationary-maps-preorders.lagda.md +++ b/src/order-theory/inflationary-maps-preorders.lagda.md @@ -1,24 +1,19 @@ # Inflationary maps on a preorder ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.inflationary-maps-preorders - (funext : function-extensionality) - where +module order-theory.inflationary-maps-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders funext -open import order-theory.preorders funext +open import order-theory.order-preserving-maps-preorders +open import order-theory.preorders ```
diff --git a/src/order-theory/inflattices.lagda.md b/src/order-theory/inflattices.lagda.md index c79f8098f2..03b68b3db8 100644 --- a/src/order-theory/inflattices.lagda.md +++ b/src/order-theory/inflattices.lagda.md @@ -1,27 +1,22 @@ # Inflattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.inflattices - (funext : function-extensionality) - where +module order-theory.inflattices where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-posets funext -open import order-theory.lower-bounds-posets funext -open import order-theory.posets funext +open import order-theory.greatest-lower-bounds-posets +open import order-theory.lower-bounds-posets +open import order-theory.posets ```
diff --git a/src/order-theory/inhabited-chains-posets.lagda.md b/src/order-theory/inhabited-chains-posets.lagda.md index f00966a114..8274e4af2a 100644 --- a/src/order-theory/inhabited-chains-posets.lagda.md +++ b/src/order-theory/inhabited-chains-posets.lagda.md @@ -1,33 +1,28 @@ # Inhabited chains in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.inhabited-chains-posets - (funext : function-extensionality) - where +module order-theory.inhabited-chains-posets where ```
Imports ```agda -open import domain-theory.directed-families-posets funext +open import domain-theory.directed-families-posets -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.existential-quantification funext -open import foundation.inhabited-subtypes funext -open import foundation.inhabited-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.disjunction +open import foundation.existential-quantification +open import foundation.inhabited-subtypes +open import foundation.inhabited-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.chains-posets funext -open import order-theory.posets funext -open import order-theory.subposets funext -open import order-theory.total-preorders funext +open import order-theory.chains-posets +open import order-theory.posets +open import order-theory.subposets +open import order-theory.total-preorders ```
diff --git a/src/order-theory/inhabited-chains-preorders.lagda.md b/src/order-theory/inhabited-chains-preorders.lagda.md index f1f79e175b..1722f40034 100644 --- a/src/order-theory/inhabited-chains-preorders.lagda.md +++ b/src/order-theory/inhabited-chains-preorders.lagda.md @@ -1,27 +1,22 @@ # Inhabited chains in preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.inhabited-chains-preorders - (funext : function-extensionality) - where +module order-theory.inhabited-chains-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-subtypes funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.inhabited-subtypes +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.chains-preorders funext -open import order-theory.preorders funext -open import order-theory.subpreorders funext -open import order-theory.total-preorders funext +open import order-theory.chains-preorders +open import order-theory.preorders +open import order-theory.subpreorders +open import order-theory.total-preorders ```
diff --git a/src/order-theory/inhabited-finite-total-orders.lagda.md b/src/order-theory/inhabited-finite-total-orders.lagda.md index ab12aafaa9..a7a49e6404 100644 --- a/src/order-theory/inhabited-finite-total-orders.lagda.md +++ b/src/order-theory/inhabited-finite-total-orders.lagda.md @@ -1,27 +1,22 @@ # Inhabited finite total orders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.inhabited-finite-total-orders - (funext : function-extensionality) - where +module order-theory.inhabited-finite-total-orders where ```
Imports ```agda -open import foundation.inhabited-types funext -open import foundation.propositions funext +open import foundation.inhabited-types +open import foundation.propositions open import foundation.universe-levels -open import order-theory.finite-posets funext -open import order-theory.finite-total-orders funext -open import order-theory.posets funext -open import order-theory.total-orders funext +open import order-theory.finite-posets +open import order-theory.finite-total-orders +open import order-theory.posets +open import order-theory.total-orders -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/order-theory/interval-subposets.lagda.md b/src/order-theory/interval-subposets.lagda.md index 699cdaaae3..5f53725119 100644 --- a/src/order-theory/interval-subposets.lagda.md +++ b/src/order-theory/interval-subposets.lagda.md @@ -1,26 +1,21 @@ # Interval subposets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.interval-subposets - (funext : function-extensionality) - where +module order-theory.interval-subposets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.inhabited-types funext -open import foundation.propositions funext +open import foundation.inhabited-types +open import foundation.propositions open import foundation.universe-levels open import foundation-core.cartesian-product-types -open import order-theory.posets funext -open import order-theory.subposets funext +open import order-theory.posets +open import order-theory.subposets ```
diff --git a/src/order-theory/join-preserving-maps-posets.lagda.md b/src/order-theory/join-preserving-maps-posets.lagda.md index 25aea8fb53..1da7506fa2 100644 --- a/src/order-theory/join-preserving-maps-posets.lagda.md +++ b/src/order-theory/join-preserving-maps-posets.lagda.md @@ -1,37 +1,32 @@ # Join preserving maps between posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.join-preserving-maps-posets - (funext : function-extensionality) - where +module order-theory.join-preserving-maps-posets where ```
Imports ```agda -open import foundation.booleans funext +open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.evaluation-functions -open import foundation.function-types funext +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.small-types funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.small-types +open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/order-theory/join-semilattices.lagda.md b/src/order-theory/join-semilattices.lagda.md index e127cd52f5..fe7f25a8cc 100644 --- a/src/order-theory/join-semilattices.lagda.md +++ b/src/order-theory/join-semilattices.lagda.md @@ -1,33 +1,28 @@ # Join-semilattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.join-semilattices - (funext : function-extensionality) - where +module order-theory.join-semilattices where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.semigroups funext +open import group-theory.semigroups -open import order-theory.least-upper-bounds-posets funext -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.upper-bounds-posets funext +open import order-theory.least-upper-bounds-posets +open import order-theory.posets +open import order-theory.preorders +open import order-theory.upper-bounds-posets ```
diff --git a/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md b/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md index dff8080920..fdc6bc2fc0 100644 --- a/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md +++ b/src/order-theory/knaster-tarski-fixed-point-theorem.lagda.md @@ -1,12 +1,7 @@ # The Knaster–Tarski fixed point theorem ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.knaster-tarski-fixed-point-theorem - (funext : function-extensionality) - where +module order-theory.knaster-tarski-fixed-point-theorem where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import foundation.dependent-pair-types open import foundation.fixed-points-endofunctions -open import foundation.identity-types funext -open import foundation.logical-equivalences funext +open import foundation.identity-types +open import foundation.logical-equivalences open import foundation.universe-levels -open import order-theory.inflattices funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext -open import order-theory.suplattices funext +open import order-theory.inflattices +open import order-theory.order-preserving-maps-posets +open import order-theory.posets +open import order-theory.suplattices ```
diff --git a/src/order-theory/large-frames.lagda.md b/src/order-theory/large-frames.lagda.md index 00b795f64d..dfd1287b72 100644 --- a/src/order-theory/large-frames.lagda.md +++ b/src/order-theory/large-frames.lagda.md @@ -1,35 +1,30 @@ # Large frames ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-frames - (funext : function-extensionality) - where +module order-theory.large-frames where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.meet-semilattices funext -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.suplattices funext -open import order-theory.top-elements-large-posets funext -open import order-theory.upper-bounds-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.meet-semilattices +open import order-theory.posets +open import order-theory.preorders +open import order-theory.suplattices +open import order-theory.top-elements-large-posets +open import order-theory.upper-bounds-large-posets ```
diff --git a/src/order-theory/large-inflattices.lagda.md b/src/order-theory/large-inflattices.lagda.md index a434a4d002..74860bf69e 100644 --- a/src/order-theory/large-inflattices.lagda.md +++ b/src/order-theory/large-inflattices.lagda.md @@ -1,28 +1,23 @@ # Large inflattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-inflattices - (funext : function-extensionality) - where +module order-theory.large-inflattices where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations funext -open import foundation.logical-equivalences funext -open import foundation.sets funext +open import foundation.large-binary-relations +open import foundation.logical-equivalences +open import foundation.sets open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.inflattices funext -open import order-theory.large-posets funext -open import order-theory.lower-bounds-large-posets funext -open import order-theory.posets funext +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.inflattices +open import order-theory.large-posets +open import order-theory.lower-bounds-large-posets +open import order-theory.posets ```
diff --git a/src/order-theory/large-join-semilattices.lagda.md b/src/order-theory/large-join-semilattices.lagda.md index 70b800058f..abd7e934e0 100644 --- a/src/order-theory/large-join-semilattices.lagda.md +++ b/src/order-theory/large-join-semilattices.lagda.md @@ -1,12 +1,7 @@ # Large join-semilattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-join-semilattices - (funext : function-extensionality) - where +module order-theory.large-join-semilattices where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.bottom-elements-large-posets funext -open import order-theory.join-semilattices funext -open import order-theory.large-posets funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.posets funext +open import order-theory.bottom-elements-large-posets +open import order-theory.join-semilattices +open import order-theory.large-posets +open import order-theory.least-upper-bounds-large-posets +open import order-theory.posets ```
diff --git a/src/order-theory/large-locales.lagda.md b/src/order-theory/large-locales.lagda.md index 6e5322766d..9c6da1d97e 100644 --- a/src/order-theory/large-locales.lagda.md +++ b/src/order-theory/large-locales.lagda.md @@ -1,35 +1,30 @@ # Large locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-locales - (funext : function-extensionality) - where +module order-theory.large-locales where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-frames funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.meet-semilattices funext -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.suplattices funext -open import order-theory.top-elements-large-posets funext -open import order-theory.upper-bounds-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-frames +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.meet-semilattices +open import order-theory.posets +open import order-theory.preorders +open import order-theory.suplattices +open import order-theory.top-elements-large-posets +open import order-theory.upper-bounds-large-posets ```
diff --git a/src/order-theory/large-meet-semilattices.lagda.md b/src/order-theory/large-meet-semilattices.lagda.md index f8cbdd9256..c9087cf742 100644 --- a/src/order-theory/large-meet-semilattices.lagda.md +++ b/src/order-theory/large-meet-semilattices.lagda.md @@ -1,12 +1,7 @@ # Large meet-semilattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-meet-semilattices - (funext : function-extensionality) - where +module order-theory.large-meet-semilattices where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-posets funext -open import order-theory.meet-semilattices funext -open import order-theory.posets funext -open import order-theory.top-elements-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-posets +open import order-theory.meet-semilattices +open import order-theory.posets +open import order-theory.top-elements-large-posets ```
diff --git a/src/order-theory/large-meet-subsemilattices.lagda.md b/src/order-theory/large-meet-subsemilattices.lagda.md index 5692ddedb5..4c2bc6364c 100644 --- a/src/order-theory/large-meet-subsemilattices.lagda.md +++ b/src/order-theory/large-meet-subsemilattices.lagda.md @@ -1,27 +1,22 @@ # Large meet-subsemilattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-meet-subsemilattices - (funext : function-extensionality) - where +module order-theory.large-meet-subsemilattices where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations funext +open import foundation.large-binary-relations open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.large-subposets funext -open import order-theory.top-elements-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.large-subposets +open import order-theory.top-elements-large-posets ```
diff --git a/src/order-theory/large-posets.lagda.md b/src/order-theory/large-posets.lagda.md index a5d73597cf..ebe0411daf 100644 --- a/src/order-theory/large-posets.lagda.md +++ b/src/order-theory/large-posets.lagda.md @@ -1,34 +1,29 @@ # Large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-posets - (funext : function-extensionality) - where +module order-theory.large-posets where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.isomorphisms-in-large-categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.large-categories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.large-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.large-preorders +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/order-theory/large-preorders.lagda.md b/src/order-theory/large-preorders.lagda.md index 78aaaf4c78..34c9170742 100644 --- a/src/order-theory/large-preorders.lagda.md +++ b/src/order-theory/large-preorders.lagda.md @@ -1,28 +1,23 @@ # Large preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-preorders - (funext : function-extensionality) - where +module order-theory.large-preorders where ```
Imports ```agda -open import category-theory.large-precategories funext +open import category-theory.large-precategories open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels -open import order-theory.preorders funext +open import order-theory.preorders ```
diff --git a/src/order-theory/large-quotient-locales.lagda.md b/src/order-theory/large-quotient-locales.lagda.md index 0f9c31f0f0..15e8cc8a46 100644 --- a/src/order-theory/large-quotient-locales.lagda.md +++ b/src/order-theory/large-quotient-locales.lagda.md @@ -1,34 +1,29 @@ # Large quotient locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-quotient-locales - (funext : function-extensionality) - where +module order-theory.large-quotient-locales where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.large-binary-relations funext +open import foundation.identity-types +open import foundation.large-binary-relations open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-locales funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-meet-subsemilattices funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.large-subframes funext -open import order-theory.large-subposets funext -open import order-theory.large-subpreorders funext -open import order-theory.large-subsuplattices funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.top-elements-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-locales +open import order-theory.large-meet-semilattices +open import order-theory.large-meet-subsemilattices +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.large-subframes +open import order-theory.large-subposets +open import order-theory.large-subpreorders +open import order-theory.large-subsuplattices +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.top-elements-large-posets ```
diff --git a/src/order-theory/large-subframes.lagda.md b/src/order-theory/large-subframes.lagda.md index aeb3387340..a425901336 100644 --- a/src/order-theory/large-subframes.lagda.md +++ b/src/order-theory/large-subframes.lagda.md @@ -1,36 +1,31 @@ # Large subframes ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-subframes - (funext : function-extensionality) - where +module order-theory.large-subframes where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-frames funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-meet-subsemilattices funext -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.large-subposets funext -open import order-theory.large-subpreorders funext -open import order-theory.large-subsuplattices funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.top-elements-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-frames +open import order-theory.large-meet-semilattices +open import order-theory.large-meet-subsemilattices +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.large-subposets +open import order-theory.large-subpreorders +open import order-theory.large-subsuplattices +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.top-elements-large-posets ```
diff --git a/src/order-theory/large-subposets.lagda.md b/src/order-theory/large-subposets.lagda.md index f918d03f32..6e2cefec16 100644 --- a/src/order-theory/large-subposets.lagda.md +++ b/src/order-theory/large-subposets.lagda.md @@ -1,26 +1,21 @@ # Large subposets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-subposets - (funext : function-extensionality) - where +module order-theory.large-subposets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations funext -open import foundation.logical-equivalences funext -open import foundation.subtypes funext +open import foundation.large-binary-relations +open import foundation.logical-equivalences +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.large-subpreorders funext +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.large-subpreorders ```
diff --git a/src/order-theory/large-subpreorders.lagda.md b/src/order-theory/large-subpreorders.lagda.md index 9c96e79e14..d69fca9bbe 100644 --- a/src/order-theory/large-subpreorders.lagda.md +++ b/src/order-theory/large-subpreorders.lagda.md @@ -1,24 +1,19 @@ # Large subpreorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-subpreorders - (funext : function-extensionality) - where +module order-theory.large-subpreorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.large-binary-relations funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.large-binary-relations +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.large-preorders funext +open import order-theory.large-preorders ```
diff --git a/src/order-theory/large-subsuplattices.lagda.md b/src/order-theory/large-subsuplattices.lagda.md index 550f7ffb0f..c2a9126cba 100644 --- a/src/order-theory/large-subsuplattices.lagda.md +++ b/src/order-theory/large-subsuplattices.lagda.md @@ -1,23 +1,18 @@ # Large subsuplattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-subsuplattices - (funext : function-extensionality) - where +module order-theory.large-subsuplattices where ```
Imports ```agda -open import foundation.large-binary-relations funext +open import foundation.large-binary-relations open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-subposets funext -open import order-theory.large-suplattices funext +open import order-theory.large-posets +open import order-theory.large-subposets +open import order-theory.large-suplattices ```
diff --git a/src/order-theory/large-suplattices.lagda.md b/src/order-theory/large-suplattices.lagda.md index 028337af4a..489330b18b 100644 --- a/src/order-theory/large-suplattices.lagda.md +++ b/src/order-theory/large-suplattices.lagda.md @@ -1,31 +1,26 @@ # Large suplattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.large-suplattices - (funext : function-extensionality) - where +module order-theory.large-suplattices where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.posets funext -open import order-theory.suplattices funext -open import order-theory.upper-bounds-large-posets funext +open import order-theory.large-posets +open import order-theory.least-upper-bounds-large-posets +open import order-theory.posets +open import order-theory.suplattices +open import order-theory.upper-bounds-large-posets ```
diff --git a/src/order-theory/lattices.lagda.md b/src/order-theory/lattices.lagda.md index 99e9a1821c..bc9d9bc466 100644 --- a/src/order-theory/lattices.lagda.md +++ b/src/order-theory/lattices.lagda.md @@ -1,26 +1,21 @@ # Lattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.lattices - (funext : function-extensionality) - where +module order-theory.lattices where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.join-semilattices funext -open import order-theory.meet-semilattices funext -open import order-theory.posets funext +open import order-theory.join-semilattices +open import order-theory.meet-semilattices +open import order-theory.posets ```
diff --git a/src/order-theory/least-upper-bounds-large-posets.lagda.md b/src/order-theory/least-upper-bounds-large-posets.lagda.md index 75972fe59a..a1ee5df25f 100644 --- a/src/order-theory/least-upper-bounds-large-posets.lagda.md +++ b/src/order-theory/least-upper-bounds-large-posets.lagda.md @@ -1,26 +1,21 @@ # Least upper bounds in large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.least-upper-bounds-large-posets - (funext : function-extensionality) - where +module order-theory.least-upper-bounds-large-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.logical-equivalences funext +open import foundation.logical-equivalences open import foundation.universe-levels -open import order-theory.dependent-products-large-posets funext -open import order-theory.large-posets funext -open import order-theory.least-upper-bounds-posets funext -open import order-theory.similarity-of-elements-large-posets funext -open import order-theory.upper-bounds-large-posets funext +open import order-theory.dependent-products-large-posets +open import order-theory.large-posets +open import order-theory.least-upper-bounds-posets +open import order-theory.similarity-of-elements-large-posets +open import order-theory.upper-bounds-large-posets ```
diff --git a/src/order-theory/least-upper-bounds-posets.lagda.md b/src/order-theory/least-upper-bounds-posets.lagda.md index c20eea66f0..d0a5e74b02 100644 --- a/src/order-theory/least-upper-bounds-posets.lagda.md +++ b/src/order-theory/least-upper-bounds-posets.lagda.md @@ -1,28 +1,23 @@ # Least upper bounds in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.least-upper-bounds-posets - (funext : function-extensionality) - where +module order-theory.least-upper-bounds-posets where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.booleans funext +open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.upper-bounds-posets funext +open import order-theory.posets +open import order-theory.upper-bounds-posets ```
diff --git a/src/order-theory/locales.lagda.md b/src/order-theory/locales.lagda.md index 0ce60c3e25..25983102a6 100644 --- a/src/order-theory/locales.lagda.md +++ b/src/order-theory/locales.lagda.md @@ -1,30 +1,25 @@ # Locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.locales - (funext : function-extensionality) - where +module order-theory.locales where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.binary-relations +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.frames funext -open import order-theory.greatest-lower-bounds-posets funext -open import order-theory.least-upper-bounds-posets funext -open import order-theory.meet-semilattices funext -open import order-theory.meet-suplattices funext -open import order-theory.posets funext -open import order-theory.suplattices funext +open import order-theory.frames +open import order-theory.greatest-lower-bounds-posets +open import order-theory.least-upper-bounds-posets +open import order-theory.meet-semilattices +open import order-theory.meet-suplattices +open import order-theory.posets +open import order-theory.suplattices ```
diff --git a/src/order-theory/locally-finite-posets.lagda.md b/src/order-theory/locally-finite-posets.lagda.md index 16dd993bc0..69a7c93beb 100644 --- a/src/order-theory/locally-finite-posets.lagda.md +++ b/src/order-theory/locally-finite-posets.lagda.md @@ -1,23 +1,18 @@ # Locally finite posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.locally-finite-posets - (funext : function-extensionality) - where +module order-theory.locally-finite-posets where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import order-theory.finite-posets funext -open import order-theory.interval-subposets funext -open import order-theory.posets funext +open import order-theory.finite-posets +open import order-theory.interval-subposets +open import order-theory.posets ```
diff --git a/src/order-theory/lower-bounds-large-posets.lagda.md b/src/order-theory/lower-bounds-large-posets.lagda.md index 38a4ee7b42..3f527ccddc 100644 --- a/src/order-theory/lower-bounds-large-posets.lagda.md +++ b/src/order-theory/lower-bounds-large-posets.lagda.md @@ -1,25 +1,20 @@ # Lower bounds in large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.lower-bounds-large-posets - (funext : function-extensionality) - where +module order-theory.lower-bounds-large-posets where ```
Imports ```agda -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.universe-levels -open import order-theory.dependent-products-large-posets funext -open import order-theory.large-posets funext +open import order-theory.dependent-products-large-posets +open import order-theory.large-posets ```
diff --git a/src/order-theory/lower-bounds-posets.lagda.md b/src/order-theory/lower-bounds-posets.lagda.md index 1db7547fc6..5ae8f55417 100644 --- a/src/order-theory/lower-bounds-posets.lagda.md +++ b/src/order-theory/lower-bounds-posets.lagda.md @@ -1,22 +1,17 @@ # Lower bounds in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.lower-bounds-posets - (funext : function-extensionality) - where +module order-theory.lower-bounds-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import order-theory.posets funext +open import order-theory.posets ```
diff --git a/src/order-theory/lower-sets-large-posets.lagda.md b/src/order-theory/lower-sets-large-posets.lagda.md index 7526a0bac3..bef92c55f0 100644 --- a/src/order-theory/lower-sets-large-posets.lagda.md +++ b/src/order-theory/lower-sets-large-posets.lagda.md @@ -1,12 +1,7 @@ # Lower sets in large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.lower-sets-large-posets - (funext : function-extensionality) - where +module order-theory.lower-sets-large-posets where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-subposets funext +open import order-theory.large-posets +open import order-theory.large-subposets ```
diff --git a/src/order-theory/lower-types-preorders.lagda.md b/src/order-theory/lower-types-preorders.lagda.md index 03254048b8..7967370856 100644 --- a/src/order-theory/lower-types-preorders.lagda.md +++ b/src/order-theory/lower-types-preorders.lagda.md @@ -1,22 +1,17 @@ # Lower types in preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.lower-types-preorders - (funext : function-extensionality) - where +module order-theory.lower-types-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.preorders funext +open import order-theory.preorders ```
diff --git a/src/order-theory/maximal-chains-posets.lagda.md b/src/order-theory/maximal-chains-posets.lagda.md index f3293d1432..e62dabcc6e 100644 --- a/src/order-theory/maximal-chains-posets.lagda.md +++ b/src/order-theory/maximal-chains-posets.lagda.md @@ -1,23 +1,18 @@ # Maximal chains in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.maximal-chains-posets - (funext : function-extensionality) - where +module order-theory.maximal-chains-posets where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import order-theory.chains-posets funext -open import order-theory.maximal-chains-preorders funext -open import order-theory.posets funext +open import order-theory.chains-posets +open import order-theory.maximal-chains-preorders +open import order-theory.posets ```
diff --git a/src/order-theory/maximal-chains-preorders.lagda.md b/src/order-theory/maximal-chains-preorders.lagda.md index 86a66aad8f..0cf6169f4f 100644 --- a/src/order-theory/maximal-chains-preorders.lagda.md +++ b/src/order-theory/maximal-chains-preorders.lagda.md @@ -1,23 +1,18 @@ # Maximal chains in preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.maximal-chains-preorders - (funext : function-extensionality) - where +module order-theory.maximal-chains-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import order-theory.chains-preorders funext -open import order-theory.preorders funext +open import order-theory.chains-preorders +open import order-theory.preorders ```
diff --git a/src/order-theory/meet-semilattices.lagda.md b/src/order-theory/meet-semilattices.lagda.md index b31f3f8c1b..4a01ec4db8 100644 --- a/src/order-theory/meet-semilattices.lagda.md +++ b/src/order-theory/meet-semilattices.lagda.md @@ -1,34 +1,29 @@ # Meet-semilattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.meet-semilattices - (funext : function-extensionality) - where +module order-theory.meet-semilattices where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.isomorphisms-semigroups funext -open import group-theory.semigroups funext +open import group-theory.isomorphisms-semigroups +open import group-theory.semigroups -open import order-theory.greatest-lower-bounds-posets funext -open import order-theory.lower-bounds-posets funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.greatest-lower-bounds-posets +open import order-theory.lower-bounds-posets +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/order-theory/meet-suplattices.lagda.md b/src/order-theory/meet-suplattices.lagda.md index 2d67301fd1..898eeb5f7a 100644 --- a/src/order-theory/meet-suplattices.lagda.md +++ b/src/order-theory/meet-suplattices.lagda.md @@ -1,26 +1,21 @@ # Meet-suplattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.meet-suplattices - (funext : function-extensionality) - where +module order-theory.meet-suplattices where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.meet-semilattices funext -open import order-theory.posets funext -open import order-theory.suplattices funext +open import order-theory.meet-semilattices +open import order-theory.posets +open import order-theory.suplattices ```
diff --git a/src/order-theory/nuclei-large-locales.lagda.md b/src/order-theory/nuclei-large-locales.lagda.md index a54ae4f7bc..b6d44973c9 100644 --- a/src/order-theory/nuclei-large-locales.lagda.md +++ b/src/order-theory/nuclei-large-locales.lagda.md @@ -1,12 +1,7 @@ # Nuclei on large locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.nuclei-large-locales - (funext : function-extensionality) - where +module order-theory.nuclei-large-locales where ```
Imports @@ -14,25 +9,25 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.homomorphisms-large-meet-semilattices funext -open import order-theory.large-frames funext -open import order-theory.large-locales funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-meet-subsemilattices funext -open import order-theory.large-posets funext -open import order-theory.large-subposets funext -open import order-theory.large-subpreorders funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext +open import order-theory.homomorphisms-large-meet-semilattices +open import order-theory.large-frames +open import order-theory.large-locales +open import order-theory.large-meet-semilattices +open import order-theory.large-meet-subsemilattices +open import order-theory.large-posets +open import order-theory.large-subposets +open import order-theory.large-subpreorders +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets ```
diff --git a/src/order-theory/opposite-large-posets.lagda.md b/src/order-theory/opposite-large-posets.lagda.md index 1566f395bd..cbb94d58f5 100644 --- a/src/order-theory/opposite-large-posets.lagda.md +++ b/src/order-theory/opposite-large-posets.lagda.md @@ -1,30 +1,25 @@ # Opposite large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.opposite-large-posets - (funext : function-extensionality) - where +module order-theory.opposite-large-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types open import foundation.large-identity-types -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.opposite-large-preorders funext -open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.opposite-large-preorders +open import order-theory.order-preserving-maps-large-posets ```
diff --git a/src/order-theory/opposite-large-preorders.lagda.md b/src/order-theory/opposite-large-preorders.lagda.md index 39124b3a83..5ecbfef3d7 100644 --- a/src/order-theory/opposite-large-preorders.lagda.md +++ b/src/order-theory/opposite-large-preorders.lagda.md @@ -1,28 +1,23 @@ # Opposite large preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.opposite-large-preorders - (funext : function-extensionality) - where +module order-theory.opposite-large-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types open import foundation.large-identity-types -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-large-preorders funext +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-large-preorders ```
diff --git a/src/order-theory/opposite-posets.lagda.md b/src/order-theory/opposite-posets.lagda.md index ef5d17eb8e..45b842294c 100644 --- a/src/order-theory/opposite-posets.lagda.md +++ b/src/order-theory/opposite-posets.lagda.md @@ -1,29 +1,24 @@ # Opposite posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.opposite-posets - (funext : function-extensionality) - where +module order-theory.opposite-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.opposite-preorders funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.opposite-preorders +open import order-theory.order-preserving-maps-posets +open import order-theory.posets +open import order-theory.preorders ```
diff --git a/src/order-theory/opposite-preorders.lagda.md b/src/order-theory/opposite-preorders.lagda.md index 39d960bd75..2e6db98be2 100644 --- a/src/order-theory/opposite-preorders.lagda.md +++ b/src/order-theory/opposite-preorders.lagda.md @@ -1,27 +1,22 @@ # Opposite preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.opposite-preorders - (funext : function-extensionality) - where +module order-theory.opposite-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders funext -open import order-theory.preorders funext +open import order-theory.order-preserving-maps-preorders +open import order-theory.preorders ```
diff --git a/src/order-theory/order-preserving-maps-large-posets.lagda.md b/src/order-theory/order-preserving-maps-large-posets.lagda.md index 556945e9fb..5c8636c874 100644 --- a/src/order-theory/order-preserving-maps-large-posets.lagda.md +++ b/src/order-theory/order-preserving-maps-large-posets.lagda.md @@ -1,12 +1,7 @@ # Order preserving maps between large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.order-preserving-maps-large-posets - (funext : function-extensionality) - where +module order-theory.order-preserving-maps-large-posets where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.order-preserving-maps-posets +open import order-theory.similarity-of-elements-large-posets ```
diff --git a/src/order-theory/order-preserving-maps-large-preorders.lagda.md b/src/order-theory/order-preserving-maps-large-preorders.lagda.md index 6a9088af23..d9150512e7 100644 --- a/src/order-theory/order-preserving-maps-large-preorders.lagda.md +++ b/src/order-theory/order-preserving-maps-large-preorders.lagda.md @@ -1,12 +1,7 @@ # Order preserving maps between large preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.order-preserving-maps-large-preorders - (funext : function-extensionality) - where +module order-theory.order-preserving-maps-large-preorders where ```
Imports @@ -18,9 +13,9 @@ open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.homotopies -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-preorders funext -open import order-theory.similarity-of-elements-large-preorders funext +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-preorders +open import order-theory.similarity-of-elements-large-preorders ```
diff --git a/src/order-theory/order-preserving-maps-posets.lagda.md b/src/order-theory/order-preserving-maps-posets.lagda.md index 6bff92ab1b..163aee3f3f 100644 --- a/src/order-theory/order-preserving-maps-posets.lagda.md +++ b/src/order-theory/order-preserving-maps-posets.lagda.md @@ -1,29 +1,24 @@ # Order preserving maps between posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.order-preserving-maps-posets - (funext : function-extensionality) - where +module order-theory.order-preserving-maps-posets where ```
Imports ```agda -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.strictly-involutive-identity-types +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders funext -open import order-theory.posets funext +open import order-theory.order-preserving-maps-preorders +open import order-theory.posets ```
diff --git a/src/order-theory/order-preserving-maps-preorders.lagda.md b/src/order-theory/order-preserving-maps-preorders.lagda.md index fd518afef5..a45df09656 100644 --- a/src/order-theory/order-preserving-maps-preorders.lagda.md +++ b/src/order-theory/order-preserving-maps-preorders.lagda.md @@ -1,32 +1,27 @@ # Order preserving maps between preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.order-preserving-maps-preorders - (funext : function-extensionality) - where +module order-theory.order-preserving-maps-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositions +open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle open import foundation.universe-levels open import foundation-core.torsorial-type-families -open import order-theory.preorders funext +open import order-theory.preorders ```
diff --git a/src/order-theory/ordinals.lagda.md b/src/order-theory/ordinals.lagda.md index 187a6a048f..7dc9994603 100644 --- a/src/order-theory/ordinals.lagda.md +++ b/src/order-theory/ordinals.lagda.md @@ -1,30 +1,25 @@ # Ordinals ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.ordinals - (funext : function-extensionality) - where +module order-theory.ordinals where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.transitive-well-founded-relations funext -open import order-theory.well-founded-relations funext +open import order-theory.posets +open import order-theory.preorders +open import order-theory.transitive-well-founded-relations +open import order-theory.well-founded-relations ```
diff --git a/src/order-theory/posets.lagda.md b/src/order-theory/posets.lagda.md index 3abd37fcfc..f1875f86f2 100644 --- a/src/order-theory/posets.lagda.md +++ b/src/order-theory/posets.lagda.md @@ -1,33 +1,28 @@ # Posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.posets - (funext : function-extensionality) - where +module order-theory.posets where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.isomorphisms-in-precategories funext -open import category-theory.precategories funext +open import category-theory.categories +open import category-theory.isomorphisms-in-precategories +open import category-theory.precategories -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.preorders funext +open import order-theory.preorders ```
diff --git a/src/order-theory/powers-of-large-locales.lagda.md b/src/order-theory/powers-of-large-locales.lagda.md index 5480b824f2..1822320130 100644 --- a/src/order-theory/powers-of-large-locales.lagda.md +++ b/src/order-theory/powers-of-large-locales.lagda.md @@ -1,30 +1,25 @@ # Powers of large locales ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.powers-of-large-locales - (funext : function-extensionality) - where +module order-theory.powers-of-large-locales where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.sets open import foundation.universe-levels -open import order-theory.dependent-products-large-locales funext -open import order-theory.greatest-lower-bounds-large-posets funext -open import order-theory.large-locales funext -open import order-theory.large-meet-semilattices funext -open import order-theory.large-posets funext -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.top-elements-large-posets funext +open import order-theory.dependent-products-large-locales +open import order-theory.greatest-lower-bounds-large-posets +open import order-theory.large-locales +open import order-theory.large-meet-semilattices +open import order-theory.large-posets +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.top-elements-large-posets ```
diff --git a/src/order-theory/precategory-of-decidable-total-orders.lagda.md b/src/order-theory/precategory-of-decidable-total-orders.lagda.md index 9186f19ba8..ee91924562 100644 --- a/src/order-theory/precategory-of-decidable-total-orders.lagda.md +++ b/src/order-theory/precategory-of-decidable-total-orders.lagda.md @@ -1,25 +1,20 @@ # The precategory of decidable total orders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.precategory-of-decidable-total-orders - (funext : function-extensionality) - where +module order-theory.precategory-of-decidable-total-orders where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.full-large-subprecategories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import order-theory.decidable-total-orders funext -open import order-theory.precategory-of-posets funext +open import order-theory.decidable-total-orders +open import order-theory.precategory-of-posets ```
diff --git a/src/order-theory/precategory-of-finite-posets.lagda.md b/src/order-theory/precategory-of-finite-posets.lagda.md index 0f5fe4aa5f..87c506290f 100644 --- a/src/order-theory/precategory-of-finite-posets.lagda.md +++ b/src/order-theory/precategory-of-finite-posets.lagda.md @@ -1,25 +1,20 @@ # The precategory of finite posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.precategory-of-finite-posets - (funext : function-extensionality) - where +module order-theory.precategory-of-finite-posets where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.full-large-subprecategories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import order-theory.finite-posets funext -open import order-theory.precategory-of-posets funext +open import order-theory.finite-posets +open import order-theory.precategory-of-posets ```
diff --git a/src/order-theory/precategory-of-finite-total-orders.lagda.md b/src/order-theory/precategory-of-finite-total-orders.lagda.md index b91b516f29..e5e28bf9c5 100644 --- a/src/order-theory/precategory-of-finite-total-orders.lagda.md +++ b/src/order-theory/precategory-of-finite-total-orders.lagda.md @@ -1,25 +1,20 @@ # The precategory of finite total orders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.precategory-of-finite-total-orders - (funext : function-extensionality) - where +module order-theory.precategory-of-finite-total-orders where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.full-large-subprecategories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import order-theory.finite-total-orders funext -open import order-theory.precategory-of-posets funext +open import order-theory.finite-total-orders +open import order-theory.precategory-of-posets ```
diff --git a/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md b/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md index c59414f1a3..cbcc011d57 100644 --- a/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md +++ b/src/order-theory/precategory-of-inhabited-finite-total-orders.lagda.md @@ -1,25 +1,20 @@ # The precategory of inhabited finite total orders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.precategory-of-inhabited-finite-total-orders - (funext : function-extensionality) - where +module order-theory.precategory-of-inhabited-finite-total-orders where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.full-large-subprecategories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import order-theory.inhabited-finite-total-orders funext -open import order-theory.precategory-of-posets funext +open import order-theory.inhabited-finite-total-orders +open import order-theory.precategory-of-posets ```
diff --git a/src/order-theory/precategory-of-posets.lagda.md b/src/order-theory/precategory-of-posets.lagda.md index 2af76d06ba..69a33a4c81 100644 --- a/src/order-theory/precategory-of-posets.lagda.md +++ b/src/order-theory/precategory-of-posets.lagda.md @@ -1,24 +1,19 @@ # The precategory of posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.precategory-of-posets - (funext : function-extensionality) - where +module order-theory.precategory-of-posets where ```
Imports ```agda -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/order-theory/precategory-of-total-orders.lagda.md b/src/order-theory/precategory-of-total-orders.lagda.md index d6ae76dfdf..aeb5d9ffd2 100644 --- a/src/order-theory/precategory-of-total-orders.lagda.md +++ b/src/order-theory/precategory-of-total-orders.lagda.md @@ -1,25 +1,20 @@ # The precategory of total orders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.precategory-of-total-orders - (funext : function-extensionality) - where +module order-theory.precategory-of-total-orders where ```
Imports ```agda -open import category-theory.full-large-subprecategories funext -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.full-large-subprecategories +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import order-theory.precategory-of-posets funext -open import order-theory.total-orders funext +open import order-theory.precategory-of-posets +open import order-theory.total-orders ```
diff --git a/src/order-theory/preorders.lagda.md b/src/order-theory/preorders.lagda.md index 0521e102ee..37293a7863 100644 --- a/src/order-theory/preorders.lagda.md +++ b/src/order-theory/preorders.lagda.md @@ -1,29 +1,24 @@ # Preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.preorders - (funext : function-extensionality) - where +module order-theory.preorders where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/order-theory/principal-lower-sets-large-posets.lagda.md b/src/order-theory/principal-lower-sets-large-posets.lagda.md index 83c700f447..6823e5413e 100644 --- a/src/order-theory/principal-lower-sets-large-posets.lagda.md +++ b/src/order-theory/principal-lower-sets-large-posets.lagda.md @@ -1,26 +1,21 @@ # Principal lower sets of large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.principal-lower-sets-large-posets - (funext : function-extensionality) - where +module order-theory.principal-lower-sets-large-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext +open import foundation.identity-types +open import foundation.logical-equivalences open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-subposets funext -open import order-theory.large-subpreorders funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-posets +open import order-theory.large-subposets +open import order-theory.large-subpreorders +open import order-theory.similarity-of-elements-large-posets ```
diff --git a/src/order-theory/principal-upper-sets-large-posets.lagda.md b/src/order-theory/principal-upper-sets-large-posets.lagda.md index 981aa11bcc..c66b312a07 100644 --- a/src/order-theory/principal-upper-sets-large-posets.lagda.md +++ b/src/order-theory/principal-upper-sets-large-posets.lagda.md @@ -1,26 +1,21 @@ # Principal upper sets of large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.principal-upper-sets-large-posets - (funext : function-extensionality) - where +module order-theory.principal-upper-sets-large-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext +open import foundation.identity-types +open import foundation.logical-equivalences open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-subposets funext -open import order-theory.large-subpreorders funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-posets +open import order-theory.large-subposets +open import order-theory.large-subpreorders +open import order-theory.similarity-of-elements-large-posets ```
diff --git a/src/order-theory/reflective-galois-connections-large-posets.lagda.md b/src/order-theory/reflective-galois-connections-large-posets.lagda.md index caec33de61..bd27be52af 100644 --- a/src/order-theory/reflective-galois-connections-large-posets.lagda.md +++ b/src/order-theory/reflective-galois-connections-large-posets.lagda.md @@ -1,23 +1,18 @@ # Reflective Galois connections between large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.reflective-galois-connections-large-posets - (funext : function-extensionality) - where +module order-theory.reflective-galois-connections-large-posets where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.universe-levels -open import order-theory.galois-connections-large-posets funext -open import order-theory.large-posets funext -open import order-theory.order-preserving-maps-large-posets funext +open import order-theory.galois-connections-large-posets +open import order-theory.large-posets +open import order-theory.order-preserving-maps-large-posets ```
diff --git a/src/order-theory/resizing-posets.lagda.md b/src/order-theory/resizing-posets.lagda.md index 9cd4a30eb3..4fcaf5e66f 100644 --- a/src/order-theory/resizing-posets.lagda.md +++ b/src/order-theory/resizing-posets.lagda.md @@ -1,38 +1,33 @@ # Resizing posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.resizing-posets - (funext : function-extensionality) - where +module order-theory.resizing-posets where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.small-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions +open import foundation.sets +open import foundation.small-types open import foundation.universe-levels -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext -open import order-theory.precategory-of-posets funext -open import order-theory.preorders funext -open import order-theory.resizing-preorders funext +open import order-theory.order-preserving-maps-posets +open import order-theory.posets +open import order-theory.precategory-of-posets +open import order-theory.preorders +open import order-theory.resizing-preorders ```
diff --git a/src/order-theory/resizing-preorders.lagda.md b/src/order-theory/resizing-preorders.lagda.md index a73cacd1c6..26a17b7682 100644 --- a/src/order-theory/resizing-preorders.lagda.md +++ b/src/order-theory/resizing-preorders.lagda.md @@ -1,32 +1,27 @@ # Resizing preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.resizing-preorders - (funext : function-extensionality) - where +module order-theory.resizing-preorders where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.small-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions +open import foundation.sets +open import foundation.small-types open import foundation.universe-levels -open import order-theory.order-preserving-maps-preorders funext -open import order-theory.preorders funext +open import order-theory.order-preserving-maps-preorders +open import order-theory.preorders ```
diff --git a/src/order-theory/resizing-suplattices.lagda.md b/src/order-theory/resizing-suplattices.lagda.md index 06cb2d0284..6c0cdeede8 100644 --- a/src/order-theory/resizing-suplattices.lagda.md +++ b/src/order-theory/resizing-suplattices.lagda.md @@ -1,36 +1,31 @@ # Resizing suplattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.resizing-suplattices - (funext : function-extensionality) - where +module order-theory.resizing-suplattices where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.small-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions +open import foundation.sets +open import foundation.small-types open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext -open import order-theory.resizing-posets funext -open import order-theory.suplattices funext +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.posets +open import order-theory.resizing-posets +open import order-theory.suplattices ```
diff --git a/src/order-theory/similarity-of-elements-large-posets.lagda.md b/src/order-theory/similarity-of-elements-large-posets.lagda.md index 1878dbc0db..5e2d8199ea 100644 --- a/src/order-theory/similarity-of-elements-large-posets.lagda.md +++ b/src/order-theory/similarity-of-elements-large-posets.lagda.md @@ -1,29 +1,24 @@ # Similarity of elements in large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.similarity-of-elements-large-posets - (funext : function-extensionality) - where +module order-theory.similarity-of-elements-large-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.propositions +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.similarity-of-elements-large-preorders funext +open import order-theory.large-posets +open import order-theory.similarity-of-elements-large-preorders ```
diff --git a/src/order-theory/similarity-of-elements-large-preorders.lagda.md b/src/order-theory/similarity-of-elements-large-preorders.lagda.md index 3e1633d49b..c027bb56db 100644 --- a/src/order-theory/similarity-of-elements-large-preorders.lagda.md +++ b/src/order-theory/similarity-of-elements-large-preorders.lagda.md @@ -1,24 +1,19 @@ # Similarity of elements in large preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.similarity-of-elements-large-preorders - (funext : function-extensionality) - where +module order-theory.similarity-of-elements-large-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.propositions open import foundation.universe-levels -open import order-theory.large-preorders funext +open import order-theory.large-preorders ```
diff --git a/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md b/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md index e75d8229a6..663ec217c0 100644 --- a/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md +++ b/src/order-theory/similarity-of-order-preserving-maps-large-posets.lagda.md @@ -1,24 +1,19 @@ # Similarity of order preserving maps between large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.similarity-of-order-preserving-maps-large-posets - (funext : function-extensionality) - where +module order-theory.similarity-of-order-preserving-maps-large-posets where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.similarity-of-elements-large-posets funext -open import order-theory.similarity-of-order-preserving-maps-large-preorders funext +open import order-theory.large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.similarity-of-elements-large-posets +open import order-theory.similarity-of-order-preserving-maps-large-preorders ```
diff --git a/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md b/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md index 4f34f8bcff..62ce3a3d85 100644 --- a/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md +++ b/src/order-theory/similarity-of-order-preserving-maps-large-preorders.lagda.md @@ -1,23 +1,18 @@ # Similarity of order preserving maps between large preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.similarity-of-order-preserving-maps-large-preorders - (funext : function-extensionality) - where +module order-theory.similarity-of-order-preserving-maps-large-preorders where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.universe-levels -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.similarity-of-elements-large-preorders funext +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.similarity-of-elements-large-preorders ```
diff --git a/src/order-theory/strict-order-preserving-maps.lagda.md b/src/order-theory/strict-order-preserving-maps.lagda.md index 4bf0892ac6..44b8225347 100644 --- a/src/order-theory/strict-order-preserving-maps.lagda.md +++ b/src/order-theory/strict-order-preserving-maps.lagda.md @@ -1,25 +1,20 @@ # Strict order preserving maps ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.strict-order-preserving-maps - (funext : function-extensionality) - where +module order-theory.strict-order-preserving-maps where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.strict-preorders funext -open import order-theory.strictly-preordered-sets funext +open import order-theory.strict-preorders +open import order-theory.strictly-preordered-sets ```
diff --git a/src/order-theory/strict-preorders.lagda.md b/src/order-theory/strict-preorders.lagda.md index 65e3f23b7d..071d017b3d 100644 --- a/src/order-theory/strict-preorders.lagda.md +++ b/src/order-theory/strict-preorders.lagda.md @@ -1,23 +1,18 @@ # Strict preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.strict-preorders - (funext : function-extensionality) - where +module order-theory.strict-preorders where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.negation +open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md b/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md index 2f63126c6d..d8a4672caa 100644 --- a/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md +++ b/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md @@ -1,24 +1,19 @@ # Strictly inflationary maps on a strictly preordered type ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.strictly-inflationary-maps-strict-preorders - (funext : function-extensionality) - where +module order-theory.strictly-inflationary-maps-strict-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.strict-order-preserving-maps funext -open import order-theory.strict-preorders funext +open import order-theory.strict-order-preserving-maps +open import order-theory.strict-preorders ```
diff --git a/src/order-theory/strictly-preordered-sets.lagda.md b/src/order-theory/strictly-preordered-sets.lagda.md index 860efc968b..c639e6fe02 100644 --- a/src/order-theory/strictly-preordered-sets.lagda.md +++ b/src/order-theory/strictly-preordered-sets.lagda.md @@ -1,27 +1,22 @@ # Strictly preordered sets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.strictly-preordered-sets - (funext : function-extensionality) - where +module order-theory.strictly-preordered-sets where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.strict-preorders funext +open import order-theory.strict-preorders ```
diff --git a/src/order-theory/subposets.lagda.md b/src/order-theory/subposets.lagda.md index 38f8a05a95..d7cd52162e 100644 --- a/src/order-theory/subposets.lagda.md +++ b/src/order-theory/subposets.lagda.md @@ -1,26 +1,21 @@ # Subposets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.subposets - (funext : function-extensionality) - where +module order-theory.subposets where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.subpreorders funext +open import order-theory.posets +open import order-theory.preorders +open import order-theory.subpreorders ```
diff --git a/src/order-theory/subpreorders.lagda.md b/src/order-theory/subpreorders.lagda.md index fce45d7c7b..8ac0925ccd 100644 --- a/src/order-theory/subpreorders.lagda.md +++ b/src/order-theory/subpreorders.lagda.md @@ -1,26 +1,21 @@ # Subpreorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.subpreorders - (funext : function-extensionality) - where +module order-theory.subpreorders where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.preorders funext +open import order-theory.preorders ```
diff --git a/src/order-theory/suplattices.lagda.md b/src/order-theory/suplattices.lagda.md index 86a1563326..e2cac7a583 100644 --- a/src/order-theory/suplattices.lagda.md +++ b/src/order-theory/suplattices.lagda.md @@ -1,30 +1,25 @@ # Suplattices ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.suplattices - (funext : function-extensionality) - where +module order-theory.suplattices where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.least-upper-bounds-posets funext -open import order-theory.posets funext -open import order-theory.upper-bounds-posets funext +open import order-theory.least-upper-bounds-posets +open import order-theory.posets +open import order-theory.upper-bounds-posets ```
diff --git a/src/order-theory/supremum-preserving-maps-posets.lagda.md b/src/order-theory/supremum-preserving-maps-posets.lagda.md index c75c301030..b5abca4ab4 100644 --- a/src/order-theory/supremum-preserving-maps-posets.lagda.md +++ b/src/order-theory/supremum-preserving-maps-posets.lagda.md @@ -1,38 +1,33 @@ # Supremum preserving maps between posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.supremum-preserving-maps-posets - (funext : function-extensionality) - where +module order-theory.supremum-preserving-maps-posets where ```
Imports ```agda -open import foundation.booleans funext +open import foundation.booleans open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.evaluation-functions -open import foundation.function-types funext +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.small-types funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.small-types +open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import order-theory.join-preserving-maps-posets funext -open import order-theory.least-upper-bounds-posets funext -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.join-preserving-maps-posets +open import order-theory.least-upper-bounds-posets +open import order-theory.order-preserving-maps-posets +open import order-theory.posets ```
diff --git a/src/order-theory/top-elements-large-posets.lagda.md b/src/order-theory/top-elements-large-posets.lagda.md index 8e760b8df5..f861a1a336 100644 --- a/src/order-theory/top-elements-large-posets.lagda.md +++ b/src/order-theory/top-elements-large-posets.lagda.md @@ -1,12 +1,7 @@ # Top elements in large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.top-elements-large-posets - (funext : function-extensionality) - where +module order-theory.top-elements-large-posets where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import order-theory.dependent-products-large-posets funext -open import order-theory.large-posets funext +open import order-theory.dependent-products-large-posets +open import order-theory.large-posets ```
diff --git a/src/order-theory/top-elements-posets.lagda.md b/src/order-theory/top-elements-posets.lagda.md index 802fcfb581..658fc977cc 100644 --- a/src/order-theory/top-elements-posets.lagda.md +++ b/src/order-theory/top-elements-posets.lagda.md @@ -1,24 +1,19 @@ # Top elements in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.top-elements-posets - (funext : function-extensionality) - where +module order-theory.top-elements-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.top-elements-preorders funext +open import order-theory.posets +open import order-theory.top-elements-preorders ```
diff --git a/src/order-theory/top-elements-preorders.lagda.md b/src/order-theory/top-elements-preorders.lagda.md index 94a3834174..1c9655f1de 100644 --- a/src/order-theory/top-elements-preorders.lagda.md +++ b/src/order-theory/top-elements-preorders.lagda.md @@ -1,22 +1,17 @@ # Top elements in preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.top-elements-preorders - (funext : function-extensionality) - where +module order-theory.top-elements-preorders where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import order-theory.preorders funext +open import order-theory.preorders ```
diff --git a/src/order-theory/total-orders.lagda.md b/src/order-theory/total-orders.lagda.md index a0dd92af88..1f84d69e67 100644 --- a/src/order-theory/total-orders.lagda.md +++ b/src/order-theory/total-orders.lagda.md @@ -1,27 +1,22 @@ # Total orders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.total-orders - (funext : function-extensionality) - where +module order-theory.total-orders where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import order-theory.posets funext -open import order-theory.preorders funext -open import order-theory.total-preorders funext +open import order-theory.posets +open import order-theory.preorders +open import order-theory.total-preorders ```
diff --git a/src/order-theory/total-preorders.lagda.md b/src/order-theory/total-preorders.lagda.md index be203bcef2..facdaddbd8 100644 --- a/src/order-theory/total-preorders.lagda.md +++ b/src/order-theory/total-preorders.lagda.md @@ -1,24 +1,19 @@ # Total preorders ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.total-preorders - (funext : function-extensionality) - where +module order-theory.total-preorders where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.propositions funext +open import foundation.disjunction +open import foundation.propositions open import foundation.universe-levels -open import order-theory.preorders funext +open import order-theory.preorders ```
diff --git a/src/order-theory/transitive-well-founded-relations.lagda.md b/src/order-theory/transitive-well-founded-relations.lagda.md index 2a95571b4f..f011a6666e 100644 --- a/src/order-theory/transitive-well-founded-relations.lagda.md +++ b/src/order-theory/transitive-well-founded-relations.lagda.md @@ -1,23 +1,18 @@ # Transitive well-founded relations ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.transitive-well-founded-relations - (funext : function-extensionality) - where +module order-theory.transitive-well-founded-relations where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import order-theory.well-founded-relations funext +open import order-theory.well-founded-relations ```
diff --git a/src/order-theory/upper-bounds-chains-posets.lagda.md b/src/order-theory/upper-bounds-chains-posets.lagda.md index 4588a2df75..3da859e4e1 100644 --- a/src/order-theory/upper-bounds-chains-posets.lagda.md +++ b/src/order-theory/upper-bounds-chains-posets.lagda.md @@ -1,26 +1,21 @@ # Upper bounds of chains in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.upper-bounds-chains-posets - (funext : function-extensionality) - where +module order-theory.upper-bounds-chains-posets where ```
Imports ```agda -open import foundation.existential-quantification funext +open import foundation.existential-quantification open import foundation.universe-levels open import foundation-core.function-types open import foundation-core.propositions -open import order-theory.chains-posets funext -open import order-theory.posets funext -open import order-theory.upper-bounds-posets funext +open import order-theory.chains-posets +open import order-theory.posets +open import order-theory.upper-bounds-posets ```
diff --git a/src/order-theory/upper-bounds-large-posets.lagda.md b/src/order-theory/upper-bounds-large-posets.lagda.md index 51321f7487..bada6644c6 100644 --- a/src/order-theory/upper-bounds-large-posets.lagda.md +++ b/src/order-theory/upper-bounds-large-posets.lagda.md @@ -1,25 +1,20 @@ # Upper bounds in large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.upper-bounds-large-posets - (funext : function-extensionality) - where +module order-theory.upper-bounds-large-posets where ```
Imports ```agda -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.universe-levels -open import order-theory.dependent-products-large-posets funext -open import order-theory.large-posets funext +open import order-theory.dependent-products-large-posets +open import order-theory.large-posets ```
diff --git a/src/order-theory/upper-bounds-posets.lagda.md b/src/order-theory/upper-bounds-posets.lagda.md index 514a58283b..0193ab6052 100644 --- a/src/order-theory/upper-bounds-posets.lagda.md +++ b/src/order-theory/upper-bounds-posets.lagda.md @@ -1,22 +1,17 @@ # Upper bounds in posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.upper-bounds-posets - (funext : function-extensionality) - where +module order-theory.upper-bounds-posets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import order-theory.posets funext +open import order-theory.posets ```
diff --git a/src/order-theory/upper-sets-large-posets.lagda.md b/src/order-theory/upper-sets-large-posets.lagda.md index 0dd83dbf8c..f5c8d8ec1c 100644 --- a/src/order-theory/upper-sets-large-posets.lagda.md +++ b/src/order-theory/upper-sets-large-posets.lagda.md @@ -1,12 +1,7 @@ # Upper sets of large posets ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.upper-sets-large-posets - (funext : function-extensionality) - where +module order-theory.upper-sets-large-posets where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-subposets funext +open import order-theory.large-posets +open import order-theory.large-subposets ```
diff --git a/src/order-theory/well-founded-relations.lagda.md b/src/order-theory/well-founded-relations.lagda.md index 05a5a53042..7ae600f45c 100644 --- a/src/order-theory/well-founded-relations.lagda.md +++ b/src/order-theory/well-founded-relations.lagda.md @@ -1,26 +1,21 @@ # Well-founded relations ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.well-founded-relations - (funext : function-extensionality) - where +module order-theory.well-founded-relations where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import order-theory.accessible-elements-relations funext -open import order-theory.preorders funext +open import order-theory.accessible-elements-relations +open import order-theory.preorders ```
diff --git a/src/order-theory/zorns-lemma.lagda.md b/src/order-theory/zorns-lemma.lagda.md index d13ce39247..8d1381868b 100644 --- a/src/order-theory/zorns-lemma.lagda.md +++ b/src/order-theory/zorns-lemma.lagda.md @@ -1,34 +1,29 @@ # Zorn's lemma ```agda -open import foundation.function-extensionality-axiom - -module - order-theory.zorns-lemma - (funext : function-extensionality) - where +module order-theory.zorns-lemma where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.inhabited-types funext -open import foundation.law-of-excluded-middle funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.dependent-products-propositions +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.inhabited-types +open import foundation.law-of-excluded-middle +open import foundation.logical-equivalences +open import foundation.propositional-truncations open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.propositions -open import order-theory.chains-posets funext -open import order-theory.posets funext -open import order-theory.top-elements-posets funext -open import order-theory.upper-bounds-chains-posets funext +open import order-theory.chains-posets +open import order-theory.posets +open import order-theory.top-elements-posets +open import order-theory.upper-bounds-chains-posets ```
diff --git a/src/organic-chemistry.lagda.md b/src/organic-chemistry.lagda.md index 7d0fc2ed59..d4b75e9bc7 100644 --- a/src/organic-chemistry.lagda.md +++ b/src/organic-chemistry.lagda.md @@ -3,19 +3,14 @@ ## Modules in the organic chemistry namespace ```agda -open import foundation.function-extensionality-axiom +module organic-chemistry where -module - organic-chemistry - (funext : function-extensionality) - where - -open import organic-chemistry.alcohols funext public -open import organic-chemistry.alkanes funext public -open import organic-chemistry.alkenes funext public -open import organic-chemistry.alkynes funext public -open import organic-chemistry.ethane funext public -open import organic-chemistry.hydrocarbons funext public -open import organic-chemistry.methane funext public -open import organic-chemistry.saturated-carbons funext public +open import organic-chemistry.alcohols public +open import organic-chemistry.alkanes public +open import organic-chemistry.alkenes public +open import organic-chemistry.alkynes public +open import organic-chemistry.ethane public +open import organic-chemistry.hydrocarbons public +open import organic-chemistry.methane public +open import organic-chemistry.saturated-carbons public ``` diff --git a/src/organic-chemistry/alcohols.lagda.md b/src/organic-chemistry/alcohols.lagda.md index cdc4500b3b..f28fc09806 100644 --- a/src/organic-chemistry/alcohols.lagda.md +++ b/src/organic-chemistry/alcohols.lagda.md @@ -1,27 +1,22 @@ # Alcohols ```agda -open import foundation.function-extensionality-axiom - -module - organic-chemistry.alcohols - (funext : function-extensionality) - where +module organic-chemistry.alcohols where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.decidable-subtypes funext +open import foundation.cartesian-product-types +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.negation funext -open import foundation.propositional-truncations funext +open import foundation.negation +open import foundation.propositional-truncations open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import organic-chemistry.hydrocarbons funext -open import organic-chemistry.saturated-carbons funext +open import organic-chemistry.hydrocarbons +open import organic-chemistry.saturated-carbons ```
diff --git a/src/organic-chemistry/alkanes.lagda.md b/src/organic-chemistry/alkanes.lagda.md index 328077f317..ae5bc42c05 100644 --- a/src/organic-chemistry/alkanes.lagda.md +++ b/src/organic-chemistry/alkanes.lagda.md @@ -1,12 +1,7 @@ # Alkanes ```agda -open import foundation.function-extensionality-axiom - -module - organic-chemistry.alkanes - (funext : function-extensionality) - where +module organic-chemistry.alkanes where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import organic-chemistry.hydrocarbons funext -open import organic-chemistry.saturated-carbons funext +open import organic-chemistry.hydrocarbons +open import organic-chemistry.saturated-carbons ```
diff --git a/src/organic-chemistry/alkenes.lagda.md b/src/organic-chemistry/alkenes.lagda.md index 9d7a7c7823..66a563f86e 100644 --- a/src/organic-chemistry/alkenes.lagda.md +++ b/src/organic-chemistry/alkenes.lagda.md @@ -1,12 +1,7 @@ # Alkenes ```agda -open import foundation.function-extensionality-axiom - -module - organic-chemistry.alkenes - (funext : function-extensionality) - where +module organic-chemistry.alkenes where ```
Imports @@ -15,13 +10,13 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.embeddings funext +open import foundation.embeddings open import foundation.universe-levels -open import organic-chemistry.hydrocarbons funext -open import organic-chemistry.saturated-carbons funext +open import organic-chemistry.hydrocarbons +open import organic-chemistry.saturated-carbons -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/organic-chemistry/alkynes.lagda.md b/src/organic-chemistry/alkynes.lagda.md index 2f4eccad47..80956732ce 100644 --- a/src/organic-chemistry/alkynes.lagda.md +++ b/src/organic-chemistry/alkynes.lagda.md @@ -1,12 +1,7 @@ # Alkynes ```agda -open import foundation.function-extensionality-axiom - -module - organic-chemistry.alkynes - (funext : function-extensionality) - where +module organic-chemistry.alkynes where ```
Imports @@ -15,13 +10,13 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.embeddings funext +open import foundation.embeddings open import foundation.universe-levels -open import organic-chemistry.hydrocarbons funext -open import organic-chemistry.saturated-carbons funext +open import organic-chemistry.hydrocarbons +open import organic-chemistry.saturated-carbons -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/organic-chemistry/ethane.lagda.md b/src/organic-chemistry/ethane.lagda.md index 644f189b87..b20b3fe687 100644 --- a/src/organic-chemistry/ethane.lagda.md +++ b/src/organic-chemistry/ethane.lagda.md @@ -1,49 +1,44 @@ # Ethane ```agda -open import foundation.function-extensionality-axiom - -module - organic-chemistry.ethane - (funext : function-extensionality) - where +module organic-chemistry.ethane where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers -open import finite-group-theory.tetrahedra-in-3-space funext +open import finite-group-theory.tetrahedra-in-3-space -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.finite-graphs funext -open import graph-theory.walks-undirected-graphs funext +open import graph-theory.finite-graphs +open import graph-theory.walks-undirected-graphs -open import organic-chemistry.alkanes funext -open import organic-chemistry.hydrocarbons funext +open import organic-chemistry.alkanes +open import organic-chemistry.hydrocarbons -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/organic-chemistry/hydrocarbons.lagda.md b/src/organic-chemistry/hydrocarbons.lagda.md index 7c2a4736df..6012140cf2 100644 --- a/src/organic-chemistry/hydrocarbons.lagda.md +++ b/src/organic-chemistry/hydrocarbons.lagda.md @@ -1,32 +1,27 @@ # Hydrocarbons ```agda -open import foundation.function-extensionality-axiom - -module - organic-chemistry.hydrocarbons - (funext : function-extensionality) - where +module organic-chemistry.hydrocarbons where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers -open import finite-group-theory.tetrahedra-in-3-space funext +open import finite-group-theory.tetrahedra-in-3-space -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.negation funext +open import foundation.embeddings +open import foundation.negation open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.connected-undirected-graphs funext -open import graph-theory.finite-graphs funext +open import graph-theory.connected-undirected-graphs +open import graph-theory.finite-graphs -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/organic-chemistry/methane.lagda.md b/src/organic-chemistry/methane.lagda.md index 64cc068f95..806fb0cbc9 100644 --- a/src/organic-chemistry/methane.lagda.md +++ b/src/organic-chemistry/methane.lagda.md @@ -1,35 +1,30 @@ # Methane ```agda -open import foundation.function-extensionality-axiom - -module - organic-chemistry.methane - (funext : function-extensionality) - where +module organic-chemistry.methane where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers -open import finite-group-theory.tetrahedra-in-3-space funext +open import finite-group-theory.tetrahedra-in-3-space open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.unit-type open import foundation.universe-levels -open import graph-theory.walks-undirected-graphs funext +open import graph-theory.walks-undirected-graphs -open import organic-chemistry.alkanes funext -open import organic-chemistry.hydrocarbons funext +open import organic-chemistry.alkanes +open import organic-chemistry.hydrocarbons -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.finite-types ```
diff --git a/src/organic-chemistry/saturated-carbons.lagda.md b/src/organic-chemistry/saturated-carbons.lagda.md index 0754610b22..f214d5aa80 100644 --- a/src/organic-chemistry/saturated-carbons.lagda.md +++ b/src/organic-chemistry/saturated-carbons.lagda.md @@ -1,26 +1,21 @@ # Saturated carbons ```agda -open import foundation.function-extensionality-axiom - -module - organic-chemistry.saturated-carbons - (funext : function-extensionality) - where +module organic-chemistry.saturated-carbons where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import organic-chemistry.hydrocarbons funext +open import organic-chemistry.hydrocarbons -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems.lagda.md index d621d09720..a167d57d4a 100644 --- a/src/orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems.lagda.md @@ -7,76 +7,71 @@ ## Modules in the orthogonal factorization systems namespace ```agda -open import foundation.function-extensionality-axiom +module orthogonal-factorization-systems where -module - orthogonal-factorization-systems - (funext : function-extensionality) - where - -open import orthogonal-factorization-systems.cd-structures funext public -open import orthogonal-factorization-systems.cellular-maps funext public -open import orthogonal-factorization-systems.closed-modalities funext public -open import orthogonal-factorization-systems.continuation-modalities funext public -open import orthogonal-factorization-systems.double-lifts-families-of-elements funext public -open import orthogonal-factorization-systems.double-negation-sheaves funext public -open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements funext public -open import orthogonal-factorization-systems.extensions-lifts-families-of-elements funext public -open import orthogonal-factorization-systems.extensions-maps funext public -open import orthogonal-factorization-systems.factorization-operations funext public -open import orthogonal-factorization-systems.factorization-operations-function-classes funext public -open import orthogonal-factorization-systems.factorization-operations-global-function-classes funext public -open import orthogonal-factorization-systems.factorizations-of-maps funext public -open import orthogonal-factorization-systems.factorizations-of-maps-function-classes funext public -open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes funext public -open import orthogonal-factorization-systems.families-of-types-local-at-maps funext public -open import orthogonal-factorization-systems.fiberwise-orthogonal-maps funext public -open import orthogonal-factorization-systems.function-classes funext public -open import orthogonal-factorization-systems.functoriality-higher-modalities funext public -open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses funext public -open import orthogonal-factorization-systems.functoriality-pullback-hom funext public -open import orthogonal-factorization-systems.functoriality-reflective-global-subuniverses funext public -open import orthogonal-factorization-systems.global-function-classes funext public -open import orthogonal-factorization-systems.higher-modalities funext public -open import orthogonal-factorization-systems.identity-modality funext public -open import orthogonal-factorization-systems.large-lawvere-tierney-topologies funext public -open import orthogonal-factorization-systems.lawvere-tierney-topologies funext public -open import orthogonal-factorization-systems.lifting-operations funext public -open import orthogonal-factorization-systems.lifting-structures-on-squares funext public -open import orthogonal-factorization-systems.lifts-families-of-elements funext public -open import orthogonal-factorization-systems.lifts-maps funext public -open import orthogonal-factorization-systems.localizations-at-global-subuniverses funext public -open import orthogonal-factorization-systems.localizations-at-maps funext public -open import orthogonal-factorization-systems.localizations-at-subuniverses funext public -open import orthogonal-factorization-systems.locally-small-modal-operators funext public -open import orthogonal-factorization-systems.maps-local-at-maps funext public -open import orthogonal-factorization-systems.mere-lifting-properties funext public -open import orthogonal-factorization-systems.modal-induction funext public -open import orthogonal-factorization-systems.modal-operators funext public -open import orthogonal-factorization-systems.modal-subuniverse-induction funext public -open import orthogonal-factorization-systems.null-families-of-types funext public -open import orthogonal-factorization-systems.null-maps funext public -open import orthogonal-factorization-systems.null-types funext public -open import orthogonal-factorization-systems.open-modalities funext public -open import orthogonal-factorization-systems.orthogonal-factorization-systems funext public -open import orthogonal-factorization-systems.orthogonal-maps funext public -open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements funext public -open import orthogonal-factorization-systems.pullback-hom funext public -open import orthogonal-factorization-systems.raise-modalities funext public -open import orthogonal-factorization-systems.reflective-global-subuniverses funext public -open import orthogonal-factorization-systems.reflective-modalities funext public -open import orthogonal-factorization-systems.reflective-subuniverses funext public +open import orthogonal-factorization-systems.cd-structures public +open import orthogonal-factorization-systems.cellular-maps public +open import orthogonal-factorization-systems.closed-modalities public +open import orthogonal-factorization-systems.continuation-modalities public +open import orthogonal-factorization-systems.double-lifts-families-of-elements public +open import orthogonal-factorization-systems.double-negation-sheaves public +open import orthogonal-factorization-systems.extensions-double-lifts-families-of-elements public +open import orthogonal-factorization-systems.extensions-lifts-families-of-elements public +open import orthogonal-factorization-systems.extensions-maps public +open import orthogonal-factorization-systems.factorization-operations public +open import orthogonal-factorization-systems.factorization-operations-function-classes public +open import orthogonal-factorization-systems.factorization-operations-global-function-classes public +open import orthogonal-factorization-systems.factorizations-of-maps public +open import orthogonal-factorization-systems.factorizations-of-maps-function-classes public +open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes public +open import orthogonal-factorization-systems.families-of-types-local-at-maps public +open import orthogonal-factorization-systems.fiberwise-orthogonal-maps public +open import orthogonal-factorization-systems.function-classes public +open import orthogonal-factorization-systems.functoriality-higher-modalities public +open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses public +open import orthogonal-factorization-systems.functoriality-pullback-hom public +open import orthogonal-factorization-systems.functoriality-reflective-global-subuniverses public +open import orthogonal-factorization-systems.global-function-classes public +open import orthogonal-factorization-systems.higher-modalities public +open import orthogonal-factorization-systems.identity-modality public +open import orthogonal-factorization-systems.large-lawvere-tierney-topologies public +open import orthogonal-factorization-systems.lawvere-tierney-topologies public +open import orthogonal-factorization-systems.lifting-operations public +open import orthogonal-factorization-systems.lifting-structures-on-squares public +open import orthogonal-factorization-systems.lifts-families-of-elements public +open import orthogonal-factorization-systems.lifts-maps public +open import orthogonal-factorization-systems.localizations-at-global-subuniverses public +open import orthogonal-factorization-systems.localizations-at-maps public +open import orthogonal-factorization-systems.localizations-at-subuniverses public +open import orthogonal-factorization-systems.locally-small-modal-operators public +open import orthogonal-factorization-systems.maps-local-at-maps public +open import orthogonal-factorization-systems.mere-lifting-properties public +open import orthogonal-factorization-systems.modal-induction public +open import orthogonal-factorization-systems.modal-operators public +open import orthogonal-factorization-systems.modal-subuniverse-induction public +open import orthogonal-factorization-systems.null-families-of-types public +open import orthogonal-factorization-systems.null-maps public +open import orthogonal-factorization-systems.null-types public +open import orthogonal-factorization-systems.open-modalities public +open import orthogonal-factorization-systems.orthogonal-factorization-systems public +open import orthogonal-factorization-systems.orthogonal-maps public +open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements public +open import orthogonal-factorization-systems.pullback-hom public +open import orthogonal-factorization-systems.raise-modalities public +open import orthogonal-factorization-systems.reflective-global-subuniverses public +open import orthogonal-factorization-systems.reflective-modalities public +open import orthogonal-factorization-systems.reflective-subuniverses public open import orthogonal-factorization-systems.regular-cd-structures public -open import orthogonal-factorization-systems.sigma-closed-modalities funext public -open import orthogonal-factorization-systems.sigma-closed-reflective-modalities funext public -open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses funext public -open import orthogonal-factorization-systems.stable-orthogonal-factorization-systems funext public -open import orthogonal-factorization-systems.types-colocal-at-maps funext public -open import orthogonal-factorization-systems.types-local-at-maps funext public -open import orthogonal-factorization-systems.types-separated-at-maps funext public -open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext public -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext public -open import orthogonal-factorization-systems.wide-function-classes funext public -open import orthogonal-factorization-systems.wide-global-function-classes funext public -open import orthogonal-factorization-systems.zero-modality funext public +open import orthogonal-factorization-systems.sigma-closed-modalities public +open import orthogonal-factorization-systems.sigma-closed-reflective-modalities public +open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses public +open import orthogonal-factorization-systems.stable-orthogonal-factorization-systems public +open import orthogonal-factorization-systems.types-colocal-at-maps public +open import orthogonal-factorization-systems.types-local-at-maps public +open import orthogonal-factorization-systems.types-separated-at-maps public +open import orthogonal-factorization-systems.uniquely-eliminating-modalities public +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses public +open import orthogonal-factorization-systems.wide-function-classes public +open import orthogonal-factorization-systems.wide-global-function-classes public +open import orthogonal-factorization-systems.zero-modality public ``` diff --git a/src/orthogonal-factorization-systems/cd-structures.lagda.md b/src/orthogonal-factorization-systems/cd-structures.lagda.md index 27013b19df..d33d5a3d4a 100644 --- a/src/orthogonal-factorization-systems/cd-structures.lagda.md +++ b/src/orthogonal-factorization-systems/cd-structures.lagda.md @@ -1,20 +1,15 @@ # Cd-structures ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.cd-structures - (funext : function-extensionality) - where +module orthogonal-factorization-systems.cd-structures where ```
Imports ```agda -open import foundation.morphisms-arrows funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.morphisms-arrows +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/cellular-maps.lagda.md b/src/orthogonal-factorization-systems/cellular-maps.lagda.md index 0544a9aac7..0bcd3a38aa 100644 --- a/src/orthogonal-factorization-systems/cellular-maps.lagda.md +++ b/src/orthogonal-factorization-systems/cellular-maps.lagda.md @@ -1,22 +1,17 @@ # Cellular maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.cellular-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.cellular-maps where ```
Imports ```agda -open import foundation.connected-maps funext +open import foundation.connected-maps open import foundation.truncation-levels open import foundation.universe-levels -open import orthogonal-factorization-systems.mere-lifting-properties funext +open import orthogonal-factorization-systems.mere-lifting-properties ```
diff --git a/src/orthogonal-factorization-systems/closed-modalities.lagda.md b/src/orthogonal-factorization-systems/closed-modalities.lagda.md index bf2bae353b..c42bfe9572 100644 --- a/src/orthogonal-factorization-systems/closed-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/closed-modalities.lagda.md @@ -1,34 +1,29 @@ # The closed modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.closed-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.closed-modalities where ```
Imports ```agda -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.reflective-subuniverses funext -open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses funext +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.reflective-subuniverses +open import orthogonal-factorization-systems.sigma-closed-reflective-subuniverses -open import synthetic-homotopy-theory.joins-of-types funext +open import synthetic-homotopy-theory.joins-of-types ```
diff --git a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md index ee6cf0a7e3..37b7855617 100644 --- a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md @@ -1,32 +1,27 @@ # Continuation modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.continuation-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.continuation-modalities where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.continuations funext +open import foundation.cartesian-product-types +open import foundation.continuations open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.large-lawvere-tierney-topologies funext -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.types-local-at-maps funext -open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext +open import orthogonal-factorization-systems.large-lawvere-tierney-topologies +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.uniquely-eliminating-modalities ```
diff --git a/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md index 251388aacc..4c248d4992 100644 --- a/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/double-lifts-families-of-elements.lagda.md @@ -1,12 +1,7 @@ # Double lifts of families of elements ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.double-lifts-families-of-elements - (funext : function-extensionality) - where +module orthogonal-factorization-systems.double-lifts-families-of-elements where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.universe-levels -open import orthogonal-factorization-systems.lifts-families-of-elements funext +open import orthogonal-factorization-systems.lifts-families-of-elements ```
diff --git a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md index f91b2b0986..d48dc64cdd 100644 --- a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md +++ b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md @@ -1,34 +1,29 @@ # Double negation sheaves ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.double-negation-sheaves - (funext : function-extensionality) - where +module orthogonal-factorization-systems.double-negation-sheaves where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-propositions funext -open import foundation.double-negation-stable-propositions funext -open import foundation.empty-types funext -open import foundation.irrefutable-propositions funext -open import foundation.logical-equivalences funext -open import foundation.negation funext +open import foundation.dependent-products-propositions +open import foundation.double-negation-stable-propositions +open import foundation.empty-types +open import foundation.irrefutable-propositions +open import foundation.logical-equivalences +open import foundation.negation open import foundation.type-arithmetic-cartesian-product-types -open import foundation.universal-property-coproduct-types funext +open import foundation.universal-property-coproduct-types open import foundation.universe-levels open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.propositions -open import orthogonal-factorization-systems.null-types funext +open import orthogonal-factorization-systems.null-types ```
diff --git a/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md index 5eb86ba4d9..c590c46263 100644 --- a/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-double-lifts-families-of-elements.lagda.md @@ -17,8 +17,8 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import orthogonal-factorization-systems.double-lifts-families-of-elements funext -open import orthogonal-factorization-systems.lifts-families-of-elements funext +open import orthogonal-factorization-systems.double-lifts-families-of-elements +open import orthogonal-factorization-systems.lifts-families-of-elements ```
@@ -60,12 +60,7 @@ elements `a : (i : I) → A i` induces an evaluation map given by `c ↦ (λ i → c i (a i) (b i))`. ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {l1 l2 l3 l4 : Level} {I : UU l1} {A : I → UU l2} {B : (i : I) → A i → UU l3} {C : (i : I) (x : A i) → B i x → UU l4} {a : (i : I) → A i} (b : dependent-lift-family-of-elements B a) diff --git a/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md index ef201d3db3..8766921e92 100644 --- a/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-lifts-families-of-elements.lagda.md @@ -17,7 +17,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types -open import orthogonal-factorization-systems.lifts-families-of-elements funext +open import orthogonal-factorization-systems.lifts-families-of-elements ```
@@ -66,12 +66,7 @@ Any family of elements `a : (i : I) → A i` induces an evaluation map defined by `b ↦ (λ i → b i (a i))`. ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {l1 l2 l3 : Level} {I : UU l1} {A : I → UU l2} {B : (i : I) → A i → UU l3} (a : (i : I) → A i) where diff --git a/src/orthogonal-factorization-systems/extensions-maps.lagda.md b/src/orthogonal-factorization-systems/extensions-maps.lagda.md index 438090583e..1afb566035 100644 --- a/src/orthogonal-factorization-systems/extensions-maps.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-maps.lagda.md @@ -1,12 +1,7 @@ # Extensions of maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.extensions-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.extensions-maps where ```
Imports @@ -14,25 +9,25 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.dependent-products-truncated-types +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.monomorphisms funext -open import foundation.postcomposition-functions funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.monomorphisms +open import foundation.postcomposition-functions +open import foundation.propositions +open import foundation.sets open import foundation.structure-identity-principle open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md index 1a5f24806b..1d51743a99 100644 --- a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md @@ -1,42 +1,37 @@ # Factorization operations into function classes ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.factorization-operations-function-classes - (funext : function-extensionality) - where +module orthogonal-factorization-systems.factorization-operations-function-classes where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions +open import foundation.subtypes open import foundation.telescopes open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorizations-of-maps funext -open import orthogonal-factorization-systems.factorizations-of-maps funext-function-classes -open import orthogonal-factorization-systems.function-classes funext -open import orthogonal-factorization-systems.lifting-structures-on-squares funext +open import orthogonal-factorization-systems.factorizations-of-maps +open import orthogonal-factorization-systems.factorizations-of-maps-function-classes +open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.lifting-structures-on-squares ```
diff --git a/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md index 708d067acb..a372c14a56 100644 --- a/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md @@ -1,23 +1,18 @@ # Factorization operations into global function classes ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.factorization-operations-global-function-classes - (funext : function-extensionality) - where +module orthogonal-factorization-systems.factorization-operations-global-function-classes where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import orthogonal-factorization-systems.factorization-operations-function-classes funext -open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes funext -open import orthogonal-factorization-systems.global-function-classes funext +open import orthogonal-factorization-systems.factorization-operations-function-classes +open import orthogonal-factorization-systems.factorizations-of-maps-global-function-classes +open import orthogonal-factorization-systems.global-function-classes ```
diff --git a/src/orthogonal-factorization-systems/factorization-operations.lagda.md b/src/orthogonal-factorization-systems/factorization-operations.lagda.md index c580cbce90..9262dfd081 100644 --- a/src/orthogonal-factorization-systems/factorization-operations.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations.lagda.md @@ -1,12 +1,7 @@ # Factorization operations ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.factorization-operations - (funext : function-extensionality) - where +module orthogonal-factorization-systems.factorization-operations where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.universe-levels -open import orthogonal-factorization-systems.factorizations-of-maps funext +open import orthogonal-factorization-systems.factorizations-of-maps ```
diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md index 369674f700..f4eee03050 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md @@ -1,39 +1,34 @@ # Factorizations of maps into function classes ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.factorizations-of-maps-function-classes - (funext : function-extensionality) - where +module orthogonal-factorization-systems.factorizations-of-maps-function-classes where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositions +open import foundation.retractions +open import foundation.sections open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorizations-of-maps funext -open import orthogonal-factorization-systems.function-classes funext -open import orthogonal-factorization-systems.global-function-classes funext +open import orthogonal-factorization-systems.factorizations-of-maps +open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.global-function-classes ```
diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md index b8190052e7..9945116577 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md @@ -1,39 +1,34 @@ # Factorizations of maps into global function classes ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.factorizations-of-maps-global-function-classes - (funext : function-extensionality) - where +module orthogonal-factorization-systems.factorizations-of-maps-global-function-classes where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositions +open import foundation.retractions +open import foundation.sections open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorizations-of-maps funext -open import orthogonal-factorization-systems.factorizations-of-maps funext-function-classes -open import orthogonal-factorization-systems.function-classes funext -open import orthogonal-factorization-systems.global-function-classes funext +open import orthogonal-factorization-systems.factorizations-of-maps +open import orthogonal-factorization-systems.factorizations-of-maps-function-classes +open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.global-function-classes ```
diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md index ef5eb84631..a4266abdd5 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps.lagda.md @@ -1,29 +1,24 @@ # Factorizations of maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.factorizations-of-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.factorizations-of-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.retracts-of-types funext +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.retracts-of-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition ``` diff --git a/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md index 79dca887c2..0d79431a42 100644 --- a/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md @@ -1,25 +1,20 @@ # Families of types local at a map ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.families-of-types-local-at-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.families-of-types-local-at-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.precomposition-functions funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.precomposition-functions +open import foundation.propositions open import foundation.universe-levels -open import orthogonal-factorization-systems.orthogonal-maps funext -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.orthogonal-maps +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md index bf6a19c7ad..544627106f 100644 --- a/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/fiberwise-orthogonal-maps.lagda.md @@ -1,32 +1,27 @@ # Fiberwise orthogonal maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.fiberwise-orthogonal-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.fiberwise-orthogonal-maps where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.homotopies funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-functions funext -open import foundation.pullbacks funext +open import foundation.cartesian-morphisms-arrows +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.homotopies +open import foundation.postcomposition-functions +open import foundation.precomposition-functions +open import foundation.pullbacks open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.null-maps funext -open import orthogonal-factorization-systems.orthogonal-maps funext -open import orthogonal-factorization-systems.pullback-hom funext +open import orthogonal-factorization-systems.null-maps +open import orthogonal-factorization-systems.orthogonal-maps +open import orthogonal-factorization-systems.pullback-hom ```
diff --git a/src/orthogonal-factorization-systems/function-classes.lagda.md b/src/orthogonal-factorization-systems/function-classes.lagda.md index 4f5fc23b8c..821f6aa51e 100644 --- a/src/orthogonal-factorization-systems/function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/function-classes.lagda.md @@ -1,33 +1,28 @@ # Function classes ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.function-classes - (funext : function-extensionality) - where +module orthogonal-factorization-systems.function-classes where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalence-induction funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.pullbacks funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalence-induction +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.pullbacks +open import foundation.subtypes open import foundation.telescopes open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md b/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md index c9f0f08cda..5bf2870bfe 100644 --- a/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-higher-modalities.lagda.md @@ -1,12 +1,7 @@ # Functoriality of higher modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.functoriality-higher-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.functoriality-higher-modalities where ```
Imports @@ -14,22 +9,21 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.path-algebra funext -open import foundation.small-types funext +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.path-algebra +open import foundation.small-types open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import orthogonal-factorization-systems.higher-modalities funext -open import orthogonal-factorization-systems.modal-induction funext -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.modal-subuniverse-induction funext +open import orthogonal-factorization-systems.higher-modalities +open import orthogonal-factorization-systems.modal-induction +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-subuniverse-induction ```
diff --git a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md index 7e561032db..2ba05b568a 100644 --- a/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-localizations-at-global-subuniverses.lagda.md @@ -1,34 +1,30 @@ # Functoriality of localizations at global subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses - (funext : function-extensionality) - where +module orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.extensions-types-global-subuniverses funext -open import foundation.function-types funext -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.retracts-of-maps funext -open import foundation.retracts-of-types funext +open import foundation.equivalences +open import foundation.extensions-types-global-subuniverses +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.retractions +open import foundation.retracts-of-maps +open import foundation.retracts-of-types open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-global-subuniverses funext -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext +open import orthogonal-factorization-systems.localizations-at-global-subuniverses +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses ```
diff --git a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md index 223a39f814..ba3af5d73b 100644 --- a/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-pullback-hom.lagda.md @@ -1,24 +1,19 @@ # Functoriality of the pullback-hom ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.functoriality-pullback-hom - (funext : function-extensionality) - where +module orthogonal-factorization-systems.functoriality-pullback-hom where ```
Imports ```agda -open import foundation.functoriality-morphisms-arrows funext -open import foundation.functoriality-pullbacks funext -open import foundation.morphisms-arrows funext +open import foundation.functoriality-morphisms-arrows +open import foundation.functoriality-pullbacks +open import foundation.morphisms-arrows open import foundation.morphisms-cospan-diagrams open import foundation.universe-levels -open import orthogonal-factorization-systems.pullback-hom funext +open import orthogonal-factorization-systems.pullback-hom ```
diff --git a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md index 9a319abc75..e3b1f8e7b4 100644 --- a/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/functoriality-reflective-global-subuniverses.lagda.md @@ -1,27 +1,22 @@ # Functoriality of reflective global subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.functoriality-reflective-global-subuniverses - (funext : function-extensionality) - where +module orthogonal-factorization-systems.functoriality-reflective-global-subuniverses where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.retracts-of-types funext +open import foundation.commuting-squares-of-maps +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.retractions +open import foundation.retracts-of-types open import foundation.universe-levels -open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses funext -open import orthogonal-factorization-systems.reflective-global-subuniverses funext +open import orthogonal-factorization-systems.functoriality-localizations-at-global-subuniverses +open import orthogonal-factorization-systems.reflective-global-subuniverses ```
diff --git a/src/orthogonal-factorization-systems/global-function-classes.lagda.md b/src/orthogonal-factorization-systems/global-function-classes.lagda.md index b0601aeb2e..b11fa84d13 100644 --- a/src/orthogonal-factorization-systems/global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/global-function-classes.lagda.md @@ -1,28 +1,23 @@ # Global function classes ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.global-function-classes - (funext : function-extensionality) - where +module orthogonal-factorization-systems.global-function-classes where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.propositions funext -open import foundation.pullbacks funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.propositions +open import foundation.pullbacks +open import foundation.subtypes open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes funext +open import orthogonal-factorization-systems.function-classes ```
diff --git a/src/orthogonal-factorization-systems/higher-modalities.lagda.md b/src/orthogonal-factorization-systems/higher-modalities.lagda.md index 6258fb3788..54408c3970 100644 --- a/src/orthogonal-factorization-systems/higher-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/higher-modalities.lagda.md @@ -1,38 +1,33 @@ # Higher modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.higher-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.higher-modalities where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.precomposition-dependent-functions funext -open import foundation.retractions funext -open import foundation.small-types funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.precomposition-dependent-functions +open import foundation.retractions +open import foundation.small-types open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.locally-small-modal-operators funext -open import orthogonal-factorization-systems.modal-induction funext -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.modal-subuniverse-induction funext -open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext +open import orthogonal-factorization-systems.locally-small-modal-operators +open import orthogonal-factorization-systems.modal-induction +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-subuniverse-induction +open import orthogonal-factorization-systems.uniquely-eliminating-modalities ```
diff --git a/src/orthogonal-factorization-systems/identity-modality.lagda.md b/src/orthogonal-factorization-systems/identity-modality.lagda.md index 583b0dd4f9..34bcadc7b1 100644 --- a/src/orthogonal-factorization-systems/identity-modality.lagda.md +++ b/src/orthogonal-factorization-systems/identity-modality.lagda.md @@ -1,24 +1,19 @@ # The identity modality ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.identity-modality - (funext : function-extensionality) - where +module orthogonal-factorization-systems.identity-modality where ```
Imports ```agda -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.types-local-at-maps funext -open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.uniquely-eliminating-modalities ```
diff --git a/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md b/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md index 78fe9cfcf8..b6fd6cabc1 100644 --- a/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md +++ b/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md @@ -1,27 +1,22 @@ # Large Lawvere–Tierney topologies ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.large-lawvere-tierney-topologies - (funext : function-extensionality) - where +module orthogonal-factorization-systems.large-lawvere-tierney-topologies where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext +open import foundation.cartesian-product-types +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.lawvere-tierney-topologies funext +open import orthogonal-factorization-systems.lawvere-tierney-topologies ```
diff --git a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md index 79dd8d9771..8976f0993e 100644 --- a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md +++ b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md @@ -1,27 +1,22 @@ # Lawvere–Tierney topologies ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.lawvere-tierney-topologies - (funext : function-extensionality) - where +module orthogonal-factorization-systems.lawvere-tierney-topologies where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext +open import foundation.cartesian-product-types +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-extensionality funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.function-types +open import foundation.logical-equivalences +open import foundation.propositional-extensionality +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.sets +open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/lifting-operations.lagda.md b/src/orthogonal-factorization-systems/lifting-operations.lagda.md index 9d26c783ed..35f437fa9b 100644 --- a/src/orthogonal-factorization-systems/lifting-operations.lagda.md +++ b/src/orthogonal-factorization-systems/lifting-operations.lagda.md @@ -1,25 +1,20 @@ # Lifting operations ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.lifting-operations - (funext : function-extensionality) - where +module orthogonal-factorization-systems.lifting-operations where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.morphisms-arrows funext -open import foundation.sections funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.morphisms-arrows +open import foundation.sections open import foundation.universe-levels -open import orthogonal-factorization-systems.pullback-hom funext +open import orthogonal-factorization-systems.pullback-hom ```
diff --git a/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md b/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md index 05b22e3cc3..cd33ef10d2 100644 --- a/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md +++ b/src/orthogonal-factorization-systems/lifting-structures-on-squares.lagda.md @@ -1,46 +1,41 @@ # Lifting structures on commuting squares of maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.lifting-structures-on-squares - (funext : function-extensionality) - where +module orthogonal-factorization-systems.lifting-structures-on-squares where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-tetrahedra-of-homotopies funext -open import foundation.commuting-triangles-of-homotopies funext -open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-maps +open import foundation.commuting-tetrahedra-of-homotopies +open import foundation.commuting-triangles-of-homotopies +open import foundation.commuting-triangles-of-identifications open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.higher-homotopies-morphisms-arrows funext -open import foundation.homotopies funext -open import foundation.homotopies funext-morphisms-arrows -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.morphisms-arrows funext -open import foundation.path-algebra funext +open import foundation.higher-homotopies-morphisms-arrows +open import foundation.homotopies +open import foundation.homotopies-morphisms-arrows +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.morphisms-arrows +open import foundation.path-algebra open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import orthogonal-factorization-systems.extensions-maps funext -open import orthogonal-factorization-systems.lifts-maps funext -open import orthogonal-factorization-systems.pullback-hom funext +open import orthogonal-factorization-systems.extensions-maps +open import orthogonal-factorization-systems.lifts-maps +open import orthogonal-factorization-systems.pullback-hom ```
diff --git a/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md index 7d1eb95bd0..2121b91eb6 100644 --- a/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/lifts-families-of-elements.lagda.md @@ -1,12 +1,7 @@ # Lifts of families of elements ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.lifts-families-of-elements - (funext : function-extensionality) - where +module orthogonal-factorization-systems.lifts-families-of-elements where ```
Imports @@ -14,12 +9,12 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.precomposition-functions funext -open import foundation.precomposition-type-families funext -open import foundation.transport-along-homotopies funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.precomposition-functions +open import foundation.precomposition-type-families +open import foundation.transport-along-homotopies open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/lifts-maps.lagda.md b/src/orthogonal-factorization-systems/lifts-maps.lagda.md index e940821bde..60cb9ba46c 100644 --- a/src/orthogonal-factorization-systems/lifts-maps.lagda.md +++ b/src/orthogonal-factorization-systems/lifts-maps.lagda.md @@ -1,33 +1,28 @@ # Lifts of maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.lifts-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.lifts-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.dependent-products-truncated-types +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.small-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.small-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.truncated-types funext +open import foundation.torsorial-type-families +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md index b42708e378..f4ba57ae36 100644 --- a/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md @@ -1,56 +1,50 @@ # Localizations at global subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.localizations-at-global-subuniverses - (funext : function-extensionality) - where +module orthogonal-factorization-systems.localizations-at-global-subuniverses where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.cones-over-cospan-diagrams funext -open import foundation.constant-maps funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.cones-over-cospan-diagrams +open import foundation.constant-maps +open import foundation.contractible-types open import foundation.cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.extensions-types funext -open import foundation.extensions-types funext-global-subuniverses -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.pullback-cones funext -open import foundation.pullbacks funext -open import foundation.sequential-limits funext +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.extensions-types +open import foundation.extensions-types-global-subuniverses +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.identity-types +open import foundation.postcomposition-functions +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.pullback-cones +open import foundation.pullbacks +open import foundation.sequential-limits open import foundation.singleton-induction -open import foundation.subuniverses funext -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.subuniverses +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.orthogonal-maps funext -open import orthogonal-factorization-systems.pullback-hom funext -open import orthogonal-factorization-systems.types-local-at-maps funext -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext +open import orthogonal-factorization-systems.orthogonal-maps +open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses ```
diff --git a/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md b/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md index 027977c69f..1144d685d4 100644 --- a/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-maps.lagda.md @@ -1,23 +1,18 @@ # Localizations at maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.localizations-at-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.localizations-at-maps where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-subuniverses funext -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.localizations-at-subuniverses +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md b/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md index 69ca59a5d0..c12ced2306 100644 --- a/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-subuniverses.lagda.md @@ -1,23 +1,18 @@ # Localizations at subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.localizations-at-subuniverses - (funext : function-extensionality) - where +module orthogonal-factorization-systems.localizations-at-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.subuniverses funext +open import foundation.subuniverses open import foundation.universe-levels -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md b/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md index d331d0bcd3..88185472d4 100644 --- a/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md +++ b/src/orthogonal-factorization-systems/locally-small-modal-operators.lagda.md @@ -1,22 +1,17 @@ # Locally small modal-operators ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.locally-small-modal-operators - (funext : function-extensionality) - where +module orthogonal-factorization-systems.locally-small-modal-operators where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.locally-small-types funext +open import foundation.locally-small-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.modal-operators ```
diff --git a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md index f6d0011b14..dd2128327c 100644 --- a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md @@ -1,27 +1,22 @@ # Maps local at maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.maps-local-at-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.maps-local-at-maps where ```
Imports ```agda -open import foundation.cartesian-morphisms-arrows funext -open import foundation.fibers-of-maps funext -open import foundation.propositions funext -open import foundation.retracts-of-maps funext +open import foundation.cartesian-morphisms-arrows +open import foundation.fibers-of-maps +open import foundation.propositions +open import foundation.retracts-of-maps open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.families-of-types-local-at-maps funext -open import orthogonal-factorization-systems.orthogonal-maps funext -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.families-of-types-local-at-maps +open import orthogonal-factorization-systems.orthogonal-maps +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md b/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md index 4f2a97b6b2..ffc220075a 100644 --- a/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md +++ b/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md @@ -1,22 +1,17 @@ # Mere lifting properties ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.mere-lifting-properties - (funext : function-extensionality) - where +module orthogonal-factorization-systems.mere-lifting-properties where ```
Imports ```agda -open import foundation.propositions funext -open import foundation.surjective-maps funext +open import foundation.propositions +open import foundation.surjective-maps open import foundation.universe-levels -open import orthogonal-factorization-systems.pullback-hom funext +open import orthogonal-factorization-systems.pullback-hom ```
diff --git a/src/orthogonal-factorization-systems/modal-induction.lagda.md b/src/orthogonal-factorization-systems/modal-induction.lagda.md index 9bb62f58cf..9329a93810 100644 --- a/src/orthogonal-factorization-systems/modal-induction.lagda.md +++ b/src/orthogonal-factorization-systems/modal-induction.lagda.md @@ -1,12 +1,7 @@ # Modal induction ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.modal-induction - (funext : function-extensionality) - where +module orthogonal-factorization-systems.modal-induction where ```
Imports @@ -14,25 +9,24 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.multivariable-sections funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.multivariable-sections +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.retractions +open import foundation.sections open import foundation.telescopes -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.modal-operators ```
diff --git a/src/orthogonal-factorization-systems/modal-operators.lagda.md b/src/orthogonal-factorization-systems/modal-operators.lagda.md index da8313d5a4..457aeddced 100644 --- a/src/orthogonal-factorization-systems/modal-operators.lagda.md +++ b/src/orthogonal-factorization-systems/modal-operators.lagda.md @@ -1,23 +1,18 @@ # Modal operators ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.modal-operators - (funext : function-extensionality) - where +module orthogonal-factorization-systems.modal-operators where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.propositions funext -open import foundation.small-types funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.propositions +open import foundation.small-types +open import foundation.subuniverses open import foundation.universe-levels ``` diff --git a/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md b/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md index 9da9f4787c..32cc226bd3 100644 --- a/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md +++ b/src/orthogonal-factorization-systems/modal-subuniverse-induction.lagda.md @@ -1,12 +1,7 @@ # Modal subuniverse induction ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.modal-subuniverse-induction - (funext : function-extensionality) - where +module orthogonal-factorization-systems.modal-subuniverse-induction where ```
Imports @@ -14,21 +9,21 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.multivariable-sections funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.retractions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.multivariable-sections +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.retractions open import foundation.telescopes -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-induction funext -open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.modal-induction +open import orthogonal-factorization-systems.modal-operators ```
diff --git a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md index f635119a73..1ea050536a 100644 --- a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md @@ -1,26 +1,21 @@ # Null families of types ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.null-families-of-types - (funext : function-extensionality) - where +module orthogonal-factorization-systems.null-families-of-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.precomposition-functions funext -open import foundation.propositions funext -open import foundation.retracts-of-types funext +open import foundation.equivalences +open import foundation.precomposition-functions +open import foundation.propositions +open import foundation.retracts-of-types open import foundation.universe-levels -open import orthogonal-factorization-systems.null-types funext -open import orthogonal-factorization-systems.orthogonal-maps funext +open import orthogonal-factorization-systems.null-types +open import orthogonal-factorization-systems.orthogonal-maps ```
diff --git a/src/orthogonal-factorization-systems/null-maps.lagda.md b/src/orthogonal-factorization-systems/null-maps.lagda.md index adfa89291d..abce4f90c5 100644 --- a/src/orthogonal-factorization-systems/null-maps.lagda.md +++ b/src/orthogonal-factorization-systems/null-maps.lagda.md @@ -1,46 +1,41 @@ # Null maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.null-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.null-maps where ```
Imports ```agda -open import foundation.cones-over-cospan-diagrams funext +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.families-of-equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-fibers-of-maps funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.morphisms-arrows funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-functions funext -open import foundation.propositions funext -open import foundation.pullbacks funext +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.families-of-equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-fibers-of-maps +open import foundation.homotopies +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.morphisms-arrows +open import foundation.postcomposition-functions +open import foundation.precomposition-functions +open import foundation.propositions +open import foundation.pullbacks open import foundation.type-arithmetic-unit-type -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type -open import foundation.universal-property-family-of-fibers-of-maps funext +open import foundation.universal-property-family-of-fibers-of-maps open import foundation.universe-levels open import foundation-core.diagonal-maps-of-types -open import orthogonal-factorization-systems.maps-local-at-maps funext -open import orthogonal-factorization-systems.null-families-of-types funext -open import orthogonal-factorization-systems.null-types funext -open import orthogonal-factorization-systems.orthogonal-maps funext -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.maps-local-at-maps +open import orthogonal-factorization-systems.null-families-of-types +open import orthogonal-factorization-systems.null-types +open import orthogonal-factorization-systems.orthogonal-maps +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/null-types.lagda.md b/src/orthogonal-factorization-systems/null-types.lagda.md index a8a932b24a..f6b07a4409 100644 --- a/src/orthogonal-factorization-systems/null-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-types.lagda.md @@ -1,50 +1,44 @@ # Null types ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.null-types - (funext : function-extensionality) - where +module orthogonal-factorization-systems.null-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types funext -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.retracts-of-maps funext -open import foundation.retracts-of-types funext -open import foundation.sections funext +open import foundation.diagonal-maps-of-types +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.postcomposition-functions +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.propositions +open import foundation.retractions +open import foundation.retracts-of-maps +open import foundation.retracts-of-types +open import foundation.sections open import foundation.type-arithmetic-unit-type -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type -open import foundation.universal-property-equivalences funext -open import foundation.universal-property-family-of-fibers-of-maps funext -open import foundation.universal-property-unit-type funext +open import foundation.universal-property-equivalences +open import foundation.universal-property-family-of-fibers-of-maps +open import foundation.universal-property-unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.maps-local-at-maps funext -open import orthogonal-factorization-systems.orthogonal-maps funext -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.maps-local-at-maps +open import orthogonal-factorization-systems.orthogonal-maps +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/open-modalities.lagda.md b/src/orthogonal-factorization-systems/open-modalities.lagda.md index e6f6bdb891..3de73e9582 100644 --- a/src/orthogonal-factorization-systems/open-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/open-modalities.lagda.md @@ -1,12 +1,7 @@ # The open modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.open-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.open-modalities where ```
Imports @@ -14,20 +9,20 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.locally-small-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.locally-small-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import orthogonal-factorization-systems.higher-modalities funext -open import orthogonal-factorization-systems.locally-small-modal-operators funext -open import orthogonal-factorization-systems.modal-induction funext -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext +open import orthogonal-factorization-systems.higher-modalities +open import orthogonal-factorization-systems.locally-small-modal-operators +open import orthogonal-factorization-systems.modal-induction +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.uniquely-eliminating-modalities ```
diff --git a/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md index 4befe136b2..ccdba0c7e2 100644 --- a/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md @@ -1,36 +1,31 @@ # Orthogonal factorization systems ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.orthogonal-factorization-systems - (funext : function-extensionality) - where +module orthogonal-factorization-systems.orthogonal-factorization-systems where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.iterated-dependent-product-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.iterated-dependent-product-types +open import foundation.propositions open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.factorization-operations-function-classes funext -open import orthogonal-factorization-systems.factorizations-of-maps funext -open import orthogonal-factorization-systems.factorizations-of-maps funext-function-classes -open import orthogonal-factorization-systems.function-classes funext -open import orthogonal-factorization-systems.lifting-structures-on-squares funext -open import orthogonal-factorization-systems.wide-function-classes funext +open import orthogonal-factorization-systems.factorization-operations-function-classes +open import orthogonal-factorization-systems.factorizations-of-maps +open import orthogonal-factorization-systems.factorizations-of-maps-function-classes +open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.lifting-structures-on-squares +open import orthogonal-factorization-systems.wide-function-classes ```
diff --git a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md index c59b8efa88..0d98e6c2ea 100644 --- a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md @@ -1,62 +1,56 @@ # Orthogonal maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.orthogonal-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.orthogonal-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-morphisms-arrows funext -open import foundation.cartesian-product-types funext -open import foundation.composition-algebra funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.coproducts-pullbacks funext +open import foundation.cartesian-morphisms-arrows +open import foundation.cartesian-product-types +open import foundation.composition-algebra +open import foundation.contractible-maps +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.coproducts-pullbacks open import foundation.dependent-pair-types -open import foundation.dependent-products-pullbacks funext -open import foundation.dependent-sums-pullbacks funext -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.fibered-maps funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-fibers-of-maps funext -open import foundation.homotopies funext -open import foundation.morphisms-arrows funext -open import foundation.postcomposition-functions funext -open import foundation.postcomposition-pullbacks funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.products-pullbacks funext -open import foundation.propositions funext -open import foundation.pullbacks funext -open import foundation.type-arithmetic-dependent-function-types funext -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.dependent-products-pullbacks +open import foundation.dependent-sums-pullbacks +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.fibered-maps +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-fibers-of-maps +open import foundation.homotopies +open import foundation.morphisms-arrows +open import foundation.postcomposition-functions +open import foundation.postcomposition-pullbacks +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.products-pullbacks +open import foundation.propositions +open import foundation.pullbacks +open import foundation.type-arithmetic-dependent-function-types +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types funext -open import foundation.universal-property-coproduct-types funext -open import foundation.universal-property-dependent-pair-types funext -open import foundation.universal-property-equivalences funext -open import foundation.universal-property-pullbacks funext +open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-coproduct-types +open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-equivalences +open import foundation.universal-property-pullbacks open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.lifting-structures-on-squares funext -open import orthogonal-factorization-systems.pullback-hom funext -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.lifting-structures-on-squares +open import orthogonal-factorization-systems.pullback-hom +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md b/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md index 7fc3bd2570..2292277230 100644 --- a/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md +++ b/src/orthogonal-factorization-systems/precomposition-lifts-families-of-elements.lagda.md @@ -1,38 +1,33 @@ # Precomposition of lifts of families of elements by maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.precomposition-lifts-families-of-elements - (funext : function-extensionality) - where +module orthogonal-factorization-systems.precomposition-lifts-families-of-elements where ```
Imports ```agda open import foundation.action-on-identifications-dependent-functions -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.precomposition-functions funext +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.precomposition-functions open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import orthogonal-factorization-systems.lifts-families-of-elements funext +open import orthogonal-factorization-systems.lifts-families-of-elements ```
diff --git a/src/orthogonal-factorization-systems/pullback-hom.lagda.md b/src/orthogonal-factorization-systems/pullback-hom.lagda.md index 74e232d104..6cd1e6d736 100644 --- a/src/orthogonal-factorization-systems/pullback-hom.lagda.md +++ b/src/orthogonal-factorization-systems/pullback-hom.lagda.md @@ -1,45 +1,40 @@ # The pullback-hom ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.pullback-hom - (funext : function-extensionality) - where +module orthogonal-factorization-systems.pullback-hom where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-fibers-of-maps funext -open import foundation.functoriality-morphisms-arrows funext -open import foundation.higher-homotopies-morphisms-arrows funext -open import foundation.homotopies funext -open import foundation.homotopies funext-morphisms-arrows -open import foundation.identity-types funext -open import foundation.morphisms-arrows funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.pullback-cones funext -open import foundation.pullbacks funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.standard-pullbacks funext -open import foundation.type-theoretic-principle-of-choice funext -open import foundation.universal-property-pullbacks funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-fibers-of-maps +open import foundation.functoriality-morphisms-arrows +open import foundation.higher-homotopies-morphisms-arrows +open import foundation.homotopies +open import foundation.homotopies-morphisms-arrows +open import foundation.identity-types +open import foundation.morphisms-arrows +open import foundation.postcomposition-functions +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.pullback-cones +open import foundation.pullbacks +open import foundation.retractions +open import foundation.sections +open import foundation.standard-pullbacks +open import foundation.type-theoretic-principle-of-choice +open import foundation.universal-property-pullbacks open import foundation.universe-levels open import foundation.whiskering-homotopies-composition ``` diff --git a/src/orthogonal-factorization-systems/raise-modalities.lagda.md b/src/orthogonal-factorization-systems/raise-modalities.lagda.md index 59844a3d8e..1f7569b41d 100644 --- a/src/orthogonal-factorization-systems/raise-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/raise-modalities.lagda.md @@ -1,24 +1,19 @@ # The raise modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.raise-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.raise-modalities where ```
Imports ```agda -open import foundation.function-types funext -open import foundation.raising-universe-levels funext +open import foundation.function-types +open import foundation.raising-universe-levels open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.types-local-at-maps funext -open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.uniquely-eliminating-modalities ```
diff --git a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md index e9d8035ec0..440719b15d 100644 --- a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md @@ -1,33 +1,28 @@ # Reflective global subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.reflective-global-subuniverses - (funext : function-extensionality) - where +module orthogonal-factorization-systems.reflective-global-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.cospan-diagrams -open import foundation.equivalences funext -open import foundation.extensions-types-global-subuniverses funext -open import foundation.global-subuniverses funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.pullback-cones funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.extensions-types-global-subuniverses +open import foundation.global-subuniverses +open import foundation.identity-types +open import foundation.propositions +open import foundation.pullback-cones +open import foundation.subuniverses open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-global-subuniverses funext -open import orthogonal-factorization-systems.types-local-at-maps funext -open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses funext +open import orthogonal-factorization-systems.localizations-at-global-subuniverses +open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses ```
diff --git a/src/orthogonal-factorization-systems/reflective-modalities.lagda.md b/src/orthogonal-factorization-systems/reflective-modalities.lagda.md index 88214ad1b2..46c235675f 100644 --- a/src/orthogonal-factorization-systems/reflective-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-modalities.lagda.md @@ -1,12 +1,7 @@ # Reflective modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.reflective-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.reflective-modalities where ```
Imports @@ -15,8 +10,8 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.reflective-subuniverses funext +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.reflective-subuniverses ```
diff --git a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md index 648aa7cc88..5c545e554c 100644 --- a/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-subuniverses.lagda.md @@ -1,28 +1,23 @@ # Reflective subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.reflective-subuniverses - (funext : function-extensionality) - where +module orthogonal-factorization-systems.reflective-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.subuniverses open import foundation.universe-levels -open import orthogonal-factorization-systems.localizations-at-subuniverses funext -open import orthogonal-factorization-systems.modal-induction funext -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.modal-subuniverse-induction funext -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.localizations-at-subuniverses +open import orthogonal-factorization-systems.modal-induction +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.modal-subuniverse-induction +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md b/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md index 8bb8d36526..20370cd516 100644 --- a/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/sigma-closed-modalities.lagda.md @@ -1,23 +1,18 @@ # Σ-closed modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.sigma-closed-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.sigma-closed-modalities where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.sigma-closed-subuniverses funext +open import foundation.function-types +open import foundation.sigma-closed-subuniverses open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext +open import orthogonal-factorization-systems.modal-operators ```
diff --git a/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md b/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md index 82e198037c..4abbb4bf5d 100644 --- a/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/sigma-closed-reflective-modalities.lagda.md @@ -1,24 +1,19 @@ # Σ-closed reflective modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.sigma-closed-reflective-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.sigma-closed-reflective-modalities where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.reflective-modalities funext -open import orthogonal-factorization-systems.sigma-closed-modalities funext +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.reflective-modalities +open import orthogonal-factorization-systems.sigma-closed-modalities ```
diff --git a/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md b/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md index 04ccf4ba15..08cd6c74fc 100644 --- a/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/sigma-closed-reflective-subuniverses.lagda.md @@ -1,22 +1,17 @@ # Σ-closed reflective subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.sigma-closed-reflective-subuniverses - (funext : function-extensionality) - where +module orthogonal-factorization-systems.sigma-closed-reflective-subuniverses where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.sigma-closed-subuniverses funext +open import foundation.sigma-closed-subuniverses open import foundation.universe-levels -open import orthogonal-factorization-systems.reflective-subuniverses funext +open import orthogonal-factorization-systems.reflective-subuniverses ```
diff --git a/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md index f2252f1b84..2d9c5958c2 100644 --- a/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems/stable-orthogonal-factorization-systems.lagda.md @@ -1,12 +1,7 @@ # Stable orthogonal factorization systems ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.stable-orthogonal-factorization-systems - (funext : function-extensionality) - where +module orthogonal-factorization-systems.stable-orthogonal-factorization-systems where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes funext -open import orthogonal-factorization-systems.orthogonal-factorization-systems funext +open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.orthogonal-factorization-systems ```
diff --git a/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md index 542779c15c..7292a82aa0 100644 --- a/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md @@ -1,38 +1,32 @@ # Types colocal at maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.types-colocal-at-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.types-colocal-at-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.postcomposition-dependent-functions funext -open import foundation.postcomposition-functions funext -open import foundation.propositions funext -open import foundation.retracts-of-maps funext -open import foundation.retracts-of-types funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.postcomposition-dependent-functions +open import foundation.postcomposition-functions +open import foundation.propositions +open import foundation.retracts-of-maps +open import foundation.retracts-of-types open import foundation.unit-type -open import foundation.universal-property-empty-type funext -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-empty-type +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation.whiskering-homotopies-composition diff --git a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md index 868cceea8c..0e261e3ed9 100644 --- a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md @@ -1,52 +1,47 @@ # Types local at maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.types-local-at-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.types-local-at-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.families-of-equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.retracts-of-maps funext -open import foundation.retracts-of-types funext -open import foundation.sections funext -open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.dependent-universal-property-equivalences +open import foundation.empty-types +open import foundation.equivalences +open import foundation.families-of-equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.postcomposition-functions +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.propositions +open import foundation.retractions +open import foundation.retracts-of-maps +open import foundation.retracts-of-types +open import foundation.sections +open import foundation.type-arithmetic-dependent-function-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-empty-type funext -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-empty-type +open import foundation.universal-property-equivalences open import foundation.universe-levels -open import orthogonal-factorization-systems.extensions-maps funext +open import orthogonal-factorization-systems.extensions-maps ```
diff --git a/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md index 2c7d92e0c2..a909c66dac 100644 --- a/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-separated-at-maps.lagda.md @@ -1,21 +1,16 @@ # Types separated at maps ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.types-separated-at-maps - (funext : function-extensionality) - where +module orthogonal-factorization-systems.types-separated-at-maps where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md index babb757ddc..d0a891d833 100644 --- a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md @@ -1,33 +1,28 @@ # Uniquely eliminating modalities ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.uniquely-eliminating-modalities - (funext : function-extensionality) - where +module orthogonal-factorization-systems.uniquely-eliminating-modalities where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.univalence funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md index 56b0e454de..59815d7643 100644 --- a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md @@ -1,35 +1,31 @@ # The universal property of localizations at global subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses - (funext : function-extensionality) - where +module orthogonal-factorization-systems.universal-property-localizations-at-global-subuniverses where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.extensions-types funext -open import foundation.extensions-types funext-global-subuniverses -open import foundation.function-types funext -open import foundation.global-subuniverses funext -open import foundation.identity-types funext -open import foundation.precomposition-functions funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.univalence funext +open import foundation.equivalences +open import foundation.extensions-types +open import foundation.extensions-types-global-subuniverses +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.global-subuniverses +open import foundation.identity-types +open import foundation.precomposition-functions +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.univalence open import foundation.universe-levels -open import orthogonal-factorization-systems.extensions-maps funext -open import orthogonal-factorization-systems.types-local-at-maps funext +open import orthogonal-factorization-systems.extensions-maps +open import orthogonal-factorization-systems.types-local-at-maps ```
diff --git a/src/orthogonal-factorization-systems/wide-function-classes.lagda.md b/src/orthogonal-factorization-systems/wide-function-classes.lagda.md index bc26079cd0..7798c4379d 100644 --- a/src/orthogonal-factorization-systems/wide-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/wide-function-classes.lagda.md @@ -1,24 +1,19 @@ # Wide function classes ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.wide-function-classes - (funext : function-extensionality) - where +module orthogonal-factorization-systems.wide-function-classes where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.propositions open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes funext +open import orthogonal-factorization-systems.function-classes ```
diff --git a/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md index 2272c231ac..e8ed36b96f 100644 --- a/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md @@ -1,26 +1,21 @@ # Wide global function classes ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.wide-global-function-classes - (funext : function-extensionality) - where +module orthogonal-factorization-systems.wide-global-function-classes where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.function-types funext -open import foundation.propositions funext +open import foundation.embeddings +open import foundation.function-types +open import foundation.propositions open import foundation.universe-levels -open import orthogonal-factorization-systems.function-classes funext -open import orthogonal-factorization-systems.global-function-classes funext +open import orthogonal-factorization-systems.function-classes +open import orthogonal-factorization-systems.global-function-classes ```
diff --git a/src/orthogonal-factorization-systems/zero-modality.lagda.md b/src/orthogonal-factorization-systems/zero-modality.lagda.md index a5861514ad..7725c93fb4 100644 --- a/src/orthogonal-factorization-systems/zero-modality.lagda.md +++ b/src/orthogonal-factorization-systems/zero-modality.lagda.md @@ -1,24 +1,19 @@ # The zero modality ```agda -open import foundation.function-extensionality-axiom - -module - orthogonal-factorization-systems.zero-modality - (funext : function-extensionality) - where +module orthogonal-factorization-systems.zero-modality where ```
Imports ```agda -open import foundation.raising-universe-levels-unit-type funext +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import orthogonal-factorization-systems.modal-operators funext -open import orthogonal-factorization-systems.types-local-at-maps funext -open import orthogonal-factorization-systems.uniquely-eliminating-modalities funext +open import orthogonal-factorization-systems.modal-operators +open import orthogonal-factorization-systems.types-local-at-maps +open import orthogonal-factorization-systems.uniquely-eliminating-modalities ```
diff --git a/src/polytopes.lagda.md b/src/polytopes.lagda.md index b90a8223bd..93741a955f 100644 --- a/src/polytopes.lagda.md +++ b/src/polytopes.lagda.md @@ -3,12 +3,7 @@ ## Modules in the polytopes namespace ```agda -open import foundation.function-extensionality-axiom +module polytopes where -module - polytopes - (funext : function-extensionality) - where - -open import polytopes.abstract-polytopes funext public +open import polytopes.abstract-polytopes public ``` diff --git a/src/polytopes/abstract-polytopes.lagda.md b/src/polytopes/abstract-polytopes.lagda.md index d611fd93cb..b2a62140af 100644 --- a/src/polytopes/abstract-polytopes.lagda.md +++ b/src/polytopes/abstract-polytopes.lagda.md @@ -1,39 +1,34 @@ # Abstract polytopes ```agda -open import foundation.function-extensionality-axiom - -module - polytopes.abstract-polytopes - (funext : function-extensionality) - where +module polytopes.abstract-polytopes where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.inequality-standard-finite-types open import elementary-number-theory.natural-numbers -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sets funext +open import foundation.disjunction +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.sets open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import order-theory.finitely-graded-posets funext -open import order-theory.posets funext +open import order-theory.finitely-graded-posets +open import order-theory.posets -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/real-numbers.lagda.md b/src/real-numbers.lagda.md index 237e02efee..ef82f3855b 100644 --- a/src/real-numbers.lagda.md +++ b/src/real-numbers.lagda.md @@ -3,28 +3,23 @@ ## Modules in the real numbers namespace ```agda -open import foundation.function-extensionality-axiom +module real-numbers where -module - real-numbers - (funext : function-extensionality) - where - -open import real-numbers.apartness-real-numbers funext public -open import real-numbers.arithmetically-located-dedekind-cuts funext public -open import real-numbers.dedekind-real-numbers funext public -open import real-numbers.inequality-lower-dedekind-real-numbers funext public -open import real-numbers.inequality-real-numbers funext public -open import real-numbers.inequality-upper-dedekind-real-numbers funext public -open import real-numbers.lower-dedekind-real-numbers funext public -open import real-numbers.metric-space-of-real-numbers funext public -open import real-numbers.negation-lower-upper-dedekind-real-numbers funext public -open import real-numbers.negation-real-numbers funext public -open import real-numbers.raising-universe-levels-real-numbers funext public -open import real-numbers.rational-lower-dedekind-real-numbers funext public -open import real-numbers.rational-real-numbers funext public -open import real-numbers.rational-upper-dedekind-real-numbers funext public -open import real-numbers.similarity-real-numbers funext public -open import real-numbers.strict-inequality-real-numbers funext public -open import real-numbers.upper-dedekind-real-numbers funext public +open import real-numbers.apartness-real-numbers public +open import real-numbers.arithmetically-located-dedekind-cuts public +open import real-numbers.dedekind-real-numbers public +open import real-numbers.inequality-lower-dedekind-real-numbers public +open import real-numbers.inequality-real-numbers public +open import real-numbers.inequality-upper-dedekind-real-numbers public +open import real-numbers.lower-dedekind-real-numbers public +open import real-numbers.metric-space-of-real-numbers public +open import real-numbers.negation-lower-upper-dedekind-real-numbers public +open import real-numbers.negation-real-numbers public +open import real-numbers.raising-universe-levels-real-numbers public +open import real-numbers.rational-lower-dedekind-real-numbers public +open import real-numbers.rational-real-numbers public +open import real-numbers.rational-upper-dedekind-real-numbers public +open import real-numbers.similarity-real-numbers public +open import real-numbers.strict-inequality-real-numbers public +open import real-numbers.upper-dedekind-real-numbers public ``` diff --git a/src/real-numbers/apartness-real-numbers.lagda.md b/src/real-numbers/apartness-real-numbers.lagda.md index 2106f4e595..610c8bcdbb 100644 --- a/src/real-numbers/apartness-real-numbers.lagda.md +++ b/src/real-numbers/apartness-real-numbers.lagda.md @@ -1,29 +1,24 @@ # Apartness of real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.apartness-real-numbers - (funext : function-extensionality) - where +module real-numbers.apartness-real-numbers where ```
Imports ```agda -open import foundation.disjunction funext -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.large-apartness-relations funext -open import foundation.large-binary-relations funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.disjunction +open import foundation.empty-types +open import foundation.function-types +open import foundation.large-apartness-relations +open import foundation.large-binary-relations +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions open import foundation.universe-levels -open import real-numbers.dedekind-real-numbers funext -open import real-numbers.strict-inequality-real-numbers funext +open import real-numbers.dedekind-real-numbers +open import real-numbers.strict-inequality-real-numbers ```
diff --git a/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md b/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md index bd7f2b0263..a378d58d72 100644 --- a/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md +++ b/src/real-numbers/arithmetically-located-dedekind-cuts.lagda.md @@ -3,39 +3,34 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - real-numbers.arithmetically-located-dedekind-cuts - (funext : function-extensionality) - where +module real-numbers.arithmetically-located-dedekind-cuts where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.additive-group-of-rational-numbers funext -open import elementary-number-theory.difference-rational-numbers funext -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext - -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext -open import foundation.coproduct-types funext +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.additive-group-of-rational-numbers +open import elementary-number-theory.difference-rational-numbers +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers + +open import foundation.cartesian-product-types +open import foundation.conjunction +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.existential-quantification funext +open import foundation.disjunction +open import foundation.existential-quantification open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.abelian-groups funext +open import group-theory.abelian-groups -open import real-numbers.dedekind-real-numbers funext -open import real-numbers.lower-dedekind-real-numbers funext -open import real-numbers.upper-dedekind-real-numbers funext +open import real-numbers.dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.upper-dedekind-real-numbers ```
diff --git a/src/real-numbers/dedekind-real-numbers.lagda.md b/src/real-numbers/dedekind-real-numbers.lagda.md index 63bc7c7cfe..36f5e8e621 100644 --- a/src/real-numbers/dedekind-real-numbers.lagda.md +++ b/src/real-numbers/dedekind-real-numbers.lagda.md @@ -1,49 +1,44 @@ # Dedekind real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.dedekind-real-numbers - (funext : function-extensionality) - where +module real-numbers.dedekind-real-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.conjunction funext -open import foundation.coproduct-types funext +open import foundation.conjunction +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.disjoint-subtypes funext -open import foundation.disjunction funext -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.powersets funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.disjoint-subtypes +open import foundation.disjunction +open import foundation.embeddings +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.powersets +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.universal-quantification funext +open import foundation.universal-quantification open import foundation.universe-levels -open import logic.functoriality-existential-quantification funext +open import logic.functoriality-existential-quantification -open import real-numbers.lower-dedekind-real-numbers funext -open import real-numbers.upper-dedekind-real-numbers funext +open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.upper-dedekind-real-numbers ```
diff --git a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md index e38906cd17..87a1154a7f 100644 --- a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md @@ -1,35 +1,30 @@ # Inequality on the lower Dedekind real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.inequality-lower-dedekind-real-numbers - (funext : function-extensionality) - where +module real-numbers.inequality-lower-dedekind-real-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext +open import order-theory.large-posets +open import order-theory.large-preorders -open import real-numbers.lower-dedekind-real-numbers funext -open import real-numbers.rational-lower-dedekind-real-numbers funext +open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.rational-lower-dedekind-real-numbers ```
diff --git a/src/real-numbers/inequality-real-numbers.lagda.md b/src/real-numbers/inequality-real-numbers.lagda.md index dfdd39e19c..06313f63bb 100644 --- a/src/real-numbers/inequality-real-numbers.lagda.md +++ b/src/real-numbers/inequality-real-numbers.lagda.md @@ -1,38 +1,33 @@ # Inequality on the real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.inequality-real-numbers - (funext : function-extensionality) - where +module real-numbers.inequality-real-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.rational-numbers -open import foundation.complements-subtypes funext +open import foundation.complements-subtypes open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.posets funext -open import order-theory.preorders funext +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.posets +open import order-theory.preorders -open import real-numbers.dedekind-real-numbers funext -open import real-numbers.inequality-lower-dedekind-real-numbers funext -open import real-numbers.inequality-upper-dedekind-real-numbers funext -open import real-numbers.rational-real-numbers funext +open import real-numbers.dedekind-real-numbers +open import real-numbers.inequality-lower-dedekind-real-numbers +open import real-numbers.inequality-upper-dedekind-real-numbers +open import real-numbers.rational-real-numbers ```
diff --git a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md index e6341b15b6..1c124e2f50 100644 --- a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md @@ -1,35 +1,30 @@ # Inequality on the upper Dedekind real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.inequality-upper-dedekind-real-numbers - (funext : function-extensionality) - where +module real-numbers.inequality-upper-dedekind-real-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext +open import order-theory.large-posets +open import order-theory.large-preorders -open import real-numbers.rational-upper-dedekind-real-numbers funext -open import real-numbers.upper-dedekind-real-numbers funext +open import real-numbers.rational-upper-dedekind-real-numbers +open import real-numbers.upper-dedekind-real-numbers ```
diff --git a/src/real-numbers/lower-dedekind-real-numbers.lagda.md b/src/real-numbers/lower-dedekind-real-numbers.lagda.md index 5f3529bd6b..2d9c8b829b 100644 --- a/src/real-numbers/lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/lower-dedekind-real-numbers.lagda.md @@ -1,36 +1,31 @@ # Lower Dedekind real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.lower-dedekind-real-numbers - (funext : function-extensionality) - where +module real-numbers.lower-dedekind-real-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.conjunction funext -open import foundation.coproduct-types funext +open import foundation.conjunction +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels -open import foundation.universal-quantification funext +open import foundation.universal-quantification open import foundation.universe-levels ``` diff --git a/src/real-numbers/metric-space-of-real-numbers.lagda.md b/src/real-numbers/metric-space-of-real-numbers.lagda.md index 74042bf1c2..7a4d12c506 100644 --- a/src/real-numbers/metric-space-of-real-numbers.lagda.md +++ b/src/real-numbers/metric-space-of-real-numbers.lagda.md @@ -3,50 +3,45 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - real-numbers.metric-space-of-real-numbers - (funext : function-extensionality) - where +module real-numbers.metric-space-of-real-numbers where ```
Imports ```agda -open import elementary-number-theory.addition-rational-numbers funext -open import elementary-number-theory.difference-rational-numbers funext -open import elementary-number-theory.positive-rational-numbers funext -open import elementary-number-theory.rational-numbers funext +open import elementary-number-theory.addition-rational-numbers +open import elementary-number-theory.difference-rational-numbers +open import elementary-number-theory.positive-rational-numbers +open import elementary-number-theory.rational-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.diagonal-maps-cartesian-products-of-types funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.diagonal-maps-cartesian-products-of-types +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import metric-spaces.extensional-premetric-structures funext -open import metric-spaces.isometries-metric-spaces funext -open import metric-spaces.metric-space-of-rational-numbers funext -open import metric-spaces.metric-spaces funext -open import metric-spaces.metric-structures funext -open import metric-spaces.premetric-spaces funext -open import metric-spaces.premetric-structures funext -open import metric-spaces.pseudometric-structures funext -open import metric-spaces.reflexive-premetric-structures funext -open import metric-spaces.saturated-metric-spaces funext -open import metric-spaces.symmetric-premetric-structures funext -open import metric-spaces.triangular-premetric-structures funext - -open import real-numbers.dedekind-real-numbers funext -open import real-numbers.rational-real-numbers funext +open import metric-spaces.extensional-premetric-structures +open import metric-spaces.isometries-metric-spaces +open import metric-spaces.metric-space-of-rational-numbers +open import metric-spaces.metric-spaces +open import metric-spaces.metric-structures +open import metric-spaces.premetric-spaces +open import metric-spaces.premetric-structures +open import metric-spaces.pseudometric-structures +open import metric-spaces.reflexive-premetric-structures +open import metric-spaces.saturated-metric-spaces +open import metric-spaces.symmetric-premetric-structures +open import metric-spaces.triangular-premetric-structures + +open import real-numbers.dedekind-real-numbers +open import real-numbers.rational-real-numbers ```
diff --git a/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md index d791c05774..0fe42bfd07 100644 --- a/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/negation-lower-upper-dedekind-real-numbers.lagda.md @@ -3,40 +3,35 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - real-numbers.negation-lower-upper-dedekind-real-numbers - (funext : function-extensionality) - where +module real-numbers.negation-lower-upper-dedekind-real-numbers where ```
Imports ```agda -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext +open import foundation.cartesian-product-types +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.retractions +open import foundation.sections +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification funext +open import logic.functoriality-existential-quantification -open import real-numbers.lower-dedekind-real-numbers funext -open import real-numbers.rational-lower-dedekind-real-numbers funext -open import real-numbers.rational-upper-dedekind-real-numbers funext -open import real-numbers.upper-dedekind-real-numbers funext +open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.rational-lower-dedekind-real-numbers +open import real-numbers.rational-upper-dedekind-real-numbers +open import real-numbers.upper-dedekind-real-numbers ```
diff --git a/src/real-numbers/negation-real-numbers.lagda.md b/src/real-numbers/negation-real-numbers.lagda.md index 60c8f216b5..54744b5d9d 100644 --- a/src/real-numbers/negation-real-numbers.lagda.md +++ b/src/real-numbers/negation-real-numbers.lagda.md @@ -3,34 +3,29 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - real-numbers.negation-real-numbers - (funext : function-extensionality) - where +module real-numbers.negation-real-numbers where ```
Imports ```agda -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.dependent-pair-types -open import foundation.disjoint-subtypes funext -open import foundation.disjunction funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.subtypes funext +open import foundation.disjoint-subtypes +open import foundation.disjunction +open import foundation.function-types +open import foundation.identity-types +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import real-numbers.dedekind-real-numbers funext -open import real-numbers.lower-dedekind-real-numbers funext -open import real-numbers.negation-lower-upper-dedekind-real-numbers funext -open import real-numbers.rational-real-numbers funext -open import real-numbers.upper-dedekind-real-numbers funext +open import real-numbers.dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.negation-lower-upper-dedekind-real-numbers +open import real-numbers.rational-real-numbers +open import real-numbers.upper-dedekind-real-numbers ```
diff --git a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md index 6cb792b364..422760c592 100644 --- a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md +++ b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md @@ -1,41 +1,36 @@ # Raising the universe levels of real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.raising-universe-levels-real-numbers - (funext : function-extensionality) - where +module real-numbers.raising-universe-levels-real-numbers where ```
Imports ```agda -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.cartesian-product-types funext -open import foundation.conjunction funext +open import foundation.cartesian-product-types +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.inhabited-subtypes funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.raising-universe-levels funext -open import foundation.subtypes funext +open import foundation.disjunction +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.inhabited-subtypes +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.raising-universe-levels +open import foundation.subtypes open import foundation.universe-levels -open import logic.functoriality-existential-quantification funext +open import logic.functoriality-existential-quantification -open import real-numbers.dedekind-real-numbers funext -open import real-numbers.lower-dedekind-real-numbers funext -open import real-numbers.similarity-real-numbers funext -open import real-numbers.upper-dedekind-real-numbers funext +open import real-numbers.dedekind-real-numbers +open import real-numbers.lower-dedekind-real-numbers +open import real-numbers.similarity-real-numbers +open import real-numbers.upper-dedekind-real-numbers ```
diff --git a/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md index 9eab421308..5176279b29 100644 --- a/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/rational-lower-dedekind-real-numbers.lagda.md @@ -1,28 +1,23 @@ # Rational lower Dedekind real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.rational-lower-dedekind-real-numbers - (funext : function-extensionality) - where +module real-numbers.rational-lower-dedekind-real-numbers where ```
Imports ```agda -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.logical-equivalences funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.logical-equivalences +open import foundation.subtypes open import foundation.universe-levels -open import real-numbers.lower-dedekind-real-numbers funext +open import real-numbers.lower-dedekind-real-numbers ```
diff --git a/src/real-numbers/rational-real-numbers.lagda.md b/src/real-numbers/rational-real-numbers.lagda.md index cfa3ebd3a2..c5dfe24fcc 100644 --- a/src/real-numbers/rational-real-numbers.lagda.md +++ b/src/real-numbers/rational-real-numbers.lagda.md @@ -3,40 +3,35 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - real-numbers.rational-real-numbers - (funext : function-extensionality) - where +module real-numbers.rational-real-numbers where ```
Imports ```agda -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.subtypes funext +open import foundation.disjunction +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import real-numbers.dedekind-real-numbers funext -open import real-numbers.rational-lower-dedekind-real-numbers funext -open import real-numbers.rational-upper-dedekind-real-numbers funext -open import real-numbers.similarity-real-numbers funext +open import real-numbers.dedekind-real-numbers +open import real-numbers.rational-lower-dedekind-real-numbers +open import real-numbers.rational-upper-dedekind-real-numbers +open import real-numbers.similarity-real-numbers ```
diff --git a/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md index 9c3b511383..f88c510a18 100644 --- a/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/rational-upper-dedekind-real-numbers.lagda.md @@ -1,28 +1,23 @@ # Rational upper Dedekind real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.rational-upper-dedekind-real-numbers - (funext : function-extensionality) - where +module real-numbers.rational-upper-dedekind-real-numbers where ```
Imports ```agda -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.conjunction funext +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.logical-equivalences funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.logical-equivalences +open import foundation.subtypes open import foundation.universe-levels -open import real-numbers.upper-dedekind-real-numbers funext +open import real-numbers.upper-dedekind-real-numbers ```
diff --git a/src/real-numbers/similarity-real-numbers.lagda.md b/src/real-numbers/similarity-real-numbers.lagda.md index 2589a0fe87..d7b13097d2 100644 --- a/src/real-numbers/similarity-real-numbers.lagda.md +++ b/src/real-numbers/similarity-real-numbers.lagda.md @@ -1,26 +1,21 @@ # Similarity of real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.similarity-real-numbers - (funext : function-extensionality) - where +module real-numbers.similarity-real-numbers where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import real-numbers.dedekind-real-numbers funext +open import real-numbers.dedekind-real-numbers ```
diff --git a/src/real-numbers/strict-inequality-real-numbers.lagda.md b/src/real-numbers/strict-inequality-real-numbers.lagda.md index 71b39f01ff..2b2ccc6a6b 100644 --- a/src/real-numbers/strict-inequality-real-numbers.lagda.md +++ b/src/real-numbers/strict-inequality-real-numbers.lagda.md @@ -3,43 +3,38 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - real-numbers.strict-inequality-real-numbers - (funext : function-extensionality) - where +module real-numbers.strict-inequality-real-numbers where ```
Imports ```agda -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.conjunction funext -open import foundation.coproduct-types funext +open import foundation.conjunction +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.disjunction +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import logic.functoriality-existential-quantification funext +open import logic.functoriality-existential-quantification -open import real-numbers.dedekind-real-numbers funext -open import real-numbers.inequality-real-numbers funext -open import real-numbers.negation-real-numbers funext -open import real-numbers.rational-real-numbers funext +open import real-numbers.dedekind-real-numbers +open import real-numbers.inequality-real-numbers +open import real-numbers.negation-real-numbers +open import real-numbers.rational-real-numbers ```
diff --git a/src/real-numbers/upper-dedekind-real-numbers.lagda.md b/src/real-numbers/upper-dedekind-real-numbers.lagda.md index 156894f09c..fa82905722 100644 --- a/src/real-numbers/upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/upper-dedekind-real-numbers.lagda.md @@ -1,36 +1,31 @@ # Upper Dedekind real numbers ```agda -open import foundation.function-extensionality-axiom - -module - real-numbers.upper-dedekind-real-numbers - (funext : function-extensionality) - where +module real-numbers.upper-dedekind-real-numbers where ```
Imports ```agda -open import elementary-number-theory.inequality-rational-numbers funext -open import elementary-number-theory.rational-numbers funext -open import elementary-number-theory.strict-inequality-rational-numbers funext +open import elementary-number-theory.inequality-rational-numbers +open import elementary-number-theory.rational-numbers +open import elementary-number-theory.strict-inequality-rational-numbers -open import foundation.conjunction funext -open import foundation.coproduct-types funext +open import foundation.conjunction +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels -open import foundation.universal-quantification funext +open import foundation.universal-quantification open import foundation.universe-levels ``` diff --git a/src/reflection.lagda.md b/src/reflection.lagda.md index 5a4df12448..0e4c56b9dc 100644 --- a/src/reflection.lagda.md +++ b/src/reflection.lagda.md @@ -7,24 +7,19 @@ ## Modules in the reflection namespace ```agda -open import foundation.function-extensionality-axiom - -module - reflection - (funext : function-extensionality) - where +module reflection where open import reflection.abstractions public open import reflection.arguments public -open import reflection.boolean-reflection funext public +open import reflection.boolean-reflection public open import reflection.definitions public open import reflection.erasing-equality public -open import reflection.fixity funext public -open import reflection.group-solver funext public +open import reflection.fixity public +open import reflection.group-solver public open import reflection.literals public open import reflection.metavariables public open import reflection.names public -open import reflection.precategory-solver funext public +open import reflection.precategory-solver public open import reflection.rewriting public open import reflection.terms public open import reflection.type-checking-monad public diff --git a/src/reflection/boolean-reflection.lagda.md b/src/reflection/boolean-reflection.lagda.md index 909f3e3e08..e4602783c7 100644 --- a/src/reflection/boolean-reflection.lagda.md +++ b/src/reflection/boolean-reflection.lagda.md @@ -1,18 +1,13 @@ # Boolean reflection ```agda -open import foundation.function-extensionality-axiom - -module - reflection.boolean-reflection - (funext : function-extensionality) - where +module reflection.boolean-reflection where ```
Imports ```agda -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.universe-levels open import foundation-core.booleans diff --git a/src/reflection/fixity.lagda.md b/src/reflection/fixity.lagda.md index 83069c171d..6f7961f5ce 100644 --- a/src/reflection/fixity.lagda.md +++ b/src/reflection/fixity.lagda.md @@ -1,18 +1,13 @@ # Fixity ```agda -open import foundation.function-extensionality-axiom - -module - reflection.fixity - (funext : function-extensionality) - where +module reflection.fixity where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import foundation.universe-levels diff --git a/src/reflection/group-solver.lagda.md b/src/reflection/group-solver.lagda.md index 32d5a7edad..6fb762b69b 100644 --- a/src/reflection/group-solver.lagda.md +++ b/src/reflection/group-solver.lagda.md @@ -1,12 +1,7 @@ # Group solver ```agda -open import foundation.function-extensionality-axiom - -module - reflection.group-solver - (funext : function-extensionality) - where +module reflection.group-solver where ```
Imports @@ -15,21 +10,21 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.identity-types -open import group-theory.groups funext +open import group-theory.groups -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import lists.concatenation-lists funext -open import lists.functoriality-lists funext +open import lists.concatenation-lists +open import lists.functoriality-lists open import lists.lists -open import lists.reversing-lists funext +open import lists.reversing-lists ```
diff --git a/src/reflection/precategory-solver.lagda.md b/src/reflection/precategory-solver.lagda.md index 62d14b4e1c..dd11d6389c 100644 --- a/src/reflection/precategory-solver.lagda.md +++ b/src/reflection/precategory-solver.lagda.md @@ -3,28 +3,23 @@ ```agda {-# OPTIONS --no-exact-split #-} -open import foundation.function-extensionality-axiom - -module - reflection.precategory-solver - (funext : function-extensionality) - where +module reflection.precategory-solver where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext +open import foundation.function-types open import foundation.unit-type open import foundation.universe-levels open import foundation-core.identity-types -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists open import reflection.arguments diff --git a/src/ring-theory.lagda.md b/src/ring-theory.lagda.md index cbc30af145..9ea7cb8d0b 100644 --- a/src/ring-theory.lagda.md +++ b/src/ring-theory.lagda.md @@ -3,88 +3,83 @@ ## Modules in the ring theory namespace ```agda -open import foundation.function-extensionality-axiom +module ring-theory where -module - ring-theory - (funext : function-extensionality) - where - -open import ring-theory.additive-orders-of-elements-rings funext public -open import ring-theory.algebras-rings funext public -open import ring-theory.binomial-theorem-rings funext public -open import ring-theory.binomial-theorem-semirings funext public -open import ring-theory.category-of-cyclic-rings funext public -open import ring-theory.category-of-rings funext public -open import ring-theory.central-elements-rings funext public -open import ring-theory.central-elements-semirings funext public -open import ring-theory.characteristics-rings funext public -open import ring-theory.commuting-elements-rings funext public -open import ring-theory.congruence-relations-rings funext public -open import ring-theory.congruence-relations-semirings funext public -open import ring-theory.cyclic-rings funext public -open import ring-theory.dependent-products-rings funext public -open import ring-theory.dependent-products-semirings funext public -open import ring-theory.division-rings funext public -open import ring-theory.free-rings-with-one-generator funext public -open import ring-theory.full-ideals-rings funext public -open import ring-theory.function-rings funext public -open import ring-theory.function-semirings funext public -open import ring-theory.generating-elements-rings funext public -open import ring-theory.groups-of-units-rings funext public -open import ring-theory.homomorphisms-cyclic-rings funext public -open import ring-theory.homomorphisms-rings funext public -open import ring-theory.homomorphisms-semirings funext public -open import ring-theory.ideals-generated-by-subsets-rings funext public -open import ring-theory.ideals-rings funext public -open import ring-theory.ideals-semirings funext public -open import ring-theory.idempotent-elements-rings funext public -open import ring-theory.initial-rings funext public -open import ring-theory.integer-multiples-of-elements-rings funext public -open import ring-theory.intersections-ideals-rings funext public -open import ring-theory.intersections-ideals-semirings funext public -open import ring-theory.invariant-basis-property-rings funext public -open import ring-theory.invertible-elements-rings funext public -open import ring-theory.isomorphisms-rings funext public -open import ring-theory.joins-ideals-rings funext public -open import ring-theory.joins-left-ideals-rings funext public -open import ring-theory.joins-right-ideals-rings funext public -open import ring-theory.kernels-of-ring-homomorphisms funext public -open import ring-theory.left-ideals-generated-by-subsets-rings funext public -open import ring-theory.left-ideals-rings funext public -open import ring-theory.local-rings funext public -open import ring-theory.localizations-rings funext public +open import ring-theory.additive-orders-of-elements-rings public +open import ring-theory.algebras-rings public +open import ring-theory.binomial-theorem-rings public +open import ring-theory.binomial-theorem-semirings public +open import ring-theory.category-of-cyclic-rings public +open import ring-theory.category-of-rings public +open import ring-theory.central-elements-rings public +open import ring-theory.central-elements-semirings public +open import ring-theory.characteristics-rings public +open import ring-theory.commuting-elements-rings public +open import ring-theory.congruence-relations-rings public +open import ring-theory.congruence-relations-semirings public +open import ring-theory.cyclic-rings public +open import ring-theory.dependent-products-rings public +open import ring-theory.dependent-products-semirings public +open import ring-theory.division-rings public +open import ring-theory.free-rings-with-one-generator public +open import ring-theory.full-ideals-rings public +open import ring-theory.function-rings public +open import ring-theory.function-semirings public +open import ring-theory.generating-elements-rings public +open import ring-theory.groups-of-units-rings public +open import ring-theory.homomorphisms-cyclic-rings public +open import ring-theory.homomorphisms-rings public +open import ring-theory.homomorphisms-semirings public +open import ring-theory.ideals-generated-by-subsets-rings public +open import ring-theory.ideals-rings public +open import ring-theory.ideals-semirings public +open import ring-theory.idempotent-elements-rings public +open import ring-theory.initial-rings public +open import ring-theory.integer-multiples-of-elements-rings public +open import ring-theory.intersections-ideals-rings public +open import ring-theory.intersections-ideals-semirings public +open import ring-theory.invariant-basis-property-rings public +open import ring-theory.invertible-elements-rings public +open import ring-theory.isomorphisms-rings public +open import ring-theory.joins-ideals-rings public +open import ring-theory.joins-left-ideals-rings public +open import ring-theory.joins-right-ideals-rings public +open import ring-theory.kernels-of-ring-homomorphisms public +open import ring-theory.left-ideals-generated-by-subsets-rings public +open import ring-theory.left-ideals-rings public +open import ring-theory.local-rings public +open import ring-theory.localizations-rings public open import ring-theory.maximal-ideals-rings public -open import ring-theory.modules-rings funext public -open import ring-theory.multiples-of-elements-rings funext public +open import ring-theory.modules-rings public +open import ring-theory.multiples-of-elements-rings public open import ring-theory.multiplicative-orders-of-units-rings public -open import ring-theory.nil-ideals-rings funext public -open import ring-theory.nilpotent-elements-rings funext public -open import ring-theory.nilpotent-elements-semirings funext public -open import ring-theory.opposite-rings funext public -open import ring-theory.poset-of-cyclic-rings funext public -open import ring-theory.poset-of-ideals-rings funext public -open import ring-theory.poset-of-left-ideals-rings funext public -open import ring-theory.poset-of-right-ideals-rings funext public -open import ring-theory.powers-of-elements-rings funext public -open import ring-theory.powers-of-elements-semirings funext public -open import ring-theory.precategory-of-rings funext public -open import ring-theory.precategory-of-semirings funext public -open import ring-theory.products-ideals-rings funext public -open import ring-theory.products-left-ideals-rings funext public -open import ring-theory.products-right-ideals-rings funext public -open import ring-theory.products-rings funext public -open import ring-theory.products-subsets-rings funext public -open import ring-theory.quotient-rings funext public -open import ring-theory.radical-ideals-rings funext public -open import ring-theory.right-ideals-generated-by-subsets-rings funext public -open import ring-theory.right-ideals-rings funext public -open import ring-theory.rings funext public -open import ring-theory.semirings funext public -open import ring-theory.subsets-rings funext public -open import ring-theory.subsets-semirings funext public -open import ring-theory.sums-rings funext public -open import ring-theory.sums-semirings funext public -open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups funext public -open import ring-theory.trivial-rings funext public +open import ring-theory.nil-ideals-rings public +open import ring-theory.nilpotent-elements-rings public +open import ring-theory.nilpotent-elements-semirings public +open import ring-theory.opposite-rings public +open import ring-theory.poset-of-cyclic-rings public +open import ring-theory.poset-of-ideals-rings public +open import ring-theory.poset-of-left-ideals-rings public +open import ring-theory.poset-of-right-ideals-rings public +open import ring-theory.powers-of-elements-rings public +open import ring-theory.powers-of-elements-semirings public +open import ring-theory.precategory-of-rings public +open import ring-theory.precategory-of-semirings public +open import ring-theory.products-ideals-rings public +open import ring-theory.products-left-ideals-rings public +open import ring-theory.products-right-ideals-rings public +open import ring-theory.products-rings public +open import ring-theory.products-subsets-rings public +open import ring-theory.quotient-rings public +open import ring-theory.radical-ideals-rings public +open import ring-theory.right-ideals-generated-by-subsets-rings public +open import ring-theory.right-ideals-rings public +open import ring-theory.rings public +open import ring-theory.semirings public +open import ring-theory.subsets-rings public +open import ring-theory.subsets-semirings public +open import ring-theory.sums-rings public +open import ring-theory.sums-semirings public +open import ring-theory.transporting-ring-structure-along-isomorphisms-abelian-groups public +open import ring-theory.trivial-rings public ``` diff --git a/src/ring-theory/additive-orders-of-elements-rings.lagda.md b/src/ring-theory/additive-orders-of-elements-rings.lagda.md index e6550b308c..8a8cf9374c 100644 --- a/src/ring-theory/additive-orders-of-elements-rings.lagda.md +++ b/src/ring-theory/additive-orders-of-elements-rings.lagda.md @@ -1,33 +1,28 @@ # Additive orders of elements of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.additive-orders-of-elements-rings - (funext : function-extensionality) - where +module ring-theory.additive-orders-of-elements-rings where ```
Imports ```agda -open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.group-of-integers open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels -open import group-theory.normal-subgroups funext -open import group-theory.orders-of-elements-groups funext -open import group-theory.subgroups funext -open import group-theory.subsets-groups funext +open import group-theory.normal-subgroups +open import group-theory.orders-of-elements-groups +open import group-theory.subgroups +open import group-theory.subsets-groups -open import ring-theory.integer-multiples-of-elements-rings funext -open import ring-theory.rings funext +open import ring-theory.integer-multiples-of-elements-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/algebras-rings.lagda.md b/src/ring-theory/algebras-rings.lagda.md index e59d256076..ff618c84d6 100644 --- a/src/ring-theory/algebras-rings.lagda.md +++ b/src/ring-theory/algebras-rings.lagda.md @@ -1,24 +1,19 @@ # Algebras over rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.algebras-rings - (funext : function-extensionality) - where +module ring-theory.algebras-rings where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.modules-rings funext -open import ring-theory.rings funext +open import ring-theory.modules-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/binomial-theorem-rings.lagda.md b/src/ring-theory/binomial-theorem-rings.lagda.md index a901e2f90e..d951452476 100644 --- a/src/ring-theory/binomial-theorem-rings.lagda.md +++ b/src/ring-theory/binomial-theorem-rings.lagda.md @@ -1,34 +1,29 @@ # The binomial theorem for rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.binomial-theorem-rings - (funext : function-extensionality) - where +module ring-theory.binomial-theorem-rings where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients funext -open import elementary-number-theory.distance-natural-numbers funext +open import elementary-number-theory.binomial-coefficients +open import elementary-number-theory.distance-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.vectors-on-rings funext +open import linear-algebra.vectors-on-rings -open import ring-theory.binomial-theorem-semirings funext -open import ring-theory.powers-of-elements-rings funext -open import ring-theory.rings funext -open import ring-theory.sums-rings funext +open import ring-theory.binomial-theorem-semirings +open import ring-theory.powers-of-elements-rings +open import ring-theory.rings +open import ring-theory.sums-rings -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/ring-theory/binomial-theorem-semirings.lagda.md b/src/ring-theory/binomial-theorem-semirings.lagda.md index 4286f0a12b..66679c0071 100644 --- a/src/ring-theory/binomial-theorem-semirings.lagda.md +++ b/src/ring-theory/binomial-theorem-semirings.lagda.md @@ -1,37 +1,32 @@ # The binomial theorem for semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.binomial-theorem-semirings - (funext : function-extensionality) - where +module ring-theory.binomial-theorem-semirings where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.binomial-coefficients funext -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.binomial-coefficients +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.vectors-on-semirings funext +open import linear-algebra.vectors-on-semirings -open import ring-theory.powers-of-elements-semirings funext -open import ring-theory.semirings funext -open import ring-theory.sums-semirings funext +open import ring-theory.powers-of-elements-semirings +open import ring-theory.semirings +open import ring-theory.sums-semirings -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/ring-theory/category-of-cyclic-rings.lagda.md b/src/ring-theory/category-of-cyclic-rings.lagda.md index 628159d38c..27c4f61a07 100644 --- a/src/ring-theory/category-of-cyclic-rings.lagda.md +++ b/src/ring-theory/category-of-cyclic-rings.lagda.md @@ -1,30 +1,25 @@ # The category of cyclic rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.category-of-cyclic-rings - (funext : function-extensionality) - where +module ring-theory.category-of-cyclic-rings where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.full-large-subprecategories funext -open import category-theory.large-categories funext -open import category-theory.large-precategories funext +open import category-theory.categories +open import category-theory.full-large-subprecategories +open import category-theory.large-categories +open import category-theory.large-precategories open import foundation.universe-levels -open import order-theory.large-posets funext +open import order-theory.large-posets -open import ring-theory.category-of-rings funext -open import ring-theory.cyclic-rings funext -open import ring-theory.homomorphisms-cyclic-rings funext -open import ring-theory.precategory-of-rings funext +open import ring-theory.category-of-rings +open import ring-theory.cyclic-rings +open import ring-theory.homomorphisms-cyclic-rings +open import ring-theory.precategory-of-rings ```
diff --git a/src/ring-theory/category-of-rings.lagda.md b/src/ring-theory/category-of-rings.lagda.md index 7e870297cf..8c06755027 100644 --- a/src/ring-theory/category-of-rings.lagda.md +++ b/src/ring-theory/category-of-rings.lagda.md @@ -1,24 +1,19 @@ # The category of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.category-of-rings - (funext : function-extensionality) - where +module ring-theory.category-of-rings where ```
Imports ```agda -open import category-theory.categories funext -open import category-theory.large-categories funext +open import category-theory.categories +open import category-theory.large-categories open import foundation.universe-levels -open import ring-theory.isomorphisms-rings funext -open import ring-theory.precategory-of-rings funext +open import ring-theory.isomorphisms-rings +open import ring-theory.precategory-of-rings ```
diff --git a/src/ring-theory/central-elements-rings.lagda.md b/src/ring-theory/central-elements-rings.lagda.md index 1cb7eb7808..7ecc9dc806 100644 --- a/src/ring-theory/central-elements-rings.lagda.md +++ b/src/ring-theory/central-elements-rings.lagda.md @@ -1,24 +1,19 @@ # Central elements of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.central-elements-rings - (funext : function-extensionality) - where +module ring-theory.central-elements-rings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import ring-theory.central-elements-semirings funext -open import ring-theory.rings funext +open import ring-theory.central-elements-semirings +open import ring-theory.rings ```
diff --git a/src/ring-theory/central-elements-semirings.lagda.md b/src/ring-theory/central-elements-semirings.lagda.md index c37711c151..41cb19f6ef 100644 --- a/src/ring-theory/central-elements-semirings.lagda.md +++ b/src/ring-theory/central-elements-semirings.lagda.md @@ -1,24 +1,19 @@ # Central elements of semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.central-elements-semirings - (funext : function-extensionality) - where +module ring-theory.central-elements-semirings where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.central-elements-monoids funext +open import group-theory.central-elements-monoids -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/ring-theory/characteristics-rings.lagda.md b/src/ring-theory/characteristics-rings.lagda.md index 9f4298e796..45bdfb7e8e 100644 --- a/src/ring-theory/characteristics-rings.lagda.md +++ b/src/ring-theory/characteristics-rings.lagda.md @@ -1,24 +1,19 @@ # Characteristics of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.characteristics-rings - (funext : function-extensionality) - where +module ring-theory.characteristics-rings where ```
Imports ```agda -open import elementary-number-theory.ring-of-integers funext +open import elementary-number-theory.ring-of-integers open import foundation.universe-levels -open import ring-theory.ideals-rings funext -open import ring-theory.kernels-of-ring-homomorphisms funext -open import ring-theory.rings funext +open import ring-theory.ideals-rings +open import ring-theory.kernels-of-ring-homomorphisms +open import ring-theory.rings ```
diff --git a/src/ring-theory/commuting-elements-rings.lagda.md b/src/ring-theory/commuting-elements-rings.lagda.md index be128ab07e..3d35949217 100644 --- a/src/ring-theory/commuting-elements-rings.lagda.md +++ b/src/ring-theory/commuting-elements-rings.lagda.md @@ -1,25 +1,20 @@ # Commuting elements of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.commuting-elements-rings - (funext : function-extensionality) - where +module ring-theory.commuting-elements-rings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.commuting-elements-monoids funext +open import group-theory.commuting-elements-monoids -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/ring-theory/congruence-relations-rings.lagda.md b/src/ring-theory/congruence-relations-rings.lagda.md index 0ca8dea892..7b12139706 100644 --- a/src/ring-theory/congruence-relations-rings.lagda.md +++ b/src/ring-theory/congruence-relations-rings.lagda.md @@ -1,31 +1,26 @@ # Congruence relations on rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.congruence-relations-rings - (funext : function-extensionality) - where +module ring-theory.congruence-relations-rings where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.congruence-relations-abelian-groups funext -open import group-theory.congruence-relations-monoids funext +open import group-theory.congruence-relations-abelian-groups +open import group-theory.congruence-relations-monoids -open import ring-theory.congruence-relations-semirings funext -open import ring-theory.rings funext +open import ring-theory.congruence-relations-semirings +open import ring-theory.rings ```
diff --git a/src/ring-theory/congruence-relations-semirings.lagda.md b/src/ring-theory/congruence-relations-semirings.lagda.md index 306af82fd4..2a0089a148 100644 --- a/src/ring-theory/congruence-relations-semirings.lagda.md +++ b/src/ring-theory/congruence-relations-semirings.lagda.md @@ -1,32 +1,27 @@ # Congruence relations on semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.congruence-relations-semirings - (funext : function-extensionality) - where +module ring-theory.congruence-relations-semirings where ```
Imports ```agda -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext +open import foundation.equivalence-relations +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.congruence-relations-monoids funext +open import group-theory.congruence-relations-monoids -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/ring-theory/cyclic-rings.lagda.md b/src/ring-theory/cyclic-rings.lagda.md index 8f6197d570..e3b3ac6fca 100644 --- a/src/ring-theory/cyclic-rings.lagda.md +++ b/src/ring-theory/cyclic-rings.lagda.md @@ -1,44 +1,39 @@ # Cyclic rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.cyclic-rings - (funext : function-extensionality) - where +module ring-theory.cyclic-rings where ```
Imports ```agda -open import commutative-algebra.commutative-rings funext +open import commutative-algebra.commutative-rings open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext -open import elementary-number-theory.ring-of-integers funext +open import elementary-number-theory.multiplication-integers +open import elementary-number-theory.ring-of-integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.cyclic-groups funext -open import group-theory.free-groups-with-one-generator funext -open import group-theory.generating-elements-groups funext -open import group-theory.groups funext +open import group-theory.abelian-groups +open import group-theory.cyclic-groups +open import group-theory.free-groups-with-one-generator +open import group-theory.generating-elements-groups +open import group-theory.groups -open import ring-theory.integer-multiples-of-elements-rings funext -open import ring-theory.invertible-elements-rings funext -open import ring-theory.rings funext +open import ring-theory.integer-multiples-of-elements-rings +open import ring-theory.invertible-elements-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/dependent-products-rings.lagda.md b/src/ring-theory/dependent-products-rings.lagda.md index eebbea2b52..409f515003 100644 --- a/src/ring-theory/dependent-products-rings.lagda.md +++ b/src/ring-theory/dependent-products-rings.lagda.md @@ -1,31 +1,26 @@ # Dependent products of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.dependent-products-rings - (funext : function-extensionality) - where +module ring-theory.dependent-products-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.dependent-products-abelian-groups funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.dependent-products-abelian-groups +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import ring-theory.dependent-products-semirings funext -open import ring-theory.rings funext -open import ring-theory.semirings funext +open import ring-theory.dependent-products-semirings +open import ring-theory.rings +open import ring-theory.semirings ```
diff --git a/src/ring-theory/dependent-products-semirings.lagda.md b/src/ring-theory/dependent-products-semirings.lagda.md index d9d4e3cfd6..5c59c14b05 100644 --- a/src/ring-theory/dependent-products-semirings.lagda.md +++ b/src/ring-theory/dependent-products-semirings.lagda.md @@ -1,31 +1,25 @@ # Dependent products of semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.dependent-products-semirings - (funext : function-extensionality) - where +module ring-theory.dependent-products-semirings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.dependent-products-commutative-monoids funext -open import group-theory.dependent-products-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.commutative-monoids +open import group-theory.dependent-products-commutative-monoids +open import group-theory.dependent-products-monoids +open import group-theory.monoids +open import group-theory.semigroups -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/ring-theory/division-rings.lagda.md b/src/ring-theory/division-rings.lagda.md index 10dd48fd8e..fcdce2df44 100644 --- a/src/ring-theory/division-rings.lagda.md +++ b/src/ring-theory/division-rings.lagda.md @@ -1,24 +1,19 @@ # Division rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.division-rings - (funext : function-extensionality) - where +module ring-theory.division-rings where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.negated-equality funext +open import foundation.cartesian-product-types +open import foundation.negated-equality open import foundation.universe-levels -open import ring-theory.invertible-elements-rings funext -open import ring-theory.rings funext -open import ring-theory.trivial-rings funext +open import ring-theory.invertible-elements-rings +open import ring-theory.rings +open import ring-theory.trivial-rings ```
diff --git a/src/ring-theory/free-rings-with-one-generator.lagda.md b/src/ring-theory/free-rings-with-one-generator.lagda.md index 43e87dff73..4131005dfa 100644 --- a/src/ring-theory/free-rings-with-one-generator.lagda.md +++ b/src/ring-theory/free-rings-with-one-generator.lagda.md @@ -1,22 +1,17 @@ # The free ring with one generator ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.free-rings-with-one-generator - (funext : function-extensionality) - where +module ring-theory.free-rings-with-one-generator where ```
Imports ```agda -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import ring-theory.homomorphisms-rings funext -open import ring-theory.rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/full-ideals-rings.lagda.md b/src/ring-theory/full-ideals-rings.lagda.md index b6444d987d..145fc154fa 100644 --- a/src/ring-theory/full-ideals-rings.lagda.md +++ b/src/ring-theory/full-ideals-rings.lagda.md @@ -1,33 +1,28 @@ # Full ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.full-ideals-rings - (funext : function-extensionality) - where +module ring-theory.full-ideals-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.full-subtypes funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.subtypes funext +open import foundation.full-subtypes +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes open import foundation.unit-type open import foundation.universe-levels -open import order-theory.top-elements-large-posets funext +open import order-theory.top-elements-large-posets -open import ring-theory.ideals-rings funext -open import ring-theory.left-ideals-rings funext -open import ring-theory.poset-of-ideals-rings funext -open import ring-theory.right-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.ideals-rings +open import ring-theory.left-ideals-rings +open import ring-theory.poset-of-ideals-rings +open import ring-theory.right-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/function-rings.lagda.md b/src/ring-theory/function-rings.lagda.md index 7005d8a569..4a3837e0ec 100644 --- a/src/ring-theory/function-rings.lagda.md +++ b/src/ring-theory/function-rings.lagda.md @@ -1,26 +1,21 @@ # Function rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.function-rings - (funext : function-extensionality) - where +module ring-theory.function-rings where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.monoids funext +open import group-theory.abelian-groups +open import group-theory.monoids -open import ring-theory.dependent-products-rings funext -open import ring-theory.rings funext +open import ring-theory.dependent-products-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/function-semirings.lagda.md b/src/ring-theory/function-semirings.lagda.md index dbb79aa450..2aa4003612 100644 --- a/src/ring-theory/function-semirings.lagda.md +++ b/src/ring-theory/function-semirings.lagda.md @@ -1,27 +1,22 @@ # Function semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.function-semirings - (funext : function-extensionality) - where +module ring-theory.function-semirings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext +open import group-theory.commutative-monoids +open import group-theory.monoids -open import ring-theory.dependent-products-semirings funext -open import ring-theory.semirings funext +open import ring-theory.dependent-products-semirings +open import ring-theory.semirings ```
diff --git a/src/ring-theory/generating-elements-rings.lagda.md b/src/ring-theory/generating-elements-rings.lagda.md index a62fb21021..f143405f0f 100644 --- a/src/ring-theory/generating-elements-rings.lagda.md +++ b/src/ring-theory/generating-elements-rings.lagda.md @@ -1,23 +1,18 @@ # Generating elements of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.generating-elements-rings - (funext : function-extensionality) - where +module ring-theory.generating-elements-rings where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import group-theory.generating-elements-groups funext +open import group-theory.generating-elements-groups -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/ring-theory/groups-of-units-rings.lagda.md b/src/ring-theory/groups-of-units-rings.lagda.md index 6cad0e0d05..16e293804e 100644 --- a/src/ring-theory/groups-of-units-rings.lagda.md +++ b/src/ring-theory/groups-of-units-rings.lagda.md @@ -1,36 +1,31 @@ # The group of multiplicative units of a ring ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.groups-of-units-rings - (funext : function-extensionality) - where +module ring-theory.groups-of-units-rings where ```
Imports ```agda -open import category-theory.functors-large-precategories funext +open import category-theory.functors-large-precategories -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.cores-monoids funext -open import group-theory.groups funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-monoids funext -open import group-theory.monoids funext -open import group-theory.precategory-of-groups funext -open import group-theory.semigroups funext -open import group-theory.submonoids funext - -open import ring-theory.homomorphisms-rings funext -open import ring-theory.invertible-elements-rings funext -open import ring-theory.precategory-of-rings funext -open import ring-theory.rings funext +open import group-theory.cores-monoids +open import group-theory.groups +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-monoids +open import group-theory.monoids +open import group-theory.precategory-of-groups +open import group-theory.semigroups +open import group-theory.submonoids + +open import ring-theory.homomorphisms-rings +open import ring-theory.invertible-elements-rings +open import ring-theory.precategory-of-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/homomorphisms-cyclic-rings.lagda.md b/src/ring-theory/homomorphisms-cyclic-rings.lagda.md index c485279eeb..8bdb6d76cf 100644 --- a/src/ring-theory/homomorphisms-cyclic-rings.lagda.md +++ b/src/ring-theory/homomorphisms-cyclic-rings.lagda.md @@ -1,12 +1,7 @@ # Homomorphisms of cyclic rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.homomorphisms-cyclic-rings - (funext : function-extensionality) - where +module ring-theory.homomorphisms-cyclic-rings where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import ring-theory.cyclic-rings funext -open import ring-theory.homomorphisms-rings funext -open import ring-theory.integer-multiples-of-elements-rings funext -open import ring-theory.rings funext +open import ring-theory.cyclic-rings +open import ring-theory.homomorphisms-rings +open import ring-theory.integer-multiples-of-elements-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/homomorphisms-rings.lagda.md b/src/ring-theory/homomorphisms-rings.lagda.md index d9b221fdbe..95f466ea7c 100644 --- a/src/ring-theory/homomorphisms-rings.lagda.md +++ b/src/ring-theory/homomorphisms-rings.lagda.md @@ -1,37 +1,32 @@ # Homomorphisms of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.homomorphisms-rings - (funext : function-extensionality) - where +module ring-theory.homomorphisms-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.homomorphisms-commutative-monoids funext -open import group-theory.homomorphisms-groups funext -open import group-theory.homomorphisms-monoids funext +open import group-theory.homomorphisms-abelian-groups +open import group-theory.homomorphisms-commutative-monoids +open import group-theory.homomorphisms-groups +open import group-theory.homomorphisms-monoids -open import ring-theory.homomorphisms-semirings funext -open import ring-theory.invertible-elements-rings funext -open import ring-theory.rings funext +open import ring-theory.homomorphisms-semirings +open import ring-theory.invertible-elements-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/homomorphisms-semirings.lagda.md b/src/ring-theory/homomorphisms-semirings.lagda.md index cddc4bd631..9bd4acad47 100644 --- a/src/ring-theory/homomorphisms-semirings.lagda.md +++ b/src/ring-theory/homomorphisms-semirings.lagda.md @@ -1,34 +1,29 @@ # Homomorphisms of semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.homomorphisms-semirings - (funext : function-extensionality) - where +module ring-theory.homomorphisms-semirings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.homomorphisms-commutative-monoids funext -open import group-theory.homomorphisms-monoids funext -open import group-theory.homomorphisms-semigroups funext +open import group-theory.homomorphisms-commutative-monoids +open import group-theory.homomorphisms-monoids +open import group-theory.homomorphisms-semigroups -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md index 77997c7ef5..641996be99 100644 --- a/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/ideals-generated-by-subsets-rings.lagda.md @@ -1,44 +1,39 @@ # Ideals generated by subsets of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.ideals-generated-by-subsets-rings - (funext : function-extensionality) - where +module ring-theory.ideals-generated-by-subsets-rings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext +open import foundation.fibers-of-maps +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.unions-subtypes funext +open import foundation.unions-subtypes open import foundation.universe-levels -open import lists.concatenation-lists funext -open import lists.functoriality-lists funext +open import lists.concatenation-lists +open import lists.functoriality-lists open import lists.lists -open import order-theory.galois-connections-large-posets funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.reflective-galois-connections-large-posets funext +open import order-theory.galois-connections-large-posets +open import order-theory.least-upper-bounds-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.reflective-galois-connections-large-posets -open import ring-theory.ideals-rings funext -open import ring-theory.poset-of-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.ideals-rings +open import ring-theory.poset-of-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/ideals-rings.lagda.md b/src/ring-theory/ideals-rings.lagda.md index da879e3efe..74b99261c9 100644 --- a/src/ring-theory/ideals-rings.lagda.md +++ b/src/ring-theory/ideals-rings.lagda.md @@ -1,42 +1,37 @@ # Ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.ideals-rings - (funext : function-extensionality) - where +module ring-theory.ideals-rings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.binary-transport -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import group-theory.congruence-relations-abelian-groups funext -open import group-theory.congruence-relations-monoids funext -open import group-theory.subgroups-abelian-groups funext +open import group-theory.congruence-relations-abelian-groups +open import group-theory.congruence-relations-monoids +open import group-theory.subgroups-abelian-groups -open import ring-theory.congruence-relations-rings funext -open import ring-theory.left-ideals-rings funext -open import ring-theory.right-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.congruence-relations-rings +open import ring-theory.left-ideals-rings +open import ring-theory.right-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/ideals-semirings.lagda.md b/src/ring-theory/ideals-semirings.lagda.md index b88f0f16a4..801c43f0b9 100644 --- a/src/ring-theory/ideals-semirings.lagda.md +++ b/src/ring-theory/ideals-semirings.lagda.md @@ -1,27 +1,22 @@ # Ideals of semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.ideals-semirings - (funext : function-extensionality) - where +module ring-theory.ideals-semirings where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.submonoids funext +open import group-theory.submonoids -open import ring-theory.semirings funext -open import ring-theory.subsets-semirings funext +open import ring-theory.semirings +open import ring-theory.subsets-semirings ```
diff --git a/src/ring-theory/idempotent-elements-rings.lagda.md b/src/ring-theory/idempotent-elements-rings.lagda.md index a3f09dee43..3d3369a849 100644 --- a/src/ring-theory/idempotent-elements-rings.lagda.md +++ b/src/ring-theory/idempotent-elements-rings.lagda.md @@ -1,23 +1,18 @@ # Idempotent elements in rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.idempotent-elements-rings - (funext : function-extensionality) - where +module ring-theory.idempotent-elements-rings where ```
Imports ```agda -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/ring-theory/initial-rings.lagda.md b/src/ring-theory/initial-rings.lagda.md index 6673cd467e..b3287aeae7 100644 --- a/src/ring-theory/initial-rings.lagda.md +++ b/src/ring-theory/initial-rings.lagda.md @@ -1,23 +1,18 @@ # Initial rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.initial-rings - (funext : function-extensionality) - where +module ring-theory.initial-rings where ```
Imports ```agda -open import category-theory.initial-objects-large-categories funext +open import category-theory.initial-objects-large-categories open import foundation.universe-levels -open import ring-theory.category-of-rings funext -open import ring-theory.rings funext +open import ring-theory.category-of-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/integer-multiples-of-elements-rings.lagda.md b/src/ring-theory/integer-multiples-of-elements-rings.lagda.md index 3eabb4b3b0..9f66654609 100644 --- a/src/ring-theory/integer-multiples-of-elements-rings.lagda.md +++ b/src/ring-theory/integer-multiples-of-elements-rings.lagda.md @@ -1,36 +1,31 @@ # Integer multiples of elements of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.integer-multiples-of-elements-rings - (funext : function-extensionality) - where +module ring-theory.integer-multiples-of-elements-rings where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers -open import elementary-number-theory.multiplication-integers funext +open import elementary-number-theory.multiplication-integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.coproduct-types +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.integer-multiples-of-elements-abelian-groups funext +open import group-theory.homomorphisms-abelian-groups +open import group-theory.integer-multiples-of-elements-abelian-groups -open import ring-theory.commuting-elements-rings funext -open import ring-theory.homomorphisms-rings funext -open import ring-theory.multiples-of-elements-rings funext -open import ring-theory.rings funext +open import ring-theory.commuting-elements-rings +open import ring-theory.homomorphisms-rings +open import ring-theory.multiples-of-elements-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/intersections-ideals-rings.lagda.md b/src/ring-theory/intersections-ideals-rings.lagda.md index f5b1623514..4444ab8716 100644 --- a/src/ring-theory/intersections-ideals-rings.lagda.md +++ b/src/ring-theory/intersections-ideals-rings.lagda.md @@ -1,27 +1,22 @@ # Intersections of ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.intersections-ideals-rings - (funext : function-extensionality) - where +module ring-theory.intersections-ideals-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.intersections-subtypes funext +open import foundation.intersections-subtypes open import foundation.universe-levels -open import order-theory.greatest-lower-bounds-large-posets funext +open import order-theory.greatest-lower-bounds-large-posets -open import ring-theory.ideals-rings funext -open import ring-theory.poset-of-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.ideals-rings +open import ring-theory.poset-of-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/intersections-ideals-semirings.lagda.md b/src/ring-theory/intersections-ideals-semirings.lagda.md index 7d114a7e64..e263dc496c 100644 --- a/src/ring-theory/intersections-ideals-semirings.lagda.md +++ b/src/ring-theory/intersections-ideals-semirings.lagda.md @@ -1,24 +1,19 @@ # Intersections of ideals of semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.intersections-ideals-semirings - (funext : function-extensionality) - where +module ring-theory.intersections-ideals-semirings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.intersections-subtypes funext +open import foundation.intersections-subtypes open import foundation.universe-levels -open import ring-theory.ideals-semirings funext -open import ring-theory.semirings funext -open import ring-theory.subsets-semirings funext +open import ring-theory.ideals-semirings +open import ring-theory.semirings +open import ring-theory.subsets-semirings ```
diff --git a/src/ring-theory/invariant-basis-property-rings.lagda.md b/src/ring-theory/invariant-basis-property-rings.lagda.md index e9e1ad24a7..ae9972819c 100644 --- a/src/ring-theory/invariant-basis-property-rings.lagda.md +++ b/src/ring-theory/invariant-basis-property-rings.lagda.md @@ -1,12 +1,7 @@ # The invariant basis property of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.invariant-basis-property-rings - (funext : function-extensionality) - where +module ring-theory.invariant-basis-property-rings where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.dependent-products-rings funext -open import ring-theory.isomorphisms-rings funext -open import ring-theory.rings funext +open import ring-theory.dependent-products-rings +open import ring-theory.isomorphisms-rings +open import ring-theory.rings -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/ring-theory/invertible-elements-rings.lagda.md b/src/ring-theory/invertible-elements-rings.lagda.md index 79b6a7de9b..5066846791 100644 --- a/src/ring-theory/invertible-elements-rings.lagda.md +++ b/src/ring-theory/invertible-elements-rings.lagda.md @@ -1,32 +1,27 @@ # Invertible elements in rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.invertible-elements-rings - (funext : function-extensionality) - where +module ring-theory.invertible-elements-rings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.contractible-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import group-theory.invertible-elements-monoids funext +open import group-theory.invertible-elements-monoids -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/ring-theory/isomorphisms-rings.lagda.md b/src/ring-theory/isomorphisms-rings.lagda.md index 1ee1eff325..9ca0051cd9 100644 --- a/src/ring-theory/isomorphisms-rings.lagda.md +++ b/src/ring-theory/isomorphisms-rings.lagda.md @@ -1,53 +1,48 @@ # Isomorphisms of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.isomorphisms-rings - (funext : function-extensionality) - where +module ring-theory.isomorphisms-rings where ```
Imports ```agda -open import category-theory.isomorphisms-in-large-precategories funext +open import category-theory.isomorphisms-in-large-precategories open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.implicit-function-types -open import foundation.iterated-dependent-product-types funext -open import foundation.multivariable-homotopies funext -open import foundation.propositions funext +open import foundation.iterated-dependent-product-types +open import foundation.multivariable-homotopies +open import foundation.propositions open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.subtypes funext +open import foundation.subtypes open import foundation.telescopes -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.homomorphisms-abelian-groups funext -open import group-theory.homomorphisms-monoids funext -open import group-theory.isomorphisms-abelian-groups funext -open import group-theory.isomorphisms-monoids funext +open import group-theory.homomorphisms-abelian-groups +open import group-theory.homomorphisms-monoids +open import group-theory.isomorphisms-abelian-groups +open import group-theory.isomorphisms-monoids -open import ring-theory.homomorphisms-rings funext -open import ring-theory.invertible-elements-rings funext -open import ring-theory.precategory-of-rings funext -open import ring-theory.rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.invertible-elements-rings +open import ring-theory.precategory-of-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/joins-ideals-rings.lagda.md b/src/ring-theory/joins-ideals-rings.lagda.md index a0d2643a44..cefa31e7f4 100644 --- a/src/ring-theory/joins-ideals-rings.lagda.md +++ b/src/ring-theory/joins-ideals-rings.lagda.md @@ -1,31 +1,26 @@ # Joins of ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.joins-ideals-rings - (funext : function-extensionality) - where +module ring-theory.joins-ideals-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.unions-subtypes funext +open import foundation.identity-types +open import foundation.unions-subtypes open import foundation.universe-levels -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.similarity-of-elements-large-posets -open import ring-theory.ideals-generated-by-subsets-rings funext -open import ring-theory.ideals-rings funext -open import ring-theory.poset-of-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.ideals-generated-by-subsets-rings +open import ring-theory.ideals-rings +open import ring-theory.poset-of-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/joins-left-ideals-rings.lagda.md b/src/ring-theory/joins-left-ideals-rings.lagda.md index 9cfb2c802b..9b93c7d3c5 100644 --- a/src/ring-theory/joins-left-ideals-rings.lagda.md +++ b/src/ring-theory/joins-left-ideals-rings.lagda.md @@ -1,31 +1,26 @@ # Joins of left ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.joins-left-ideals-rings - (funext : function-extensionality) - where +module ring-theory.joins-left-ideals-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.unions-subtypes funext +open import foundation.identity-types +open import foundation.unions-subtypes open import foundation.universe-levels -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.similarity-of-elements-large-posets -open import ring-theory.left-ideals-generated-by-subsets-rings funext -open import ring-theory.left-ideals-rings funext -open import ring-theory.poset-of-left-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.left-ideals-generated-by-subsets-rings +open import ring-theory.left-ideals-rings +open import ring-theory.poset-of-left-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/joins-right-ideals-rings.lagda.md b/src/ring-theory/joins-right-ideals-rings.lagda.md index 1c02382c76..f1ce158230 100644 --- a/src/ring-theory/joins-right-ideals-rings.lagda.md +++ b/src/ring-theory/joins-right-ideals-rings.lagda.md @@ -1,31 +1,26 @@ # Joins of right ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.joins-right-ideals-rings - (funext : function-extensionality) - where +module ring-theory.joins-right-ideals-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.unions-subtypes funext +open import foundation.identity-types +open import foundation.unions-subtypes open import foundation.universe-levels -open import order-theory.large-suplattices funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-suplattices +open import order-theory.least-upper-bounds-large-posets +open import order-theory.similarity-of-elements-large-posets -open import ring-theory.poset-of-right-ideals-rings funext -open import ring-theory.right-ideals-generated-by-subsets-rings funext -open import ring-theory.right-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.poset-of-right-ideals-rings +open import ring-theory.right-ideals-generated-by-subsets-rings +open import ring-theory.right-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md b/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md index 7802312942..905d2411ee 100644 --- a/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md +++ b/src/ring-theory/kernels-of-ring-homomorphisms.lagda.md @@ -1,12 +1,7 @@ # Kernels of ring homomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.kernels-of-ring-homomorphisms - (funext : function-extensionality) - where +module ring-theory.kernels-of-ring-homomorphisms where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.kernels-homomorphisms-groups funext -open import group-theory.subgroups-abelian-groups funext +open import group-theory.kernels-homomorphisms-groups +open import group-theory.subgroups-abelian-groups -open import ring-theory.homomorphisms-rings funext -open import ring-theory.ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md index ea7458694a..45001b74cb 100644 --- a/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md @@ -1,46 +1,41 @@ # Left ideals generated by subsets of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.left-ideals-generated-by-subsets-rings - (funext : function-extensionality) - where +module ring-theory.left-ideals-generated-by-subsets-rings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.unions-subtypes funext +open import foundation.unions-subtypes open import foundation.universe-levels -open import lists.concatenation-lists funext -open import lists.functoriality-lists funext +open import lists.concatenation-lists +open import lists.functoriality-lists open import lists.lists -open import order-theory.galois-connections-large-posets funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.reflective-galois-connections-large-posets funext +open import order-theory.galois-connections-large-posets +open import order-theory.least-upper-bounds-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.reflective-galois-connections-large-posets -open import ring-theory.left-ideals-rings funext -open import ring-theory.poset-of-left-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.left-ideals-rings +open import ring-theory.poset-of-left-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/left-ideals-rings.lagda.md b/src/ring-theory/left-ideals-rings.lagda.md index dd924a061a..c0d2710a89 100644 --- a/src/ring-theory/left-ideals-rings.lagda.md +++ b/src/ring-theory/left-ideals-rings.lagda.md @@ -1,30 +1,25 @@ # Left ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.left-ideals-rings - (funext : function-extensionality) - where +module ring-theory.left-ideals-rings where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/local-rings.lagda.md b/src/ring-theory/local-rings.lagda.md index dbf1bb60da..6ec65472c7 100644 --- a/src/ring-theory/local-rings.lagda.md +++ b/src/ring-theory/local-rings.lagda.md @@ -1,25 +1,20 @@ # Local rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.local-rings - (funext : function-extensionality) - where +module ring-theory.local-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.disjunction +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import ring-theory.invertible-elements-rings funext -open import ring-theory.rings funext +open import ring-theory.invertible-elements-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/localizations-rings.lagda.md b/src/ring-theory/localizations-rings.lagda.md index 2a82dcf8f3..0c3aeb511a 100644 --- a/src/ring-theory/localizations-rings.lagda.md +++ b/src/ring-theory/localizations-rings.lagda.md @@ -1,33 +1,28 @@ # Localizations of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.localizations-rings - (funext : function-extensionality) - where +module ring-theory.localizations-rings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import ring-theory.homomorphisms-rings funext -open import ring-theory.invertible-elements-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.invertible-elements-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/modules-rings.lagda.md b/src/ring-theory/modules-rings.lagda.md index 430896e153..dd09b187e4 100644 --- a/src/ring-theory/modules-rings.lagda.md +++ b/src/ring-theory/modules-rings.lagda.md @@ -1,30 +1,25 @@ # Modules over rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.modules-rings - (funext : function-extensionality) - where +module ring-theory.modules-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.addition-homomorphisms-abelian-groups funext -open import group-theory.endomorphism-rings-abelian-groups funext -open import group-theory.homomorphisms-abelian-groups funext +open import group-theory.abelian-groups +open import group-theory.addition-homomorphisms-abelian-groups +open import group-theory.endomorphism-rings-abelian-groups +open import group-theory.homomorphisms-abelian-groups -open import ring-theory.homomorphisms-rings funext -open import ring-theory.opposite-rings funext -open import ring-theory.rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.opposite-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/multiples-of-elements-rings.lagda.md b/src/ring-theory/multiples-of-elements-rings.lagda.md index 20a8f02d82..f0bf36215a 100644 --- a/src/ring-theory/multiples-of-elements-rings.lagda.md +++ b/src/ring-theory/multiples-of-elements-rings.lagda.md @@ -1,12 +1,7 @@ # Multiples of elements in rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.multiples-of-elements-rings - (funext : function-extensionality) - where +module ring-theory.multiples-of-elements-rings where ```
Imports @@ -16,13 +11,13 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.multiples-of-elements-abelian-groups funext +open import group-theory.multiples-of-elements-abelian-groups -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/ring-theory/nil-ideals-rings.lagda.md b/src/ring-theory/nil-ideals-rings.lagda.md index 06662923ea..22688c8e4c 100644 --- a/src/ring-theory/nil-ideals-rings.lagda.md +++ b/src/ring-theory/nil-ideals-rings.lagda.md @@ -1,25 +1,20 @@ # Nil ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.nil-ideals-rings - (funext : function-extensionality) - where +module ring-theory.nil-ideals-rings where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import ring-theory.ideals-rings funext -open import ring-theory.left-ideals-rings funext -open import ring-theory.nilpotent-elements-rings funext -open import ring-theory.right-ideals-rings funext -open import ring-theory.rings funext +open import ring-theory.ideals-rings +open import ring-theory.left-ideals-rings +open import ring-theory.nilpotent-elements-rings +open import ring-theory.right-ideals-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/nilpotent-elements-rings.lagda.md b/src/ring-theory/nilpotent-elements-rings.lagda.md index 39b2ac18c8..96f8512935 100644 --- a/src/ring-theory/nilpotent-elements-rings.lagda.md +++ b/src/ring-theory/nilpotent-elements-rings.lagda.md @@ -1,12 +1,7 @@ # Nilpotent elements in rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.nilpotent-elements-rings - (funext : function-extensionality) - where +module ring-theory.nilpotent-elements-rings where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.universe-levels -open import ring-theory.nilpotent-elements-semirings funext -open import ring-theory.powers-of-elements-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.nilpotent-elements-semirings +open import ring-theory.powers-of-elements-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/nilpotent-elements-semirings.lagda.md b/src/ring-theory/nilpotent-elements-semirings.lagda.md index e3895705f5..434bdf7fb8 100644 --- a/src/ring-theory/nilpotent-elements-semirings.lagda.md +++ b/src/ring-theory/nilpotent-elements-semirings.lagda.md @@ -1,12 +1,7 @@ # Nilpotent elements in semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.nilpotent-elements-semirings - (funext : function-extensionality) - where +module ring-theory.nilpotent-elements-semirings where ```
Imports @@ -17,16 +12,16 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import ring-theory.binomial-theorem-semirings funext -open import ring-theory.powers-of-elements-semirings funext -open import ring-theory.semirings funext +open import ring-theory.binomial-theorem-semirings +open import ring-theory.powers-of-elements-semirings +open import ring-theory.semirings ```
diff --git a/src/ring-theory/opposite-rings.lagda.md b/src/ring-theory/opposite-rings.lagda.md index 7d6540b83b..824b49515c 100644 --- a/src/ring-theory/opposite-rings.lagda.md +++ b/src/ring-theory/opposite-rings.lagda.md @@ -1,22 +1,17 @@ # Opposite rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.opposite-rings - (funext : function-extensionality) - where +module ring-theory.opposite-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/ring-theory/poset-of-cyclic-rings.lagda.md b/src/ring-theory/poset-of-cyclic-rings.lagda.md index 4bda70c7f1..ef3023bcd0 100644 --- a/src/ring-theory/poset-of-cyclic-rings.lagda.md +++ b/src/ring-theory/poset-of-cyclic-rings.lagda.md @@ -1,12 +1,7 @@ # The poset of cyclic rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.poset-of-cyclic-rings - (funext : function-extensionality) - where +module ring-theory.poset-of-cyclic-rings where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.universe-levels -open import order-theory.large-posets funext +open import order-theory.large-posets -open import ring-theory.category-of-cyclic-rings funext +open import ring-theory.category-of-cyclic-rings ```
diff --git a/src/ring-theory/poset-of-ideals-rings.lagda.md b/src/ring-theory/poset-of-ideals-rings.lagda.md index b5fc9b2f77..7ac68be10d 100644 --- a/src/ring-theory/poset-of-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-ideals-rings.lagda.md @@ -1,33 +1,28 @@ # The poset of ideals of a ring ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.poset-of-ideals-rings - (funext : function-extensionality) - where +module ring-theory.poset-of-ideals-rings where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.powersets funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.powersets +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.similarity-of-elements-large-posets -open import ring-theory.ideals-rings funext -open import ring-theory.rings funext +open import ring-theory.ideals-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/poset-of-left-ideals-rings.lagda.md b/src/ring-theory/poset-of-left-ideals-rings.lagda.md index 885b1c7e7a..a34d3bad4a 100644 --- a/src/ring-theory/poset-of-left-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-left-ideals-rings.lagda.md @@ -1,33 +1,28 @@ # The poset of left ideals of a ring ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.poset-of-left-ideals-rings - (funext : function-extensionality) - where +module ring-theory.poset-of-left-ideals-rings where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.powersets funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.powersets +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.similarity-of-elements-large-posets -open import ring-theory.left-ideals-rings funext -open import ring-theory.rings funext +open import ring-theory.left-ideals-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/poset-of-right-ideals-rings.lagda.md b/src/ring-theory/poset-of-right-ideals-rings.lagda.md index 04854226db..9ddb7754b7 100644 --- a/src/ring-theory/poset-of-right-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-right-ideals-rings.lagda.md @@ -1,33 +1,28 @@ # The poset of right ideals of a ring ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.poset-of-right-ideals-rings - (funext : function-extensionality) - where +module ring-theory.poset-of-right-ideals-rings where ```
Imports ```agda -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.powersets funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.powersets +open import foundation.propositions +open import foundation.subtypes open import foundation.universe-levels -open import order-theory.large-posets funext -open import order-theory.large-preorders funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.similarity-of-elements-large-posets funext +open import order-theory.large-posets +open import order-theory.large-preorders +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.similarity-of-elements-large-posets -open import ring-theory.right-ideals-rings funext -open import ring-theory.rings funext +open import ring-theory.right-ideals-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/powers-of-elements-rings.lagda.md b/src/ring-theory/powers-of-elements-rings.lagda.md index 452f666b71..e7a4956cc4 100644 --- a/src/ring-theory/powers-of-elements-rings.lagda.md +++ b/src/ring-theory/powers-of-elements-rings.lagda.md @@ -1,12 +1,7 @@ # Powers of elements in rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.powers-of-elements-rings - (funext : function-extensionality) - where +module ring-theory.powers-of-elements-rings where ```
Imports @@ -15,17 +10,17 @@ module open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.parity-natural-numbers funext +open import elementary-number-theory.parity-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.empty-types funext -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.central-elements-rings funext -open import ring-theory.powers-of-elements-semirings funext -open import ring-theory.rings funext +open import ring-theory.central-elements-rings +open import ring-theory.powers-of-elements-semirings +open import ring-theory.rings ```
diff --git a/src/ring-theory/powers-of-elements-semirings.lagda.md b/src/ring-theory/powers-of-elements-semirings.lagda.md index 40ff6b2692..ca2f29b47c 100644 --- a/src/ring-theory/powers-of-elements-semirings.lagda.md +++ b/src/ring-theory/powers-of-elements-semirings.lagda.md @@ -1,12 +1,7 @@ # Powers of elements in semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.powers-of-elements-semirings - (funext : function-extensionality) - where +module ring-theory.powers-of-elements-semirings where ```
Imports @@ -16,12 +11,12 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.powers-of-elements-monoids funext +open import group-theory.powers-of-elements-monoids -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/ring-theory/precategory-of-rings.lagda.md b/src/ring-theory/precategory-of-rings.lagda.md index e7e15052ef..e22cb72547 100644 --- a/src/ring-theory/precategory-of-rings.lagda.md +++ b/src/ring-theory/precategory-of-rings.lagda.md @@ -1,24 +1,19 @@ # The precategory of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.precategory-of-rings - (funext : function-extensionality) - where +module ring-theory.precategory-of-rings where ```
Imports ```agda -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import ring-theory.homomorphisms-rings funext -open import ring-theory.rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/precategory-of-semirings.lagda.md b/src/ring-theory/precategory-of-semirings.lagda.md index b23ef29f64..8b84a0d3e0 100644 --- a/src/ring-theory/precategory-of-semirings.lagda.md +++ b/src/ring-theory/precategory-of-semirings.lagda.md @@ -1,24 +1,19 @@ # The precategory of semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.precategory-of-semirings - (funext : function-extensionality) - where +module ring-theory.precategory-of-semirings where ```
Imports ```agda -open import category-theory.large-precategories funext -open import category-theory.precategories funext +open import category-theory.large-precategories +open import category-theory.precategories open import foundation.universe-levels -open import ring-theory.homomorphisms-semirings funext -open import ring-theory.semirings funext +open import ring-theory.homomorphisms-semirings +open import ring-theory.semirings ```
diff --git a/src/ring-theory/products-ideals-rings.lagda.md b/src/ring-theory/products-ideals-rings.lagda.md index 6ea7eea658..73cb6e9253 100644 --- a/src/ring-theory/products-ideals-rings.lagda.md +++ b/src/ring-theory/products-ideals-rings.lagda.md @@ -1,28 +1,23 @@ # Products of ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.products-ideals-rings - (funext : function-extensionality) - where +module ring-theory.products-ideals-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels -open import ring-theory.ideals-generated-by-subsets-rings funext -open import ring-theory.ideals-rings funext -open import ring-theory.poset-of-ideals-rings funext -open import ring-theory.products-subsets-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.ideals-generated-by-subsets-rings +open import ring-theory.ideals-rings +open import ring-theory.poset-of-ideals-rings +open import ring-theory.products-subsets-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/products-left-ideals-rings.lagda.md b/src/ring-theory/products-left-ideals-rings.lagda.md index e9f4ece37a..553c0eacf9 100644 --- a/src/ring-theory/products-left-ideals-rings.lagda.md +++ b/src/ring-theory/products-left-ideals-rings.lagda.md @@ -1,28 +1,23 @@ # Products of left ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.products-left-ideals-rings - (funext : function-extensionality) - where +module ring-theory.products-left-ideals-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels -open import ring-theory.left-ideals-generated-by-subsets-rings funext -open import ring-theory.left-ideals-rings funext -open import ring-theory.poset-of-left-ideals-rings funext -open import ring-theory.products-subsets-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.left-ideals-generated-by-subsets-rings +open import ring-theory.left-ideals-rings +open import ring-theory.poset-of-left-ideals-rings +open import ring-theory.products-subsets-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/products-right-ideals-rings.lagda.md b/src/ring-theory/products-right-ideals-rings.lagda.md index 4cbb7bca31..22cf1b4cfe 100644 --- a/src/ring-theory/products-right-ideals-rings.lagda.md +++ b/src/ring-theory/products-right-ideals-rings.lagda.md @@ -1,28 +1,23 @@ # Products of right ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.products-right-ideals-rings - (funext : function-extensionality) - where +module ring-theory.products-right-ideals-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels -open import ring-theory.poset-of-right-ideals-rings funext -open import ring-theory.products-subsets-rings funext -open import ring-theory.right-ideals-generated-by-subsets-rings funext -open import ring-theory.right-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.poset-of-right-ideals-rings +open import ring-theory.products-subsets-rings +open import ring-theory.right-ideals-generated-by-subsets-rings +open import ring-theory.right-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/products-rings.lagda.md b/src/ring-theory/products-rings.lagda.md index 29e2312b8b..fcebad162a 100644 --- a/src/ring-theory/products-rings.lagda.md +++ b/src/ring-theory/products-rings.lagda.md @@ -1,12 +1,7 @@ # Products of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.products-rings - (funext : function-extensionality) - where +module ring-theory.products-rings where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.groups +open import group-theory.semigroups -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/ring-theory/products-subsets-rings.lagda.md b/src/ring-theory/products-subsets-rings.lagda.md index dfeb1ae9a1..157d8910ef 100644 --- a/src/ring-theory/products-subsets-rings.lagda.md +++ b/src/ring-theory/products-subsets-rings.lagda.md @@ -1,26 +1,21 @@ # Products of subsets of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.products-subsets-rings - (funext : function-extensionality) - where +module ring-theory.products-subsets-rings where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext -open import foundation.unions-subtypes funext +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.subtypes +open import foundation.unions-subtypes open import foundation.universe-levels -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/quotient-rings.lagda.md b/src/ring-theory/quotient-rings.lagda.md index 4554e40a56..cf3fdbe28f 100644 --- a/src/ring-theory/quotient-rings.lagda.md +++ b/src/ring-theory/quotient-rings.lagda.md @@ -1,12 +1,7 @@ # Quotient rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.quotient-rings - (funext : function-extensionality) - where +module ring-theory.quotient-rings where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import ring-theory.homomorphisms-rings funext -open import ring-theory.ideals-rings funext -open import ring-theory.rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.ideals-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/radical-ideals-rings.lagda.md b/src/ring-theory/radical-ideals-rings.lagda.md index 894236432b..964017ee37 100644 --- a/src/ring-theory/radical-ideals-rings.lagda.md +++ b/src/ring-theory/radical-ideals-rings.lagda.md @@ -1,23 +1,18 @@ # Radical ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.radical-ideals-rings - (funext : function-extensionality) - where +module ring-theory.radical-ideals-rings where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import ring-theory.ideals-rings funext -open import ring-theory.invertible-elements-rings funext -open import ring-theory.rings funext +open import ring-theory.ideals-rings +open import ring-theory.invertible-elements-rings +open import ring-theory.rings ```
diff --git a/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md index 03e141f826..ec913d21e3 100644 --- a/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md @@ -1,46 +1,41 @@ # Right ideals generated by subsets of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.right-ideals-generated-by-subsets-rings - (funext : function-extensionality) - where +module ring-theory.right-ideals-generated-by-subsets-rings where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.powersets funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.powersets +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.unions-subtypes funext +open import foundation.unions-subtypes open import foundation.universe-levels -open import lists.concatenation-lists funext -open import lists.functoriality-lists funext +open import lists.concatenation-lists +open import lists.functoriality-lists open import lists.lists -open import order-theory.galois-connections-large-posets funext -open import order-theory.least-upper-bounds-large-posets funext -open import order-theory.order-preserving-maps-large-posets funext -open import order-theory.order-preserving-maps-large-preorders funext -open import order-theory.reflective-galois-connections-large-posets funext +open import order-theory.galois-connections-large-posets +open import order-theory.least-upper-bounds-large-posets +open import order-theory.order-preserving-maps-large-posets +open import order-theory.order-preserving-maps-large-preorders +open import order-theory.reflective-galois-connections-large-posets -open import ring-theory.poset-of-right-ideals-rings funext -open import ring-theory.right-ideals-rings funext -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.poset-of-right-ideals-rings +open import ring-theory.right-ideals-rings +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/right-ideals-rings.lagda.md b/src/ring-theory/right-ideals-rings.lagda.md index d564389a3c..1da87674fc 100644 --- a/src/ring-theory/right-ideals-rings.lagda.md +++ b/src/ring-theory/right-ideals-rings.lagda.md @@ -1,30 +1,25 @@ # Right ideals of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.right-ideals-rings - (funext : function-extensionality) - where +module ring-theory.right-ideals-rings where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.universe-levels -open import ring-theory.rings funext -open import ring-theory.subsets-rings funext +open import ring-theory.rings +open import ring-theory.subsets-rings ```
diff --git a/src/ring-theory/rings.lagda.md b/src/ring-theory/rings.lagda.md index 29ba5a4d4d..757f7994ee 100644 --- a/src/ring-theory/rings.lagda.md +++ b/src/ring-theory/rings.lagda.md @@ -1,12 +1,7 @@ # Rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.rings - (funext : function-extensionality) - where +module ring-theory.rings where ```
Imports @@ -17,33 +12,33 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-embeddings funext +open import foundation.binary-embeddings open import foundation.binary-equivalences -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.involutions funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.involutions +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.commutative-monoids funext -open import group-theory.groups funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.commutative-monoids +open import group-theory.groups +open import group-theory.monoids +open import group-theory.semigroups -open import lists.concatenation-lists funext +open import lists.concatenation-lists open import lists.lists -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/ring-theory/semirings.lagda.md b/src/ring-theory/semirings.lagda.md index ba4782e20c..982869d8d3 100644 --- a/src/ring-theory/semirings.lagda.md +++ b/src/ring-theory/semirings.lagda.md @@ -1,12 +1,7 @@ # Semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.semirings - (funext : function-extensionality) - where +module ring-theory.semirings where ```
Imports @@ -17,18 +12,18 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.commutative-monoids funext -open import group-theory.monoids funext -open import group-theory.semigroups funext +open import group-theory.commutative-monoids +open import group-theory.monoids +open import group-theory.semigroups ```
diff --git a/src/ring-theory/subsets-rings.lagda.md b/src/ring-theory/subsets-rings.lagda.md index 0a31ce5a5b..df9a3f2c84 100644 --- a/src/ring-theory/subsets-rings.lagda.md +++ b/src/ring-theory/subsets-rings.lagda.md @@ -1,27 +1,22 @@ # Subsets of rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.subsets-rings - (funext : function-extensionality) - where +module ring-theory.subsets-rings where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.propositional-extensionality funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositional-extensionality +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import group-theory.subgroups-abelian-groups funext +open import group-theory.subgroups-abelian-groups -open import ring-theory.rings funext +open import ring-theory.rings ```
diff --git a/src/ring-theory/subsets-semirings.lagda.md b/src/ring-theory/subsets-semirings.lagda.md index ea24d6e52f..0236a79809 100644 --- a/src/ring-theory/subsets-semirings.lagda.md +++ b/src/ring-theory/subsets-semirings.lagda.md @@ -1,25 +1,20 @@ # Subsets of semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.subsets-semirings - (funext : function-extensionality) - where +module ring-theory.subsets-semirings where ```
Imports ```agda -open import foundation.identity-types funext -open import foundation.propositional-extensionality funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositional-extensionality +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels -open import ring-theory.semirings funext +open import ring-theory.semirings ```
diff --git a/src/ring-theory/sums-rings.lagda.md b/src/ring-theory/sums-rings.lagda.md index eeb6852f08..f2f5859aa9 100644 --- a/src/ring-theory/sums-rings.lagda.md +++ b/src/ring-theory/sums-rings.lagda.md @@ -1,12 +1,7 @@ # Sums of elements in rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.sums-rings - (funext : function-extensionality) - where +module ring-theory.sums-rings where ```
Imports @@ -15,19 +10,19 @@ module open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.vectors funext -open import linear-algebra.vectors funext-on-rings +open import linear-algebra.vectors +open import linear-algebra.vectors-on-rings -open import ring-theory.rings funext -open import ring-theory.sums-semirings funext +open import ring-theory.rings +open import ring-theory.sums-semirings -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/ring-theory/sums-semirings.lagda.md b/src/ring-theory/sums-semirings.lagda.md index dc618859b3..3f42f0a446 100644 --- a/src/ring-theory/sums-semirings.lagda.md +++ b/src/ring-theory/sums-semirings.lagda.md @@ -1,12 +1,7 @@ # Sums of elements in semirings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.sums-semirings - (funext : function-extensionality) - where +module ring-theory.sums-semirings where ```
Imports @@ -16,21 +11,21 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.coproduct-types +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import linear-algebra.vectors funext -open import linear-algebra.vectors funext-on-semirings +open import linear-algebra.vectors +open import linear-algebra.vectors-on-semirings -open import ring-theory.semirings funext +open import ring-theory.semirings -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md b/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md index db394a93e7..d69f003772 100644 --- a/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md +++ b/src/ring-theory/transporting-ring-structure-along-isomorphisms-abelian-groups.lagda.md @@ -11,17 +11,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import group-theory.abelian-groups funext -open import group-theory.isomorphisms-abelian-groups funext -open import group-theory.semigroups funext +open import group-theory.abelian-groups +open import group-theory.isomorphisms-abelian-groups +open import group-theory.semigroups -open import ring-theory.homomorphisms-rings funext -open import ring-theory.isomorphisms-rings funext -open import ring-theory.rings funext +open import ring-theory.homomorphisms-rings +open import ring-theory.isomorphisms-rings +open import ring-theory.rings ```
@@ -44,12 +44,7 @@ transported ring structure. ### Transporting the multiplicative structure of a ring along an isomorphism of abelian groups ```agda -open import foundation.function-extensionality-axiom - -module - _ - (funext : function-extensionality) - where +module _ {l1 l2 : Level} (R : Ring l1) (A : Ab l2) (f : iso-Ab (ab-Ring R) A) where diff --git a/src/ring-theory/trivial-rings.lagda.md b/src/ring-theory/trivial-rings.lagda.md index c0b8c06b3d..4173514622 100644 --- a/src/ring-theory/trivial-rings.lagda.md +++ b/src/ring-theory/trivial-rings.lagda.md @@ -1,12 +1,7 @@ # Trivial rings ```agda -open import foundation.function-extensionality-axiom - -module - ring-theory.trivial-rings - (funext : function-extensionality) - where +module ring-theory.trivial-rings where ```
Imports @@ -14,17 +9,17 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import ring-theory.invertible-elements-rings funext -open import ring-theory.rings funext +open import ring-theory.invertible-elements-rings +open import ring-theory.rings ```
diff --git a/src/set-theory.lagda.md b/src/set-theory.lagda.md index 17685338a6..054f1135dc 100644 --- a/src/set-theory.lagda.md +++ b/src/set-theory.lagda.md @@ -42,22 +42,17 @@ theory, and [Russell's paradox](set-theory.russells-paradox.md). ## Modules in the set theory namespace ```agda -open import foundation.function-extensionality-axiom - -module - set-theory - (funext : function-extensionality) - where - -open import set-theory.baire-space funext public -open import set-theory.cantor-space funext public -open import set-theory.cantors-diagonal-argument funext public -open import set-theory.cardinalities funext public -open import set-theory.countable-sets funext public -open import set-theory.cumulative-hierarchy funext public -open import set-theory.infinite-sets funext public -open import set-theory.russells-paradox funext public -open import set-theory.uncountable-sets funext public +module set-theory where + +open import set-theory.baire-space public +open import set-theory.cantor-space public +open import set-theory.cantors-diagonal-argument public +open import set-theory.cardinalities public +open import set-theory.countable-sets public +open import set-theory.cumulative-hierarchy public +open import set-theory.infinite-sets public +open import set-theory.russells-paradox public +open import set-theory.uncountable-sets public ``` ## References diff --git a/src/set-theory/baire-space.lagda.md b/src/set-theory/baire-space.lagda.md index c261f2ca38..884e7587bd 100644 --- a/src/set-theory/baire-space.lagda.md +++ b/src/set-theory/baire-space.lagda.md @@ -1,34 +1,29 @@ # Baire space ```agda -open import foundation.function-extensionality-axiom - -module - set-theory.baire-space - (funext : function-extensionality) - where +module set-theory.baire-space where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.lawveres-fixed-point-theorem funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.lawveres-fixed-point-theorem +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.sets open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.identity-types -open import set-theory.cantors-diagonal-argument funext -open import set-theory.countable-sets funext -open import set-theory.uncountable-sets funext +open import set-theory.cantors-diagonal-argument +open import set-theory.countable-sets +open import set-theory.uncountable-sets ```
diff --git a/src/set-theory/cantor-space.lagda.md b/src/set-theory/cantor-space.lagda.md index 26a7b5356d..41ea6e9e47 100644 --- a/src/set-theory/cantor-space.lagda.md +++ b/src/set-theory/cantor-space.lagda.md @@ -1,12 +1,7 @@ # Cantor space ```agda -open import foundation.function-extensionality-axiom - -module - set-theory.cantor-space - (funext : function-extensionality) - where +module set-theory.cantor-space where ```
Imports @@ -14,24 +9,24 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.booleans funext -open import foundation.coproduct-types funext +open import foundation.booleans +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.lawveres-fixed-point-theorem funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.sets funext -open import foundation.tight-apartness-relations funext +open import foundation.empty-types +open import foundation.lawveres-fixed-point-theorem +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.sets +open import foundation.tight-apartness-relations open import foundation.unit-type open import foundation.universe-levels -open import set-theory.cantors-diagonal-argument funext -open import set-theory.countable-sets funext -open import set-theory.uncountable-sets funext +open import set-theory.cantors-diagonal-argument +open import set-theory.countable-sets +open import set-theory.uncountable-sets -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/set-theory/cantors-diagonal-argument.lagda.md b/src/set-theory/cantors-diagonal-argument.lagda.md index 4907c2ed28..1ff1284a90 100644 --- a/src/set-theory/cantors-diagonal-argument.lagda.md +++ b/src/set-theory/cantors-diagonal-argument.lagda.md @@ -1,12 +1,7 @@ # Cantor's diagonal argument ```agda -open import foundation.function-extensionality-axiom - -module - set-theory.cantors-diagonal-argument - (funext : function-extensionality) - where +module set-theory.cantors-diagonal-argument where ```
Imports @@ -15,24 +10,25 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.discrete-types funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.sets funext -open import foundation.surjective-maps funext +open import foundation.discrete-types +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.sets +open import foundation.surjective-maps open import foundation.universe-levels open import foundation-core.empty-types open import foundation-core.fibers-of-maps open import foundation-core.propositions -open import set-theory.countable-sets funext -open import set-theory.uncountable-sets funext +open import set-theory.countable-sets +open import set-theory.uncountable-sets ```
diff --git a/src/set-theory/cardinalities.lagda.md b/src/set-theory/cardinalities.lagda.md index 8a21df98be..27c781d4cc 100644 --- a/src/set-theory/cardinalities.lagda.md +++ b/src/set-theory/cardinalities.lagda.md @@ -1,29 +1,25 @@ # Cardinalities of sets ```agda -open import foundation.function-extensionality-axiom - -module - set-theory.cardinalities - (funext : function-extensionality) - where +module set-theory.cardinalities where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.identity-types funext -open import foundation.large-binary-relations funext -open import foundation.law-of-excluded-middle funext -open import foundation.mere-embeddings funext -open import foundation.mere-equivalences funext -open import foundation.propositional-extensionality funext -open import foundation.propositions funext -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.functoriality-propositional-truncation +open import foundation.identity-types +open import foundation.large-binary-relations +open import foundation.law-of-excluded-middle +open import foundation.mere-embeddings +open import foundation.mere-equivalences +open import foundation.propositional-extensionality +open import foundation.propositions +open import foundation.set-truncations +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/set-theory/countable-sets.lagda.md b/src/set-theory/countable-sets.lagda.md index f6bc29f075..ab92a803d5 100644 --- a/src/set-theory/countable-sets.lagda.md +++ b/src/set-theory/countable-sets.lagda.md @@ -1,46 +1,41 @@ # Countable sets ```agda -open import foundation.function-extensionality-axiom - -module - set-theory.countable-sets - (funext : function-extensionality) - where +module set-theory.countable-sets where ```
Imports ```agda -open import elementary-number-theory.equality-integers funext -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-integers +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.type-arithmetic-natural-numbers funext +open import elementary-number-theory.type-arithmetic-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-subtypes funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-subtypes +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-coproduct-types funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.maybe funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.retracts-of-types funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equality-coproduct-types +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.maybe +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.retracts-of-types +open import foundation.sets open import foundation.shifting-sequences -open import foundation.surjective-maps funext +open import foundation.surjective-maps open import foundation.unit-type open import foundation.universe-levels @@ -48,7 +43,7 @@ open import foundation-core.cartesian-product-types open import foundation-core.fibers-of-maps open import foundation-core.identity-types -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/set-theory/cumulative-hierarchy.lagda.md b/src/set-theory/cumulative-hierarchy.lagda.md index bb385bf185..baa1ddad21 100644 --- a/src/set-theory/cumulative-hierarchy.lagda.md +++ b/src/set-theory/cumulative-hierarchy.lagda.md @@ -1,12 +1,7 @@ # Cumulative hierarchy ```agda -open import foundation.function-extensionality-axiom - -module - set-theory.cumulative-hierarchy - (funext : function-extensionality) - where +module set-theory.cumulative-hierarchy where ```
Imports @@ -15,27 +10,27 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.booleans funext -open import foundation.cartesian-product-types funext -open import foundation.constant-type-families funext -open import foundation.coproduct-types funext +open import foundation.booleans +open import foundation.cartesian-product-types +open import foundation.constant-type-families +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-booleans -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-propositional-truncation +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositional-extensionality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-booleans +open import foundation.raising-universe-levels-unit-type +open import foundation.sets open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.unit-type open import foundation.universe-levels ``` diff --git a/src/set-theory/infinite-sets.lagda.md b/src/set-theory/infinite-sets.lagda.md index 481cb50381..d94e6be82f 100644 --- a/src/set-theory/infinite-sets.lagda.md +++ b/src/set-theory/infinite-sets.lagda.md @@ -1,12 +1,7 @@ # Infinite sets ```agda -open import foundation.function-extensionality-axiom - -module - set-theory.infinite-sets - (funext : function-extensionality) - where +module set-theory.infinite-sets where ```
Imports @@ -15,12 +10,12 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.mere-embeddings funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.mere-embeddings +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/set-theory/russells-paradox.lagda.md b/src/set-theory/russells-paradox.lagda.md index 94750c0c21..9ca07432a8 100644 --- a/src/set-theory/russells-paradox.lagda.md +++ b/src/set-theory/russells-paradox.lagda.md @@ -3,29 +3,24 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - set-theory.russells-paradox - (funext : function-extensionality) - where +module set-theory.russells-paradox where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types funext -open import foundation.identity-types funext -open import foundation.locally-small-types funext -open import foundation.negation funext -open import foundation.small-types funext -open import foundation.small-universes funext -open import foundation.surjective-maps funext -open import foundation.torsorial-type-families funext +open import foundation.functoriality-cartesian-product-types +open import foundation.identity-types +open import foundation.locally-small-types +open import foundation.negation +open import foundation.small-types +open import foundation.small-universes +open import foundation.surjective-maps +open import foundation.torsorial-type-families open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation-core.contractible-types @@ -33,9 +28,9 @@ open import foundation-core.empty-types open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types -open import trees.multisets funext -open import trees.small-multisets funext -open import trees.universal-multiset funext +open import trees.multisets +open import trees.small-multisets +open import trees.universal-multiset ```
diff --git a/src/set-theory/uncountable-sets.lagda.md b/src/set-theory/uncountable-sets.lagda.md index b5f767514c..f1cb306d08 100644 --- a/src/set-theory/uncountable-sets.lagda.md +++ b/src/set-theory/uncountable-sets.lagda.md @@ -1,23 +1,18 @@ # Uncountable sets ```agda -open import foundation.function-extensionality-axiom - -module - set-theory.uncountable-sets - (funext : function-extensionality) - where +module set-theory.uncountable-sets where ```
Imports ```agda -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.negation +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import set-theory.countable-sets funext +open import set-theory.countable-sets ```
diff --git a/src/species.lagda.md b/src/species.lagda.md index 35e8d68e99..c36d98ea52 100644 --- a/src/species.lagda.md +++ b/src/species.lagda.md @@ -3,58 +3,53 @@ ## Modules in the species namespace ```agda -open import foundation.function-extensionality-axiom +module species where -module - species - (funext : function-extensionality) - where - -open import species.cartesian-exponents-species-of-types funext public -open import species.cartesian-products-species-of-types funext public -open import species.cauchy-composition-species-of-types funext public -open import species.cauchy-composition-species-of-types-in-subuniverses funext public -open import species.cauchy-exponentials-species-of-types funext public -open import species.cauchy-exponentials-species-of-types-in-subuniverses funext public -open import species.cauchy-products-species-of-types funext public -open import species.cauchy-products-species-of-types-in-subuniverses funext public -open import species.cauchy-series-species-of-types funext public -open import species.cauchy-series-species-of-types-in-subuniverses funext public -open import species.composition-cauchy-series-species-of-types funext public -open import species.composition-cauchy-series-species-of-types-in-subuniverses funext public -open import species.coproducts-species-of-types funext public -open import species.coproducts-species-of-types-in-subuniverses funext public -open import species.cycle-index-series-species-of-types funext public -open import species.derivatives-species-of-types funext public -open import species.dirichlet-exponentials-species-of-types funext public -open import species.dirichlet-exponentials-species-of-types-in-subuniverses funext public -open import species.dirichlet-products-species-of-types funext public -open import species.dirichlet-products-species-of-types-in-subuniverses funext public -open import species.dirichlet-series-species-of-finite-inhabited-types funext public -open import species.dirichlet-series-species-of-types funext public -open import species.dirichlet-series-species-of-types-in-subuniverses funext public -open import species.equivalences-species-of-types funext public -open import species.equivalences-species-of-types-in-subuniverses funext public -open import species.exponentials-cauchy-series-of-types funext public -open import species.exponentials-cauchy-series-of-types-in-subuniverses funext public -open import species.hasse-weil-species funext public -open import species.morphisms-finite-species funext public -open import species.morphisms-species-of-types funext public -open import species.pointing-species-of-types funext public -open import species.precategory-of-finite-species funext public -open import species.products-cauchy-series-species-of-types funext public -open import species.products-cauchy-series-species-of-types-in-subuniverses funext public -open import species.products-dirichlet-series-species-of-finite-inhabited-types funext public -open import species.products-dirichlet-series-species-of-types funext public -open import species.products-dirichlet-series-species-of-types-in-subuniverses funext public -open import species.small-cauchy-composition-species-of-finite-inhabited-types funext public -open import species.small-cauchy-composition-species-of-types-in-subuniverses funext public -open import species.species-of-finite-inhabited-types funext public -open import species.species-of-finite-types funext public -open import species.species-of-inhabited-types funext public -open import species.species-of-types funext public -open import species.species-of-types-in-subuniverses funext public -open import species.unit-cauchy-composition-species-of-types funext public -open import species.unit-cauchy-composition-species-of-types-in-subuniverses funext public -open import species.unlabeled-structures-species funext public +open import species.cartesian-exponents-species-of-types public +open import species.cartesian-products-species-of-types public +open import species.cauchy-composition-species-of-types public +open import species.cauchy-composition-species-of-types-in-subuniverses public +open import species.cauchy-exponentials-species-of-types public +open import species.cauchy-exponentials-species-of-types-in-subuniverses public +open import species.cauchy-products-species-of-types public +open import species.cauchy-products-species-of-types-in-subuniverses public +open import species.cauchy-series-species-of-types public +open import species.cauchy-series-species-of-types-in-subuniverses public +open import species.composition-cauchy-series-species-of-types public +open import species.composition-cauchy-series-species-of-types-in-subuniverses public +open import species.coproducts-species-of-types public +open import species.coproducts-species-of-types-in-subuniverses public +open import species.cycle-index-series-species-of-types public +open import species.derivatives-species-of-types public +open import species.dirichlet-exponentials-species-of-types public +open import species.dirichlet-exponentials-species-of-types-in-subuniverses public +open import species.dirichlet-products-species-of-types public +open import species.dirichlet-products-species-of-types-in-subuniverses public +open import species.dirichlet-series-species-of-finite-inhabited-types public +open import species.dirichlet-series-species-of-types public +open import species.dirichlet-series-species-of-types-in-subuniverses public +open import species.equivalences-species-of-types public +open import species.equivalences-species-of-types-in-subuniverses public +open import species.exponentials-cauchy-series-of-types public +open import species.exponentials-cauchy-series-of-types-in-subuniverses public +open import species.hasse-weil-species public +open import species.morphisms-finite-species public +open import species.morphisms-species-of-types public +open import species.pointing-species-of-types public +open import species.precategory-of-finite-species public +open import species.products-cauchy-series-species-of-types public +open import species.products-cauchy-series-species-of-types-in-subuniverses public +open import species.products-dirichlet-series-species-of-finite-inhabited-types public +open import species.products-dirichlet-series-species-of-types public +open import species.products-dirichlet-series-species-of-types-in-subuniverses public +open import species.small-cauchy-composition-species-of-finite-inhabited-types public +open import species.small-cauchy-composition-species-of-types-in-subuniverses public +open import species.species-of-finite-inhabited-types public +open import species.species-of-finite-types public +open import species.species-of-inhabited-types public +open import species.species-of-types public +open import species.species-of-types-in-subuniverses public +open import species.unit-cauchy-composition-species-of-types public +open import species.unit-cauchy-composition-species-of-types-in-subuniverses public +open import species.unlabeled-structures-species public ``` diff --git a/src/species/cartesian-exponents-species-of-types.lagda.md b/src/species/cartesian-exponents-species-of-types.lagda.md index cd335ba1b7..8f07241384 100644 --- a/src/species/cartesian-exponents-species-of-types.lagda.md +++ b/src/species/cartesian-exponents-species-of-types.lagda.md @@ -1,12 +1,7 @@ # Cartesian exponents of species ```agda -open import foundation.function-extensionality-axiom - -module - species.cartesian-exponents-species-of-types - (funext : function-extensionality) - where +module species.cartesian-exponents-species-of-types where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/cartesian-products-species-of-types.lagda.md b/src/species/cartesian-products-species-of-types.lagda.md index 02d73fcc99..60e524d6b4 100644 --- a/src/species/cartesian-products-species-of-types.lagda.md +++ b/src/species/cartesian-products-species-of-types.lagda.md @@ -1,26 +1,21 @@ # Cartesian products of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.cartesian-products-species-of-types - (funext : function-extensionality) - where +module species.cartesian-products-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.universal-property-dependent-pair-types funext +open import foundation.cartesian-product-types +open import foundation.equivalences +open import foundation.functoriality-dependent-function-types +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels -open import species.cartesian-exponents-species-of-types funext -open import species.morphisms-species-of-types funext -open import species.species-of-types funext +open import species.cartesian-exponents-species-of-types +open import species.morphisms-species-of-types +open import species.species-of-types ```
diff --git a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md index 8686388d7e..d3642b399f 100644 --- a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -1,46 +1,41 @@ # Cauchy composition of species of types in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - species.cauchy-composition-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.cauchy-composition-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.relaxed-sigma-decompositions funext -open import foundation.sigma-closed-subuniverses funext -open import foundation.sigma-decomposition-subuniverse funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions +open import foundation.sigma-closed-subuniverses +open import foundation.sigma-decomposition-subuniverse +open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import species.cauchy-composition-species-of-types funext -open import species.species-of-types-in-subuniverses funext -open import species.unit-cauchy-composition-species-of-types funext -open import species.unit-cauchy-composition-species-of-types funext-in-subuniverses +open import species.cauchy-composition-species-of-types +open import species.species-of-types-in-subuniverses +open import species.unit-cauchy-composition-species-of-types +open import species.unit-cauchy-composition-species-of-types-in-subuniverses ```
diff --git a/src/species/cauchy-composition-species-of-types.lagda.md b/src/species/cauchy-composition-species-of-types.lagda.md index 6539d0e6ac..05943435c9 100644 --- a/src/species/cauchy-composition-species-of-types.lagda.md +++ b/src/species/cauchy-composition-species-of-types.lagda.md @@ -1,41 +1,35 @@ # Cauchy composition of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.cauchy-composition-species-of-types - (funext : function-extensionality) - where +module species.cauchy-composition-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.discrete-relaxed-sigma-decompositions funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.relaxed-sigma-decompositions funext -open import foundation.trivial-relaxed-sigma-decompositions funext +open import foundation.dependent-universal-property-equivalences +open import foundation.discrete-relaxed-sigma-decompositions +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.relaxed-sigma-decompositions +open import foundation.trivial-relaxed-sigma-decompositions open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-dependent-function-types funext +open import foundation.type-arithmetic-dependent-function-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext -open import foundation.univalence funext -open import foundation.universal-property-dependent-pair-types funext +open import foundation.type-theoretic-principle-of-choice +open import foundation.univalence +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels -open import species.species-of-types funext -open import species.unit-cauchy-composition-species-of-types funext +open import species.species-of-types +open import species.unit-cauchy-composition-species-of-types ```
diff --git a/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md index 388b504def..a5d3b8b486 100644 --- a/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md @@ -1,45 +1,40 @@ # Cauchy exponentials of species of types in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - species.cauchy-exponentials-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.cauchy-exponentials-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-decompositions funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-decompositions +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.propositions funext -open import foundation.relaxed-sigma-decompositions funext -open import foundation.sigma-closed-subuniverses funext -open import foundation.sigma-decomposition-subuniverse funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.propositions +open import foundation.relaxed-sigma-decompositions +open import foundation.sigma-closed-subuniverses +open import foundation.sigma-decomposition-subuniverse +open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import species.cauchy-composition-species-of-types-in-subuniverses funext -open import species.cauchy-exponentials-species-of-types funext -open import species.cauchy-products-species-of-types-in-subuniverses funext -open import species.coproducts-species-of-types funext -open import species.coproducts-species-of-types funext-in-subuniverses -open import species.species-of-types-in-subuniverses funext +open import species.cauchy-composition-species-of-types-in-subuniverses +open import species.cauchy-exponentials-species-of-types +open import species.cauchy-products-species-of-types-in-subuniverses +open import species.coproducts-species-of-types +open import species.coproducts-species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/cauchy-exponentials-species-of-types.lagda.md b/src/species/cauchy-exponentials-species-of-types.lagda.md index b2dd239580..0a4e3d7d9c 100644 --- a/src/species/cauchy-exponentials-species-of-types.lagda.md +++ b/src/species/cauchy-exponentials-species-of-types.lagda.md @@ -1,41 +1,36 @@ # Cauchy exponentials of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.cauchy-exponentials-species-of-types - (funext : function-extensionality) - where +module species.cauchy-exponentials-species-of-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.arithmetic-law-coproduct-and-sigma-decompositions funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-decompositions funext -open import foundation.dependent-binomial-theorem funext +open import foundation.arithmetic-law-coproduct-and-sigma-decompositions +open import foundation.cartesian-product-types +open import foundation.coproduct-decompositions +open import foundation.dependent-binomial-theorem open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.relaxed-sigma-decompositions funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.relaxed-sigma-decompositions open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import species.cauchy-composition-species-of-types funext -open import species.cauchy-products-species-of-types funext -open import species.coproducts-species-of-types funext -open import species.equivalences-species-of-types funext -open import species.species-of-types funext +open import species.cauchy-composition-species-of-types +open import species.cauchy-products-species-of-types +open import species.coproducts-species-of-types +open import species.equivalences-species-of-types +open import species.species-of-types ```
diff --git a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md index e3e23f69d6..dc5f62299c 100644 --- a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md @@ -1,39 +1,34 @@ # Cauchy products of species of types in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - species.cauchy-products-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.cauchy-products-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-decompositions funext -open import foundation.coproduct-decompositions funext-subuniverse -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-decompositions +open import foundation.coproduct-decompositions-subuniverse +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subuniverses funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import species.cauchy-products-species-of-types funext -open import species.species-of-types-in-subuniverses funext +open import species.cauchy-products-species-of-types +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/cauchy-products-species-of-types.lagda.md b/src/species/cauchy-products-species-of-types.lagda.md index 3c778bb522..1d4560f78f 100644 --- a/src/species/cauchy-products-species-of-types.lagda.md +++ b/src/species/cauchy-products-species-of-types.lagda.md @@ -1,23 +1,18 @@ # Cauchy products of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.cauchy-products-species-of-types - (funext : function-extensionality) - where +module species.cauchy-products-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-decompositions funext +open import foundation.cartesian-product-types +open import foundation.coproduct-decompositions open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md index 9c73385dc2..4e9a36c29a 100644 --- a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -1,31 +1,26 @@ # Cauchy series of species of types in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - species.cauchy-series-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.cauchy-series-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.global-subuniverses funext -open import foundation.postcomposition-functions funext -open import foundation.propositions funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.global-subuniverses +open import foundation.postcomposition-functions +open import foundation.propositions +open import foundation.subuniverses open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import species.cauchy-series-species-of-types funext -open import species.species-of-types-in-subuniverses funext +open import species.cauchy-series-species-of-types +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/cauchy-series-species-of-types.lagda.md b/src/species/cauchy-series-species-of-types.lagda.md index aa420f1ccc..a7a7a35a51 100644 --- a/src/species/cauchy-series-species-of-types.lagda.md +++ b/src/species/cauchy-series-species-of-types.lagda.md @@ -1,26 +1,21 @@ # Cauchy series of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.cauchy-series-species-of-types - (funext : function-extensionality) - where +module species.cauchy-series-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.postcomposition-functions funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.postcomposition-functions open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md index b4845f33c2..e0eb8cc904 100644 --- a/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/composition-cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -1,29 +1,24 @@ # Composition of Cauchy series of species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.composition-cauchy-series-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.composition-cauchy-series-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.equivalences funext -open import foundation.global-subuniverses funext -open import foundation.sigma-closed-subuniverses funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.global-subuniverses +open import foundation.sigma-closed-subuniverses +open import foundation.subuniverses open import foundation.universe-levels -open import species.cauchy-composition-species-of-types funext -open import species.cauchy-composition-species-of-types funext-in-subuniverses -open import species.cauchy-series-species-of-types funext -open import species.cauchy-series-species-of-types funext-in-subuniverses -open import species.composition-cauchy-series-species-of-types funext -open import species.species-of-types-in-subuniverses funext +open import species.cauchy-composition-species-of-types +open import species.cauchy-composition-species-of-types-in-subuniverses +open import species.cauchy-series-species-of-types +open import species.cauchy-series-species-of-types-in-subuniverses +open import species.composition-cauchy-series-species-of-types +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/composition-cauchy-series-species-of-types.lagda.md b/src/species/composition-cauchy-series-species-of-types.lagda.md index f74867851e..729af0a56f 100644 --- a/src/species/composition-cauchy-series-species-of-types.lagda.md +++ b/src/species/composition-cauchy-series-species-of-types.lagda.md @@ -1,33 +1,28 @@ # Composition of Cauchy series of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.composition-cauchy-series-species-of-types - (funext : function-extensionality) - where +module species.composition-cauchy-series-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext -open import foundation.univalence funext -open import foundation.universal-property-cartesian-product-types funext -open import foundation.universal-property-dependent-pair-types funext +open import foundation.type-theoretic-principle-of-choice +open import foundation.univalence +open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels -open import species.cauchy-composition-species-of-types funext -open import species.cauchy-series-species-of-types funext -open import species.species-of-types funext +open import species.cauchy-composition-species-of-types +open import species.cauchy-series-species-of-types +open import species.species-of-types ```
diff --git a/src/species/coproducts-species-of-types-in-subuniverses.lagda.md b/src/species/coproducts-species-of-types-in-subuniverses.lagda.md index a2cc54e8a5..2900441e71 100644 --- a/src/species/coproducts-species-of-types-in-subuniverses.lagda.md +++ b/src/species/coproducts-species-of-types-in-subuniverses.lagda.md @@ -1,29 +1,24 @@ # Coproducts of species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.coproducts-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.coproducts-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.identity-types +open import foundation.subuniverses open import foundation.universe-levels -open import species.coproducts-species-of-types funext -open import species.species-of-types-in-subuniverses funext +open import species.coproducts-species-of-types +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/coproducts-species-of-types.lagda.md b/src/species/coproducts-species-of-types.lagda.md index b37ad6b34e..b38a5e44ee 100644 --- a/src/species/coproducts-species-of-types.lagda.md +++ b/src/species/coproducts-species-of-types.lagda.md @@ -1,27 +1,22 @@ # Coproducts of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.coproducts-species-of-types - (funext : function-extensionality) - where +module species.coproducts-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.type-theoretic-principle-of-choice funext -open import foundation.universal-property-coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.equivalences +open import foundation.functoriality-dependent-function-types +open import foundation.type-theoretic-principle-of-choice +open import foundation.universal-property-coproduct-types open import foundation.universe-levels -open import species.morphisms-species-of-types funext -open import species.species-of-types funext +open import species.morphisms-species-of-types +open import species.species-of-types ```
diff --git a/src/species/cycle-index-series-species-of-types.lagda.md b/src/species/cycle-index-series-species-of-types.lagda.md index 874f031816..36fe229ae9 100644 --- a/src/species/cycle-index-series-species-of-types.lagda.md +++ b/src/species/cycle-index-series-species-of-types.lagda.md @@ -1,12 +1,7 @@ # Cycle index series of species ```agda -open import foundation.function-extensionality-axiom - -module - species.cycle-index-series-species-of-types - (funext : function-extensionality) - where +module species.cycle-index-series-species-of-types where ```
Imports @@ -17,7 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.cyclic-finite-types funext +open import univalent-combinatorics.cyclic-finite-types ```
diff --git a/src/species/derivatives-species-of-types.lagda.md b/src/species/derivatives-species-of-types.lagda.md index 4d714901e7..089dca1f20 100644 --- a/src/species/derivatives-species-of-types.lagda.md +++ b/src/species/derivatives-species-of-types.lagda.md @@ -1,22 +1,17 @@ # Derivatives of species ```agda -open import foundation.function-extensionality-axiom - -module - species.derivatives-species-of-types - (funext : function-extensionality) - where +module species.derivatives-species-of-types where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.unit-type open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md index ab945e06e9..caf7c99d4d 100644 --- a/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md @@ -1,41 +1,36 @@ # Dirichlet exponentials of species of types in a subuniverse ```agda -open import foundation.function-extensionality-axiom - -module - species.dirichlet-exponentials-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.dirichlet-exponentials-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.pi-decompositions funext -open import foundation.pi-decompositions funext-subuniverse +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.pi-decompositions +open import foundation.pi-decompositions-subuniverse open import foundation.product-decompositions -open import foundation.propositions funext -open import foundation.subuniverses funext +open import foundation.propositions +open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import species.coproducts-species-of-types funext -open import species.coproducts-species-of-types funext-in-subuniverses -open import species.dirichlet-exponentials-species-of-types funext -open import species.dirichlet-products-species-of-types-in-subuniverses funext -open import species.species-of-types-in-subuniverses funext +open import species.coproducts-species-of-types +open import species.coproducts-species-of-types-in-subuniverses +open import species.dirichlet-exponentials-species-of-types +open import species.dirichlet-products-species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/dirichlet-exponentials-species-of-types.lagda.md b/src/species/dirichlet-exponentials-species-of-types.lagda.md index ab3b1a07a5..4a1ac22104 100644 --- a/src/species/dirichlet-exponentials-species-of-types.lagda.md +++ b/src/species/dirichlet-exponentials-species-of-types.lagda.md @@ -1,39 +1,34 @@ # Dirichlet exponentials of a species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.dirichlet-exponentials-species-of-types - (funext : function-extensionality) - where +module species.dirichlet-exponentials-species-of-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.arithmetic-law-product-and-pi-decompositions funext -open import foundation.cartesian-product-types funext -open import foundation.coproduct-decompositions funext -open import foundation.dependent-binomial-theorem funext +open import foundation.arithmetic-law-product-and-pi-decompositions +open import foundation.cartesian-product-types +open import foundation.coproduct-decompositions +open import foundation.dependent-binomial-theorem open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.pi-decompositions funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.pi-decompositions open import foundation.product-decompositions open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import species.coproducts-species-of-types funext -open import species.dirichlet-products-species-of-types funext -open import species.equivalences-species-of-types funext -open import species.species-of-types funext +open import species.coproducts-species-of-types +open import species.dirichlet-products-species-of-types +open import species.equivalences-species-of-types +open import species.species-of-types ```
diff --git a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md index c05eaabfc0..b2e6b43e7c 100644 --- a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md @@ -1,39 +1,34 @@ # Dirichlet products of species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.dirichlet-products-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.dirichlet-products-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.identity-types open import foundation.product-decompositions -open import foundation.product-decompositions-subuniverse funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.subuniverses funext +open import foundation.product-decompositions-subuniverse +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import species.dirichlet-products-species-of-types funext -open import species.species-of-types-in-subuniverses funext +open import species.dirichlet-products-species-of-types +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/dirichlet-products-species-of-types.lagda.md b/src/species/dirichlet-products-species-of-types.lagda.md index 16108a12e8..ba7ab3e640 100644 --- a/src/species/dirichlet-products-species-of-types.lagda.md +++ b/src/species/dirichlet-products-species-of-types.lagda.md @@ -1,23 +1,18 @@ # Dirichlet products of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.dirichlet-products-species-of-types - (funext : function-extensionality) - where +module species.dirichlet-products-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.product-decompositions open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md b/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md index 22f7e833c2..d5d0a07c20 100644 --- a/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md +++ b/src/species/dirichlet-series-species-of-finite-inhabited-types.lagda.md @@ -1,12 +1,7 @@ # Dirichlet series of species of finite inhabited types ```agda -open import foundation.function-extensionality-axiom - -module - species.dirichlet-series-species-of-finite-inhabited-types - (funext : function-extensionality) - where +module species.dirichlet-series-species-of-finite-inhabited-types where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-finite-inhabited-types funext +open import species.species-of-finite-inhabited-types -open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.inhabited-finite-types funext +open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.inhabited-finite-types ```
diff --git a/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md index 8cb57f62c4..22ff7d6265 100644 --- a/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-series-species-of-types-in-subuniverses.lagda.md @@ -1,23 +1,18 @@ # Dirichlet series of species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.dirichlet-series-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.dirichlet-series-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.subuniverses funext +open import foundation.subuniverses open import foundation.universe-levels -open import species.species-of-types-in-subuniverses funext +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/dirichlet-series-species-of-types.lagda.md b/src/species/dirichlet-series-species-of-types.lagda.md index 64a77cd91c..a3e2595e36 100644 --- a/src/species/dirichlet-series-species-of-types.lagda.md +++ b/src/species/dirichlet-series-species-of-types.lagda.md @@ -1,22 +1,17 @@ # Dirichlet series of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.dirichlet-series-species-of-types - (funext : function-extensionality) - where +module species.dirichlet-series-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/equivalences-species-of-types-in-subuniverses.lagda.md b/src/species/equivalences-species-of-types-in-subuniverses.lagda.md index 471813f816..e2a0f54a3f 100644 --- a/src/species/equivalences-species-of-types-in-subuniverses.lagda.md +++ b/src/species/equivalences-species-of-types-in-subuniverses.lagda.md @@ -1,23 +1,18 @@ # Equivalences of species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.equivalences-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.equivalences-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.subuniverses open import foundation.universe-levels -open import species.species-of-types-in-subuniverses funext +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/equivalences-species-of-types.lagda.md b/src/species/equivalences-species-of-types.lagda.md index 8e24168356..a0e35581a6 100644 --- a/src/species/equivalences-species-of-types.lagda.md +++ b/src/species/equivalences-species-of-types.lagda.md @@ -1,23 +1,18 @@ # Equivalences of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.equivalences-species-of-types - (funext : function-extensionality) - where +module species.equivalences-species-of-types where ```
Imports ```agda -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.univalence funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.univalence open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md b/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md index 356d4f4345..4f1628ab45 100644 --- a/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md +++ b/src/species/exponentials-cauchy-series-of-types-in-subuniverses.lagda.md @@ -1,33 +1,28 @@ # Exponential of Cauchy series of species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.exponentials-cauchy-series-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.exponentials-cauchy-series-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.global-subuniverses funext -open import foundation.sigma-closed-subuniverses funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.global-subuniverses +open import foundation.sigma-closed-subuniverses +open import foundation.subuniverses open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type open import foundation.universe-levels -open import species.cauchy-composition-species-of-types-in-subuniverses funext -open import species.cauchy-exponentials-species-of-types-in-subuniverses funext -open import species.cauchy-series-species-of-types-in-subuniverses funext -open import species.composition-cauchy-series-species-of-types-in-subuniverses funext -open import species.species-of-types-in-subuniverses funext +open import species.cauchy-composition-species-of-types-in-subuniverses +open import species.cauchy-exponentials-species-of-types-in-subuniverses +open import species.cauchy-series-species-of-types-in-subuniverses +open import species.composition-cauchy-series-species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/exponentials-cauchy-series-of-types.lagda.md b/src/species/exponentials-cauchy-series-of-types.lagda.md index fd94d9755b..39cbfbf9be 100644 --- a/src/species/exponentials-cauchy-series-of-types.lagda.md +++ b/src/species/exponentials-cauchy-series-of-types.lagda.md @@ -1,30 +1,25 @@ # Exponential of Cauchy series of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.exponentials-cauchy-series-of-types - (funext : function-extensionality) - where +module species.exponentials-cauchy-series-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type open import foundation.universe-levels -open import species.cauchy-composition-species-of-types funext -open import species.cauchy-exponentials-species-of-types funext -open import species.cauchy-series-species-of-types funext -open import species.composition-cauchy-series-species-of-types funext -open import species.species-of-types funext +open import species.cauchy-composition-species-of-types +open import species.cauchy-exponentials-species-of-types +open import species.cauchy-series-species-of-types +open import species.composition-cauchy-series-species-of-types +open import species.species-of-types ```
diff --git a/src/species/hasse-weil-species.lagda.md b/src/species/hasse-weil-species.lagda.md index a1d8cee721..4538f31367 100644 --- a/src/species/hasse-weil-species.lagda.md +++ b/src/species/hasse-weil-species.lagda.md @@ -1,25 +1,20 @@ # Hasse-Weil species ```agda -open import foundation.function-extensionality-axiom - -module - species.hasse-weil-species - (funext : function-extensionality) - where +module species.hasse-weil-species where ```
Imports ```agda -open import finite-algebra.commutative-finite-rings funext -open import finite-algebra.products-commutative-finite-rings funext +open import finite-algebra.commutative-finite-rings +open import finite-algebra.products-commutative-finite-rings -open import foundation.cartesian-product-types funext -open import foundation.equivalences funext +open import foundation.cartesian-product-types +open import foundation.equivalences open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/species/morphisms-finite-species.lagda.md b/src/species/morphisms-finite-species.lagda.md index 92b58f06ad..52f2991b25 100644 --- a/src/species/morphisms-finite-species.lagda.md +++ b/src/species/morphisms-finite-species.lagda.md @@ -1,33 +1,28 @@ # Morphisms of finite species ```agda -open import foundation.function-extensionality-axiom - -module - species.morphisms-finite-species - (funext : function-extensionality) - where +module species.morphisms-finite-species where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.universe-levels -open import species.species-of-finite-types funext +open import species.species-of-finite-types -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/species/morphisms-species-of-types.lagda.md b/src/species/morphisms-species-of-types.lagda.md index e21ab35cbe..713b51777c 100644 --- a/src/species/morphisms-species-of-types.lagda.md +++ b/src/species/morphisms-species-of-types.lagda.md @@ -1,28 +1,23 @@ # Morphisms of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.morphisms-species-of-types - (funext : function-extensionality) - where +module species.morphisms-species-of-types where ```
Imports ```agda -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/pointing-species-of-types.lagda.md b/src/species/pointing-species-of-types.lagda.md index ea7ff88b07..6761bb997f 100644 --- a/src/species/pointing-species-of-types.lagda.md +++ b/src/species/pointing-species-of-types.lagda.md @@ -1,21 +1,16 @@ # Pointing of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.pointing-species-of-types - (funext : function-extensionality) - where +module species.pointing-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/precategory-of-finite-species.lagda.md b/src/species/precategory-of-finite-species.lagda.md index c51432d6a4..d2de76dfc8 100644 --- a/src/species/precategory-of-finite-species.lagda.md +++ b/src/species/precategory-of-finite-species.lagda.md @@ -1,23 +1,18 @@ # The precategory of finite species ```agda -open import foundation.function-extensionality-axiom - -module - species.precategory-of-finite-species - (funext : function-extensionality) - where +module species.precategory-of-finite-species where ```
Imports ```agda -open import category-theory.large-precategories funext +open import category-theory.large-precategories open import foundation.universe-levels -open import species.morphisms-finite-species funext -open import species.species-of-finite-types funext +open import species.morphisms-finite-species +open import species.species-of-finite-types ```
diff --git a/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md index 4633f412b4..946d2dd088 100644 --- a/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/products-cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -1,31 +1,26 @@ # Products of Cauchy series of species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.products-cauchy-series-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.products-cauchy-series-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.global-subuniverses funext -open import foundation.subuniverses funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.global-subuniverses +open import foundation.subuniverses open import foundation.universe-levels -open import species.cauchy-products-species-of-types funext -open import species.cauchy-products-species-of-types funext-in-subuniverses -open import species.cauchy-series-species-of-types funext -open import species.cauchy-series-species-of-types funext-in-subuniverses -open import species.products-cauchy-series-species-of-types funext -open import species.species-of-types-in-subuniverses funext +open import species.cauchy-products-species-of-types +open import species.cauchy-products-species-of-types-in-subuniverses +open import species.cauchy-series-species-of-types +open import species.cauchy-series-species-of-types-in-subuniverses +open import species.products-cauchy-series-species-of-types +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/products-cauchy-series-species-of-types.lagda.md b/src/species/products-cauchy-series-species-of-types.lagda.md index f466a8705c..347682538c 100644 --- a/src/species/products-cauchy-series-species-of-types.lagda.md +++ b/src/species/products-cauchy-series-species-of-types.lagda.md @@ -1,32 +1,27 @@ # Products of Cauchy series of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.products-cauchy-series-species-of-types - (funext : function-extensionality) - where +module species.products-cauchy-series-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext -open import foundation.universal-property-coproduct-types funext +open import foundation.univalence +open import foundation.universal-property-coproduct-types open import foundation.universe-levels -open import species.cauchy-products-species-of-types funext -open import species.cauchy-series-species-of-types funext -open import species.species-of-types funext +open import species.cauchy-products-species-of-types +open import species.cauchy-series-species-of-types +open import species.species-of-types ```
diff --git a/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md b/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md index 188a806322..26fac97788 100644 --- a/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md +++ b/src/species/products-dirichlet-series-species-of-finite-inhabited-types.lagda.md @@ -1,22 +1,17 @@ # Products of Dirichlet series of species of finite inhabited types ```agda -open import foundation.function-extensionality-axiom - -module - species.products-dirichlet-series-species-of-finite-inhabited-types - (funext : function-extensionality) - where +module species.products-dirichlet-series-species-of-finite-inhabited-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.universe-levels -open import species.dirichlet-series-species-of-finite-inhabited-types funext -open import species.species-of-finite-inhabited-types funext +open import species.dirichlet-series-species-of-finite-inhabited-types +open import species.species-of-finite-inhabited-types ```
diff --git a/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md b/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md index 67e447d388..0618179c6c 100644 --- a/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/products-dirichlet-series-species-of-types-in-subuniverses.lagda.md @@ -1,34 +1,29 @@ # Products of Dirichlet series of species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.products-dirichlet-series-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.products-dirichlet-series-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.global-subuniverses funext -open import foundation.homotopies funext -open import foundation.postcomposition-functions funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.global-subuniverses +open import foundation.homotopies +open import foundation.postcomposition-functions +open import foundation.subuniverses open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-cartesian-product-types funext +open import foundation.universal-property-cartesian-product-types open import foundation.universe-levels -open import species.dirichlet-products-species-of-types-in-subuniverses funext -open import species.dirichlet-series-species-of-types-in-subuniverses funext -open import species.species-of-types-in-subuniverses funext +open import species.dirichlet-products-species-of-types-in-subuniverses +open import species.dirichlet-series-species-of-types-in-subuniverses +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/products-dirichlet-series-species-of-types.lagda.md b/src/species/products-dirichlet-series-species-of-types.lagda.md index cd625482e8..1b015bd412 100644 --- a/src/species/products-dirichlet-series-species-of-types.lagda.md +++ b/src/species/products-dirichlet-series-species-of-types.lagda.md @@ -1,32 +1,27 @@ # Products of Dirichlet series of species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.products-dirichlet-series-species-of-types - (funext : function-extensionality) - where +module species.products-dirichlet-series-species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.postcomposition-functions funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.postcomposition-functions open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext -open import foundation.universal-property-cartesian-product-types funext +open import foundation.univalence +open import foundation.universal-property-cartesian-product-types open import foundation.universe-levels -open import species.dirichlet-products-species-of-types funext -open import species.dirichlet-series-species-of-types funext -open import species.species-of-types funext +open import species.dirichlet-products-species-of-types +open import species.dirichlet-series-species-of-types +open import species.species-of-types ```
diff --git a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md index c2cee7d1ae..2b7b0202fd 100644 --- a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md +++ b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md @@ -3,46 +3,41 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - species.small-cauchy-composition-species-of-finite-inhabited-types - (funext : function-extensionality) - where +module species.small-cauchy-composition-species-of-finite-inhabited-types where ```
Imports ```agda -open import foundation.contractible-types funext -open import foundation.decidable-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.relaxed-sigma-decompositions funext -open import foundation.sigma-closed-subuniverses funext -open import foundation.sigma-decomposition-subuniverse funext -open import foundation.subuniverses funext +open import foundation.contractible-types +open import foundation.decidable-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions +open import foundation.sigma-closed-subuniverses +open import foundation.sigma-decomposition-subuniverse +open import foundation.subuniverses open import foundation.type-arithmetic-cartesian-product-types open import foundation.unit-type open import foundation.universe-levels -open import species.small-cauchy-composition-species-of-types-in-subuniverses funext -open import species.species-of-finite-inhabited-types funext +open import species.small-cauchy-composition-species-of-types-in-subuniverses +open import species.species-of-finite-inhabited-types -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.inhabited-finite-types funext -open import univalent-combinatorics.sigma-decompositions funext -open import univalent-combinatorics.small-types funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.inhabited-finite-types +open import univalent-combinatorics.sigma-decompositions +open import univalent-combinatorics.small-types ```
diff --git a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md index 8b8d8645df..22cb26f896 100644 --- a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -1,44 +1,39 @@ # Small Cauchy composition of species types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.small-cauchy-composition-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.small-cauchy-composition-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.relaxed-sigma-decompositions funext -open import foundation.sigma-closed-subuniverses funext -open import foundation.sigma-decomposition-subuniverse funext -open import foundation.small-types funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.relaxed-sigma-decompositions +open import foundation.sigma-closed-subuniverses +open import foundation.sigma-decomposition-subuniverse +open import foundation.small-types +open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import species.cauchy-composition-species-of-types funext -open import species.species-of-types-in-subuniverses funext -open import species.unit-cauchy-composition-species-of-types funext +open import species.cauchy-composition-species-of-types +open import species.species-of-types-in-subuniverses +open import species.unit-cauchy-composition-species-of-types ```
diff --git a/src/species/species-of-finite-inhabited-types.lagda.md b/src/species/species-of-finite-inhabited-types.lagda.md index 01a25fa4ee..fa9ba4bc14 100644 --- a/src/species/species-of-finite-inhabited-types.lagda.md +++ b/src/species/species-of-finite-inhabited-types.lagda.md @@ -1,12 +1,7 @@ # Species of finite inhabited types ```agda -open import foundation.function-extensionality-axiom - -module - species.species-of-finite-inhabited-types - (funext : function-extensionality) - where +module species.species-of-finite-inhabited-types where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.universe-levels -open import species.species-of-types-in-subuniverses funext +open import species.species-of-types-in-subuniverses -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.inhabited-finite-types funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.inhabited-finite-types ```
diff --git a/src/species/species-of-finite-types.lagda.md b/src/species/species-of-finite-types.lagda.md index fb9d783a82..24eb4eb3b3 100644 --- a/src/species/species-of-finite-types.lagda.md +++ b/src/species/species-of-finite-types.lagda.md @@ -1,12 +1,7 @@ # Species of finite types ```agda -open import foundation.function-extensionality-axiom - -module - species.species-of-finite-types - (funext : function-extensionality) - where +module species.species-of-finite-types where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.universe-levels -open import species.species-of-types-in-subuniverses funext +open import species.species-of-types-in-subuniverses -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/species/species-of-inhabited-types.lagda.md b/src/species/species-of-inhabited-types.lagda.md index 0c4f53809b..92c51b4adf 100644 --- a/src/species/species-of-inhabited-types.lagda.md +++ b/src/species/species-of-inhabited-types.lagda.md @@ -1,22 +1,17 @@ # Species of inhabited types ```agda -open import foundation.function-extensionality-axiom - -module - species.species-of-inhabited-types - (funext : function-extensionality) - where +module species.species-of-inhabited-types where ```
Imports ```agda -open import foundation.inhabited-types funext +open import foundation.inhabited-types open import foundation.unit-type open import foundation.universe-levels -open import species.species-of-types-in-subuniverses funext +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/species-of-types-in-subuniverses.lagda.md b/src/species/species-of-types-in-subuniverses.lagda.md index 4421d6d350..1ef1c85fec 100644 --- a/src/species/species-of-types-in-subuniverses.lagda.md +++ b/src/species/species-of-types-in-subuniverses.lagda.md @@ -1,28 +1,23 @@ # Species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.propositions funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.propositions +open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/species-of-types.lagda.md b/src/species/species-of-types.lagda.md index 5e36e13616..e300981b9b 100644 --- a/src/species/species-of-types.lagda.md +++ b/src/species/species-of-types.lagda.md @@ -1,21 +1,16 @@ # Species of types ```agda -open import foundation.function-extensionality-axiom - -module - species.species-of-types - (funext : function-extensionality) - where +module species.species-of-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.equivalences funext +open import foundation.cartesian-product-types +open import foundation.equivalences open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels ``` diff --git a/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md index b068d199c2..030f8440d0 100644 --- a/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -1,24 +1,19 @@ # The unit of Cauchy composition of species of types in subuniverses ```agda -open import foundation.function-extensionality-axiom - -module - species.unit-cauchy-composition-species-of-types-in-subuniverses - (funext : function-extensionality) - where +module species.unit-cauchy-composition-species-of-types-in-subuniverses where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.global-subuniverses funext -open import foundation.subuniverses funext +open import foundation.global-subuniverses +open import foundation.subuniverses open import foundation.universe-levels -open import species.species-of-types-in-subuniverses funext +open import species.species-of-types-in-subuniverses ```
diff --git a/src/species/unit-cauchy-composition-species-of-types.lagda.md b/src/species/unit-cauchy-composition-species-of-types.lagda.md index 8667d9812c..15884d5b45 100644 --- a/src/species/unit-cauchy-composition-species-of-types.lagda.md +++ b/src/species/unit-cauchy-composition-species-of-types.lagda.md @@ -1,21 +1,16 @@ # The unit of Cauchy composition of types ```agda -open import foundation.function-extensionality-axiom - -module - species.unit-cauchy-composition-species-of-types - (funext : function-extensionality) - where +module species.unit-cauchy-composition-species-of-types where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types ```
diff --git a/src/species/unlabeled-structures-species.lagda.md b/src/species/unlabeled-structures-species.lagda.md index cf4e2d290a..2ed30b8522 100644 --- a/src/species/unlabeled-structures-species.lagda.md +++ b/src/species/unlabeled-structures-species.lagda.md @@ -1,12 +1,7 @@ # Unlabeled structures of finite species ```agda -open import foundation.function-extensionality-axiom - -module - species.unlabeled-structures-species - (funext : function-extensionality) - where +module species.unlabeled-structures-species where ```
Imports @@ -17,9 +12,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import species.species-of-types funext +open import species.species-of-types -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/structured-types.lagda.md b/src/structured-types.lagda.md index d2f064bebf..081ebda794 100644 --- a/src/structured-types.lagda.md +++ b/src/structured-types.lagda.md @@ -7,88 +7,83 @@ ## Modules in the structured types namespace ```agda -open import foundation.function-extensionality-axiom +module structured-types where -module - structured-types - (funext : function-extensionality) - where - -open import structured-types.cartesian-products-types-equipped-with-endomorphisms funext public -open import structured-types.central-h-spaces funext public -open import structured-types.commuting-squares-of-pointed-homotopies funext public -open import structured-types.commuting-squares-of-pointed-maps funext public -open import structured-types.commuting-triangles-of-pointed-maps funext public -open import structured-types.conjugation-pointed-types funext public -open import structured-types.constant-pointed-maps funext public -open import structured-types.contractible-pointed-types funext public -open import structured-types.cyclic-types funext public -open import structured-types.dependent-products-h-spaces funext public +open import structured-types.cartesian-products-types-equipped-with-endomorphisms public +open import structured-types.central-h-spaces public +open import structured-types.commuting-squares-of-pointed-homotopies public +open import structured-types.commuting-squares-of-pointed-maps public +open import structured-types.commuting-triangles-of-pointed-maps public +open import structured-types.conjugation-pointed-types public +open import structured-types.constant-pointed-maps public +open import structured-types.contractible-pointed-types public +open import structured-types.cyclic-types public +open import structured-types.dependent-products-h-spaces public open import structured-types.dependent-products-pointed-types public -open import structured-types.dependent-products-wild-monoids funext public -open import structured-types.dependent-types-equipped-with-automorphisms funext public -open import structured-types.equivalences-h-spaces funext public -open import structured-types.equivalences-pointed-arrows funext public -open import structured-types.equivalences-types-equipped-with-automorphisms funext public -open import structured-types.equivalences-types-equipped-with-endomorphisms funext public -open import structured-types.faithful-pointed-maps funext public -open import structured-types.fibers-of-pointed-maps funext public -open import structured-types.finite-multiplication-magmas funext public -open import structured-types.function-h-spaces funext public -open import structured-types.function-magmas funext public -open import structured-types.function-wild-monoids funext public -open import structured-types.h-spaces funext public -open import structured-types.initial-pointed-type-equipped-with-automorphism funext public -open import structured-types.involutive-type-of-h-space-structures funext public -open import structured-types.involutive-types funext public -open import structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms funext public -open import structured-types.iterated-pointed-cartesian-product-types funext public -open import structured-types.magmas funext public -open import structured-types.mere-equivalences-types-equipped-with-endomorphisms funext public -open import structured-types.morphisms-h-spaces funext public -open import structured-types.morphisms-magmas funext public -open import structured-types.morphisms-pointed-arrows funext public -open import structured-types.morphisms-twisted-pointed-arrows funext public -open import structured-types.morphisms-types-equipped-with-automorphisms funext public -open import structured-types.morphisms-types-equipped-with-endomorphisms funext public -open import structured-types.morphisms-wild-monoids funext public -open import structured-types.noncoherent-h-spaces funext public -open import structured-types.opposite-pointed-spans funext public -open import structured-types.pointed-2-homotopies funext public -open import structured-types.pointed-cartesian-product-types funext public -open import structured-types.pointed-dependent-functions funext public +open import structured-types.dependent-products-wild-monoids public +open import structured-types.dependent-types-equipped-with-automorphisms public +open import structured-types.equivalences-h-spaces public +open import structured-types.equivalences-pointed-arrows public +open import structured-types.equivalences-types-equipped-with-automorphisms public +open import structured-types.equivalences-types-equipped-with-endomorphisms public +open import structured-types.faithful-pointed-maps public +open import structured-types.fibers-of-pointed-maps public +open import structured-types.finite-multiplication-magmas public +open import structured-types.function-h-spaces public +open import structured-types.function-magmas public +open import structured-types.function-wild-monoids public +open import structured-types.h-spaces public +open import structured-types.initial-pointed-type-equipped-with-automorphism public +open import structured-types.involutive-type-of-h-space-structures public +open import structured-types.involutive-types public +open import structured-types.iterated-cartesian-products-types-equipped-with-endomorphisms public +open import structured-types.iterated-pointed-cartesian-product-types public +open import structured-types.magmas public +open import structured-types.mere-equivalences-types-equipped-with-endomorphisms public +open import structured-types.morphisms-h-spaces public +open import structured-types.morphisms-magmas public +open import structured-types.morphisms-pointed-arrows public +open import structured-types.morphisms-twisted-pointed-arrows public +open import structured-types.morphisms-types-equipped-with-automorphisms public +open import structured-types.morphisms-types-equipped-with-endomorphisms public +open import structured-types.morphisms-wild-monoids public +open import structured-types.noncoherent-h-spaces public +open import structured-types.opposite-pointed-spans public +open import structured-types.pointed-2-homotopies public +open import structured-types.pointed-cartesian-product-types public +open import structured-types.pointed-dependent-functions public open import structured-types.pointed-dependent-pair-types public -open import structured-types.pointed-equivalences funext public +open import structured-types.pointed-equivalences public open import structured-types.pointed-families-of-types public -open import structured-types.pointed-homotopies funext public -open import structured-types.pointed-isomorphisms funext public -open import structured-types.pointed-maps funext public -open import structured-types.pointed-retractions funext public -open import structured-types.pointed-sections funext public -open import structured-types.pointed-span-diagrams funext public -open import structured-types.pointed-spans funext public +open import structured-types.pointed-homotopies public +open import structured-types.pointed-isomorphisms public +open import structured-types.pointed-maps public +open import structured-types.pointed-retractions public +open import structured-types.pointed-sections public +open import structured-types.pointed-span-diagrams public +open import structured-types.pointed-spans public open import structured-types.pointed-types public -open import structured-types.pointed-types-equipped-with-automorphisms funext public -open import structured-types.pointed-unit-type funext public -open import structured-types.pointed-universal-property-contractible-types funext public -open import structured-types.postcomposition-pointed-maps funext public -open import structured-types.precomposition-pointed-maps funext public -open import structured-types.sets-equipped-with-automorphisms funext public -open import structured-types.small-pointed-types funext public -open import structured-types.symmetric-elements-involutive-types funext public -open import structured-types.symmetric-h-spaces funext public -open import structured-types.transposition-pointed-span-diagrams funext public -open import structured-types.types-equipped-with-automorphisms funext public -open import structured-types.types-equipped-with-endomorphisms funext public -open import structured-types.uniform-pointed-homotopies funext public -open import structured-types.universal-property-pointed-equivalences funext public +open import structured-types.pointed-types-equipped-with-automorphisms public +open import structured-types.pointed-unit-type public +open import structured-types.pointed-universal-property-contractible-types public +open import structured-types.postcomposition-pointed-maps public +open import structured-types.precomposition-pointed-maps public +open import structured-types.sets-equipped-with-automorphisms public +open import structured-types.small-pointed-types public +open import structured-types.symmetric-elements-involutive-types public +open import structured-types.symmetric-h-spaces public +open import structured-types.transposition-pointed-span-diagrams public +open import structured-types.types-equipped-with-automorphisms public +open import structured-types.types-equipped-with-endomorphisms public +open import structured-types.uniform-pointed-homotopies public +open import structured-types.universal-property-pointed-equivalences public open import structured-types.unpointed-maps public -open import structured-types.whiskering-pointed-2-homotopies-concatenation funext public -open import structured-types.whiskering-pointed-homotopies-composition funext public -open import structured-types.wild-category-of-pointed-types funext public -open import structured-types.wild-groups funext public -open import structured-types.wild-loops funext public -open import structured-types.wild-monoids funext public -open import structured-types.wild-quasigroups funext public -open import structured-types.wild-semigroups funext public +open import structured-types.whiskering-pointed-2-homotopies-concatenation public +open import structured-types.whiskering-pointed-homotopies-composition public +open import structured-types.wild-category-of-pointed-types public +open import structured-types.wild-groups public +open import structured-types.wild-loops public +open import structured-types.wild-monoids public +open import structured-types.wild-quasigroups public +open import structured-types.wild-semigroups public ``` diff --git a/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md index 7c06bfbf56..e8593cf7cf 100644 --- a/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/cartesian-products-types-equipped-with-endomorphisms.lagda.md @@ -1,23 +1,18 @@ # Cartesian products of types equipped with endomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.cartesian-products-types-equipped-with-endomorphisms - (funext : function-extensionality) - where +module structured-types.cartesian-products-types-equipped-with-endomorphisms where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.functoriality-cartesian-product-types funext +open import foundation.functoriality-cartesian-product-types open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms ```
diff --git a/src/structured-types/central-h-spaces.lagda.md b/src/structured-types/central-h-spaces.lagda.md index 0039b94c9f..c0ea967513 100644 --- a/src/structured-types/central-h-spaces.lagda.md +++ b/src/structured-types/central-h-spaces.lagda.md @@ -1,18 +1,13 @@ # Central H-spaces ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.central-h-spaces - (funext : function-extensionality) - where +module structured-types.central-h-spaces where ```
Imports ```agda -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels open import structured-types.pointed-types diff --git a/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md b/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md index 377f09fc97..0bd38407d8 100644 --- a/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md +++ b/src/structured-types/commuting-squares-of-pointed-homotopies.lagda.md @@ -1,12 +1,7 @@ # Commuting squares of pointed homotopies ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.commuting-squares-of-pointed-homotopies - (funext : function-extensionality) - where +module structured-types.commuting-squares-of-pointed-homotopies where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.universe-levels -open import structured-types.pointed-2-homotopies funext -open import structured-types.pointed-dependent-functions funext +open import structured-types.pointed-2-homotopies +open import structured-types.pointed-dependent-functions open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies funext +open import structured-types.pointed-homotopies open import structured-types.pointed-types ``` diff --git a/src/structured-types/commuting-squares-of-pointed-maps.lagda.md b/src/structured-types/commuting-squares-of-pointed-maps.lagda.md index 6346fde801..ed8779ac44 100644 --- a/src/structured-types/commuting-squares-of-pointed-maps.lagda.md +++ b/src/structured-types/commuting-squares-of-pointed-maps.lagda.md @@ -1,30 +1,25 @@ # Commuting squares of pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.commuting-squares-of-pointed-maps - (funext : function-extensionality) - where +module structured-types.commuting-squares-of-pointed-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.whiskering-pointed-homotopies-composition funext +open import structured-types.whiskering-pointed-homotopies-composition ```
diff --git a/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md b/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md index fe4041fece..34a14fabd0 100644 --- a/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md +++ b/src/structured-types/commuting-triangles-of-pointed-maps.lagda.md @@ -1,12 +1,7 @@ # Commuting triangles of pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.commuting-triangles-of-pointed-maps - (funext : function-extensionality) - where +module structured-types.commuting-triangles-of-pointed-maps where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import foundation.universe-levels -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.whiskering-pointed-homotopies-composition funext +open import structured-types.whiskering-pointed-homotopies-composition ```
diff --git a/src/structured-types/conjugation-pointed-types.lagda.md b/src/structured-types/conjugation-pointed-types.lagda.md index a60f1c08d9..fb95e9ed66 100644 --- a/src/structured-types/conjugation-pointed-types.lagda.md +++ b/src/structured-types/conjugation-pointed-types.lagda.md @@ -1,12 +1,7 @@ # Conjugation of pointed types ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.conjugation-pointed-types - (funext : function-extensionality) - where +module structured-types.conjugation-pointed-types where ```
Imports @@ -14,18 +9,18 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.conjugation-loops funext -open import synthetic-homotopy-theory.functoriality-loop-spaces funext -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.conjugation-loops +open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/structured-types/constant-pointed-maps.lagda.md b/src/structured-types/constant-pointed-maps.lagda.md index 0fce81e7ff..327fb4e80a 100644 --- a/src/structured-types/constant-pointed-maps.lagda.md +++ b/src/structured-types/constant-pointed-maps.lagda.md @@ -1,23 +1,18 @@ # Constant pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.constant-pointed-maps - (funext : function-extensionality) - where +module structured-types.constant-pointed-maps where ```
Imports ```agda -open import foundation.constant-maps funext +open import foundation.constant-maps open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/contractible-pointed-types.lagda.md b/src/structured-types/contractible-pointed-types.lagda.md index 255e3d3930..67d5b144e8 100644 --- a/src/structured-types/contractible-pointed-types.lagda.md +++ b/src/structured-types/contractible-pointed-types.lagda.md @@ -1,19 +1,14 @@ # Contractible pointed types ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.contractible-pointed-types - (funext : function-extensionality) - where +module structured-types.contractible-pointed-types where ```
Imports ```agda -open import foundation.contractible-types funext -open import foundation.propositions funext +open import foundation.contractible-types +open import foundation.propositions open import foundation.universe-levels open import structured-types.pointed-types diff --git a/src/structured-types/cyclic-types.lagda.md b/src/structured-types/cyclic-types.lagda.md index 906df221eb..dcd59c7116 100644 --- a/src/structured-types/cyclic-types.lagda.md +++ b/src/structured-types/cyclic-types.lagda.md @@ -1,27 +1,22 @@ # Cyclic types ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.cyclic-types - (funext : function-extensionality) - where +module structured-types.cyclic-types where ```
Imports ```agda -open import foundation.automorphisms funext +open import foundation.automorphisms open import foundation.dependent-pair-types -open import foundation.iterating-automorphisms funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.surjective-maps funext +open import foundation.iterating-automorphisms +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.surjective-maps open import foundation.universe-levels -open import structured-types.sets-equipped-with-automorphisms funext +open import structured-types.sets-equipped-with-automorphisms ```
diff --git a/src/structured-types/dependent-products-h-spaces.lagda.md b/src/structured-types/dependent-products-h-spaces.lagda.md index 84afbe86e8..535481be7f 100644 --- a/src/structured-types/dependent-products-h-spaces.lagda.md +++ b/src/structured-types/dependent-products-h-spaces.lagda.md @@ -1,12 +1,7 @@ # Dependent products of H-spaces ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.dependent-products-h-spaces - (funext : function-extensionality) - where +module structured-types.dependent-products-h-spaces where ```
Imports @@ -14,14 +9,13 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.identity-types funext +open import foundation.function-extensionality +open import foundation.identity-types open import foundation.unital-binary-operations open import foundation.universe-levels open import structured-types.dependent-products-pointed-types -open import structured-types.h-spaces funext +open import structured-types.h-spaces open import structured-types.pointed-types ``` diff --git a/src/structured-types/dependent-products-wild-monoids.lagda.md b/src/structured-types/dependent-products-wild-monoids.lagda.md index f84c7fcf7d..183ccb58a5 100644 --- a/src/structured-types/dependent-products-wild-monoids.lagda.md +++ b/src/structured-types/dependent-products-wild-monoids.lagda.md @@ -1,12 +1,7 @@ # Dependent products of wild monoids ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.dependent-products-wild-monoids - (funext : function-extensionality) - where +module structured-types.dependent-products-wild-monoids where ```
Imports @@ -14,17 +9,16 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.function-extensionality +open import foundation.homotopies +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels -open import structured-types.dependent-products-h-spaces funext -open import structured-types.h-spaces funext +open import structured-types.dependent-products-h-spaces +open import structured-types.h-spaces open import structured-types.pointed-types -open import structured-types.wild-monoids funext +open import structured-types.wild-monoids ```
diff --git a/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md b/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md index 155f82ba02..5cc34bb515 100644 --- a/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/dependent-types-equipped-with-automorphisms.lagda.md @@ -1,32 +1,27 @@ # Dependent types equipped with automorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.dependent-types-equipped-with-automorphisms - (funext : function-extensionality) - where +module structured-types.dependent-types-equipped-with-automorphisms where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels -open import structured-types.types-equipped-with-automorphisms funext +open import structured-types.types-equipped-with-automorphisms ```
diff --git a/src/structured-types/equivalences-h-spaces.lagda.md b/src/structured-types/equivalences-h-spaces.lagda.md index 27d83b75f0..3a8285ea5c 100644 --- a/src/structured-types/equivalences-h-spaces.lagda.md +++ b/src/structured-types/equivalences-h-spaces.lagda.md @@ -1,36 +1,31 @@ # Equivalences of H-spaces ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.equivalences-h-spaces - (funext : function-extensionality) - where +module structured-types.equivalences-h-spaces where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-squares-of-identifications +open import foundation.commuting-triangles-of-identifications open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.path-algebra funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.path-algebra open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import group-theory.homomorphisms-semigroups funext +open import group-theory.homomorphisms-semigroups -open import structured-types.h-spaces funext -open import structured-types.morphisms-h-spaces funext -open import structured-types.pointed-equivalences funext -open import structured-types.pointed-maps funext +open import structured-types.h-spaces +open import structured-types.morphisms-h-spaces +open import structured-types.pointed-equivalences +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/equivalences-pointed-arrows.lagda.md b/src/structured-types/equivalences-pointed-arrows.lagda.md index 97b3a7d133..0d1aacbfd7 100644 --- a/src/structured-types/equivalences-pointed-arrows.lagda.md +++ b/src/structured-types/equivalences-pointed-arrows.lagda.md @@ -1,28 +1,23 @@ # Equivalences of pointed arrows ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.equivalences-pointed-arrows - (funext : function-extensionality) - where +module structured-types.equivalences-pointed-arrows where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.commuting-squares-of-pointed-maps funext -open import structured-types.pointed-equivalences funext -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.commuting-squares-of-pointed-maps +open import structured-types.pointed-equivalences +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md b/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md index 55101f97bd..a9d7268372 100644 --- a/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/equivalences-types-equipped-with-automorphisms.lagda.md @@ -1,31 +1,26 @@ # Equivalences of types equipped with automorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.equivalences-types-equipped-with-automorphisms - (funext : function-extensionality) - where +module structured-types.equivalences-types-equipped-with-automorphisms where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext +open import foundation.equivalence-extensionality +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-endomorphisms funext -open import structured-types.morphisms-types-equipped-with-automorphisms funext -open import structured-types.types-equipped-with-automorphisms funext +open import structured-types.equivalences-types-equipped-with-endomorphisms +open import structured-types.morphisms-types-equipped-with-automorphisms +open import structured-types.types-equipped-with-automorphisms ```
diff --git a/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md index fe4ae4cfb3..3b8b45fb50 100644 --- a/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md @@ -1,37 +1,32 @@ # Equivalences of types equipped with endomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.equivalences-types-equipped-with-endomorphisms - (funext : function-extensionality) - where +module structured-types.equivalences-types-equipped-with-endomorphisms where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import structured-types.morphisms-types-equipped-with-endomorphisms funext -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.morphisms-types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms ```
diff --git a/src/structured-types/faithful-pointed-maps.lagda.md b/src/structured-types/faithful-pointed-maps.lagda.md index a88ec96450..eeb654cf27 100644 --- a/src/structured-types/faithful-pointed-maps.lagda.md +++ b/src/structured-types/faithful-pointed-maps.lagda.md @@ -1,23 +1,18 @@ # Faithful pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.faithful-pointed-maps - (funext : function-extensionality) - where +module structured-types.faithful-pointed-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.faithful-maps funext -open import foundation.identity-types funext +open import foundation.faithful-maps +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/fibers-of-pointed-maps.lagda.md b/src/structured-types/fibers-of-pointed-maps.lagda.md index cdcaf5a39e..3564027bd2 100644 --- a/src/structured-types/fibers-of-pointed-maps.lagda.md +++ b/src/structured-types/fibers-of-pointed-maps.lagda.md @@ -1,22 +1,17 @@ # Fibers of pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.fibers-of-pointed-maps - (funext : function-extensionality) - where +module structured-types.fibers-of-pointed-maps where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext +open import foundation.fibers-of-maps open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/finite-multiplication-magmas.lagda.md b/src/structured-types/finite-multiplication-magmas.lagda.md index b7a529952e..6c31a6bd9a 100644 --- a/src/structured-types/finite-multiplication-magmas.lagda.md +++ b/src/structured-types/finite-multiplication-magmas.lagda.md @@ -1,12 +1,7 @@ # Finite multiplication in magmas ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.finite-multiplication-magmas - (funext : function-extensionality) - where +module structured-types.finite-multiplication-magmas where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.coproduct-types +open import foundation.equivalences +open import foundation.function-types open import foundation.unit-type open import foundation.universe-levels -open import structured-types.magmas funext +open import structured-types.magmas -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/structured-types/function-h-spaces.lagda.md b/src/structured-types/function-h-spaces.lagda.md index 67488bbb24..05b8a63e3c 100644 --- a/src/structured-types/function-h-spaces.lagda.md +++ b/src/structured-types/function-h-spaces.lagda.md @@ -1,23 +1,18 @@ # Function H-spaces ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.function-h-spaces - (funext : function-extensionality) - where +module structured-types.function-h-spaces where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import structured-types.dependent-products-h-spaces funext -open import structured-types.h-spaces funext +open import structured-types.dependent-products-h-spaces +open import structured-types.h-spaces open import structured-types.pointed-types ``` diff --git a/src/structured-types/function-magmas.lagda.md b/src/structured-types/function-magmas.lagda.md index d1d767239a..e5eef3f42a 100644 --- a/src/structured-types/function-magmas.lagda.md +++ b/src/structured-types/function-magmas.lagda.md @@ -1,12 +1,7 @@ # Function magmas ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.function-magmas - (funext : function-extensionality) - where +module structured-types.function-magmas where ```
Imports @@ -15,7 +10,7 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.magmas funext +open import structured-types.magmas ```
diff --git a/src/structured-types/function-wild-monoids.lagda.md b/src/structured-types/function-wild-monoids.lagda.md index 079a8ec6a6..154a0e8116 100644 --- a/src/structured-types/function-wild-monoids.lagda.md +++ b/src/structured-types/function-wild-monoids.lagda.md @@ -1,24 +1,19 @@ # Function wild monoids ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.function-wild-monoids - (funext : function-extensionality) - where +module structured-types.function-wild-monoids where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.dependent-products-wild-monoids funext -open import structured-types.h-spaces funext +open import structured-types.dependent-products-wild-monoids +open import structured-types.h-spaces open import structured-types.pointed-types -open import structured-types.wild-monoids funext +open import structured-types.wild-monoids ```
diff --git a/src/structured-types/h-spaces.lagda.md b/src/structured-types/h-spaces.lagda.md index 8cec45ccce..be217b8539 100644 --- a/src/structured-types/h-spaces.lagda.md +++ b/src/structured-types/h-spaces.lagda.md @@ -1,12 +1,7 @@ # H-spaces ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.h-spaces - (funext : function-extensionality) - where +module structured-types.h-spaces where ```
Imports @@ -15,25 +10,24 @@ module open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.evaluation-functions -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.unital-binary-operations open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import foundation-core.endomorphisms funext +open import foundation-core.endomorphisms -open import structured-types.magmas funext -open import structured-types.noncoherent-h-spaces funext -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext -open import structured-types.pointed-sections funext +open import structured-types.magmas +open import structured-types.noncoherent-h-spaces +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps +open import structured-types.pointed-sections open import structured-types.pointed-types ``` diff --git a/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md b/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md index 2eceaeb464..cab4124961 100644 --- a/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md +++ b/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md @@ -1,12 +1,7 @@ # The initial pointed type equipped with an automorphism ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.initial-pointed-type-equipped-with-automorphism - (funext : function-extensionality) - where +module structured-types.initial-pointed-type-equipped-with-automorphism where ```
Imports @@ -16,18 +11,18 @@ open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.iterating-automorphisms funext -open import foundation.transposition-identifications-along-equivalences funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types +open import foundation.iterating-automorphisms +open import foundation.transposition-identifications-along-equivalences open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-types-equipped-with-automorphisms funext +open import structured-types.pointed-types-equipped-with-automorphisms ```
diff --git a/src/structured-types/involutive-type-of-h-space-structures.lagda.md b/src/structured-types/involutive-type-of-h-space-structures.lagda.md index efe2dc3aa8..a9109305c2 100644 --- a/src/structured-types/involutive-type-of-h-space-structures.lagda.md +++ b/src/structured-types/involutive-type-of-h-space-structures.lagda.md @@ -1,12 +1,7 @@ # The involutive type of H-space structures on a pointed type ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.involutive-type-of-h-space-structures - (funext : function-extensionality) - where +module structured-types.involutive-type-of-h-space-structures where ```
Imports @@ -14,25 +9,25 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.constant-maps funext -open import foundation.contractible-types funext +open import foundation.constant-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.symmetric-identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.symmetric-identity-types +open import foundation.torsorial-type-families open import foundation.universe-levels -open import structured-types.constant-pointed-maps funext +open import structured-types.constant-pointed-maps open import structured-types.pointed-types -open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.2-element-types ```
diff --git a/src/structured-types/involutive-types.lagda.md b/src/structured-types/involutive-types.lagda.md index af59a2318f..14c1459d5d 100644 --- a/src/structured-types/involutive-types.lagda.md +++ b/src/structured-types/involutive-types.lagda.md @@ -1,22 +1,17 @@ # Involutive types ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.involutive-types - (funext : function-extensionality) - where +module structured-types.involutive-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.2-element-types ```
diff --git a/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md index 1f15dde562..58ed426a9e 100644 --- a/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/iterated-cartesian-products-types-equipped-with-endomorphisms.lagda.md @@ -13,8 +13,8 @@ open import foundation.universe-levels open import lists.lists -open import structured-types.cartesian-products-types-equipped-with-endomorphisms funext -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.cartesian-products-types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms ```
diff --git a/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md b/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md index b2f70f218f..305993ecf4 100644 --- a/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md +++ b/src/structured-types/iterated-pointed-cartesian-product-types.lagda.md @@ -1,25 +1,20 @@ # Iterated cartesian products of pointed types ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.iterated-pointed-cartesian-product-types - (funext : function-extensionality) - where +module structured-types.iterated-pointed-cartesian-product-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.raising-universe-levels-unit-type funext +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels open import lists.lists -open import structured-types.pointed-cartesian-product-types funext +open import structured-types.pointed-cartesian-product-types open import structured-types.pointed-types ``` diff --git a/src/structured-types/magmas.lagda.md b/src/structured-types/magmas.lagda.md index da402fe17b..13372059eb 100644 --- a/src/structured-types/magmas.lagda.md +++ b/src/structured-types/magmas.lagda.md @@ -1,20 +1,15 @@ # Magmas ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.magmas - (funext : function-extensionality) - where +module structured-types.magmas where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unital-binary-operations open import foundation.universe-levels ``` diff --git a/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md index ab90827857..0d43b47932 100644 --- a/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md @@ -1,30 +1,25 @@ # Mere equivalences of types equipped with endomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.mere-equivalences-types-equipped-with-endomorphisms - (funext : function-extensionality) - where +module structured-types.mere-equivalences-types-equipped-with-endomorphisms where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-endomorphisms funext -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.equivalences-types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-endomorphisms ```
diff --git a/src/structured-types/morphisms-h-spaces.lagda.md b/src/structured-types/morphisms-h-spaces.lagda.md index f0b746e082..15fe75ebf3 100644 --- a/src/structured-types/morphisms-h-spaces.lagda.md +++ b/src/structured-types/morphisms-h-spaces.lagda.md @@ -1,34 +1,29 @@ # Morphisms of H-spaces ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.morphisms-h-spaces - (funext : function-extensionality) - where +module structured-types.morphisms-h-spaces where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-squares-of-identifications +open import foundation.commuting-triangles-of-identifications open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.path-algebra funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.path-algebra open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import group-theory.homomorphisms-semigroups funext +open import group-theory.homomorphisms-semigroups -open import structured-types.h-spaces funext -open import structured-types.pointed-maps funext +open import structured-types.h-spaces +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/morphisms-magmas.lagda.md b/src/structured-types/morphisms-magmas.lagda.md index fab320fe37..e5d3920e3b 100644 --- a/src/structured-types/morphisms-magmas.lagda.md +++ b/src/structured-types/morphisms-magmas.lagda.md @@ -1,22 +1,17 @@ # Morphisms of magmas ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.morphisms-magmas - (funext : function-extensionality) - where +module structured-types.morphisms-magmas where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.magmas funext +open import structured-types.magmas ```
diff --git a/src/structured-types/morphisms-pointed-arrows.lagda.md b/src/structured-types/morphisms-pointed-arrows.lagda.md index 7e730463c2..a7f8e2d3fe 100644 --- a/src/structured-types/morphisms-pointed-arrows.lagda.md +++ b/src/structured-types/morphisms-pointed-arrows.lagda.md @@ -1,47 +1,42 @@ # Morphisms of pointed arrows ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.morphisms-pointed-arrows - (funext : function-extensionality) - where +module structured-types.morphisms-pointed-arrows where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-identifications funext -open import foundation.commuting-triangles-of-identifications funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-identifications +open import foundation.commuting-triangles-of-identifications +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types funext +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopy-induction funext -open import foundation.morphisms-arrows funext -open import foundation.path-algebra funext +open import foundation.homotopy-induction +open import foundation.morphisms-arrows +open import foundation.path-algebra open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.torsorial-type-families -open import structured-types.commuting-squares-of-pointed-homotopies funext -open import structured-types.commuting-squares-of-pointed-maps funext -open import structured-types.pointed-2-homotopies funext -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.commuting-squares-of-pointed-homotopies +open import structured-types.commuting-squares-of-pointed-maps +open import structured-types.pointed-2-homotopies +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.whiskering-pointed-2-homotopies-concatenation funext -open import structured-types.whiskering-pointed-homotopies-composition funext +open import structured-types.whiskering-pointed-2-homotopies-concatenation +open import structured-types.whiskering-pointed-homotopies-composition ```
diff --git a/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md b/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md index 2c770f6a7e..42373c4872 100644 --- a/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md +++ b/src/structured-types/morphisms-twisted-pointed-arrows.lagda.md @@ -1,25 +1,20 @@ # Morphisms of twisted pointed arrows ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.morphisms-twisted-pointed-arrows - (funext : function-extensionality) - where +module structured-types.morphisms-twisted-pointed-arrows where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.morphisms-twisted-arrows open import foundation.universe-levels -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md b/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md index ea6be7b259..2f74c32b78 100644 --- a/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/morphisms-types-equipped-with-automorphisms.lagda.md @@ -1,25 +1,20 @@ # Morphisms of types equipped with automorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.morphisms-types-equipped-with-automorphisms - (funext : function-extensionality) - where +module structured-types.morphisms-types-equipped-with-automorphisms where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.commuting-squares-of-maps +open import foundation.equivalences +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.universe-levels -open import structured-types.morphisms-types-equipped-with-endomorphisms funext -open import structured-types.types-equipped-with-automorphisms funext +open import structured-types.morphisms-types-equipped-with-endomorphisms +open import structured-types.types-equipped-with-automorphisms ```
diff --git a/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md index e16a617d4d..3215246b06 100644 --- a/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md @@ -1,32 +1,27 @@ # Morphisms of types equipped with endomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.morphisms-types-equipped-with-endomorphisms - (funext : function-extensionality) - where +module structured-types.morphisms-types-equipped-with-endomorphisms where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms ```
diff --git a/src/structured-types/morphisms-wild-monoids.lagda.md b/src/structured-types/morphisms-wild-monoids.lagda.md index 16f5633889..93df4f6dd1 100644 --- a/src/structured-types/morphisms-wild-monoids.lagda.md +++ b/src/structured-types/morphisms-wild-monoids.lagda.md @@ -1,26 +1,21 @@ # Morphisms of wild monoids ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.morphisms-wild-monoids - (funext : function-extensionality) - where +module structured-types.morphisms-wild-monoids where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import group-theory.homomorphisms-semigroups funext +open import group-theory.homomorphisms-semigroups -open import structured-types.morphisms-h-spaces funext -open import structured-types.pointed-maps funext -open import structured-types.wild-monoids funext +open import structured-types.morphisms-h-spaces +open import structured-types.pointed-maps +open import structured-types.wild-monoids ```
diff --git a/src/structured-types/noncoherent-h-spaces.lagda.md b/src/structured-types/noncoherent-h-spaces.lagda.md index 0fec4a09e3..bf3ba3b5d1 100644 --- a/src/structured-types/noncoherent-h-spaces.lagda.md +++ b/src/structured-types/noncoherent-h-spaces.lagda.md @@ -1,19 +1,14 @@ # Noncoherent H-spaces ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.noncoherent-h-spaces - (funext : function-extensionality) - where +module structured-types.noncoherent-h-spaces where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unital-binary-operations open import foundation.universe-levels diff --git a/src/structured-types/opposite-pointed-spans.lagda.md b/src/structured-types/opposite-pointed-spans.lagda.md index 3b902c2967..2c29bc256f 100644 --- a/src/structured-types/opposite-pointed-spans.lagda.md +++ b/src/structured-types/opposite-pointed-spans.lagda.md @@ -1,12 +1,7 @@ # Opposite pointed spans ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.opposite-pointed-spans - (funext : function-extensionality) - where +module structured-types.opposite-pointed-spans where ```
Imports @@ -15,7 +10,7 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-spans funext +open import structured-types.pointed-spans open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-2-homotopies.lagda.md b/src/structured-types/pointed-2-homotopies.lagda.md index dbe1306d42..7b40b04004 100644 --- a/src/structured-types/pointed-2-homotopies.lagda.md +++ b/src/structured-types/pointed-2-homotopies.lagda.md @@ -1,12 +1,7 @@ # Pointed `2`-homotopies ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-2-homotopies - (funext : function-extensionality) - where +module structured-types.pointed-2-homotopies where ```
Imports @@ -14,27 +9,27 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-equivalences -open import foundation.commuting-triangles-of-identifications funext -open import foundation.contractible-types funext +open import foundation.commuting-triangles-of-identifications +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.path-algebra funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.path-algebra open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import structured-types.pointed-dependent-functions funext +open import structured-types.pointed-dependent-functions open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.uniform-pointed-homotopies funext +open import structured-types.uniform-pointed-homotopies ```
diff --git a/src/structured-types/pointed-cartesian-product-types.lagda.md b/src/structured-types/pointed-cartesian-product-types.lagda.md index 0429868475..6e40cdb641 100644 --- a/src/structured-types/pointed-cartesian-product-types.lagda.md +++ b/src/structured-types/pointed-cartesian-product-types.lagda.md @@ -1,26 +1,21 @@ # Pointed cartesian product types ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-cartesian-product-types - (funext : function-extensionality) - where +module structured-types.pointed-cartesian-product-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-dependent-functions.lagda.md b/src/structured-types/pointed-dependent-functions.lagda.md index fcf95c937e..7df9e3085d 100644 --- a/src/structured-types/pointed-dependent-functions.lagda.md +++ b/src/structured-types/pointed-dependent-functions.lagda.md @@ -1,21 +1,16 @@ # Pointed dependent functions ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-dependent-functions - (funext : function-extensionality) - where +module structured-types.pointed-dependent-functions where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels open import structured-types.pointed-families-of-types diff --git a/src/structured-types/pointed-equivalences.lagda.md b/src/structured-types/pointed-equivalences.lagda.md index fb9819cb19..0305b2134d 100644 --- a/src/structured-types/pointed-equivalences.lagda.md +++ b/src/structured-types/pointed-equivalences.lagda.md @@ -1,12 +1,7 @@ # Pointed equivalences ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-equivalences - (funext : function-extensionality) - where +module structured-types.pointed-equivalences where ```
Imports @@ -15,32 +10,32 @@ module open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.path-algebra funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.path-algebra +open import foundation.propositions +open import foundation.retractions +open import foundation.sections open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext -open import structured-types.pointed-retractions funext -open import structured-types.pointed-sections funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps +open import structured-types.pointed-retractions +open import structured-types.pointed-sections open import structured-types.pointed-types -open import structured-types.postcomposition-pointed-maps funext -open import structured-types.precomposition-pointed-maps funext -open import structured-types.universal-property-pointed-equivalences funext -open import structured-types.whiskering-pointed-homotopies-composition funext +open import structured-types.postcomposition-pointed-maps +open import structured-types.precomposition-pointed-maps +open import structured-types.universal-property-pointed-equivalences +open import structured-types.whiskering-pointed-homotopies-composition ```
diff --git a/src/structured-types/pointed-homotopies.lagda.md b/src/structured-types/pointed-homotopies.lagda.md index 6d1ca2e57c..dabdeef3c9 100644 --- a/src/structured-types/pointed-homotopies.lagda.md +++ b/src/structured-types/pointed-homotopies.lagda.md @@ -1,12 +1,7 @@ # Pointed homotopies ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-homotopies - (funext : function-extensionality) - where +module structured-types.pointed-homotopies where ```
Imports @@ -14,24 +9,24 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-equivalences -open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-triangles-of-identifications open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation open import foundation-core.torsorial-type-families -open import structured-types.pointed-dependent-functions funext +open import structured-types.pointed-dependent-functions open import structured-types.pointed-families-of-types -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-isomorphisms.lagda.md b/src/structured-types/pointed-isomorphisms.lagda.md index cc30482f74..f38534a262 100644 --- a/src/structured-types/pointed-isomorphisms.lagda.md +++ b/src/structured-types/pointed-isomorphisms.lagda.md @@ -1,35 +1,30 @@ # Pointed isomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-isomorphisms - (funext : function-extensionality) - where +module structured-types.pointed-isomorphisms where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.retractions +open import foundation.sections open import foundation.structure-identity-principle open import foundation.universe-levels -open import structured-types.pointed-equivalences funext -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext -open import structured-types.pointed-retractions funext -open import structured-types.pointed-sections funext +open import structured-types.pointed-equivalences +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps +open import structured-types.pointed-retractions +open import structured-types.pointed-sections open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-maps.lagda.md b/src/structured-types/pointed-maps.lagda.md index 674bd77994..1a8de69535 100644 --- a/src/structured-types/pointed-maps.lagda.md +++ b/src/structured-types/pointed-maps.lagda.md @@ -1,12 +1,7 @@ # Pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-maps - (funext : function-extensionality) - where +module structured-types.pointed-maps where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.constant-maps funext +open import foundation.constant-maps open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import structured-types.pointed-dependent-functions funext +open import structured-types.pointed-dependent-functions open import structured-types.pointed-families-of-types open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-retractions.lagda.md b/src/structured-types/pointed-retractions.lagda.md index 5571cf61d5..d4b837ac66 100644 --- a/src/structured-types/pointed-retractions.lagda.md +++ b/src/structured-types/pointed-retractions.lagda.md @@ -1,29 +1,24 @@ # Pointed retractions of pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-retractions - (funext : function-extensionality) - where +module structured-types.pointed-retractions where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-identifications open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels open import foundation-core.contractible-maps open import foundation-core.contractible-types open import foundation-core.retractions -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-sections.lagda.md b/src/structured-types/pointed-sections.lagda.md index 8fd23278e9..a3dfdb69f3 100644 --- a/src/structured-types/pointed-sections.lagda.md +++ b/src/structured-types/pointed-sections.lagda.md @@ -1,24 +1,19 @@ # Pointed sections of pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-sections - (funext : function-extensionality) - where +module structured-types.pointed-sections where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sections funext +open import foundation.identity-types +open import foundation.sections open import foundation.universe-levels -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-span-diagrams.lagda.md b/src/structured-types/pointed-span-diagrams.lagda.md index d5db510a0a..95f98ce716 100644 --- a/src/structured-types/pointed-span-diagrams.lagda.md +++ b/src/structured-types/pointed-span-diagrams.lagda.md @@ -1,25 +1,20 @@ # Pointed span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-span-diagrams - (funext : function-extensionality) - where +module structured-types.pointed-span-diagrams where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.morphisms-arrows funext +open import foundation.identity-types +open import foundation.morphisms-arrows open import foundation.universe-levels -open import structured-types.morphisms-pointed-arrows funext -open import structured-types.pointed-maps funext -open import structured-types.pointed-spans funext +open import structured-types.morphisms-pointed-arrows +open import structured-types.pointed-maps +open import structured-types.pointed-spans open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-spans.lagda.md b/src/structured-types/pointed-spans.lagda.md index 5e96e5bf17..125e01bee5 100644 --- a/src/structured-types/pointed-spans.lagda.md +++ b/src/structured-types/pointed-spans.lagda.md @@ -1,24 +1,19 @@ # Pointed spans ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-spans - (funext : function-extensionality) - where +module structured-types.pointed-spans where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.spans open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md b/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md index b82f5b5f20..b97e8e7ae3 100644 --- a/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md @@ -1,31 +1,26 @@ # Pointed types equipped with automorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-types-equipped-with-automorphisms - (funext : function-extensionality) - where +module structured-types.pointed-types-equipped-with-automorphisms where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.automorphisms funext -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.automorphisms +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import structured-types.pointed-types diff --git a/src/structured-types/pointed-unit-type.lagda.md b/src/structured-types/pointed-unit-type.lagda.md index 927a96670b..af2130cf0b 100644 --- a/src/structured-types/pointed-unit-type.lagda.md +++ b/src/structured-types/pointed-unit-type.lagda.md @@ -1,24 +1,19 @@ # The pointed unit type ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-unit-type - (funext : function-extensionality) - where +module structured-types.pointed-unit-type where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/pointed-universal-property-contractible-types.lagda.md b/src/structured-types/pointed-universal-property-contractible-types.lagda.md index 64e79fd00d..296b91ee4b 100644 --- a/src/structured-types/pointed-universal-property-contractible-types.lagda.md +++ b/src/structured-types/pointed-universal-property-contractible-types.lagda.md @@ -1,29 +1,24 @@ # Universal property of contractible types with respect to pointed types and maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.pointed-universal-property-contractible-types - (funext : function-extensionality) - where +module structured-types.pointed-universal-property-contractible-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types -open import foundation.universal-property-contractible-types funext +open import foundation.universal-property-contractible-types open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/postcomposition-pointed-maps.lagda.md b/src/structured-types/postcomposition-pointed-maps.lagda.md index 21c5ec0f02..03629c2259 100644 --- a/src/structured-types/postcomposition-pointed-maps.lagda.md +++ b/src/structured-types/postcomposition-pointed-maps.lagda.md @@ -1,12 +1,7 @@ # Postcomposition of pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.postcomposition-pointed-maps - (funext : function-extensionality) - where +module structured-types.postcomposition-pointed-maps where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/precomposition-pointed-maps.lagda.md b/src/structured-types/precomposition-pointed-maps.lagda.md index ba3e2ada46..da91cbc088 100644 --- a/src/structured-types/precomposition-pointed-maps.lagda.md +++ b/src/structured-types/precomposition-pointed-maps.lagda.md @@ -1,12 +1,7 @@ # Precomposition of pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.precomposition-pointed-maps - (funext : function-extensionality) - where +module structured-types.precomposition-pointed-maps where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/sets-equipped-with-automorphisms.lagda.md b/src/structured-types/sets-equipped-with-automorphisms.lagda.md index ca24903b47..2d0431fa3f 100644 --- a/src/structured-types/sets-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/sets-equipped-with-automorphisms.lagda.md @@ -1,22 +1,17 @@ # Sets equipped with automorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.sets-equipped-with-automorphisms - (funext : function-extensionality) - where +module structured-types.sets-equipped-with-automorphisms where ```
Imports ```agda -open import foundation.automorphisms funext +open import foundation.automorphisms open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/structured-types/small-pointed-types.lagda.md b/src/structured-types/small-pointed-types.lagda.md index 30ebe6bcb9..c1ee5d36fa 100644 --- a/src/structured-types/small-pointed-types.lagda.md +++ b/src/structured-types/small-pointed-types.lagda.md @@ -1,27 +1,22 @@ # Small pointed types ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.small-pointed-types - (funext : function-extensionality) - where +module structured-types.small-pointed-types where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.small-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.small-types open import foundation.universe-levels -open import structured-types.pointed-equivalences funext +open import structured-types.pointed-equivalences open import structured-types.pointed-types ``` diff --git a/src/structured-types/symmetric-elements-involutive-types.lagda.md b/src/structured-types/symmetric-elements-involutive-types.lagda.md index 4c2621cab5..d9f5ee8705 100644 --- a/src/structured-types/symmetric-elements-involutive-types.lagda.md +++ b/src/structured-types/symmetric-elements-involutive-types.lagda.md @@ -1,12 +1,7 @@ # Symmetric elements of involutive types ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.symmetric-elements-involutive-types - (funext : function-extensionality) - where +module structured-types.symmetric-elements-involutive-types where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import foundation.universe-levels -open import structured-types.involutive-types funext +open import structured-types.involutive-types -open import univalent-combinatorics.2-element-types funext +open import univalent-combinatorics.2-element-types ```
diff --git a/src/structured-types/symmetric-h-spaces.lagda.md b/src/structured-types/symmetric-h-spaces.lagda.md index 1de28b6122..95d5e73667 100644 --- a/src/structured-types/symmetric-h-spaces.lagda.md +++ b/src/structured-types/symmetric-h-spaces.lagda.md @@ -1,24 +1,19 @@ # Symmetric H-spaces ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.symmetric-h-spaces - (funext : function-extensionality) - where +module structured-types.symmetric-h-spaces where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.symmetric-operations funext +open import foundation.symmetric-operations open import foundation.universe-levels -open import structured-types.involutive-type-of-h-space-structures funext +open import structured-types.involutive-type-of-h-space-structures open import structured-types.pointed-types -open import structured-types.symmetric-elements-involutive-types funext +open import structured-types.symmetric-elements-involutive-types ```
diff --git a/src/structured-types/transposition-pointed-span-diagrams.lagda.md b/src/structured-types/transposition-pointed-span-diagrams.lagda.md index 460b11fa1c..3b21a8cd57 100644 --- a/src/structured-types/transposition-pointed-span-diagrams.lagda.md +++ b/src/structured-types/transposition-pointed-span-diagrams.lagda.md @@ -1,12 +1,7 @@ # Transposition of pointed span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.transposition-pointed-span-diagrams - (funext : function-extensionality) - where +module structured-types.transposition-pointed-span-diagrams where ```
Imports @@ -15,8 +10,8 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.opposite-pointed-spans funext -open import structured-types.pointed-span-diagrams funext +open import structured-types.opposite-pointed-spans +open import structured-types.pointed-span-diagrams ```
diff --git a/src/structured-types/types-equipped-with-automorphisms.lagda.md b/src/structured-types/types-equipped-with-automorphisms.lagda.md index 551a3e2493..56e43e8efd 100644 --- a/src/structured-types/types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/types-equipped-with-automorphisms.lagda.md @@ -1,23 +1,18 @@ # Types equipped with automorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.types-equipped-with-automorphisms - (funext : function-extensionality) - where +module structured-types.types-equipped-with-automorphisms where ```
Imports ```agda -open import foundation.automorphisms funext +open import foundation.automorphisms open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms ```
diff --git a/src/structured-types/types-equipped-with-endomorphisms.lagda.md b/src/structured-types/types-equipped-with-endomorphisms.lagda.md index 499c2977f8..beffcc9d59 100644 --- a/src/structured-types/types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/types-equipped-with-endomorphisms.lagda.md @@ -1,23 +1,18 @@ # Types equipped with endomorphisms ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.types-equipped-with-endomorphisms - (funext : function-extensionality) - where +module structured-types.types-equipped-with-endomorphisms where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.raising-universe-levels-unit-type funext +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.endomorphisms funext +open import foundation-core.endomorphisms open import foundation-core.function-types ``` diff --git a/src/structured-types/uniform-pointed-homotopies.lagda.md b/src/structured-types/uniform-pointed-homotopies.lagda.md index f2fa6b4349..eb98f22918 100644 --- a/src/structured-types/uniform-pointed-homotopies.lagda.md +++ b/src/structured-types/uniform-pointed-homotopies.lagda.md @@ -1,33 +1,27 @@ # Uniform pointed homotopies ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.uniform-pointed-homotopies - (funext : function-extensionality) - where +module structured-types.uniform-pointed-homotopies where ```
Imports ```agda -open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-triangles-of-identifications open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.universe-levels -open import structured-types.pointed-dependent-functions funext +open import structured-types.pointed-dependent-functions open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/universal-property-pointed-equivalences.lagda.md b/src/structured-types/universal-property-pointed-equivalences.lagda.md index e6acc824ac..1ed069812f 100644 --- a/src/structured-types/universal-property-pointed-equivalences.lagda.md +++ b/src/structured-types/universal-property-pointed-equivalences.lagda.md @@ -1,23 +1,18 @@ # The universal property of pointed equivalences ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.universal-property-pointed-equivalences - (funext : function-extensionality) - where +module structured-types.universal-property-pointed-equivalences where ```
Imports ```agda -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.precomposition-pointed-maps funext +open import structured-types.precomposition-pointed-maps ```
diff --git a/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md b/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md index c211e5bcde..7e99884c46 100644 --- a/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md +++ b/src/structured-types/whiskering-pointed-2-homotopies-concatenation.lagda.md @@ -1,29 +1,24 @@ # Whiskering pointed homotopies with respect to concatenation ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.whiskering-pointed-2-homotopies-concatenation - (funext : function-extensionality) - where +module structured-types.whiskering-pointed-2-homotopies-concatenation where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-triangles-of-identifications open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.path-algebra funext +open import foundation.identity-types +open import foundation.path-algebra open import foundation.universe-levels -open import foundation.whiskering-homotopies-concatenation funext -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-homotopies-concatenation +open import foundation.whiskering-identifications-concatenation -open import structured-types.pointed-2-homotopies funext -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-2-homotopies +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md b/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md index 0819340370..ce71678ce6 100644 --- a/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md +++ b/src/structured-types/whiskering-pointed-homotopies-composition.lagda.md @@ -1,12 +1,7 @@ # Whiskering of pointed homotopies with respect to composition of pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.whiskering-pointed-homotopies-composition - (funext : function-extensionality) - where +module structured-types.whiskering-pointed-homotopies-composition where ```
Imports @@ -14,19 +9,19 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.commuting-triangles-of-identifications funext +open import foundation.commuting-squares-of-identifications +open import foundation.commuting-triangles-of-identifications open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import structured-types.pointed-2-homotopies funext +open import structured-types.pointed-2-homotopies open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/structured-types/wild-category-of-pointed-types.lagda.md b/src/structured-types/wild-category-of-pointed-types.lagda.md index e421500afe..3ff1429d27 100644 --- a/src/structured-types/wild-category-of-pointed-types.lagda.md +++ b/src/structured-types/wild-category-of-pointed-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - structured-types.wild-category-of-pointed-types - (funext : function-extensionality) - where +module structured-types.wild-category-of-pointed-types where ```
Imports @@ -16,29 +11,29 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import globular-types.discrete-reflexive-globular-types funext +open import globular-types.discrete-reflexive-globular-types open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.large-reflexive-globular-types funext -open import globular-types.large-transitive-globular-types funext -open import globular-types.reflexive-globular-types funext -open import globular-types.transitive-globular-types funext +open import globular-types.large-reflexive-globular-types +open import globular-types.large-transitive-globular-types +open import globular-types.reflexive-globular-types +open import globular-types.transitive-globular-types -open import structured-types.pointed-2-homotopies funext -open import structured-types.pointed-dependent-functions funext +open import structured-types.pointed-2-homotopies +open import structured-types.pointed-dependent-functions open import structured-types.pointed-families-of-types -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.uniform-pointed-homotopies funext +open import structured-types.uniform-pointed-homotopies -open import wild-category-theory.noncoherent-large-omega-precategories funext -open import wild-category-theory.noncoherent-omega-precategories funext +open import wild-category-theory.noncoherent-large-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories ```
diff --git a/src/structured-types/wild-groups.lagda.md b/src/structured-types/wild-groups.lagda.md index 2620052ec1..a743c1d556 100644 --- a/src/structured-types/wild-groups.lagda.md +++ b/src/structured-types/wild-groups.lagda.md @@ -1,12 +1,7 @@ # Wild groups ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.wild-groups - (funext : function-extensionality) - where +module structured-types.wild-groups where ```
Imports @@ -16,7 +11,7 @@ open import foundation.binary-equivalences open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.wild-monoids funext +open import structured-types.wild-monoids ```
diff --git a/src/structured-types/wild-loops.lagda.md b/src/structured-types/wild-loops.lagda.md index 9aad4b47a9..0abc01f7c2 100644 --- a/src/structured-types/wild-loops.lagda.md +++ b/src/structured-types/wild-loops.lagda.md @@ -1,28 +1,23 @@ # Wild loops ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.wild-loops - (funext : function-extensionality) - where +module structured-types.wild-loops where ```
Imports ```agda -open import foundation.automorphisms funext +open import foundation.automorphisms open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.h-spaces funext -open import structured-types.magmas funext +open import structured-types.h-spaces +open import structured-types.magmas open import structured-types.pointed-types -open import structured-types.wild-quasigroups funext +open import structured-types.wild-quasigroups ```
diff --git a/src/structured-types/wild-monoids.lagda.md b/src/structured-types/wild-monoids.lagda.md index 289302fb1e..250cabb823 100644 --- a/src/structured-types/wild-monoids.lagda.md +++ b/src/structured-types/wild-monoids.lagda.md @@ -1,12 +1,7 @@ # Wild monoids ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.wild-monoids - (funext : function-extensionality) - where +module structured-types.wild-monoids where ```
Imports @@ -14,11 +9,11 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels -open import structured-types.h-spaces funext +open import structured-types.h-spaces open import structured-types.pointed-types ``` diff --git a/src/structured-types/wild-quasigroups.lagda.md b/src/structured-types/wild-quasigroups.lagda.md index e878fbd92d..a9e84acf35 100644 --- a/src/structured-types/wild-quasigroups.lagda.md +++ b/src/structured-types/wild-quasigroups.lagda.md @@ -1,24 +1,19 @@ # Wild quasigroups ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.wild-quasigroups - (funext : function-extensionality) - where +module structured-types.wild-quasigroups where ```
Imports ```agda -open import foundation.automorphisms funext +open import foundation.automorphisms open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import structured-types.magmas funext +open import structured-types.magmas ```
diff --git a/src/structured-types/wild-semigroups.lagda.md b/src/structured-types/wild-semigroups.lagda.md index fdd37df39b..f1a0642256 100644 --- a/src/structured-types/wild-semigroups.lagda.md +++ b/src/structured-types/wild-semigroups.lagda.md @@ -1,22 +1,17 @@ # Wild semigroups ```agda -open import foundation.function-extensionality-axiom - -module - structured-types.wild-semigroups - (funext : function-extensionality) - where +module structured-types.wild-semigroups where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.magmas funext +open import structured-types.magmas ```
diff --git a/src/synthetic-category-theory.lagda.md b/src/synthetic-category-theory.lagda.md index 666571a2ad..5ff89a2169 100644 --- a/src/synthetic-category-theory.lagda.md +++ b/src/synthetic-category-theory.lagda.md @@ -23,18 +23,13 @@ Some core principles of higher category theory include: ## Modules in the synthetic category theory namespace ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-category-theory - (funext : function-extensionality) - where - -open import synthetic-category-theory.cone-diagrams-synthetic-categories funext public -open import synthetic-category-theory.cospans-synthetic-categories funext public -open import synthetic-category-theory.equivalences-synthetic-categories funext public -open import synthetic-category-theory.invertible-functors-synthetic-categories funext public -open import synthetic-category-theory.pullbacks-synthetic-categories funext public +module synthetic-category-theory where + +open import synthetic-category-theory.cone-diagrams-synthetic-categories public +open import synthetic-category-theory.cospans-synthetic-categories public +open import synthetic-category-theory.equivalences-synthetic-categories public +open import synthetic-category-theory.invertible-functors-synthetic-categories public +open import synthetic-category-theory.pullbacks-synthetic-categories public open import synthetic-category-theory.retractions-synthetic-categories public open import synthetic-category-theory.sections-synthetic-categories public open import synthetic-category-theory.synthetic-categories public diff --git a/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md b/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md index 796eb45698..793041a163 100644 --- a/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/cone-diagrams-synthetic-categories.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - synthetic-category-theory.cone-diagrams-synthetic-categories - (funext : function-extensionality) - where +module synthetic-category-theory.cone-diagrams-synthetic-categories where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.cospans-synthetic-categories funext +open import synthetic-category-theory.cospans-synthetic-categories open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md b/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md index ec90b69f08..d4385ae17e 100644 --- a/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/cospans-synthetic-categories.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - synthetic-category-theory.cospans-synthetic-categories - (funext : function-extensionality) - where +module synthetic-category-theory.cospans-synthetic-categories where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.equivalences-synthetic-categories funext +open import synthetic-category-theory.equivalences-synthetic-categories open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md b/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md index d4f6753834..e616153e9f 100644 --- a/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/equivalences-synthetic-categories.lagda.md @@ -3,18 +3,13 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - synthetic-category-theory.equivalences-synthetic-categories - (funext : function-extensionality) - where +module synthetic-category-theory.equivalences-synthetic-categories where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels diff --git a/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md b/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md index 237d8a69db..79a237ffc1 100644 --- a/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/invertible-functors-synthetic-categories.lagda.md @@ -3,24 +3,19 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - synthetic-category-theory.invertible-functors-synthetic-categories - (funext : function-extensionality) - where +module synthetic-category-theory.invertible-functors-synthetic-categories where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.equivalences-synthetic-categories funext +open import synthetic-category-theory.equivalences-synthetic-categories open import synthetic-category-theory.retractions-synthetic-categories open import synthetic-category-theory.sections-synthetic-categories open import synthetic-category-theory.synthetic-categories diff --git a/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md b/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md index 05bba2ff48..c57580a72d 100644 --- a/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md +++ b/src/synthetic-category-theory/pullbacks-synthetic-categories.lagda.md @@ -3,26 +3,21 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - synthetic-category-theory.pullbacks-synthetic-categories - (funext : function-extensionality) - where +module synthetic-category-theory.pullbacks-synthetic-categories where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels open import globular-types.globular-types -open import synthetic-category-theory.cone-diagrams-synthetic-categories funext -open import synthetic-category-theory.cospans-synthetic-categories funext -open import synthetic-category-theory.equivalences-synthetic-categories funext +open import synthetic-category-theory.cone-diagrams-synthetic-categories +open import synthetic-category-theory.cospans-synthetic-categories +open import synthetic-category-theory.equivalences-synthetic-categories open import synthetic-category-theory.synthetic-categories ``` diff --git a/src/synthetic-homotopy-theory.lagda.md b/src/synthetic-homotopy-theory.lagda.md index f7c74a60b0..f05ba2976d 100644 --- a/src/synthetic-homotopy-theory.lagda.md +++ b/src/synthetic-homotopy-theory.lagda.md @@ -7,142 +7,137 @@ ## Modules in the synthetic homotopy theory namespace ```agda -open import foundation.function-extensionality-axiom +module synthetic-homotopy-theory where -module - synthetic-homotopy-theory - (funext : function-extensionality) - where - -open import synthetic-homotopy-theory.0-acyclic-maps funext public -open import synthetic-homotopy-theory.0-acyclic-types funext public -open import synthetic-homotopy-theory.1-acyclic-types funext public -open import synthetic-homotopy-theory.acyclic-maps funext public -open import synthetic-homotopy-theory.acyclic-types funext public -open import synthetic-homotopy-theory.category-of-connected-set-bundles-circle funext public -open import synthetic-homotopy-theory.cavallos-trick funext public -open import synthetic-homotopy-theory.circle funext public -open import synthetic-homotopy-theory.cocartesian-morphisms-arrows funext public -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext public -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext public -open import synthetic-homotopy-theory.cocones-under-spans funext public -open import synthetic-homotopy-theory.codiagonals-of-maps funext public -open import synthetic-homotopy-theory.coequalizers funext public -open import synthetic-homotopy-theory.cofibers-of-maps funext public -open import synthetic-homotopy-theory.cofibers-of-pointed-maps funext public -open import synthetic-homotopy-theory.coforks funext public -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams funext public -open import synthetic-homotopy-theory.conjugation-loops funext public -open import synthetic-homotopy-theory.connected-set-bundles-circle funext public -open import synthetic-homotopy-theory.connective-prespectra funext public -open import synthetic-homotopy-theory.connective-spectra funext public -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext public -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext public -open import synthetic-homotopy-theory.dependent-coforks funext public -open import synthetic-homotopy-theory.dependent-descent-circle funext public -open import synthetic-homotopy-theory.dependent-pullback-property-pushouts funext public -open import synthetic-homotopy-theory.dependent-pushout-products funext public -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext public -open import synthetic-homotopy-theory.dependent-suspension-structures funext public -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext public -open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext public -open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits funext public -open import synthetic-homotopy-theory.dependent-universal-property-suspensions funext public -open import synthetic-homotopy-theory.descent-circle funext public -open import synthetic-homotopy-theory.descent-circle-constant-families funext public -open import synthetic-homotopy-theory.descent-circle-dependent-pair-types funext public -open import synthetic-homotopy-theory.descent-circle-equivalence-types funext public -open import synthetic-homotopy-theory.descent-circle-function-types funext public -open import synthetic-homotopy-theory.descent-circle-subtypes funext public -open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts funext public -open import synthetic-homotopy-theory.descent-data-function-types-over-pushouts funext public -open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts funext public -open import synthetic-homotopy-theory.descent-data-pushouts funext public -open import synthetic-homotopy-theory.descent-data-sequential-colimits funext public -open import synthetic-homotopy-theory.descent-property-pushouts funext public -open import synthetic-homotopy-theory.descent-property-sequential-colimits funext public -open import synthetic-homotopy-theory.double-loop-spaces funext public -open import synthetic-homotopy-theory.eckmann-hilton-argument funext public -open import synthetic-homotopy-theory.equifibered-sequential-diagrams funext public -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext public -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext public -open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams funext public -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext public -open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext public -open import synthetic-homotopy-theory.families-descent-data-pushouts funext public -open import synthetic-homotopy-theory.families-descent-data-sequential-colimits funext public -open import synthetic-homotopy-theory.flattening-lemma-coequalizers funext public -open import synthetic-homotopy-theory.flattening-lemma-pushouts funext public -open import synthetic-homotopy-theory.flattening-lemma-sequential-colimits funext public -open import synthetic-homotopy-theory.free-loops funext public -open import synthetic-homotopy-theory.functoriality-loop-spaces funext public -open import synthetic-homotopy-theory.functoriality-sequential-colimits funext public -open import synthetic-homotopy-theory.functoriality-suspensions funext public -open import synthetic-homotopy-theory.groups-of-loops-in-1-types funext public -open import synthetic-homotopy-theory.hatchers-acyclic-type funext public -open import synthetic-homotopy-theory.homotopy-groups funext public -open import synthetic-homotopy-theory.identity-systems-descent-data-pushouts funext public -open import synthetic-homotopy-theory.induction-principle-pushouts funext public -open import synthetic-homotopy-theory.infinite-complex-projective-space funext public -open import synthetic-homotopy-theory.infinite-cyclic-types funext public -open import synthetic-homotopy-theory.interval-type funext public -open import synthetic-homotopy-theory.iterated-loop-spaces funext public -open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types funext public -open import synthetic-homotopy-theory.join-powers-of-types funext public -open import synthetic-homotopy-theory.joins-of-maps funext public -open import synthetic-homotopy-theory.joins-of-types funext public -open import synthetic-homotopy-theory.left-half-smash-products funext public -open import synthetic-homotopy-theory.loop-homotopy-circle funext public -open import synthetic-homotopy-theory.loop-spaces funext public -open import synthetic-homotopy-theory.maps-of-prespectra funext public -open import synthetic-homotopy-theory.mere-spheres funext public -open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams funext public -open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows funext public -open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams funext public -open import synthetic-homotopy-theory.morphisms-descent-data-circle funext public -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext public -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext public -open import synthetic-homotopy-theory.multiplication-circle funext public -open import synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams funext public -open import synthetic-homotopy-theory.plus-principle funext public -open import synthetic-homotopy-theory.powers-of-loops funext public -open import synthetic-homotopy-theory.premanifolds funext public -open import synthetic-homotopy-theory.prespectra funext public -open import synthetic-homotopy-theory.pullback-property-pushouts funext public -open import synthetic-homotopy-theory.pushout-products funext public -open import synthetic-homotopy-theory.pushouts funext public -open import synthetic-homotopy-theory.pushouts-of-pointed-types funext public -open import synthetic-homotopy-theory.recursion-principle-pushouts funext public -open import synthetic-homotopy-theory.retracts-of-sequential-diagrams funext public -open import synthetic-homotopy-theory.rewriting-pushouts funext public -open import synthetic-homotopy-theory.sections-descent-circle funext public -open import synthetic-homotopy-theory.sections-descent-data-pushouts funext public -open import synthetic-homotopy-theory.sequential-colimits funext public -open import synthetic-homotopy-theory.sequential-diagrams funext public -open import synthetic-homotopy-theory.sequentially-compact-types funext public -open import synthetic-homotopy-theory.shifts-sequential-diagrams funext public -open import synthetic-homotopy-theory.smash-products-of-pointed-types funext public -open import synthetic-homotopy-theory.spectra funext public -open import synthetic-homotopy-theory.sphere-prespectrum funext public -open import synthetic-homotopy-theory.spheres funext public -open import synthetic-homotopy-theory.suspension-prespectra funext public -open import synthetic-homotopy-theory.suspension-structures funext public -open import synthetic-homotopy-theory.suspensions-of-pointed-types funext public -open import synthetic-homotopy-theory.suspensions-of-propositions funext public -open import synthetic-homotopy-theory.suspensions-of-types funext public -open import synthetic-homotopy-theory.tangent-spheres funext public -open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams funext public -open import synthetic-homotopy-theory.total-sequential-diagrams funext public -open import synthetic-homotopy-theory.triple-loop-spaces funext public -open import synthetic-homotopy-theory.truncated-acyclic-maps funext public -open import synthetic-homotopy-theory.truncated-acyclic-types funext public -open import synthetic-homotopy-theory.universal-cover-circle funext public -open import synthetic-homotopy-theory.universal-property-circle funext public -open import synthetic-homotopy-theory.universal-property-coequalizers funext public -open import synthetic-homotopy-theory.universal-property-pushouts funext public -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext public -open import synthetic-homotopy-theory.universal-property-suspensions funext public -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext public -open import synthetic-homotopy-theory.wedges-of-pointed-types funext public -open import synthetic-homotopy-theory.zigzags-sequential-diagrams funext public +open import synthetic-homotopy-theory.0-acyclic-maps public +open import synthetic-homotopy-theory.0-acyclic-types public +open import synthetic-homotopy-theory.1-acyclic-types public +open import synthetic-homotopy-theory.acyclic-maps public +open import synthetic-homotopy-theory.acyclic-types public +open import synthetic-homotopy-theory.category-of-connected-set-bundles-circle public +open import synthetic-homotopy-theory.cavallos-trick public +open import synthetic-homotopy-theory.circle public +open import synthetic-homotopy-theory.cocartesian-morphisms-arrows public +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams public +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams public +open import synthetic-homotopy-theory.cocones-under-spans public +open import synthetic-homotopy-theory.codiagonals-of-maps public +open import synthetic-homotopy-theory.coequalizers public +open import synthetic-homotopy-theory.cofibers-of-maps public +open import synthetic-homotopy-theory.cofibers-of-pointed-maps public +open import synthetic-homotopy-theory.coforks public +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams public +open import synthetic-homotopy-theory.conjugation-loops public +open import synthetic-homotopy-theory.connected-set-bundles-circle public +open import synthetic-homotopy-theory.connective-prespectra public +open import synthetic-homotopy-theory.connective-spectra public +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams public +open import synthetic-homotopy-theory.dependent-cocones-under-spans public +open import synthetic-homotopy-theory.dependent-coforks public +open import synthetic-homotopy-theory.dependent-descent-circle public +open import synthetic-homotopy-theory.dependent-pullback-property-pushouts public +open import synthetic-homotopy-theory.dependent-pushout-products public +open import synthetic-homotopy-theory.dependent-sequential-diagrams public +open import synthetic-homotopy-theory.dependent-suspension-structures public +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers public +open import synthetic-homotopy-theory.dependent-universal-property-pushouts public +open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits public +open import synthetic-homotopy-theory.dependent-universal-property-suspensions public +open import synthetic-homotopy-theory.descent-circle public +open import synthetic-homotopy-theory.descent-circle-constant-families public +open import synthetic-homotopy-theory.descent-circle-dependent-pair-types public +open import synthetic-homotopy-theory.descent-circle-equivalence-types public +open import synthetic-homotopy-theory.descent-circle-function-types public +open import synthetic-homotopy-theory.descent-circle-subtypes public +open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts public +open import synthetic-homotopy-theory.descent-data-function-types-over-pushouts public +open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts public +open import synthetic-homotopy-theory.descent-data-pushouts public +open import synthetic-homotopy-theory.descent-data-sequential-colimits public +open import synthetic-homotopy-theory.descent-property-pushouts public +open import synthetic-homotopy-theory.descent-property-sequential-colimits public +open import synthetic-homotopy-theory.double-loop-spaces public +open import synthetic-homotopy-theory.eckmann-hilton-argument public +open import synthetic-homotopy-theory.equifibered-sequential-diagrams public +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams public +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows public +open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams public +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts public +open import synthetic-homotopy-theory.equivalences-sequential-diagrams public +open import synthetic-homotopy-theory.families-descent-data-pushouts public +open import synthetic-homotopy-theory.families-descent-data-sequential-colimits public +open import synthetic-homotopy-theory.flattening-lemma-coequalizers public +open import synthetic-homotopy-theory.flattening-lemma-pushouts public +open import synthetic-homotopy-theory.flattening-lemma-sequential-colimits public +open import synthetic-homotopy-theory.free-loops public +open import synthetic-homotopy-theory.functoriality-loop-spaces public +open import synthetic-homotopy-theory.functoriality-sequential-colimits public +open import synthetic-homotopy-theory.functoriality-suspensions public +open import synthetic-homotopy-theory.groups-of-loops-in-1-types public +open import synthetic-homotopy-theory.hatchers-acyclic-type public +open import synthetic-homotopy-theory.homotopy-groups public +open import synthetic-homotopy-theory.identity-systems-descent-data-pushouts public +open import synthetic-homotopy-theory.induction-principle-pushouts public +open import synthetic-homotopy-theory.infinite-complex-projective-space public +open import synthetic-homotopy-theory.infinite-cyclic-types public +open import synthetic-homotopy-theory.interval-type public +open import synthetic-homotopy-theory.iterated-loop-spaces public +open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types public +open import synthetic-homotopy-theory.join-powers-of-types public +open import synthetic-homotopy-theory.joins-of-maps public +open import synthetic-homotopy-theory.joins-of-types public +open import synthetic-homotopy-theory.left-half-smash-products public +open import synthetic-homotopy-theory.loop-homotopy-circle public +open import synthetic-homotopy-theory.loop-spaces public +open import synthetic-homotopy-theory.maps-of-prespectra public +open import synthetic-homotopy-theory.mere-spheres public +open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams public +open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows public +open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams public +open import synthetic-homotopy-theory.morphisms-descent-data-circle public +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts public +open import synthetic-homotopy-theory.morphisms-sequential-diagrams public +open import synthetic-homotopy-theory.multiplication-circle public +open import synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams public +open import synthetic-homotopy-theory.plus-principle public +open import synthetic-homotopy-theory.powers-of-loops public +open import synthetic-homotopy-theory.premanifolds public +open import synthetic-homotopy-theory.prespectra public +open import synthetic-homotopy-theory.pullback-property-pushouts public +open import synthetic-homotopy-theory.pushout-products public +open import synthetic-homotopy-theory.pushouts public +open import synthetic-homotopy-theory.pushouts-of-pointed-types public +open import synthetic-homotopy-theory.recursion-principle-pushouts public +open import synthetic-homotopy-theory.retracts-of-sequential-diagrams public +open import synthetic-homotopy-theory.rewriting-pushouts public +open import synthetic-homotopy-theory.sections-descent-circle public +open import synthetic-homotopy-theory.sections-descent-data-pushouts public +open import synthetic-homotopy-theory.sequential-colimits public +open import synthetic-homotopy-theory.sequential-diagrams public +open import synthetic-homotopy-theory.sequentially-compact-types public +open import synthetic-homotopy-theory.shifts-sequential-diagrams public +open import synthetic-homotopy-theory.smash-products-of-pointed-types public +open import synthetic-homotopy-theory.spectra public +open import synthetic-homotopy-theory.sphere-prespectrum public +open import synthetic-homotopy-theory.spheres public +open import synthetic-homotopy-theory.suspension-prespectra public +open import synthetic-homotopy-theory.suspension-structures public +open import synthetic-homotopy-theory.suspensions-of-pointed-types public +open import synthetic-homotopy-theory.suspensions-of-propositions public +open import synthetic-homotopy-theory.suspensions-of-types public +open import synthetic-homotopy-theory.tangent-spheres public +open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams public +open import synthetic-homotopy-theory.total-sequential-diagrams public +open import synthetic-homotopy-theory.triple-loop-spaces public +open import synthetic-homotopy-theory.truncated-acyclic-maps public +open import synthetic-homotopy-theory.truncated-acyclic-types public +open import synthetic-homotopy-theory.universal-cover-circle public +open import synthetic-homotopy-theory.universal-property-circle public +open import synthetic-homotopy-theory.universal-property-coequalizers public +open import synthetic-homotopy-theory.universal-property-pushouts public +open import synthetic-homotopy-theory.universal-property-sequential-colimits public +open import synthetic-homotopy-theory.universal-property-suspensions public +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types public +open import synthetic-homotopy-theory.wedges-of-pointed-types public +open import synthetic-homotopy-theory.zigzags-sequential-diagrams public ``` diff --git a/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md index 421e64fe72..aaa7ec0e76 100644 --- a/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md @@ -1,24 +1,19 @@ # `0`-acyclic maps ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.0-acyclic-maps - (funext : function-extensionality) - where +module synthetic-homotopy-theory.0-acyclic-maps where ```
Imports ```agda -open import foundation.epimorphisms-with-respect-to-sets funext -open import foundation.propositions funext -open import foundation.surjective-maps funext +open import foundation.epimorphisms-with-respect-to-sets +open import foundation.propositions +open import foundation.surjective-maps open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.truncated-acyclic-maps funext +open import synthetic-homotopy-theory.truncated-acyclic-maps ```
diff --git a/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md index e3bb2c9e31..cdfaabba69 100644 --- a/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md @@ -1,30 +1,25 @@ # `0`-acyclic types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.0-acyclic-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.0-acyclic-types where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.functoriality-propositional-truncation funext -open import foundation.inhabited-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.functoriality-propositional-truncation +open import foundation.inhabited-types +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.0-acyclic-maps funext -open import synthetic-homotopy-theory.truncated-acyclic-maps funext -open import synthetic-homotopy-theory.truncated-acyclic-types funext +open import synthetic-homotopy-theory.0-acyclic-maps +open import synthetic-homotopy-theory.truncated-acyclic-maps +open import synthetic-homotopy-theory.truncated-acyclic-types ```
diff --git a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md index 170977c1ec..c7e47d89d0 100644 --- a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md @@ -1,37 +1,33 @@ # `1`-acyclic types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.1-acyclic-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.1-acyclic-types where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.binary-transport -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types funext -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.injective-maps funext -open import foundation.propositions funext -open import foundation.set-truncations funext -open import foundation.sets funext -open import foundation.truncated-types funext +open import foundation.diagonal-maps-of-types +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.injective-maps +open import foundation.propositions +open import foundation.set-truncations +open import foundation.sets +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.0-acyclic-types funext -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.truncated-acyclic-maps funext -open import synthetic-homotopy-theory.truncated-acyclic-types funext +open import synthetic-homotopy-theory.0-acyclic-types +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.truncated-acyclic-maps +open import synthetic-homotopy-theory.truncated-acyclic-types ```
diff --git a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md index a14c63cb25..3bf63f4ed1 100644 --- a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md @@ -1,60 +1,55 @@ # Acyclic maps ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.acyclic-maps - (funext : function-extensionality) - where +module synthetic-homotopy-theory.acyclic-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.cones-over-cospan-diagrams funext -open import foundation.constant-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext -open import foundation.dependent-epimorphisms funext +open import foundation.cartesian-product-types +open import foundation.cones-over-cospan-diagrams +open import foundation.constant-maps +open import foundation.contractible-maps +open import foundation.contractible-types +open import foundation.dependent-epimorphisms open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.diagonal-maps-of-types funext -open import foundation.embeddings funext -open import foundation.epimorphisms funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-fibers-of-maps funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.pullbacks funext -open import foundation.retracts-of-maps funext -open import foundation.torsorial-type-families funext +open import foundation.dependent-universal-property-equivalences +open import foundation.diagonal-maps-of-types +open import foundation.embeddings +open import foundation.epimorphisms +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-fibers-of-maps +open import foundation.homotopies +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.pullbacks +open import foundation.retracts-of-maps +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types funext -open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.acyclic-types funext -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.codiagonals-of-maps funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.suspensions-of-types funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.acyclic-types +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.codiagonals-of-maps +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/acyclic-types.lagda.md b/src/synthetic-homotopy-theory/acyclic-types.lagda.md index 5072fb7fcd..35473b70bf 100644 --- a/src/synthetic-homotopy-theory/acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/acyclic-types.lagda.md @@ -1,26 +1,21 @@ # Acyclic types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.acyclic-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.acyclic-types where ```
Imports ```agda -open import foundation.contractible-types funext -open import foundation.equivalences funext -open import foundation.propositions funext -open import foundation.retracts-of-types funext +open import foundation.contractible-types +open import foundation.equivalences +open import foundation.propositions +open import foundation.retracts-of-types open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.functoriality-suspensions funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.functoriality-suspensions +open import synthetic-homotopy-theory.suspensions-of-types ```
diff --git a/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md b/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md index 3b590c8193..c03b92fe6a 100644 --- a/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md +++ b/src/synthetic-homotopy-theory/category-of-connected-set-bundles-circle.lagda.md @@ -1,25 +1,20 @@ # The category of connected set bundles over the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.category-of-connected-set-bundles-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.category-of-connected-set-bundles-circle where ```
Imports ```agda -open import category-theory.full-large-subcategories funext -open import category-theory.large-categories funext +open import category-theory.full-large-subcategories +open import category-theory.large-categories -open import foundation.category-of-families-of-sets funext +open import foundation.category-of-families-of-sets open import foundation.universe-levels -open import synthetic-homotopy-theory.circle funext -open import synthetic-homotopy-theory.connected-set-bundles-circle funext +open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.connected-set-bundles-circle ```
diff --git a/src/synthetic-homotopy-theory/cavallos-trick.lagda.md b/src/synthetic-homotopy-theory/cavallos-trick.lagda.md index e3475c89d8..54d3a7e599 100644 --- a/src/synthetic-homotopy-theory/cavallos-trick.lagda.md +++ b/src/synthetic-homotopy-theory/cavallos-trick.lagda.md @@ -1,12 +1,7 @@ # Cavallo's trick ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.cavallos-trick - (funext : function-extensionality) - where +module synthetic-homotopy-theory.cavallos-trick where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sections funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sections open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types ``` diff --git a/src/synthetic-homotopy-theory/circle.lagda.md b/src/synthetic-homotopy-theory/circle.lagda.md index 457a1c3e27..0340db0b69 100644 --- a/src/synthetic-homotopy-theory/circle.lagda.md +++ b/src/synthetic-homotopy-theory/circle.lagda.md @@ -1,53 +1,48 @@ # The circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.circle where ```
Imports ```agda -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.dependent-identifications funext +open import foundation.commuting-squares-of-identifications +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.retractions +open import foundation.sections open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups open import structured-types.pointed-types -open import synthetic-homotopy-theory.dependent-suspension-structures funext -open import synthetic-homotopy-theory.free-loops funext -open import synthetic-homotopy-theory.spheres funext -open import synthetic-homotopy-theory.suspension-structures funext -open import synthetic-homotopy-theory.suspensions-of-types funext -open import synthetic-homotopy-theory.universal-cover-circle funext -open import synthetic-homotopy-theory.universal-property-circle funext +open import synthetic-homotopy-theory.dependent-suspension-structures +open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.spheres +open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.universal-cover-circle +open import synthetic-homotopy-theory.universal-property-circle -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md b/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md index 75632d5143..9e34713e9c 100644 --- a/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md @@ -1,26 +1,21 @@ # Cocartesian morphisms of arrows ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.cocartesian-morphisms-arrows - (funext : function-extensionality) - where +module synthetic-homotopy-theory.cocartesian-morphisms-arrows where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.morphisms-arrows funext -open import foundation.propositions funext +open import foundation.morphisms-arrows +open import foundation.propositions open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md b/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md index 18cf55cc98..cec36cef2d 100644 --- a/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/cocones-under-pointed-span-diagrams.lagda.md @@ -1,12 +1,7 @@ # Cocones under pointed span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.cocones-under-pointed-span-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.cocones-under-pointed-span-diagrams where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.commuting-squares-of-pointed-maps funext -open import structured-types.pointed-maps funext +open import structured-types.commuting-squares-of-pointed-maps +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.cocones-under-spans ```
diff --git a/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md index bb328e7bd9..ca4adb47b0 100644 --- a/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/cocones-under-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Cocones under sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.cocones-under-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.cocones-under-sequential-diagrams where ```
Imports @@ -14,25 +9,25 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies funext -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-triangles-of-maps funext +open import foundation.binary-homotopies +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.postcomposition-functions open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.equifibered-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-sequential-diagrams +open import synthetic-homotopy-theory.equifibered-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md b/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md index 384f3ad2c6..b3ac5c1716 100644 --- a/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md +++ b/src/synthetic-homotopy-theory/cocones-under-spans.lagda.md @@ -1,12 +1,7 @@ # Cocones under spans ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.cocones-under-spans - (funext : function-extensionality) - where +module synthetic-homotopy-theory.cocones-under-spans where ```
Imports @@ -14,18 +9,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - +open import foundation.function-extensionality open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.morphisms-arrows funext -open import foundation.span-diagrams funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.morphisms-arrows +open import foundation.span-diagrams open import foundation.structure-identity-principle open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation-core.commuting-squares-of-maps funext +open import foundation-core.commuting-squares-of-maps open import foundation-core.contractible-types open import foundation-core.equality-dependent-pair-types open import foundation-core.equivalences diff --git a/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md b/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md index 10693a275b..b483d3e9a8 100644 --- a/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md @@ -1,32 +1,27 @@ # Codiagonals of maps ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.codiagonals-of-maps - (funext : function-extensionality) - where +module synthetic-homotopy-theory.codiagonals-of-maps where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.homotopies +open import foundation.torsorial-type-families open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.suspension-structures funext -open import synthetic-homotopy-theory.suspensions-of-types funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/coequalizers.lagda.md b/src/synthetic-homotopy-theory/coequalizers.lagda.md index afcd7476f2..a89b394839 100644 --- a/src/synthetic-homotopy-theory/coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/coequalizers.lagda.md @@ -1,28 +1,23 @@ # Coequalizers ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.coequalizers - (funext : function-extensionality) - where +module synthetic-homotopy-theory.coequalizers where ```
Imports ```agda open import foundation.double-arrows -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.universal-property-coequalizers funext +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.universal-property-coequalizers ```
diff --git a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md index 41d78c8b42..e14dce732d 100644 --- a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md @@ -1,32 +1,27 @@ # Cofibers of maps ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.cofibers-of-maps - (funext : function-extensionality) - where +module synthetic-homotopy-theory.cofibers-of-maps where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.unit-type open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.pointed-unit-type funext +open import structured-types.pointed-unit-type -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.dependent-universal-property-pushouts +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md b/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md index 837ac0ff8b..0da2de0601 100644 --- a/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md +++ b/src/synthetic-homotopy-theory/cofibers-of-pointed-maps.lagda.md @@ -1,12 +1,7 @@ # Cofibers of pointed maps ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.cofibers-of-pointed-maps - (funext : function-extensionality) - where +module synthetic-homotopy-theory.cofibers-of-pointed-maps where ```
Imports @@ -14,12 +9,12 @@ module ```agda open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.pointed-unit-type funext +open import structured-types.pointed-unit-type -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext -open import synthetic-homotopy-theory.pushouts-of-pointed-types funext +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams +open import synthetic-homotopy-theory.pushouts-of-pointed-types ```
diff --git a/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md index e746026b2a..0efd91005f 100644 --- a/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/coforks-cocones-under-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Correspondence between cocones under sequential diagrams and certain coforks ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams where ```
Imports @@ -14,33 +9,33 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-prisms-of-maps funext -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-prisms-of-maps +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences funext -open import foundation.equivalences funext-double-arrows -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.morphisms-double-arrows funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.equivalences-double-arrows +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.morphisms-double-arrows +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation funext - -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.dependent-coforks funext -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext -open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext -open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows funext -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import foundation.whiskering-homotopies-concatenation + +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-coforks +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows +open import synthetic-homotopy-theory.equivalences-sequential-diagrams +open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams +open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows +open import synthetic-homotopy-theory.morphisms-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/coforks.lagda.md b/src/synthetic-homotopy-theory/coforks.lagda.md index 12aaa42f23..fa5ea65e19 100644 --- a/src/synthetic-homotopy-theory/coforks.lagda.md +++ b/src/synthetic-homotopy-theory/coforks.lagda.md @@ -1,43 +1,38 @@ # Coforks ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.coforks - (funext : function-extensionality) - where +module synthetic-homotopy-theory.coforks where ```
Imports ```agda open import foundation.codiagonal-maps-of-types -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences funext -open import foundation.equivalences funext-double-arrows -open import foundation.equivalences-span-diagrams funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.equivalences-double-arrows +open import foundation.equivalences-span-diagrams +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.morphisms-double-arrows funext -open import foundation.morphisms-span-diagrams funext -open import foundation.span-diagrams funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.morphisms-double-arrows +open import foundation.morphisms-span-diagrams +open import foundation.span-diagrams open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.cocones-under-spans ```
diff --git a/src/synthetic-homotopy-theory/conjugation-loops.lagda.md b/src/synthetic-homotopy-theory/conjugation-loops.lagda.md index 82521cbf9b..589c5d457d 100644 --- a/src/synthetic-homotopy-theory/conjugation-loops.lagda.md +++ b/src/synthetic-homotopy-theory/conjugation-loops.lagda.md @@ -1,26 +1,21 @@ # Conjugation of loops ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.conjugation-loops - (funext : function-extensionality) - where +module synthetic-homotopy-theory.conjugation-loops where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md b/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md index a7dcac5657..46a02e248f 100644 --- a/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md +++ b/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md @@ -1,37 +1,32 @@ # Connected set bundles over the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.connected-set-bundles-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.connected-set-bundles-circle where ```
Imports ```agda -open import foundation.0-connected-types funext -open import foundation.automorphisms funext +open import foundation.0-connected-types +open import foundation.automorphisms open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.mere-equality funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.mere-equality +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.transport-along-identifications open import foundation.universe-levels -open import higher-group-theory.transitive-higher-group-actions funext +open import higher-group-theory.transitive-higher-group-actions -open import structured-types.sets-equipped-with-automorphisms funext +open import structured-types.sets-equipped-with-automorphisms -open import synthetic-homotopy-theory.circle funext +open import synthetic-homotopy-theory.circle ```
diff --git a/src/synthetic-homotopy-theory/connective-prespectra.lagda.md b/src/synthetic-homotopy-theory/connective-prespectra.lagda.md index 55e1d7c8e0..db0ebe5577 100644 --- a/src/synthetic-homotopy-theory/connective-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/connective-prespectra.lagda.md @@ -1,12 +1,7 @@ # Connective prespectra ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.connective-prespectra - (funext : function-extensionality) - where +module synthetic-homotopy-theory.connective-prespectra where ```
Imports @@ -14,23 +9,23 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-types funext +open import foundation.connected-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.truncation-levels open import foundation.universe-levels -open import structured-types.pointed-equivalences funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-equivalences +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.prespectra funext -open import synthetic-homotopy-theory.suspensions-of-pointed-types funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.prespectra +open import synthetic-homotopy-theory.suspensions-of-pointed-types +open import synthetic-homotopy-theory.suspensions-of-types ```
diff --git a/src/synthetic-homotopy-theory/connective-spectra.lagda.md b/src/synthetic-homotopy-theory/connective-spectra.lagda.md index 99c4bd7a0f..939ec9243c 100644 --- a/src/synthetic-homotopy-theory/connective-spectra.lagda.md +++ b/src/synthetic-homotopy-theory/connective-spectra.lagda.md @@ -1,12 +1,7 @@ # Connective spectra ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.connective-spectra - (funext : function-extensionality) - where +module synthetic-homotopy-theory.connective-spectra where ```
Imports @@ -14,25 +9,25 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.connected-types funext +open import foundation.connected-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.truncation-levels open import foundation.universe-levels -open import structured-types.pointed-equivalences funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-equivalences +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.connective-prespectra funext -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.prespectra funext -open import synthetic-homotopy-theory.spectra funext -open import synthetic-homotopy-theory.suspensions-of-pointed-types funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.connective-prespectra +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.prespectra +open import synthetic-homotopy-theory.spectra +open import synthetic-homotopy-theory.suspensions-of-pointed-types +open import synthetic-homotopy-theory.suspensions-of-types ```
diff --git a/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md index 81829edd7c..debb9262d7 100644 --- a/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-cocones-under-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Dependent cocones under sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams where ```
Imports @@ -16,27 +11,27 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.binary-homotopies funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.constant-type-families funext +open import foundation.binary-homotopies +open import foundation.commuting-triangles-of-maps +open import foundation.constant-type-families open import foundation.dependent-homotopies -open import foundation.dependent-identifications funext +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.dependent-coforks funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-coforks +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md b/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md index df585aa620..cfba684dd3 100644 --- a/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md @@ -1,12 +1,7 @@ # Dependent cocones under spans ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-cocones-under-spans - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-cocones-under-spans where ```
Imports @@ -14,36 +9,35 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.commuting-squares-of-maps funext -open import foundation.constant-type-families funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-identifications +open import foundation.commuting-squares-of-maps +open import foundation.constant-type-families +open import foundation.contractible-types open import foundation.dependent-homotopies -open import foundation.dependent-identifications funext +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.span-diagrams funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections +open import foundation.span-diagrams open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.transport-along-higher-identifications funext +open import foundation.torsorial-type-families +open import foundation.transport-along-higher-identifications open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import foundation-core.injective-maps -open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.cocones-under-spans ```
diff --git a/src/synthetic-homotopy-theory/dependent-coforks.lagda.md b/src/synthetic-homotopy-theory/dependent-coforks.lagda.md index 5e039920db..39b40000f5 100644 --- a/src/synthetic-homotopy-theory/dependent-coforks.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-coforks.lagda.md @@ -1,12 +1,7 @@ # Dependent coforks ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-coforks - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-coforks where ```
Imports @@ -14,29 +9,29 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps funext -open import foundation.constant-type-families funext -open import foundation.coproduct-types funext -open import foundation.dependent-identifications funext +open import foundation.commuting-triangles-of-maps +open import foundation.constant-type-families +open import foundation.coproduct-types +open import foundation.dependent-identifications open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.dependent-cocones-under-spans ```
diff --git a/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md b/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md index 78add2c3cf..a847a0abfa 100644 --- a/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md @@ -1,33 +1,28 @@ # Dependent descent for the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-descent-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-descent-circle where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import structured-types.dependent-types-equipped-with-automorphisms funext +open import structured-types.dependent-types-equipped-with-automorphisms -open import synthetic-homotopy-theory.descent-circle funext -open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.free-loops ```
diff --git a/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md index e7dbf83999..977930ff08 100644 --- a/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-pullback-property-pushouts.lagda.md @@ -1,12 +1,7 @@ # The dependent pullback property of pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-pullback-property-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-pullback-property-pushouts where ```
Imports @@ -14,27 +9,26 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.cones-over-cospan-diagrams funext -open import foundation.constant-type-families funext +open import foundation.cones-over-cospan-diagrams +open import foundation.constant-type-families open import foundation.dependent-pair-types -open import foundation.dependent-sums-pullbacks funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.precomposition-functions funext -open import foundation.pullbacks funext +open import foundation.dependent-sums-pullbacks +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.precomposition-functions +open import foundation.pullbacks open import foundation.transport-along-identifications -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import orthogonal-factorization-systems.lifts-families-of-elements funext -open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements funext +open import orthogonal-factorization-systems.lifts-families-of-elements +open import orthogonal-factorization-systems.precomposition-lifts-families-of-elements -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.pullback-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.pullback-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md b/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md index cee4079b6e..265ce6a2c9 100644 --- a/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md @@ -1,27 +1,22 @@ # Dependent pushout-products ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-pushout-products - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-pushout-products where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md index 364b0efc04..04bd1a9b0a 100644 --- a/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Dependent sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-sequential-diagrams where ```
Imports @@ -15,11 +10,11 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext +open import foundation.function-types +open import foundation.homotopies open import foundation.universe-levels -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md b/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md index 58edce6886..8000b52d60 100644 --- a/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-suspension-structures.lagda.md @@ -1,38 +1,32 @@ # Dependent suspension structures ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-suspension-structures - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-suspension-structures where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.constant-maps funext -open import foundation.dependent-identifications funext +open import foundation.commuting-squares-of-identifications +open import foundation.constant-maps +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps open import foundation.structure-identity-principle open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-unit-type funext +open import foundation.universal-property-unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.suspension-structures funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.suspension-structures ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md index 0a6329a395..ba60811fcb 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md @@ -1,31 +1,26 @@ # The dependent universal property of coequalizers ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-universal-property-coequalizers - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-universal-property-coequalizers where ```
Imports ```agda -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.functoriality-dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-coforks funext -open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext -open import synthetic-homotopy-theory.universal-property-coequalizers funext +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.dependent-coforks +open import synthetic-homotopy-theory.dependent-universal-property-pushouts +open import synthetic-homotopy-theory.universal-property-coequalizers ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md index 797539c2c8..c0b9760150 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md @@ -1,40 +1,35 @@ # The dependent universal property of pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-universal-property-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-universal-property-pushouts where ```
Imports ```agda open import foundation.action-on-identifications-dependent-functions -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.standard-pullbacks funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.retractions +open import foundation.standard-pullbacks open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-pullback-property-pushouts funext -open import synthetic-homotopy-theory.induction-principle-pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.dependent-pullback-property-pushouts +open import synthetic-homotopy-theory.induction-principle-pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md index 8b8c92ef2b..449c744b8e 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md @@ -1,43 +1,38 @@ # The dependent universal property of sequential colimits ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-universal-property-sequential-colimits - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-universal-property-sequential-colimits where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions open import foundation.subtype-identity-principle -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.coforks funext-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.dependent-coforks funext -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-coequalizers funext -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-coforks +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.universal-property-coequalizers +open import synthetic-homotopy-theory.universal-property-sequential-colimits ```
diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md index 80adcdfb9c..0b545c7c69 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-suspensions.lagda.md @@ -1,29 +1,24 @@ # Dependent universal property of suspensions ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.dependent-universal-property-suspensions - (funext : function-extensionality) - where +module synthetic-homotopy-theory.dependent-universal-property-suspensions where ```
Imports ```agda open import foundation.action-on-identifications-dependent-functions -open import foundation.constant-maps funext +open import foundation.constant-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-suspension-structures funext -open import synthetic-homotopy-theory.suspension-structures funext +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.dependent-suspension-structures +open import synthetic-homotopy-theory.suspension-structures ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md b/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md index 0faaa8a8c5..8ae23e0e55 100644 --- a/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-constant-families.lagda.md @@ -1,25 +1,20 @@ # Descent data for constant type families over the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-circle-constant-families - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-circle-constant-families where ```
Imports ```agda -open import foundation.constant-type-families funext +open import foundation.constant-type-families open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-circle funext -open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.free-loops ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md index d8a7c20093..b9abaf71f4 100644 --- a/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-dependent-pair-types.lagda.md @@ -1,26 +1,21 @@ # Descent data for families of dependent pair types over the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-circle-dependent-pair-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-circle-dependent-pair-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext +open import foundation.equality-dependent-pair-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-descent-circle funext -open import synthetic-homotopy-theory.descent-circle funext -open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.dependent-descent-circle +open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.free-loops ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md index a9d8e53450..cec4371a5e 100644 --- a/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md @@ -1,32 +1,27 @@ # Descent data for families of equivalence types over the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-circle-equivalence-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-circle-equivalence-types where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-descent-circle funext -open import synthetic-homotopy-theory.descent-circle funext -open import synthetic-homotopy-theory.descent-circle funext-dependent-pair-types -open import synthetic-homotopy-theory.descent-circle-function-types funext -open import synthetic-homotopy-theory.descent-circle-subtypes funext -open import synthetic-homotopy-theory.free-loops funext -open import synthetic-homotopy-theory.morphisms-descent-data-circle funext -open import synthetic-homotopy-theory.sections-descent-circle funext -open import synthetic-homotopy-theory.universal-property-circle funext +open import synthetic-homotopy-theory.dependent-descent-circle +open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.descent-circle-dependent-pair-types +open import synthetic-homotopy-theory.descent-circle-function-types +open import synthetic-homotopy-theory.descent-circle-subtypes +open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.morphisms-descent-data-circle +open import synthetic-homotopy-theory.sections-descent-circle +open import synthetic-homotopy-theory.universal-property-circle ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md index 8bd7885ece..447911b467 100644 --- a/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-function-types.lagda.md @@ -1,40 +1,34 @@ # Descent data for families of function types over the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-circle-function-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-circle-function-types where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-function-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-function-types +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext +open import foundation.identity-types +open import foundation.postcomposition-functions open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.descent-circle funext -open import synthetic-homotopy-theory.free-loops funext -open import synthetic-homotopy-theory.morphisms-descent-data-circle funext -open import synthetic-homotopy-theory.sections-descent-circle funext -open import synthetic-homotopy-theory.universal-property-circle funext +open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.morphisms-descent-data-circle +open import synthetic-homotopy-theory.sections-descent-circle +open import synthetic-homotopy-theory.universal-property-circle ```
diff --git a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md index 2623c2b279..8b2ed00fc2 100644 --- a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md @@ -1,34 +1,29 @@ # Subtypes of descent data for the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-circle-subtypes - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-circle-subtypes where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositions +open import foundation.subtypes open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-descent-circle funext -open import synthetic-homotopy-theory.descent-circle funext -open import synthetic-homotopy-theory.descent-circle funext-dependent-pair-types -open import synthetic-homotopy-theory.free-loops funext -open import synthetic-homotopy-theory.sections-descent-circle funext -open import synthetic-homotopy-theory.universal-property-circle funext +open import synthetic-homotopy-theory.dependent-descent-circle +open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.descent-circle-dependent-pair-types +open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.sections-descent-circle +open import synthetic-homotopy-theory.universal-property-circle ```
diff --git a/src/synthetic-homotopy-theory/descent-circle.lagda.md b/src/synthetic-homotopy-theory/descent-circle.lagda.md index bbaf503df4..26cb9592d3 100644 --- a/src/synthetic-homotopy-theory/descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle.lagda.md @@ -1,38 +1,34 @@ # The descent property of the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-circle where ```
Imports ```agda -open import foundation.automorphisms funext -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.automorphisms +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-automorphisms funext -open import structured-types.types-equipped-with-automorphisms funext +open import structured-types.equivalences-types-equipped-with-automorphisms +open import structured-types.types-equipped-with-automorphisms -open import synthetic-homotopy-theory.free-loops funext -open import synthetic-homotopy-theory.universal-property-circle funext +open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.universal-property-circle ```
diff --git a/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md index c1665cbf15..7095433e23 100644 --- a/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md @@ -3,44 +3,39 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.postcomposition-functions funext -open import foundation.span-diagrams funext +open import foundation.postcomposition-functions +open import foundation.span-diagrams open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.descent-data-pushouts funext -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext -open import synthetic-homotopy-theory.families-descent-data-pushouts funext -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext -open import synthetic-homotopy-theory.sections-descent-data-pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts +open import synthetic-homotopy-theory.families-descent-data-pushouts +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts +open import synthetic-homotopy-theory.sections-descent-data-pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md index 1b2df64c8a..35a5f3e58d 100644 --- a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md @@ -3,45 +3,40 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-data-function-types-over-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-data-function-types-over-pushouts where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.postcomposition-functions funext -open import foundation.span-diagrams funext +open import foundation.postcomposition-functions +open import foundation.span-diagrams open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.descent-data-pushouts funext -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext -open import synthetic-homotopy-theory.families-descent-data-pushouts funext -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext -open import synthetic-homotopy-theory.sections-descent-data-pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts +open import synthetic-homotopy-theory.families-descent-data-pushouts +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts +open import synthetic-homotopy-theory.sections-descent-data-pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md index dd8fc5ce36..6244d587ce 100644 --- a/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-identity-types-over-pushouts.lagda.md @@ -3,28 +3,23 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-data-identity-types-over-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-data-identity-types-over-pushouts where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.span-diagrams funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.span-diagrams open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.descent-data-pushouts funext -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext -open import synthetic-homotopy-theory.families-descent-data-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts +open import synthetic-homotopy-theory.families-descent-data-pushouts ```
diff --git a/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md index 50e8d40c6f..020d2dcefb 100644 --- a/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-pushouts.lagda.md @@ -1,25 +1,20 @@ # Descent data for pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-data-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-data-pushouts where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.span-diagrams funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.span-diagrams open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.cocones-under-spans ```
diff --git a/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md index 650fb7ea21..d498ebe3db 100644 --- a/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-sequential-colimits.lagda.md @@ -1,12 +1,7 @@ # Descent data for sequential colimits ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-data-sequential-colimits - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-data-sequential-colimits where ```
Imports @@ -15,15 +10,15 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.equifibered-sequential-diagrams funext -open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams +open import synthetic-homotopy-theory.equifibered-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams +open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md index 65369c9ba4..6d1f56638f 100644 --- a/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md @@ -1,38 +1,32 @@ # Descent property of pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-property-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-property-pushouts where ```
Imports ```agda -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.span-diagrams funext -open import foundation.univalence funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.span-diagrams +open import foundation.univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.descent-data-pushouts funext -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext -open import synthetic-homotopy-theory.families-descent-data-pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts +open import synthetic-homotopy-theory.families-descent-data-pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md index a49fc3bf86..20b9c33dc7 100644 --- a/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/descent-property-sequential-colimits.lagda.md @@ -1,12 +1,7 @@ # Descent property of sequential colimits ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.descent-property-sequential-colimits - (funext : function-extensionality) - where +module synthetic-homotopy-theory.descent-property-sequential-colimits where ```
Imports @@ -14,21 +9,21 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies funext -open import foundation.commuting-triangles-of-maps funext +open import foundation.binary-homotopies +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.univalence funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.descent-data-sequential-colimits funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.descent-data-sequential-colimits +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.universal-property-sequential-colimits ```
diff --git a/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md index 9d29be2407..03c7e352fa 100644 --- a/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/double-loop-spaces.lagda.md @@ -1,31 +1,26 @@ # Double loop spaces ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.double-loop-spaces - (funext : function-extensionality) - where +module synthetic-homotopy-theory.double-loop-spaces where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-identifications open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.path-algebra funext +open import foundation.identity-types +open import foundation.path-algebra open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import structured-types.pointed-equivalences funext +open import structured-types.pointed-equivalences open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces funext -open import synthetic-homotopy-theory.iterated-loop-spaces funext -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.iterated-loop-spaces +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md b/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md index 5bdd946f71..bef7699d56 100644 --- a/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md +++ b/src/synthetic-homotopy-theory/eckmann-hilton-argument.lagda.md @@ -1,38 +1,33 @@ # The Eckmann-Hilton argument ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.eckmann-hilton-argument - (funext : function-extensionality) - where +module synthetic-homotopy-theory.eckmann-hilton-argument where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies funext +open import foundation.commuting-squares-of-homotopies open import foundation.dependent-pair-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.interchange-law -open import foundation.path-algebra funext -open import foundation.transport-along-higher-identifications funext +open import foundation.path-algebra +open import foundation.transport-along-higher-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation funext -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-homotopies-concatenation +open import foundation.whiskering-identifications-concatenation -open import structured-types.pointed-equivalences funext +open import structured-types.pointed-equivalences open import structured-types.pointed-types -open import synthetic-homotopy-theory.double-loop-spaces funext -open import synthetic-homotopy-theory.functoriality-loop-spaces funext -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.triple-loop-spaces funext +open import synthetic-homotopy-theory.double-loop-spaces +open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.triple-loop-spaces ```
diff --git a/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md index b758442881..07cb2a030f 100644 --- a/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equifibered-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Equifibered sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.equifibered-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.equifibered-sequential-diagrams where ```
Imports @@ -15,11 +10,11 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md index edf12de7c8..c8954be17c 100644 --- a/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-cocones-under-equivalences-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Equivalences of cocones under sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-prisms-of-maps funext -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-prisms-of-maps +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext -open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-sequential-diagrams +open import synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md b/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md index 88675b25e2..a5fa74bee9 100644 --- a/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-coforks-under-equivalences-double-arrows.lagda.md @@ -1,30 +1,25 @@ # Equivalences of coforks ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows - (funext : function-extensionality) - where +module synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences funext -open import foundation.equivalences funext-arrows -open import foundation.equivalences-double-arrows funext -open import foundation.homotopies funext -open import foundation.morphisms-arrows funext +open import foundation.equivalences +open import foundation.equivalences-arrows +open import foundation.equivalences-double-arrows +open import foundation.homotopies +open import foundation.morphisms-arrows open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows funext +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows ```
diff --git a/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md index 11fbe8e7a8..54b42eb7ca 100644 --- a/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-dependent-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Equivalances of dependent sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams where ```
Imports @@ -14,22 +9,22 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-sequential-diagrams +open import synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md index 5990d72846..a95a4a12a1 100644 --- a/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-descent-data-pushouts.lagda.md @@ -1,34 +1,29 @@ # Equivalences of descent data for pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.equivalences-descent-data-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.equivalences-descent-data-pushouts where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext +open import foundation.equality-dependent-function-types +open import foundation.equivalence-extensionality +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.span-diagrams funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.span-diagrams open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-data-pushouts funext -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext +open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts ```
diff --git a/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md index 85781c6581..b82afe8957 100644 --- a/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/equivalences-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Equivalences of sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.equivalences-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.equivalences-sequential-diagrams where ```
Imports @@ -14,23 +9,23 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.retracts-of-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.morphisms-sequential-diagrams +open import synthetic-homotopy-theory.retracts-of-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md index f22adb8742..0a68a9200c 100644 --- a/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/families-descent-data-pushouts.lagda.md @@ -1,27 +1,22 @@ # Families with descent data for pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.families-descent-data-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.families-descent-data-pushouts where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.span-diagrams funext +open import foundation.equivalences +open import foundation.span-diagrams open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.descent-data-pushouts funext -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts ```
diff --git a/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md index c8aff2bd82..4343695a69 100644 --- a/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/families-descent-data-sequential-colimits.lagda.md @@ -1,12 +1,7 @@ # Families with descent data for sequential colimits ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.families-descent-data-sequential-colimits - (funext : function-extensionality) - where +module synthetic-homotopy-theory.families-descent-data-sequential-colimits where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.descent-data-sequential-colimits funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams +open import synthetic-homotopy-theory.descent-data-sequential-colimits +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md index bc01c56688..552c91b146 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-coequalizers.lagda.md @@ -1,35 +1,30 @@ # The flattening lemma for coequalizers ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.flattening-lemma-coequalizers - (funext : function-extensionality) - where +module synthetic-homotopy-theory.flattening-lemma-coequalizers where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.universe-levels -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.dependent-universal-property-coequalizers funext -open import synthetic-homotopy-theory.flattening-lemma-pushouts funext -open import synthetic-homotopy-theory.universal-property-coequalizers funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.dependent-universal-property-coequalizers +open import synthetic-homotopy-theory.flattening-lemma-pushouts +open import synthetic-homotopy-theory.universal-property-coequalizers +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md index b36252fc9b..a5842aaa89 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-pushouts.lagda.md @@ -1,42 +1,36 @@ # The flattening lemma for pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.flattening-lemma-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.flattening-lemma-pushouts where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-cubes-of-maps funext -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-cubes-of-maps +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.span-diagrams funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.span-diagrams open import foundation.transport-along-identifications -open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext -open import synthetic-homotopy-theory.descent-data-pushouts funext -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.dependent-universal-property-pushouts +open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md index 90f2b602a3..1e014f974d 100644 --- a/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/flattening-lemma-sequential-colimits.lagda.md @@ -1,12 +1,7 @@ # The flattening lemma for sequential colimits ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.flattening-lemma-sequential-colimits - (funext : function-extensionality) - where +module synthetic-homotopy-theory.flattening-lemma-sequential-colimits where ```
Imports @@ -15,26 +10,26 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-double-arrows -open import foundation.function-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.equivalences-double-arrows +open import foundation.function-types +open import foundation.homotopies open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.coforks funext-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits funext -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext -open import synthetic-homotopy-theory.families-descent-data-sequential-colimits funext -open import synthetic-homotopy-theory.flattening-lemma-coequalizers funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams funext -open import synthetic-homotopy-theory.total-sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-coequalizers funext -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows +open import synthetic-homotopy-theory.families-descent-data-sequential-colimits +open import synthetic-homotopy-theory.flattening-lemma-coequalizers +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.total-cocones-families-sequential-diagrams +open import synthetic-homotopy-theory.total-sequential-diagrams +open import synthetic-homotopy-theory.universal-property-coequalizers +open import synthetic-homotopy-theory.universal-property-sequential-colimits ```
diff --git a/src/synthetic-homotopy-theory/free-loops.lagda.md b/src/synthetic-homotopy-theory/free-loops.lagda.md index 7af38afed2..2ca408cc36 100644 --- a/src/synthetic-homotopy-theory/free-loops.lagda.md +++ b/src/synthetic-homotopy-theory/free-loops.lagda.md @@ -1,27 +1,22 @@ # Free loops ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.free-loops - (funext : function-extensionality) - where +module synthetic-homotopy-theory.free-loops where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.constant-type-families funext -open import foundation.contractible-types funext +open import foundation.constant-type-families +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md index 86a7ec2a31..32cc8a5ffa 100644 --- a/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-loop-spaces.lagda.md @@ -1,12 +1,7 @@ # Functoriality of the loop space operation ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.functoriality-loop-spaces - (funext : function-extensionality) - where +module synthetic-homotopy-theory.functoriality-loop-spaces where ```
Imports @@ -14,21 +9,21 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.faithful-maps funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.faithful-maps +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.faithful-pointed-maps funext -open import structured-types.pointed-equivalences funext -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.faithful-pointed-maps +open import structured-types.pointed-equivalences +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md index 34eb9ddcfb..52944f00cd 100644 --- a/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-sequential-colimits.lagda.md @@ -1,12 +1,7 @@ # Functoriality of sequential colimits ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.functoriality-sequential-colimits - (funext : function-extensionality) - where +module synthetic-homotopy-theory.functoriality-sequential-colimits where ```
Imports @@ -15,26 +10,27 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-prisms-of-maps funext -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-prisms-of-maps +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.retractions funext -open import foundation.retracts-of-types funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.homotopies +open import foundation.retractions +open import foundation.retracts-of-types +open import foundation.sections open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.retracts-of-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-colimits funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-sequential-diagrams +open import synthetic-homotopy-theory.morphisms-sequential-diagrams +open import synthetic-homotopy-theory.retracts-of-sequential-diagrams +open import synthetic-homotopy-theory.sequential-colimits +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.universal-property-sequential-colimits ```
diff --git a/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md b/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md index a86b0a0faf..477236e983 100644 --- a/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/functoriality-suspensions.lagda.md @@ -1,33 +1,28 @@ # Functoriality of suspensions ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.functoriality-suspensions - (funext : function-extensionality) - where +module synthetic-homotopy-theory.functoriality-suspensions where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext +open import foundation.commuting-squares-of-identifications open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.retracts-of-types funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.retractions +open import foundation.retracts-of-types +open import foundation.sections open import foundation.universe-levels -open import synthetic-homotopy-theory.suspension-structures funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.suspensions-of-types ```
diff --git a/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md b/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md index c7ff512efa..cfa1ef495a 100644 --- a/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md +++ b/src/synthetic-homotopy-theory/groups-of-loops-in-1-types.lagda.md @@ -1,29 +1,24 @@ # Groups of loops in `1`-types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.groups-of-loops-in-1-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.groups-of-loops-in-1-types where ```
Imports ```agda -open import foundation.1-types funext +open import foundation.1-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels -open import group-theory.groups funext -open import group-theory.semigroups funext +open import group-theory.groups +open import group-theory.semigroups open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md index c4d417fc81..10609483e0 100644 --- a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md +++ b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md @@ -1,12 +1,7 @@ # Hatcher's acyclic type ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.hatchers-acyclic-type - (funext : function-extensionality) - where +module synthetic-homotopy-theory.hatchers-acyclic-type where ```
Imports @@ -14,33 +9,33 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.commuting-squares-of-identifications funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.commuting-squares-of-identifications +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.path-algebra funext +open import foundation.identity-types +open import foundation.path-algebra open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.pointed-universal-property-contractible-types funext - -open import synthetic-homotopy-theory.acyclic-types funext -open import synthetic-homotopy-theory.eckmann-hilton-argument funext -open import synthetic-homotopy-theory.functoriality-loop-spaces funext -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.powers-of-loops funext -open import synthetic-homotopy-theory.suspensions-of-pointed-types funext -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext +open import structured-types.pointed-universal-property-contractible-types + +open import synthetic-homotopy-theory.acyclic-types +open import synthetic-homotopy-theory.eckmann-hilton-argument +open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.powers-of-loops +open import synthetic-homotopy-theory.suspensions-of-pointed-types +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types ```
diff --git a/src/synthetic-homotopy-theory/homotopy-groups.lagda.md b/src/synthetic-homotopy-theory/homotopy-groups.lagda.md index 27341b92b0..2576e23f3b 100644 --- a/src/synthetic-homotopy-theory/homotopy-groups.lagda.md +++ b/src/synthetic-homotopy-theory/homotopy-groups.lagda.md @@ -1,12 +1,7 @@ # Homotopy groups ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.homotopy-groups - (funext : function-extensionality) - where +module synthetic-homotopy-theory.homotopy-groups where ```
Imports @@ -15,16 +10,16 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.set-truncations +open import foundation.sets open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.homotopy-automorphism-groups funext +open import group-theory.concrete-groups +open import group-theory.homotopy-automorphism-groups open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-loop-spaces funext +open import synthetic-homotopy-theory.iterated-loop-spaces ```
diff --git a/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md index 1bb8968baf..ed4ca2232d 100644 --- a/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md @@ -3,48 +3,43 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.identity-systems-descent-data-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.identity-systems-descent-data-pushouts where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.identity-systems -open import foundation.identity-types funext -open import foundation.sections funext +open import foundation.identity-types +open import foundation.sections open import foundation.singleton-induction -open import foundation.span-diagrams funext -open import foundation.torsorial-type-families funext -open import foundation.transposition-identifications-along-equivalences funext -open import foundation.universal-property-dependent-pair-types funext -open import foundation.universal-property-identity-types funext +open import foundation.span-diagrams +open import foundation.torsorial-type-families +open import foundation.transposition-identifications-along-equivalences +open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-identity-types open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext -open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts funext -open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts funext -open import synthetic-homotopy-theory.descent-data-pushouts funext -open import synthetic-homotopy-theory.descent-property-pushouts funext -open import synthetic-homotopy-theory.equivalences-descent-data-pushouts funext -open import synthetic-homotopy-theory.families-descent-data-pushouts funext -open import synthetic-homotopy-theory.flattening-lemma-pushouts funext -open import synthetic-homotopy-theory.morphisms-descent-data-pushouts funext -open import synthetic-homotopy-theory.sections-descent-data-pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-universal-property-pushouts +open import synthetic-homotopy-theory.descent-data-equivalence-types-over-pushouts +open import synthetic-homotopy-theory.descent-data-identity-types-over-pushouts +open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.descent-property-pushouts +open import synthetic-homotopy-theory.equivalences-descent-data-pushouts +open import synthetic-homotopy-theory.families-descent-data-pushouts +open import synthetic-homotopy-theory.flattening-lemma-pushouts +open import synthetic-homotopy-theory.morphisms-descent-data-pushouts +open import synthetic-homotopy-theory.sections-descent-data-pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md b/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md index d9df3600e1..f18ec14ff3 100644 --- a/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/induction-principle-pushouts.lagda.md @@ -1,24 +1,19 @@ # The induction principle of pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.induction-principle-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.induction-principle-pushouts where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sections funext +open import foundation.identity-types +open import foundation.sections open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans ```
diff --git a/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md b/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md index 9c14ed1e0b..3492b6e4ea 100644 --- a/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-complex-projective-space.lagda.md @@ -1,23 +1,18 @@ # The infinite complex projective space ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.infinite-complex-projective-space - (funext : function-extensionality) - where +module synthetic-homotopy-theory.infinite-complex-projective-space where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.set-truncations funext +open import foundation.equivalences +open import foundation.set-truncations open import foundation.universe-levels -open import synthetic-homotopy-theory.circle funext +open import synthetic-homotopy-theory.circle ```
diff --git a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md index 104da02fe0..c651ce59fa 100644 --- a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md @@ -1,49 +1,45 @@ # Infinite cyclic types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.infinite-cyclic-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.infinite-cyclic-types where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext -open import elementary-number-theory.group-of-integers funext +open import elementary-number-theory.addition-integers +open import elementary-number-theory.group-of-integers open import elementary-number-theory.integers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import structured-types.equivalences-types-equipped-with-endomorphisms funext -open import structured-types.initial-pointed-type-equipped-with-automorphism funext -open import structured-types.mere-equivalences-types-equipped-with-endomorphisms funext +open import structured-types.equivalences-types-equipped-with-endomorphisms +open import structured-types.initial-pointed-type-equipped-with-automorphism +open import structured-types.mere-equivalences-types-equipped-with-endomorphisms open import structured-types.pointed-types -open import structured-types.pointed-types-equipped-with-automorphisms funext -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.pointed-types-equipped-with-automorphisms +open import structured-types.types-equipped-with-endomorphisms -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces -open import univalent-combinatorics.cyclic-finite-types funext +open import univalent-combinatorics.cyclic-finite-types ```
diff --git a/src/synthetic-homotopy-theory/interval-type.lagda.md b/src/synthetic-homotopy-theory/interval-type.lagda.md index 1279234515..eb421618ba 100644 --- a/src/synthetic-homotopy-theory/interval-type.lagda.md +++ b/src/synthetic-homotopy-theory/interval-type.lagda.md @@ -1,12 +1,7 @@ # The interval ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.interval-type - (funext : function-extensionality) - where +module synthetic-homotopy-theory.interval-type where ```
Imports @@ -14,15 +9,14 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.contractible-types funext -open import foundation.dependent-identifications funext +open import foundation.commuting-squares-of-identifications +open import foundation.contractible-types +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.homotopies +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md index 4f642d0a7a..22f8b3630e 100644 --- a/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/iterated-loop-spaces.lagda.md @@ -1,12 +1,7 @@ # Iterated loop spaces ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.iterated-loop-spaces - (funext : function-extensionality) - where +module synthetic-homotopy-theory.iterated-loop-spaces where ```
Imports @@ -14,13 +9,13 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.iterating-functions funext +open import foundation.iterating-functions open import foundation.universe-levels -open import structured-types.h-spaces funext +open import structured-types.h-spaces open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md index 4d97b08cd3..831ae41a13 100644 --- a/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/iterated-suspensions-of-pointed-types.lagda.md @@ -1,12 +1,7 @@ # Iterated suspensions of pointed types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.iterated-suspensions-of-pointed-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.iterated-suspensions-of-pointed-types where ```
Imports @@ -14,12 +9,12 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.iterating-functions funext +open import foundation.iterating-functions open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.suspensions-of-pointed-types ```
diff --git a/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md b/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md index e493c45aaa..3229530426 100644 --- a/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/join-powers-of-types.lagda.md @@ -1,12 +1,7 @@ # Join powers of types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.join-powers-of-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.join-powers-of-types where ```
Imports @@ -14,11 +9,11 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.empty-types funext -open import foundation.iterating-functions funext +open import foundation.empty-types +open import foundation.iterating-functions open import foundation.universe-levels -open import synthetic-homotopy-theory.joins-of-types funext +open import synthetic-homotopy-theory.joins-of-types ```
diff --git a/src/synthetic-homotopy-theory/joins-of-maps.lagda.md b/src/synthetic-homotopy-theory/joins-of-maps.lagda.md index 4afa049b9f..d31b23c331 100644 --- a/src/synthetic-homotopy-theory/joins-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/joins-of-maps.lagda.md @@ -1,27 +1,22 @@ # Joins of maps ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.joins-of-maps - (funext : function-extensionality) - where +module synthetic-homotopy-theory.joins-of-maps where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.standard-pullbacks funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.standard-pullbacks open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/joins-of-types.lagda.md b/src/synthetic-homotopy-theory/joins-of-types.lagda.md index 564a43a008..8b6ea38172 100644 --- a/src/synthetic-homotopy-theory/joins-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/joins-of-types.lagda.md @@ -1,41 +1,36 @@ # Joins of types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.joins-of-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.joins-of-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.disjunction funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext +open import foundation.disjunction +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositions open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md b/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md index c6a9f2fbe7..73c0d3f6e8 100644 --- a/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md +++ b/src/synthetic-homotopy-theory/left-half-smash-products.lagda.md @@ -1,24 +1,19 @@ # Left half-smash products ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.left-half-smash-products - (funext : function-extensionality) - where +module synthetic-homotopy-theory.left-half-smash-products where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.cofibers-of-maps funext +open import synthetic-homotopy-theory.cofibers-of-maps ```
diff --git a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md index d4b3bf0018..350415b83a 100644 --- a/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md +++ b/src/synthetic-homotopy-theory/loop-homotopy-circle.lagda.md @@ -1,24 +1,19 @@ # The loop homotopy on the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.loop-homotopy-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.loop-homotopy-circle where ```
Imports ```agda -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.negated-equality funext -open import foundation.negation funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.negated-equality +open import foundation.negation -open import synthetic-homotopy-theory.circle funext +open import synthetic-homotopy-theory.circle ```
diff --git a/src/synthetic-homotopy-theory/loop-spaces.lagda.md b/src/synthetic-homotopy-theory/loop-spaces.lagda.md index 561ea93724..d150a83996 100644 --- a/src/synthetic-homotopy-theory/loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/loop-spaces.lagda.md @@ -1,27 +1,22 @@ # Loop spaces ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.loop-spaces - (funext : function-extensionality) - where +module synthetic-homotopy-theory.loop-spaces where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.h-spaces funext -open import structured-types.magmas funext -open import structured-types.pointed-equivalences funext +open import structured-types.h-spaces +open import structured-types.magmas +open import structured-types.pointed-equivalences open import structured-types.pointed-types -open import structured-types.wild-quasigroups funext +open import structured-types.wild-quasigroups ```
diff --git a/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md b/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md index 70071200f9..4f3e139b27 100644 --- a/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/maps-of-prespectra.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.maps-of-prespectra - (funext : function-extensionality) - where +module synthetic-homotopy-theory.maps-of-prespectra where ```
Imports @@ -18,17 +13,17 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.universe-levels -open import structured-types.commuting-squares-of-pointed-maps funext -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext -open import structured-types.whiskering-pointed-homotopies-composition funext -open import structured-types.wild-category-of-pointed-types funext +open import structured-types.commuting-squares-of-pointed-maps +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps +open import structured-types.whiskering-pointed-homotopies-composition +open import structured-types.wild-category-of-pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces funext -open import synthetic-homotopy-theory.prespectra funext +open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.prespectra ```
diff --git a/src/synthetic-homotopy-theory/mere-spheres.lagda.md b/src/synthetic-homotopy-theory/mere-spheres.lagda.md index fa698acf51..70a895594b 100644 --- a/src/synthetic-homotopy-theory/mere-spheres.lagda.md +++ b/src/synthetic-homotopy-theory/mere-spheres.lagda.md @@ -1,12 +1,7 @@ # Mere spheres ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.mere-spheres - (funext : function-extensionality) - where +module synthetic-homotopy-theory.mere-spheres where ```
Imports
 @@ -15,11 +10,11 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.mere-equivalences funext -open import foundation.propositions funext +open import foundation.mere-equivalences +open import foundation.propositions open import foundation.universe-levels -open import synthetic-homotopy-theory.spheres funext +open import synthetic-homotopy-theory.spheres ```
diff --git a/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md index 44d7ec9623..ab2a8b89e3 100644 --- a/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-cocones-under-morphisms-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Morphisms of cocones under morphisms of sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.morphisms-cocones-under-morphisms-sequential-diagrams where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-prisms-of-maps funext -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-prisms-of-maps +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.morphisms-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md b/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md index 45e10d9cdb..05c6762c56 100644 --- a/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-coforks-under-morphisms-double-arrows.lagda.md @@ -1,27 +1,22 @@ # Morphisms of coforks ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows - (funext : function-extensionality) - where +module synthetic-homotopy-theory.morphisms-coforks-under-morphisms-double-arrows where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.homotopies funext -open import foundation.morphisms-arrows funext -open import foundation.morphisms-double-arrows funext +open import foundation.homotopies +open import foundation.morphisms-arrows +open import foundation.morphisms-double-arrows open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.coforks funext +open import synthetic-homotopy-theory.coforks ```
diff --git a/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md index 43ef1ed44e..129a0c0eca 100644 --- a/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-dependent-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Morphisms of dependent sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.morphisms-dependent-sequential-diagrams where ```
Imports @@ -14,12 +9,12 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md b/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md index 30b97f9572..d579804e93 100644 --- a/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-descent-data-circle.lagda.md @@ -1,23 +1,18 @@ # Morphisms of descent data of the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.morphisms-descent-data-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.morphisms-descent-data-circle where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.universe-levels -open import structured-types.morphisms-types-equipped-with-automorphisms funext +open import structured-types.morphisms-types-equipped-with-automorphisms -open import synthetic-homotopy-theory.descent-circle funext +open import synthetic-homotopy-theory.descent-circle ```
diff --git a/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md index 6f13b42ecb..27f747d90f 100644 --- a/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-descent-data-pushouts.lagda.md @@ -1,34 +1,29 @@ # Morphisms of descent data for pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.morphisms-descent-data-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.morphisms-descent-data-pushouts where ```
Imports ```agda -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.span-diagrams funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.span-diagrams open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.descent-data-pushouts funext +open import synthetic-homotopy-theory.descent-data-pushouts ```
diff --git a/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md index 3fc192fa7b..a094834153 100644 --- a/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/morphisms-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Morphisms of sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.morphisms-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.morphisms-sequential-diagrams where ```
Imports @@ -14,24 +9,24 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-homotopies funext -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-maps funext +open import foundation.binary-homotopies +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.dependent-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md index f95542e0be..7e6b3a6784 100644 --- a/src/synthetic-homotopy-theory/multiplication-circle.lagda.md +++ b/src/synthetic-homotopy-theory/multiplication-circle.lagda.md @@ -1,12 +1,7 @@ # The multiplication operation on the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.multiplication-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.multiplication-circle where ```
Imports @@ -14,16 +9,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.function-extensionality-axiom +open import foundation.homotopies +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps -open import synthetic-homotopy-theory.circle funext -open import synthetic-homotopy-theory.loop-homotopy-circle funext +open import synthetic-homotopy-theory.circle +open import synthetic-homotopy-theory.loop-homotopy-circle ```
diff --git a/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md b/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md index 9c3a69fe06..277a8788fb 100644 --- a/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/null-cocones-under-pointed-span-diagrams.lagda.md @@ -1,33 +1,28 @@ # Null cocones under pointed span diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.null-cocones-under-pointed-span-diagrams where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import structured-types.commuting-squares-of-pointed-maps funext -open import structured-types.constant-pointed-maps funext -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext -open import structured-types.pointed-span-diagrams funext +open import structured-types.commuting-squares-of-pointed-maps +open import structured-types.constant-pointed-maps +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps +open import structured-types.pointed-span-diagrams open import structured-types.pointed-types -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams ```
diff --git a/src/synthetic-homotopy-theory/plus-principle.lagda.md b/src/synthetic-homotopy-theory/plus-principle.lagda.md index 40eeda9f18..30af8ac24a 100644 --- a/src/synthetic-homotopy-theory/plus-principle.lagda.md +++ b/src/synthetic-homotopy-theory/plus-principle.lagda.md @@ -1,23 +1,18 @@ # The plus-principle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.plus-principle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.plus-principle where ```
Imports ```agda -open import foundation.connected-types funext -open import foundation.contractible-types funext +open import foundation.connected-types +open import foundation.contractible-types open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.acyclic-types funext +open import synthetic-homotopy-theory.acyclic-types ```
diff --git a/src/synthetic-homotopy-theory/powers-of-loops.lagda.md b/src/synthetic-homotopy-theory/powers-of-loops.lagda.md index 4b9e1ef197..37c127d6f1 100644 --- a/src/synthetic-homotopy-theory/powers-of-loops.lagda.md +++ b/src/synthetic-homotopy-theory/powers-of-loops.lagda.md @@ -1,12 +1,7 @@ # Powers of loops ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.powers-of-loops - (funext : function-extensionality) - where +module synthetic-homotopy-theory.powers-of-loops where ```
Imports @@ -18,18 +13,18 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.iterating-automorphisms funext -open import foundation.iterating-functions funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.iterating-automorphisms +open import foundation.iterating-functions open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces funext -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/synthetic-homotopy-theory/premanifolds.lagda.md b/src/synthetic-homotopy-theory/premanifolds.lagda.md index cf0e9d0e14..9702bfc037 100644 --- a/src/synthetic-homotopy-theory/premanifolds.lagda.md +++ b/src/synthetic-homotopy-theory/premanifolds.lagda.md @@ -1,12 +1,7 @@ # Premanifolds ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.premanifolds - (funext : function-extensionality) - where +module synthetic-homotopy-theory.premanifolds where ```
Imports @@ -14,17 +9,17 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.mere-equivalences funext +open import foundation.mere-equivalences open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.mere-spheres funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.spheres funext -open import synthetic-homotopy-theory.tangent-spheres funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.mere-spheres +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.spheres +open import synthetic-homotopy-theory.tangent-spheres ```
diff --git a/src/synthetic-homotopy-theory/prespectra.lagda.md b/src/synthetic-homotopy-theory/prespectra.lagda.md index 742a13954c..b4318725d3 100644 --- a/src/synthetic-homotopy-theory/prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/prespectra.lagda.md @@ -1,12 +1,7 @@ # Prespectra ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.prespectra - (funext : function-extensionality) - where +module synthetic-homotopy-theory.prespectra where ```
Imports @@ -15,16 +10,16 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.suspensions-of-pointed-types funext -open import synthetic-homotopy-theory.suspensions-of-types funext -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.suspensions-of-pointed-types +open import synthetic-homotopy-theory.suspensions-of-types +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types ```
diff --git a/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md index 080d6ce7b5..73103fae01 100644 --- a/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/pullback-property-pushouts.lagda.md @@ -1,26 +1,21 @@ # The pullback property of pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.pullback-property-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.pullback-property-pushouts where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.cones-over-cospan-diagrams funext +open import foundation.commuting-squares-of-maps +open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.precomposition-functions funext -open import foundation.pullbacks funext +open import foundation.function-types +open import foundation.precomposition-functions +open import foundation.pullbacks open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.cocones-under-spans ```
diff --git a/src/synthetic-homotopy-theory/pushout-products.lagda.md b/src/synthetic-homotopy-theory/pushout-products.lagda.md index 579ea2e75c..5756497b68 100644 --- a/src/synthetic-homotopy-theory/pushout-products.lagda.md +++ b/src/synthetic-homotopy-theory/pushout-products.lagda.md @@ -1,28 +1,23 @@ # Pushout-products ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.pushout-products - (funext : function-extensionality) - where +module synthetic-homotopy-theory.pushout-products where ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.homotopies funext +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.homotopies open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md index 0ee383c19b..53105ba5b8 100644 --- a/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/pushouts-of-pointed-types.lagda.md @@ -1,12 +1,7 @@ # Pushouts of pointed types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.pushouts-of-pointed-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.pushouts-of-pointed-types where ```
Imports @@ -14,14 +9,14 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext -open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams +open import synthetic-homotopy-theory.pushouts ```
diff --git a/src/synthetic-homotopy-theory/pushouts.lagda.md b/src/synthetic-homotopy-theory/pushouts.lagda.md index 308f91b3ad..1b5112681f 100644 --- a/src/synthetic-homotopy-theory/pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/pushouts.lagda.md @@ -1,12 +1,7 @@ # Pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.pushouts where ```
Imports @@ -14,31 +9,31 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.constant-type-families funext +open import foundation.commuting-squares-of-maps +open import foundation.constant-type-families open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.transport-along-homotopies funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.transport-along-homotopies open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition open import reflection.erasing-equality -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext -open import synthetic-homotopy-theory.flattening-lemma-pushouts funext -open import synthetic-homotopy-theory.induction-principle-pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.dependent-universal-property-pushouts +open import synthetic-homotopy-theory.flattening-lemma-pushouts +open import synthetic-homotopy-theory.induction-principle-pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md b/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md index 9c82dd1347..af0fa511a5 100644 --- a/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/recursion-principle-pushouts.lagda.md @@ -1,24 +1,19 @@ # The recursion principle of pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.recursion-principle-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.recursion-principle-pushouts where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sections funext +open import foundation.identity-types +open import foundation.sections open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans ```
diff --git a/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md index abb60c401a..13ad9399bb 100644 --- a/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/retracts-of-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Retracts of sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.retracts-of-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.retracts-of-sequential-diagrams where ```
Imports @@ -14,20 +9,20 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.retracts-of-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.retractions +open import foundation.retracts-of-types open import foundation.universe-levels -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext +open import synthetic-homotopy-theory.morphisms-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md b/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md index 52f521c9fd..5b471fe9ff 100644 --- a/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/rewriting-pushouts.lagda.md @@ -3,26 +3,21 @@ ```agda {-# OPTIONS --rewriting #-} -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.rewriting-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.rewriting-pushouts where ```
Imports ```agda -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels open import reflection.rewriting -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.pushouts ```
diff --git a/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md b/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md index 585cd39b97..77c8924b1c 100644 --- a/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md @@ -1,12 +1,7 @@ # Sections of families over the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.sections-descent-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.sections-descent-circle where ```
Imports @@ -14,27 +9,27 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-identifications funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext -open import foundation.dependent-identifications funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-identifications +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.path-algebra funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.path-algebra open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-circle funext -open import synthetic-homotopy-theory.free-loops funext -open import synthetic-homotopy-theory.universal-property-circle funext +open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.universal-property-circle ```
diff --git a/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md index 067f3b3aab..583235db13 100644 --- a/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md @@ -1,12 +1,7 @@ # Sections of descent data for pushouts ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.sections-descent-data-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.sections-descent-data-pushouts where ```
Imports @@ -14,31 +9,31 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-identifications +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.span-diagrams funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.span-diagrams open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-universal-property-pushouts funext -open import synthetic-homotopy-theory.descent-data-pushouts funext -open import synthetic-homotopy-theory.families-descent-data-pushouts funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.dependent-universal-property-pushouts +open import synthetic-homotopy-theory.descent-data-pushouts +open import synthetic-homotopy-theory.families-descent-data-pushouts +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/sequential-colimits.lagda.md index d5337cad00..e0767413bd 100644 --- a/src/synthetic-homotopy-theory/sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/sequential-colimits.lagda.md @@ -1,12 +1,7 @@ # Sequential colimits ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.sequential-colimits - (funext : function-extensionality) - where +module synthetic-homotopy-theory.sequential-colimits where ```
Imports @@ -14,23 +9,23 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.propositions open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.coequalizers funext -open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.coequalizers +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-universal-property-sequential-colimits +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.universal-property-sequential-colimits ```
diff --git a/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md index 6e44a4ffbc..44b7e094cb 100644 --- a/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.sequential-diagrams where ```
Imports @@ -14,9 +9,9 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels ``` diff --git a/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md b/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md index b73928730b..bd20d04559 100644 --- a/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md +++ b/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md @@ -1,23 +1,18 @@ # Sequentially compact types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.sequentially-compact-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.sequentially-compact-types where ```
Imports ```agda -open import foundation.propositions funext +open import foundation.propositions open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.universal-property-sequential-colimits ```
diff --git a/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md index 5387d22e66..c7c6e22f6f 100644 --- a/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Shifts of sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.shifts-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.shifts-sequential-diagrams where ```
Imports @@ -14,26 +9,26 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies open import foundation.homotopy-algebra -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-homotopies-concatenation funext - -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.functoriality-sequential-colimits funext -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-colimits funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext +open import foundation.whiskering-homotopies-concatenation + +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.functoriality-sequential-colimits +open import synthetic-homotopy-theory.morphisms-sequential-diagrams +open import synthetic-homotopy-theory.sequential-colimits +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.universal-property-sequential-colimits ```
diff --git a/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md index c77a7759b1..92f38de1c4 100644 --- a/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/smash-products-of-pointed-types.lagda.md @@ -1,38 +1,33 @@ # Smash products of pointed types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.smash-products-of-pointed-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.smash-products-of-pointed-types where ```
Imports ```agda -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import structured-types.constant-pointed-maps funext -open import structured-types.pointed-cartesian-product-types funext -open import structured-types.pointed-homotopies funext -open import structured-types.pointed-maps funext +open import structured-types.constant-pointed-maps +open import structured-types.pointed-cartesian-product-types +open import structured-types.pointed-homotopies +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.pointed-unit-type funext +open import structured-types.pointed-unit-type -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext -open import synthetic-homotopy-theory.cofibers-of-pointed-maps funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.wedges-of-pointed-types funext +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams +open import synthetic-homotopy-theory.cofibers-of-pointed-maps +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.wedges-of-pointed-types ```
diff --git a/src/synthetic-homotopy-theory/spectra.lagda.md b/src/synthetic-homotopy-theory/spectra.lagda.md index ebec793c9c..ba8278a8ec 100644 --- a/src/synthetic-homotopy-theory/spectra.lagda.md +++ b/src/synthetic-homotopy-theory/spectra.lagda.md @@ -1,12 +1,7 @@ # Spectra ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.spectra - (funext : function-extensionality) - where +module synthetic-homotopy-theory.spectra where ```
Imports @@ -15,20 +10,20 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import structured-types.pointed-equivalences funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-equivalences +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.prespectra funext -open import synthetic-homotopy-theory.suspensions-of-pointed-types funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.prespectra +open import synthetic-homotopy-theory.suspensions-of-pointed-types +open import synthetic-homotopy-theory.suspensions-of-types ```
diff --git a/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md b/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md index 75b682c38d..2a8ad9eab1 100644 --- a/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md +++ b/src/synthetic-homotopy-theory/sphere-prespectrum.lagda.md @@ -1,12 +1,7 @@ # The sphere prespectrum ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.sphere-prespectrum - (funext : function-extensionality) - where +module synthetic-homotopy-theory.sphere-prespectrum where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.prespectra funext -open import synthetic-homotopy-theory.suspension-prespectra funext +open import synthetic-homotopy-theory.prespectra +open import synthetic-homotopy-theory.suspension-prespectra -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/synthetic-homotopy-theory/spheres.lagda.md b/src/synthetic-homotopy-theory/spheres.lagda.md index 228674efbb..85490fc5db 100644 --- a/src/synthetic-homotopy-theory/spheres.lagda.md +++ b/src/synthetic-homotopy-theory/spheres.lagda.md @@ -1,12 +1,7 @@ # Spheres ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.spheres - (funext : function-extensionality) - where +module synthetic-homotopy-theory.spheres where ```
Imports @@ -15,16 +10,16 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types +open import synthetic-homotopy-theory.suspensions-of-types -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md b/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md index 9e38e39644..54a0453fb9 100644 --- a/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/suspension-prespectra.lagda.md @@ -1,12 +1,7 @@ # Suspension prespectra ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.suspension-prespectra - (funext : function-extensionality) - where +module synthetic-homotopy-theory.suspension-prespectra where ```
Imports @@ -17,14 +12,14 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-maps funext +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types funext -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.prespectra funext -open import synthetic-homotopy-theory.suspensions-of-pointed-types funext -open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types funext +open import synthetic-homotopy-theory.iterated-suspensions-of-pointed-types +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.prespectra +open import synthetic-homotopy-theory.suspensions-of-pointed-types +open import synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types ```
diff --git a/src/synthetic-homotopy-theory/suspension-structures.lagda.md b/src/synthetic-homotopy-theory/suspension-structures.lagda.md index 15166954da..7d579d350f 100644 --- a/src/synthetic-homotopy-theory/suspension-structures.lagda.md +++ b/src/synthetic-homotopy-theory/suspension-structures.lagda.md @@ -1,39 +1,33 @@ # Suspension Structures ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.suspension-structures - (funext : function-extensionality) - where +module synthetic-homotopy-theory.suspension-structures where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-identifications funext -open import foundation.constant-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-identifications +open import foundation.constant-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies open import foundation.identity-systems -open import foundation.identity-types funext -open import foundation.injective-maps funext +open import foundation.identity-types +open import foundation.injective-maps open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.unit-type -open import foundation.universal-property-unit-type funext +open import foundation.universal-property-unit-type open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation -open import synthetic-homotopy-theory.cocones-under-spans funext +open import synthetic-homotopy-theory.cocones-under-spans ```
diff --git a/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md index 2436f70d05..3e57879259 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-pointed-types.lagda.md @@ -1,27 +1,22 @@ # Suspensions of pointed types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.suspensions-of-pointed-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.suspensions-of-pointed-types where ```
Imports ```agda -open import foundation.constant-maps funext +open import foundation.constant-maps open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.suspension-structures funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.suspensions-of-types ```
diff --git a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md index c9d20286ff..511ff1e9b6 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md @@ -1,44 +1,39 @@ # Suspensions of propositions ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.suspensions-of-propositions - (funext : function-extensionality) - where +module synthetic-homotopy-theory.suspensions-of-propositions where ```
Imports ```agda -open import foundation.booleans funext -open import foundation.contractible-types funext +open import foundation.booleans +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.sets open import foundation.subsingleton-induction -open import foundation.surjective-maps funext -open import foundation.torsorial-type-families funext +open import foundation.surjective-maps +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import synthetic-homotopy-theory.dependent-suspension-structures funext -open import synthetic-homotopy-theory.suspension-structures funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.dependent-suspension-structures +open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.suspensions-of-types -open import univalent-combinatorics.kuratowski-finite-sets funext +open import univalent-combinatorics.kuratowski-finite-sets ```
diff --git a/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md index d899fd67dd..b0d6084cbc 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md @@ -1,12 +1,7 @@ # Suspensions of types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.suspensions-of-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.suspensions-of-types where ```
Imports @@ -14,47 +9,46 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.booleans funext -open import foundation.commuting-squares-of-identifications funext -open import foundation.connected-types funext -open import foundation.constant-maps funext -open import foundation.contractible-types funext -open import foundation.dependent-identifications funext +open import foundation.booleans +open import foundation.commuting-squares-of-identifications +open import foundation.connected-types +open import foundation.constant-maps +open import foundation.contractible-types +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.diagonal-maps-of-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.path-algebra funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.retractions funext -open import foundation.sections funext -open import foundation.surjective-maps funext -open import foundation.torsorial-type-families funext +open import foundation.diagonal-maps-of-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.path-algebra +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.retractions +open import foundation.sections +open import foundation.surjective-maps +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-cocones-under-spans funext -open import synthetic-homotopy-theory.dependent-suspension-structures funext -open import synthetic-homotopy-theory.dependent-universal-property-suspensions funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.suspension-structures funext -open import synthetic-homotopy-theory.universal-property-pushouts funext -open import synthetic-homotopy-theory.universal-property-suspensions funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.dependent-cocones-under-spans +open import synthetic-homotopy-theory.dependent-suspension-structures +open import synthetic-homotopy-theory.dependent-universal-property-suspensions +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.universal-property-pushouts +open import synthetic-homotopy-theory.universal-property-suspensions ```
diff --git a/src/synthetic-homotopy-theory/tangent-spheres.lagda.md b/src/synthetic-homotopy-theory/tangent-spheres.lagda.md index e8436abc95..ec35fb7cab 100644 --- a/src/synthetic-homotopy-theory/tangent-spheres.lagda.md +++ b/src/synthetic-homotopy-theory/tangent-spheres.lagda.md @@ -1,12 +1,7 @@ # Tangent spheres ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.tangent-spheres - (funext : function-extensionality) - where +module synthetic-homotopy-theory.tangent-spheres where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.commuting-squares-of-maps funext +open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types -open import foundation.mere-equivalences funext +open import foundation.mere-equivalences open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.mere-spheres funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.spheres funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.mere-spheres +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.spheres ```
diff --git a/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md index 428f47fd7e..5c6d86df34 100644 --- a/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/total-cocones-families-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Total cocones of type families over cocones under sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.total-cocones-families-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.total-cocones-families-sequential-diagrams where ```
Imports @@ -16,20 +11,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext - -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext -open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext -open import synthetic-homotopy-theory.families-descent-data-sequential-colimits funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.total-sequential-diagrams funext +open import foundation.whiskering-identifications-concatenation + +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-sequential-diagrams +open import synthetic-homotopy-theory.families-descent-data-sequential-colimits +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.total-sequential-diagrams ```
diff --git a/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md index 48730d7cd2..22e1060a68 100644 --- a/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/total-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Total sequential diagrams of dependent sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.total-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.total-sequential-diagrams where ```
Imports @@ -15,19 +10,19 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams funext -open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext -open import synthetic-homotopy-theory.functoriality-sequential-colimits funext -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-colimits funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.dependent-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-dependent-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-sequential-diagrams +open import synthetic-homotopy-theory.functoriality-sequential-colimits +open import synthetic-homotopy-theory.morphisms-sequential-diagrams +open import synthetic-homotopy-theory.sequential-colimits +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.universal-property-sequential-colimits ```
diff --git a/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md b/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md index 2454018226..cdb70b73bf 100644 --- a/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md +++ b/src/synthetic-homotopy-theory/triple-loop-spaces.lagda.md @@ -1,12 +1,7 @@ # Triple loop spaces ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.triple-loop-spaces - (funext : function-extensionality) - where +module synthetic-homotopy-theory.triple-loop-spaces where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.path-algebra funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.path-algebra open import foundation.universe-levels open import structured-types.pointed-types -open import synthetic-homotopy-theory.double-loop-spaces funext -open import synthetic-homotopy-theory.iterated-loop-spaces funext +open import synthetic-homotopy-theory.double-loop-spaces +open import synthetic-homotopy-theory.iterated-loop-spaces ```
diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md index 5135298f66..95872ea9f7 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md @@ -1,63 +1,58 @@ # `k`-acyclic maps ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.truncated-acyclic-maps - (funext : function-extensionality) - where +module synthetic-homotopy-theory.truncated-acyclic-maps where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.cones-over-cospan-diagrams funext -open import foundation.connected-maps funext -open import foundation.connected-types funext -open import foundation.constant-maps funext -open import foundation.dependent-epimorphisms-with-respect-to-truncated-types funext +open import foundation.cartesian-product-types +open import foundation.cones-over-cospan-diagrams +open import foundation.connected-maps +open import foundation.connected-types +open import foundation.constant-maps +open import foundation.dependent-epimorphisms-with-respect-to-truncated-types open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.diagonal-maps-of-types funext -open import foundation.embeddings funext -open import foundation.epimorphisms-with-respect-to-truncated-types funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-fibers-of-maps funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.pullbacks funext -open import foundation.retracts-of-maps funext -open import foundation.torsorial-type-families funext -open import foundation.truncated-types funext -open import foundation.truncation-equivalences funext +open import foundation.dependent-universal-property-equivalences +open import foundation.diagonal-maps-of-types +open import foundation.embeddings +open import foundation.epimorphisms-with-respect-to-truncated-types +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-fibers-of-maps +open import foundation.homotopies +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.pullbacks +open import foundation.retracts-of-maps +open import foundation.torsorial-type-families +open import foundation.truncated-types +open import foundation.truncation-equivalences open import foundation.truncation-levels -open import foundation.truncations funext +open import foundation.truncations open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-cartesian-product-types funext -open import foundation.universal-property-dependent-pair-types funext +open import foundation.universal-property-cartesian-product-types +open import foundation.universal-property-dependent-pair-types open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.codiagonals-of-maps funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.truncated-acyclic-types funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.codiagonals-of-maps +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.truncated-acyclic-types +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md index aa46246c1f..6324c36e58 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md @@ -1,28 +1,23 @@ # `k`-acyclic types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.truncated-acyclic-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.truncated-acyclic-types where ```
Imports ```agda -open import foundation.connected-types funext -open import foundation.contractible-types funext -open import foundation.equivalences funext -open import foundation.propositions funext -open import foundation.retracts-of-types funext +open import foundation.connected-types +open import foundation.contractible-types +open import foundation.equivalences +open import foundation.propositions +open import foundation.retracts-of-types open import foundation.truncation-levels open import foundation.unit-type open import foundation.universe-levels -open import synthetic-homotopy-theory.functoriality-suspensions funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.functoriality-suspensions +open import synthetic-homotopy-theory.suspensions-of-types ```
diff --git a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md index 957dfac0e1..55603d9eb5 100644 --- a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md @@ -3,54 +3,48 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.universal-cover-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.universal-cover-circle where ```
Imports ```agda -open import elementary-number-theory.equality-integers funext +open import elementary-number-theory.equality-integers open import elementary-number-theory.integers -open import elementary-number-theory.nonzero-integers funext -open import elementary-number-theory.universal-property-integers funext +open import elementary-number-theory.nonzero-integers +open import elementary-number-theory.universal-property-integers open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.dependent-identifications funext +open import foundation.commuting-squares-of-maps +open import foundation.dependent-identifications open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.dependent-universal-property-equivalences +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.precomposition-dependent-functions funext -open import foundation.raising-universe-levels funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation +open import foundation.precomposition-dependent-functions +open import foundation.raising-universe-levels +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels -open import synthetic-homotopy-theory.descent-circle funext -open import synthetic-homotopy-theory.free-loops funext -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.universal-property-circle funext +open import synthetic-homotopy-theory.descent-circle +open import synthetic-homotopy-theory.free-loops +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.universal-property-circle ```
diff --git a/src/synthetic-homotopy-theory/universal-property-circle.lagda.md b/src/synthetic-homotopy-theory/universal-property-circle.lagda.md index 01bec1af5c..9698cb554f 100644 --- a/src/synthetic-homotopy-theory/universal-property-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-circle.lagda.md @@ -1,12 +1,7 @@ # The universal property of the circle ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.universal-property-circle - (funext : function-extensionality) - where +module synthetic-homotopy-theory.universal-property-circle where ```
Imports @@ -14,24 +9,23 @@ module ```agda open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions -open import foundation.constant-type-families funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.constant-type-families +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.sections open import foundation.transport-along-identifications open import foundation.universe-levels -open import synthetic-homotopy-theory.free-loops funext +open import synthetic-homotopy-theory.free-loops ```
diff --git a/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md b/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md index 2c545c540a..14abaccfc2 100644 --- a/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md @@ -1,36 +1,31 @@ # The universal property of coequalizers ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.universal-property-coequalizers - (funext : function-extensionality) - where +module synthetic-homotopy-theory.universal-property-coequalizers where ```
Imports ```agda -open import foundation.commuting-cubes-of-maps funext -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.commuting-cubes-of-maps +open import foundation.commuting-squares-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.double-arrows -open import foundation.equivalences funext -open import foundation.equivalences funext-double-arrows -open import foundation.fibers-of-maps funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext +open import foundation.equivalences +open import foundation.equivalences-double-arrows +open import foundation.fibers-of-maps +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies open import foundation.universe-levels -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.equivalences-coforks-under-equivalences-double-arrows +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md index 96dcee0752..171038972c 100644 --- a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md @@ -3,44 +3,39 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.universal-property-pushouts - (funext : function-extensionality) - where +module synthetic-homotopy-theory.universal-property-pushouts where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-cubes-of-maps funext -open import foundation.commuting-squares-of-maps funext -open import foundation.cones-over-cospan-diagrams funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-cubes-of-maps +open import foundation.commuting-squares-of-maps +open import foundation.cones-over-cospan-diagrams +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.precomposition-functions funext -open import foundation.pullbacks funext -open import foundation.standard-pullbacks funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.precomposition-functions +open import foundation.pullbacks +open import foundation.standard-pullbacks open import foundation.subtype-identity-principle open import foundation.transport-along-identifications -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.pullback-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.pullback-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md index 1af2f81977..7969ee8012 100644 --- a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md @@ -1,12 +1,7 @@ # The universal property of sequential colimits ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.universal-property-sequential-colimits - (funext : function-extensionality) - where +module synthetic-homotopy-theory.universal-property-sequential-colimits where ```
Imports @@ -15,33 +10,34 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.precomposition-functions funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.precomposition-functions +open import foundation.retractions +open import foundation.sections open import foundation.subtype-identity-principle -open import foundation.universal-property-equivalences funext +open import foundation.universal-property-equivalences open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.coforks funext -open import synthetic-homotopy-theory.coforks funext-cocones-under-sequential-diagrams -open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams funext -open import synthetic-homotopy-theory.equivalences-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-coequalizers funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.coforks +open import synthetic-homotopy-theory.coforks-cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-cocones-under-equivalences-sequential-diagrams +open import synthetic-homotopy-theory.equivalences-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.universal-property-coequalizers ```
diff --git a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md index 64ed2338e3..a8b0a7025c 100644 --- a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md @@ -1,35 +1,30 @@ # Universal Property of suspensions of pointed types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import structured-types.pointed-equivalences funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-equivalences +open import structured-types.pointed-maps open import structured-types.pointed-types -open import synthetic-homotopy-theory.functoriality-loop-spaces funext -open import synthetic-homotopy-theory.loop-spaces funext -open import synthetic-homotopy-theory.suspensions-of-pointed-types funext -open import synthetic-homotopy-theory.suspensions-of-types funext +open import synthetic-homotopy-theory.functoriality-loop-spaces +open import synthetic-homotopy-theory.loop-spaces +open import synthetic-homotopy-theory.suspensions-of-pointed-types +open import synthetic-homotopy-theory.suspensions-of-types ```
diff --git a/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md b/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md index 4dbb9eeb18..b990b79bed 100644 --- a/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-suspensions.lagda.md @@ -1,30 +1,25 @@ # Universal property of suspensions ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.universal-property-suspensions - (funext : function-extensionality) - where +module synthetic-homotopy-theory.universal-property-suspensions where ```
Imports ```agda -open import foundation.constant-maps funext +open import foundation.constant-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-spans funext -open import synthetic-homotopy-theory.suspension-structures funext -open import synthetic-homotopy-theory.universal-property-pushouts funext +open import synthetic-homotopy-theory.cocones-under-spans +open import synthetic-homotopy-theory.suspension-structures +open import synthetic-homotopy-theory.universal-property-pushouts ```
diff --git a/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md index 2d0d184d5a..669ca31a56 100644 --- a/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/wedges-of-pointed-types.lagda.md @@ -1,31 +1,26 @@ # Wedges of pointed types ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.wedges-of-pointed-types - (funext : function-extensionality) - where +module synthetic-homotopy-theory.wedges-of-pointed-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import structured-types.pointed-cartesian-product-types funext -open import structured-types.pointed-maps funext +open import structured-types.pointed-cartesian-product-types +open import structured-types.pointed-maps open import structured-types.pointed-types -open import structured-types.pointed-unit-type funext +open import structured-types.pointed-unit-type -open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams funext -open import synthetic-homotopy-theory.cofibers-of-maps funext -open import synthetic-homotopy-theory.pushouts funext -open import synthetic-homotopy-theory.pushouts funext-of-pointed-types +open import synthetic-homotopy-theory.cocones-under-pointed-span-diagrams +open import synthetic-homotopy-theory.cofibers-of-maps +open import synthetic-homotopy-theory.pushouts +open import synthetic-homotopy-theory.pushouts-of-pointed-types ```
diff --git a/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md index 0e7729232d..71068b80e1 100644 --- a/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/zigzags-sequential-diagrams.lagda.md @@ -1,12 +1,7 @@ # Zigzags between sequential diagrams ```agda -open import foundation.function-extensionality-axiom - -module - synthetic-homotopy-theory.zigzags-sequential-diagrams - (funext : function-extensionality) - where +module synthetic-homotopy-theory.zigzags-sequential-diagrams where ```
Imports @@ -14,24 +9,24 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.commuting-squares-of-homotopies funext -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext +open import foundation.cartesian-product-types +open import foundation.commuting-squares-of-homotopies +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.retractions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.retractions open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import synthetic-homotopy-theory.cocones-under-sequential-diagrams funext -open import synthetic-homotopy-theory.functoriality-sequential-colimits funext -open import synthetic-homotopy-theory.morphisms-sequential-diagrams funext -open import synthetic-homotopy-theory.sequential-diagrams funext -open import synthetic-homotopy-theory.shifts-sequential-diagrams funext -open import synthetic-homotopy-theory.universal-property-sequential-colimits funext +open import synthetic-homotopy-theory.cocones-under-sequential-diagrams +open import synthetic-homotopy-theory.functoriality-sequential-colimits +open import synthetic-homotopy-theory.morphisms-sequential-diagrams +open import synthetic-homotopy-theory.sequential-diagrams +open import synthetic-homotopy-theory.shifts-sequential-diagrams +open import synthetic-homotopy-theory.universal-property-sequential-colimits ```
diff --git a/src/trees.lagda.md b/src/trees.lagda.md index c1258e38c7..4da5e8d445 100644 --- a/src/trees.lagda.md +++ b/src/trees.lagda.md @@ -7,66 +7,61 @@ ## Files in the `trees` module ```agda -open import foundation.function-extensionality-axiom +module trees where -module - trees - (funext : function-extensionality) - where - -open import trees.algebras-polynomial-endofunctors funext public -open import trees.bases-directed-trees funext public -open import trees.bases-enriched-directed-trees funext public +open import trees.algebras-polynomial-endofunctors public +open import trees.bases-directed-trees public +open import trees.bases-enriched-directed-trees public open import trees.binary-w-types public -open import trees.bounded-multisets funext public -open import trees.coalgebra-of-directed-trees funext public -open import trees.coalgebra-of-enriched-directed-trees funext public -open import trees.coalgebras-polynomial-endofunctors funext public -open import trees.combinator-directed-trees funext public -open import trees.combinator-enriched-directed-trees funext public -open import trees.directed-trees funext public -open import trees.elementhood-relation-coalgebras-polynomial-endofunctors funext public -open import trees.elementhood-relation-w-types funext public -open import trees.empty-multisets funext public -open import trees.enriched-directed-trees funext public -open import trees.equivalences-directed-trees funext public -open import trees.equivalences-enriched-directed-trees funext public -open import trees.extensional-w-types funext public -open import trees.fibers-directed-trees funext public -open import trees.fibers-enriched-directed-trees funext public -open import trees.full-binary-trees funext public -open import trees.functoriality-combinator-directed-trees funext public -open import trees.functoriality-fiber-directed-tree funext public -open import trees.functoriality-w-types funext public -open import trees.hereditary-w-types funext public +open import trees.bounded-multisets public +open import trees.coalgebra-of-directed-trees public +open import trees.coalgebra-of-enriched-directed-trees public +open import trees.coalgebras-polynomial-endofunctors public +open import trees.combinator-directed-trees public +open import trees.combinator-enriched-directed-trees public +open import trees.directed-trees public +open import trees.elementhood-relation-coalgebras-polynomial-endofunctors public +open import trees.elementhood-relation-w-types public +open import trees.empty-multisets public +open import trees.enriched-directed-trees public +open import trees.equivalences-directed-trees public +open import trees.equivalences-enriched-directed-trees public +open import trees.extensional-w-types public +open import trees.fibers-directed-trees public +open import trees.fibers-enriched-directed-trees public +open import trees.full-binary-trees public +open import trees.functoriality-combinator-directed-trees public +open import trees.functoriality-fiber-directed-tree public +open import trees.functoriality-w-types public +open import trees.hereditary-w-types public open import trees.indexed-w-types public -open import trees.induction-w-types funext public -open import trees.inequality-w-types funext public -open import trees.lower-types-w-types funext public -open import trees.morphisms-algebras-polynomial-endofunctors funext public -open import trees.morphisms-coalgebras-polynomial-endofunctors funext public -open import trees.morphisms-directed-trees funext public -open import trees.morphisms-enriched-directed-trees funext public -open import trees.multiset-indexed-dependent-products-of-types funext public -open import trees.multisets funext public -open import trees.planar-binary-trees funext public -open import trees.plane-trees funext public -open import trees.polynomial-endofunctors funext public -open import trees.raising-universe-levels-directed-trees funext public -open import trees.ranks-of-elements-w-types funext public -open import trees.rooted-morphisms-directed-trees funext public -open import trees.rooted-morphisms-enriched-directed-trees funext public -open import trees.rooted-quasitrees funext public -open import trees.rooted-undirected-trees funext public -open import trees.small-multisets funext public -open import trees.submultisets funext public -open import trees.transitive-multisets funext public -open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors funext public -open import trees.underlying-trees-of-elements-of-w-types funext public -open import trees.undirected-trees funext public -open import trees.universal-multiset funext public +open import trees.induction-w-types public +open import trees.inequality-w-types public +open import trees.lower-types-w-types public +open import trees.morphisms-algebras-polynomial-endofunctors public +open import trees.morphisms-coalgebras-polynomial-endofunctors public +open import trees.morphisms-directed-trees public +open import trees.morphisms-enriched-directed-trees public +open import trees.multiset-indexed-dependent-products-of-types public +open import trees.multisets public +open import trees.planar-binary-trees public +open import trees.plane-trees public +open import trees.polynomial-endofunctors public +open import trees.raising-universe-levels-directed-trees public +open import trees.ranks-of-elements-w-types public +open import trees.rooted-morphisms-directed-trees public +open import trees.rooted-morphisms-enriched-directed-trees public +open import trees.rooted-quasitrees public +open import trees.rooted-undirected-trees public +open import trees.small-multisets public +open import trees.submultisets public +open import trees.transitive-multisets public +open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors public +open import trees.underlying-trees-of-elements-of-w-types public +open import trees.undirected-trees public +open import trees.universal-multiset public open import trees.universal-tree public -open import trees.w-type-of-natural-numbers funext public -open import trees.w-type-of-propositions funext public -open import trees.w-types funext public +open import trees.w-type-of-natural-numbers public +open import trees.w-type-of-propositions public +open import trees.w-types public ``` diff --git a/src/trees/algebras-polynomial-endofunctors.lagda.md b/src/trees/algebras-polynomial-endofunctors.lagda.md index 8964993518..ca1ac4e432 100644 --- a/src/trees/algebras-polynomial-endofunctors.lagda.md +++ b/src/trees/algebras-polynomial-endofunctors.lagda.md @@ -1,12 +1,7 @@ # Algebras for polynomial endofunctors ```agda -open import foundation.function-extensionality-axiom - -module - trees.algebras-polynomial-endofunctors - (funext : function-extensionality) - where +module trees.algebras-polynomial-endofunctors where ```
Imports @@ -15,7 +10,7 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.polynomial-endofunctors funext +open import trees.polynomial-endofunctors ```
diff --git a/src/trees/bases-directed-trees.lagda.md b/src/trees/bases-directed-trees.lagda.md index 966f29407a..2e96641277 100644 --- a/src/trees/bases-directed-trees.lagda.md +++ b/src/trees/bases-directed-trees.lagda.md @@ -1,12 +1,7 @@ # Bases of directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.bases-directed-trees - (funext : function-extensionality) - where +module trees.bases-directed-trees where ```
Imports @@ -15,26 +10,26 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negation +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.universe-levels -open import graph-theory.walks-directed-graphs funext +open import graph-theory.walks-directed-graphs -open import trees.directed-trees funext +open import trees.directed-trees ```
diff --git a/src/trees/bases-enriched-directed-trees.lagda.md b/src/trees/bases-enriched-directed-trees.lagda.md index 8d55af2aa4..6d2feee2cc 100644 --- a/src/trees/bases-enriched-directed-trees.lagda.md +++ b/src/trees/bases-enriched-directed-trees.lagda.md @@ -1,31 +1,26 @@ # Bases of enriched directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.bases-enriched-directed-trees - (funext : function-extensionality) - where +module trees.bases-enriched-directed-trees where ```
Imports ```agda -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.negation +open import foundation.type-arithmetic-empty-type open import foundation.universe-levels -open import trees.bases-directed-trees funext -open import trees.enriched-directed-trees funext +open import trees.bases-directed-trees +open import trees.enriched-directed-trees ```
diff --git a/src/trees/bounded-multisets.lagda.md b/src/trees/bounded-multisets.lagda.md index c9cd740194..ceda35ae57 100644 --- a/src/trees/bounded-multisets.lagda.md +++ b/src/trees/bounded-multisets.lagda.md @@ -1,12 +1,7 @@ # Bounded multisets ```agda -open import foundation.function-extensionality-axiom - -module - trees.bounded-multisets - (funext : function-extensionality) - where +module trees.bounded-multisets where ```
Imports @@ -15,14 +10,14 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.propositions open import foundation.universe-levels -open import trees.empty-multisets funext -open import trees.multisets funext -open import trees.w-types funext +open import trees.empty-multisets +open import trees.multisets +open import trees.w-types ```
diff --git a/src/trees/coalgebra-of-directed-trees.lagda.md b/src/trees/coalgebra-of-directed-trees.lagda.md index a6deaa23a7..e581169de0 100644 --- a/src/trees/coalgebra-of-directed-trees.lagda.md +++ b/src/trees/coalgebra-of-directed-trees.lagda.md @@ -1,12 +1,7 @@ # The coalgebra of directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.coalgebra-of-directed-trees - (funext : function-extensionality) - where +module trees.coalgebra-of-directed-trees where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.bases-directed-trees funext -open import trees.coalgebras-polynomial-endofunctors funext -open import trees.directed-trees funext -open import trees.fibers-directed-trees funext +open import trees.bases-directed-trees +open import trees.coalgebras-polynomial-endofunctors +open import trees.directed-trees +open import trees.fibers-directed-trees ```
diff --git a/src/trees/coalgebra-of-enriched-directed-trees.lagda.md b/src/trees/coalgebra-of-enriched-directed-trees.lagda.md index 688785211f..32cae5c137 100644 --- a/src/trees/coalgebra-of-enriched-directed-trees.lagda.md +++ b/src/trees/coalgebra-of-enriched-directed-trees.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - trees.coalgebra-of-enriched-directed-trees - (funext : function-extensionality) - where +module trees.coalgebra-of-enriched-directed-trees where ```
Imports @@ -17,10 +12,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.coalgebras-polynomial-endofunctors funext -open import trees.enriched-directed-trees funext -open import trees.fibers-enriched-directed-trees funext -open import trees.polynomial-endofunctors funext +open import trees.coalgebras-polynomial-endofunctors +open import trees.enriched-directed-trees +open import trees.fibers-enriched-directed-trees +open import trees.polynomial-endofunctors ```
diff --git a/src/trees/coalgebras-polynomial-endofunctors.lagda.md b/src/trees/coalgebras-polynomial-endofunctors.lagda.md index 66f271ca4c..85f9f915c3 100644 --- a/src/trees/coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/coalgebras-polynomial-endofunctors.lagda.md @@ -1,12 +1,7 @@ # Coalgebras of polynomial endofunctors ```agda -open import foundation.function-extensionality-axiom - -module - trees.coalgebras-polynomial-endofunctors - (funext : function-extensionality) - where +module trees.coalgebras-polynomial-endofunctors where ```
Imports @@ -15,7 +10,7 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import trees.polynomial-endofunctors funext +open import trees.polynomial-endofunctors ```
diff --git a/src/trees/combinator-directed-trees.lagda.md b/src/trees/combinator-directed-trees.lagda.md index f09ad142bc..4d2862298f 100644 --- a/src/trees/combinator-directed-trees.lagda.md +++ b/src/trees/combinator-directed-trees.lagda.md @@ -1,44 +1,39 @@ # The combinator of directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.combinator-directed-trees - (funext : function-extensionality) - where +module trees.combinator-directed-trees where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.isolated-elements funext -open import foundation.maybe funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.isolated-elements +open import foundation.maybe +open import foundation.negation +open import foundation.propositions open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.walks-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.walks-directed-graphs -open import trees.bases-directed-trees funext -open import trees.directed-trees funext -open import trees.equivalences-directed-trees funext -open import trees.fibers-directed-trees funext -open import trees.morphisms-directed-trees funext +open import trees.bases-directed-trees +open import trees.directed-trees +open import trees.equivalences-directed-trees +open import trees.fibers-directed-trees +open import trees.morphisms-directed-trees ```
diff --git a/src/trees/combinator-enriched-directed-trees.lagda.md b/src/trees/combinator-enriched-directed-trees.lagda.md index 5fdd7fc5ea..87f07372ae 100644 --- a/src/trees/combinator-enriched-directed-trees.lagda.md +++ b/src/trees/combinator-enriched-directed-trees.lagda.md @@ -1,34 +1,29 @@ # Combinators of enriched directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.combinator-enriched-directed-trees - (funext : function-extensionality) - where +module trees.combinator-enriched-directed-trees where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.maybe funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.maybe open import foundation.universe-levels -open import graph-theory.directed-graphs funext +open import graph-theory.directed-graphs -open import trees.combinator-directed-trees funext -open import trees.directed-trees funext -open import trees.enriched-directed-trees funext -open import trees.equivalences-directed-trees funext -open import trees.equivalences-enriched-directed-trees funext -open import trees.fibers-enriched-directed-trees funext -open import trees.morphisms-directed-trees funext +open import trees.combinator-directed-trees +open import trees.directed-trees +open import trees.enriched-directed-trees +open import trees.equivalences-directed-trees +open import trees.equivalences-enriched-directed-trees +open import trees.fibers-enriched-directed-trees +open import trees.morphisms-directed-trees ```
diff --git a/src/trees/directed-trees.lagda.md b/src/trees/directed-trees.lagda.md index 989a36041e..5c60f5b264 100644 --- a/src/trees/directed-trees.lagda.md +++ b/src/trees/directed-trees.lagda.md @@ -1,12 +1,7 @@ # Directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.directed-trees - (funext : function-extensionality) - where +module trees.directed-trees where ```
Imports @@ -15,31 +10,31 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.isolated-elements funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.isolated-elements +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.walks-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.walks-directed-graphs ```
diff --git a/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md index 531dae4498..283aa1f4a3 100644 --- a/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/elementhood-relation-coalgebras-polynomial-endofunctors.lagda.md @@ -1,25 +1,20 @@ # The elementhood relation on coalgebras of polynomial endofunctors ```agda -open import foundation.function-extensionality-axiom - -module - trees.elementhood-relation-coalgebras-polynomial-endofunctors - (funext : function-extensionality) - where +module trees.elementhood-relation-coalgebras-polynomial-endofunctors where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.fibers-of-maps funext +open import foundation.fibers-of-maps open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.walks-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.walks-directed-graphs -open import trees.coalgebras-polynomial-endofunctors funext +open import trees.coalgebras-polynomial-endofunctors ```
diff --git a/src/trees/elementhood-relation-w-types.lagda.md b/src/trees/elementhood-relation-w-types.lagda.md index f8ced8f4fb..df5c81a9b4 100644 --- a/src/trees/elementhood-relation-w-types.lagda.md +++ b/src/trees/elementhood-relation-w-types.lagda.md @@ -1,25 +1,20 @@ # The elementhood relation on W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.elementhood-relation-w-types - (funext : function-extensionality) - where +module trees.elementhood-relation-w-types where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.elementhood-relation-coalgebras-polynomial-endofunctors funext -open import trees.w-types funext +open import trees.elementhood-relation-coalgebras-polynomial-endofunctors +open import trees.w-types ```
diff --git a/src/trees/empty-multisets.lagda.md b/src/trees/empty-multisets.lagda.md index 58b29eed59..d31b3e8a6b 100644 --- a/src/trees/empty-multisets.lagda.md +++ b/src/trees/empty-multisets.lagda.md @@ -1,26 +1,21 @@ # Empty multisets ```agda -open import foundation.function-extensionality-axiom - -module - trees.empty-multisets - (funext : function-extensionality) - where +module trees.empty-multisets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import trees.elementhood-relation-w-types funext -open import trees.multisets funext -open import trees.w-types funext +open import trees.elementhood-relation-w-types +open import trees.multisets +open import trees.w-types ```
diff --git a/src/trees/enriched-directed-trees.lagda.md b/src/trees/enriched-directed-trees.lagda.md index 6cc8a8817c..f17320ca15 100644 --- a/src/trees/enriched-directed-trees.lagda.md +++ b/src/trees/enriched-directed-trees.lagda.md @@ -1,12 +1,7 @@ # Enriched directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.enriched-directed-trees - (funext : function-extensionality) - where +module trees.enriched-directed-trees where ```
Imports @@ -15,22 +10,22 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.isolated-elements funext -open import foundation.negation funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.isolated-elements +open import foundation.negation +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.directed-graphs funext +open import graph-theory.directed-graphs -open import trees.directed-trees funext +open import trees.directed-trees ```
diff --git a/src/trees/equivalences-directed-trees.lagda.md b/src/trees/equivalences-directed-trees.lagda.md index d54a63691a..5b7a6ffa00 100644 --- a/src/trees/equivalences-directed-trees.lagda.md +++ b/src/trees/equivalences-directed-trees.lagda.md @@ -1,12 +1,7 @@ # Equivalences of directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.equivalences-directed-trees - (funext : function-extensionality) - where +module trees.equivalences-directed-trees where ```
Imports @@ -14,26 +9,26 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.equivalences-directed-graphs funext -open import graph-theory.walks-directed-graphs funext +open import graph-theory.equivalences-directed-graphs +open import graph-theory.walks-directed-graphs -open import trees.directed-trees funext -open import trees.morphisms-directed-trees funext -open import trees.rooted-morphisms-directed-trees funext +open import trees.directed-trees +open import trees.morphisms-directed-trees +open import trees.rooted-morphisms-directed-trees ```
diff --git a/src/trees/equivalences-enriched-directed-trees.lagda.md b/src/trees/equivalences-enriched-directed-trees.lagda.md index 4f30a8d34a..410b7c1709 100644 --- a/src/trees/equivalences-enriched-directed-trees.lagda.md +++ b/src/trees/equivalences-enriched-directed-trees.lagda.md @@ -1,40 +1,34 @@ # Equivalences of enriched directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.equivalences-enriched-directed-trees - (funext : function-extensionality) - where +module trees.equivalences-enriched-directed-trees where ```
Imports ```agda -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.enriched-directed-trees funext -open import trees.equivalences-directed-trees funext -open import trees.morphisms-directed-trees funext -open import trees.morphisms-enriched-directed-trees funext -open import trees.rooted-morphisms-enriched-directed-trees funext +open import trees.enriched-directed-trees +open import trees.equivalences-directed-trees +open import trees.morphisms-directed-trees +open import trees.morphisms-enriched-directed-trees +open import trees.rooted-morphisms-enriched-directed-trees ```
diff --git a/src/trees/extensional-w-types.lagda.md b/src/trees/extensional-w-types.lagda.md index cb3d332cca..257d84375e 100644 --- a/src/trees/extensional-w-types.lagda.md +++ b/src/trees/extensional-w-types.lagda.md @@ -1,41 +1,36 @@ # Extensional W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.extensional-w-types - (funext : function-extensionality) - where +module trees.extensional-w-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.slice funext -open import foundation.torsorial-type-families funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.slice +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.univalent-type-families funext +open import foundation.univalent-type-families open import foundation.universe-levels -open import trees.elementhood-relation-w-types funext -open import trees.w-types funext +open import trees.elementhood-relation-w-types +open import trees.w-types ```
diff --git a/src/trees/fibers-directed-trees.lagda.md b/src/trees/fibers-directed-trees.lagda.md index 1646230d0a..b1cff222b1 100644 --- a/src/trees/fibers-directed-trees.lagda.md +++ b/src/trees/fibers-directed-trees.lagda.md @@ -1,30 +1,25 @@ # Fibers of directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.fibers-directed-trees - (funext : function-extensionality) - where +module trees.fibers-directed-trees where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.homotopies +open import foundation.identity-types open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.fibers-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.fibers-directed-graphs -open import trees.bases-directed-trees funext -open import trees.directed-trees funext -open import trees.morphisms-directed-trees funext +open import trees.bases-directed-trees +open import trees.directed-trees +open import trees.morphisms-directed-trees ```
diff --git a/src/trees/fibers-enriched-directed-trees.lagda.md b/src/trees/fibers-enriched-directed-trees.lagda.md index 11d459fafc..d6c2a7b325 100644 --- a/src/trees/fibers-enriched-directed-trees.lagda.md +++ b/src/trees/fibers-enriched-directed-trees.lagda.md @@ -1,31 +1,26 @@ # Fibers of enriched directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.fibers-enriched-directed-trees - (funext : function-extensionality) - where +module trees.fibers-enriched-directed-trees where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import graph-theory.walks-directed-graphs funext +open import graph-theory.walks-directed-graphs -open import trees.bases-enriched-directed-trees funext -open import trees.directed-trees funext -open import trees.enriched-directed-trees funext -open import trees.fibers-directed-trees funext +open import trees.bases-enriched-directed-trees +open import trees.directed-trees +open import trees.enriched-directed-trees +open import trees.fibers-directed-trees ```
diff --git a/src/trees/full-binary-trees.lagda.md b/src/trees/full-binary-trees.lagda.md index 70a7583c13..00ed1e42a8 100644 --- a/src/trees/full-binary-trees.lagda.md +++ b/src/trees/full-binary-trees.lagda.md @@ -1,12 +1,7 @@ # Full binary trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.full-binary-trees - (funext : function-extensionality) - where +module trees.full-binary-trees where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.empty-types funext +open import foundation.empty-types open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/trees/functoriality-combinator-directed-trees.lagda.md b/src/trees/functoriality-combinator-directed-trees.lagda.md index e1b2c4d747..62ecdf2b9c 100644 --- a/src/trees/functoriality-combinator-directed-trees.lagda.md +++ b/src/trees/functoriality-combinator-directed-trees.lagda.md @@ -1,12 +1,7 @@ # Functoriality of the combinator of directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.functoriality-combinator-directed-trees - (funext : function-extensionality) - where +module trees.functoriality-combinator-directed-trees where ```
Imports @@ -14,19 +9,19 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.combinator-directed-trees funext -open import trees.directed-trees funext -open import trees.equivalences-directed-trees funext -open import trees.morphisms-directed-trees funext -open import trees.rooted-morphisms-directed-trees funext +open import trees.combinator-directed-trees +open import trees.directed-trees +open import trees.equivalences-directed-trees +open import trees.morphisms-directed-trees +open import trees.rooted-morphisms-directed-trees ```
diff --git a/src/trees/functoriality-fiber-directed-tree.lagda.md b/src/trees/functoriality-fiber-directed-tree.lagda.md index 2613cbf555..2338441e60 100644 --- a/src/trees/functoriality-fiber-directed-tree.lagda.md +++ b/src/trees/functoriality-fiber-directed-tree.lagda.md @@ -1,12 +1,7 @@ # Functoriality of the fiber operation on directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.functoriality-fiber-directed-tree - (funext : function-extensionality) - where +module trees.functoriality-fiber-directed-tree where ```
Imports @@ -14,17 +9,17 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types open import foundation.universe-levels -open import graph-theory.walks-directed-graphs funext +open import graph-theory.walks-directed-graphs -open import trees.directed-trees funext -open import trees.equivalences-directed-trees funext -open import trees.fibers-directed-trees funext -open import trees.morphisms-directed-trees funext +open import trees.directed-trees +open import trees.equivalences-directed-trees +open import trees.fibers-directed-trees +open import trees.morphisms-directed-trees ```
diff --git a/src/trees/functoriality-w-types.lagda.md b/src/trees/functoriality-w-types.lagda.md index f8f0370cf0..b664531fd5 100644 --- a/src/trees/functoriality-w-types.lagda.md +++ b/src/trees/functoriality-w-types.lagda.md @@ -1,39 +1,34 @@ # Functoriality of W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.functoriality-w-types - (funext : function-extensionality) - where +module trees.functoriality-w-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-maps funext +open import foundation.cartesian-product-types +open import foundation.contractible-maps open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositional-maps funext +open import foundation.dependent-products-truncated-types +open import foundation.embeddings +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositional-maps open import foundation.transport-along-identifications -open import foundation.truncated-maps funext -open import foundation.truncated-types funext +open import foundation.truncated-maps +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels -open import trees.w-types funext +open import trees.w-types ```
diff --git a/src/trees/hereditary-w-types.lagda.md b/src/trees/hereditary-w-types.lagda.md index b27bf69b19..3e0ff510c9 100644 --- a/src/trees/hereditary-w-types.lagda.md +++ b/src/trees/hereditary-w-types.lagda.md @@ -1,12 +1,7 @@ # Hereditary W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.hereditary-w-types - (funext : function-extensionality) - where +module trees.hereditary-w-types where ```
Imports @@ -15,13 +10,12 @@ module open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.identity-types +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels open import trees.binary-w-types diff --git a/src/trees/induction-w-types.lagda.md b/src/trees/induction-w-types.lagda.md index 91f71f5c9b..1805b55311 100644 --- a/src/trees/induction-w-types.lagda.md +++ b/src/trees/induction-w-types.lagda.md @@ -1,12 +1,7 @@ # Induction principles on W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.induction-w-types - (funext : function-extensionality) - where +module trees.induction-w-types where ```
Imports @@ -16,17 +11,16 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.negation funext +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.identity-types +open import foundation.negation open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.elementhood-relation-w-types funext -open import trees.inequality-w-types funext -open import trees.w-types funext +open import trees.elementhood-relation-w-types +open import trees.inequality-w-types +open import trees.w-types ```
diff --git a/src/trees/inequality-w-types.lagda.md b/src/trees/inequality-w-types.lagda.md index 3c1342ee17..e8ba671c13 100644 --- a/src/trees/inequality-w-types.lagda.md +++ b/src/trees/inequality-w-types.lagda.md @@ -1,12 +1,7 @@ # Inequality on W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.inequality-w-types - (funext : function-extensionality) - where +module trees.inequality-w-types where ```
Imports @@ -15,13 +10,13 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.negation funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.negation open import foundation.universe-levels -open import trees.elementhood-relation-w-types funext -open import trees.w-types funext +open import trees.elementhood-relation-w-types +open import trees.w-types ```
diff --git a/src/trees/lower-types-w-types.lagda.md b/src/trees/lower-types-w-types.lagda.md index 8d1d225009..5e283be7bb 100644 --- a/src/trees/lower-types-w-types.lagda.md +++ b/src/trees/lower-types-w-types.lagda.md @@ -1,22 +1,17 @@ # Lower types of elements in W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.lower-types-w-types - (funext : function-extensionality) - where +module trees.lower-types-w-types where ```
Imports ```agda -open import foundation.existential-quantification funext +open import foundation.existential-quantification open import foundation.universe-levels -open import trees.ranks-of-elements-w-types funext -open import trees.w-types funext +open import trees.ranks-of-elements-w-types +open import trees.w-types ```
diff --git a/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md b/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md index c73e9fc746..12364a1b34 100644 --- a/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md +++ b/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md @@ -1,34 +1,29 @@ # Morphisms of algebras of polynomial endofunctors ```agda -open import foundation.function-extensionality-axiom - -module - trees.morphisms-algebras-polynomial-endofunctors - (funext : function-extensionality) - where +module trees.morphisms-algebras-polynomial-endofunctors where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.algebras-polynomial-endofunctors funext -open import trees.polynomial-endofunctors funext +open import trees.algebras-polynomial-endofunctors +open import trees.polynomial-endofunctors ```
diff --git a/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md index fbb67bf1e8..f6771ba67b 100644 --- a/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md @@ -1,34 +1,29 @@ # Morphisms of coalgebras of polynomial endofunctors ```agda -open import foundation.function-extensionality-axiom - -module - trees.morphisms-coalgebras-polynomial-endofunctors - (funext : function-extensionality) - where +module trees.morphisms-coalgebras-polynomial-endofunctors where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.coalgebras-polynomial-endofunctors funext -open import trees.polynomial-endofunctors funext +open import trees.coalgebras-polynomial-endofunctors +open import trees.polynomial-endofunctors ```
diff --git a/src/trees/morphisms-directed-trees.lagda.md b/src/trees/morphisms-directed-trees.lagda.md index 12c9df167c..925111eb85 100644 --- a/src/trees/morphisms-directed-trees.lagda.md +++ b/src/trees/morphisms-directed-trees.lagda.md @@ -1,36 +1,31 @@ # Morphisms of directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.morphisms-directed-trees - (funext : function-extensionality) - where +module trees.morphisms-directed-trees where ```
Imports ```agda open import foundation.binary-transport -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.torsorial-type-families funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.negation +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.universe-levels -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.walks-directed-graphs funext +open import graph-theory.morphisms-directed-graphs +open import graph-theory.walks-directed-graphs -open import trees.directed-trees funext +open import trees.directed-trees ```
diff --git a/src/trees/morphisms-enriched-directed-trees.lagda.md b/src/trees/morphisms-enriched-directed-trees.lagda.md index f3c8aea77f..968efd173c 100644 --- a/src/trees/morphisms-enriched-directed-trees.lagda.md +++ b/src/trees/morphisms-enriched-directed-trees.lagda.md @@ -1,30 +1,25 @@ # Morphisms of enriched directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.morphisms-enriched-directed-trees - (funext : function-extensionality) - where +module trees.morphisms-enriched-directed-trees where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.commuting-triangles-of-maps funext +open import foundation.commuting-squares-of-maps +open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.enriched-directed-trees funext -open import trees.morphisms-directed-trees funext +open import trees.enriched-directed-trees +open import trees.morphisms-directed-trees ```
diff --git a/src/trees/multiset-indexed-dependent-products-of-types.lagda.md b/src/trees/multiset-indexed-dependent-products-of-types.lagda.md index f06a12883f..ed16d82c4d 100644 --- a/src/trees/multiset-indexed-dependent-products-of-types.lagda.md +++ b/src/trees/multiset-indexed-dependent-products-of-types.lagda.md @@ -1,12 +1,7 @@ # Multiset-indexed dependent products of types ```agda -open import foundation.function-extensionality-axiom - -module - trees.multiset-indexed-dependent-products-of-types - (funext : function-extensionality) - where +module trees.multiset-indexed-dependent-products-of-types where ```
Imports @@ -16,8 +11,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import trees.multisets funext -open import trees.w-types funext +open import trees.multisets +open import trees.w-types ```
diff --git a/src/trees/multisets.lagda.md b/src/trees/multisets.lagda.md index 4aa26286ad..ed24b4339c 100644 --- a/src/trees/multisets.lagda.md +++ b/src/trees/multisets.lagda.md @@ -1,24 +1,19 @@ # Multisets ```agda -open import foundation.function-extensionality-axiom - -module - trees.multisets - (funext : function-extensionality) - where +module trees.multisets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.function-types funext +open import foundation.empty-types +open import foundation.function-types open import foundation.universe-levels -open import trees.elementhood-relation-w-types funext -open import trees.w-types funext +open import trees.elementhood-relation-w-types +open import trees.w-types ```
diff --git a/src/trees/planar-binary-trees.lagda.md b/src/trees/planar-binary-trees.lagda.md index 5495fe9e73..3e60500e59 100644 --- a/src/trees/planar-binary-trees.lagda.md +++ b/src/trees/planar-binary-trees.lagda.md @@ -1,23 +1,18 @@ # Planar binary trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.planar-binary-trees - (funext : function-extensionality) - where +module trees.planar-binary-trees where ```
Imports ```agda -open import foundation.booleans funext -open import foundation.empty-types funext -open import foundation.function-types funext +open import foundation.booleans +open import foundation.empty-types +open import foundation.function-types open import foundation.universe-levels -open import trees.w-types funext +open import trees.w-types ```
diff --git a/src/trees/plane-trees.lagda.md b/src/trees/plane-trees.lagda.md index 4b0f2c3477..12c443c8e3 100644 --- a/src/trees/plane-trees.lagda.md +++ b/src/trees/plane-trees.lagda.md @@ -1,12 +1,7 @@ # Plane trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.plane-trees - (funext : function-extensionality) - where +module trees.plane-trees where ```
Imports @@ -17,20 +12,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.maybe funext -open import foundation.retractions funext -open import foundation.sections funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.maybe +open import foundation.retractions +open import foundation.sections open import foundation.universe-levels open import lists.lists -open import trees.full-binary-trees funext -open import trees.w-types funext +open import trees.full-binary-trees +open import trees.w-types -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/trees/polynomial-endofunctors.lagda.md b/src/trees/polynomial-endofunctors.lagda.md index cca3de9d96..793fbf9b59 100644 --- a/src/trees/polynomial-endofunctors.lagda.md +++ b/src/trees/polynomial-endofunctors.lagda.md @@ -1,26 +1,21 @@ # Polynomial endofunctors ```agda -open import foundation.function-extensionality-axiom - -module - trees.polynomial-endofunctors - (funext : function-extensionality) - where +module trees.polynomial-endofunctors where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.transport-along-identifications open import foundation.universe-levels diff --git a/src/trees/raising-universe-levels-directed-trees.lagda.md b/src/trees/raising-universe-levels-directed-trees.lagda.md index 8e60821837..8f1e1ac294 100644 --- a/src/trees/raising-universe-levels-directed-trees.lagda.md +++ b/src/trees/raising-universe-levels-directed-trees.lagda.md @@ -1,29 +1,24 @@ # Raising universe levels of directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.raising-universe-levels-directed-trees - (funext : function-extensionality) - where +module trees.raising-universe-levels-directed-trees where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.raising-universe-levels funext +open import foundation.equivalences +open import foundation.raising-universe-levels open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.raising-universe-levels-directed-graphs funext -open import graph-theory.walks-directed-graphs funext +open import graph-theory.directed-graphs +open import graph-theory.raising-universe-levels-directed-graphs +open import graph-theory.walks-directed-graphs -open import trees.directed-trees funext -open import trees.equivalences-directed-trees funext +open import trees.directed-trees +open import trees.equivalences-directed-trees ```
diff --git a/src/trees/ranks-of-elements-w-types.lagda.md b/src/trees/ranks-of-elements-w-types.lagda.md index 4026e6eb34..26e9e63740 100644 --- a/src/trees/ranks-of-elements-w-types.lagda.md +++ b/src/trees/ranks-of-elements-w-types.lagda.md @@ -1,31 +1,26 @@ # Ranks of elements in W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.ranks-of-elements-w-types - (funext : function-extensionality) - where +module trees.ranks-of-elements-w-types where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.existential-quantification funext -open import foundation.identity-types funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.empty-types +open import foundation.existential-quantification +open import foundation.identity-types +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.elementhood-relation-w-types funext -open import trees.inequality-w-types funext -open import trees.w-types funext +open import trees.elementhood-relation-w-types +open import trees.inequality-w-types +open import trees.w-types ```
diff --git a/src/trees/rooted-morphisms-directed-trees.lagda.md b/src/trees/rooted-morphisms-directed-trees.lagda.md index 74f5ec2274..81c9d5fc01 100644 --- a/src/trees/rooted-morphisms-directed-trees.lagda.md +++ b/src/trees/rooted-morphisms-directed-trees.lagda.md @@ -1,12 +1,7 @@ # Rooted morphisms of directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.rooted-morphisms-directed-trees - (funext : function-extensionality) - where +module trees.rooted-morphisms-directed-trees where ```
Imports @@ -14,22 +9,22 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.bases-directed-trees funext -open import trees.directed-trees funext -open import trees.morphisms-directed-trees funext +open import trees.bases-directed-trees +open import trees.directed-trees +open import trees.morphisms-directed-trees ```
diff --git a/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md b/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md index 2cae2ec1d1..f876ff518a 100644 --- a/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md +++ b/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md @@ -1,28 +1,23 @@ # Rooted morphisms of enriched directed trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.rooted-morphisms-enriched-directed-trees - (funext : function-extensionality) - where +module trees.rooted-morphisms-enriched-directed-trees where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.enriched-directed-trees funext -open import trees.morphisms-enriched-directed-trees funext -open import trees.rooted-morphisms-directed-trees funext +open import trees.enriched-directed-trees +open import trees.morphisms-enriched-directed-trees +open import trees.rooted-morphisms-directed-trees ```
diff --git a/src/trees/rooted-quasitrees.lagda.md b/src/trees/rooted-quasitrees.lagda.md index a89cb5c584..596e9e1061 100644 --- a/src/trees/rooted-quasitrees.lagda.md +++ b/src/trees/rooted-quasitrees.lagda.md @@ -1,23 +1,18 @@ # Rooted quasitrees ```agda -open import foundation.function-extensionality-axiom - -module - trees.rooted-quasitrees - (funext : function-extensionality) - where +module trees.rooted-quasitrees where ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.trails-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.trails-undirected-graphs +open import graph-theory.undirected-graphs ```
diff --git a/src/trees/rooted-undirected-trees.lagda.md b/src/trees/rooted-undirected-trees.lagda.md index bbe771ca31..52cf306b9b 100644 --- a/src/trees/rooted-undirected-trees.lagda.md +++ b/src/trees/rooted-undirected-trees.lagda.md @@ -1,12 +1,7 @@ # Rooted undirected trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.rooted-undirected-trees - (funext : function-extensionality) - where +module trees.rooted-undirected-trees where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types open import foundation.unit-type open import foundation.universe-levels -open import foundation.unordered-pairs funext +open import foundation.unordered-pairs -open import graph-theory.trails-undirected-graphs funext -open import graph-theory.undirected-graphs funext +open import graph-theory.trails-undirected-graphs +open import graph-theory.undirected-graphs -open import trees.undirected-trees funext +open import trees.undirected-trees ```
diff --git a/src/trees/small-multisets.lagda.md b/src/trees/small-multisets.lagda.md index a7af9b7537..6a8bc2b79f 100644 --- a/src/trees/small-multisets.lagda.md +++ b/src/trees/small-multisets.lagda.md @@ -1,12 +1,7 @@ # Small multisets ```agda -open import foundation.function-extensionality-axiom - -module - trees.small-multisets - (funext : function-extensionality) - where +module trees.small-multisets where ```
Imports @@ -14,22 +9,22 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.small-types funext -open import foundation.subtypes funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.small-types +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import trees.multisets funext -open import trees.w-types funext +open import trees.multisets +open import trees.w-types ```
diff --git a/src/trees/submultisets.lagda.md b/src/trees/submultisets.lagda.md index c23122b0f7..f04365fa46 100644 --- a/src/trees/submultisets.lagda.md +++ b/src/trees/submultisets.lagda.md @@ -1,22 +1,17 @@ # Submultisets ```agda -open import foundation.function-extensionality-axiom - -module - trees.submultisets - (funext : function-extensionality) - where +module trees.submultisets where ```
Imports ```agda -open import foundation.embeddings funext -open import foundation.equivalences funext +open import foundation.embeddings +open import foundation.equivalences open import foundation.universe-levels -open import trees.multisets funext +open import trees.multisets ```
diff --git a/src/trees/transitive-multisets.lagda.md b/src/trees/transitive-multisets.lagda.md index 6b1fda3d71..e09627c816 100644 --- a/src/trees/transitive-multisets.lagda.md +++ b/src/trees/transitive-multisets.lagda.md @@ -1,12 +1,7 @@ # Transitive multisets ```agda -open import foundation.function-extensionality-axiom - -module - trees.transitive-multisets - (funext : function-extensionality) - where +module trees.transitive-multisets where ```
Imports @@ -14,8 +9,8 @@ module ```agda open import foundation.universe-levels -open import trees.multisets funext -open import trees.submultisets funext +open import trees.multisets +open import trees.submultisets ```
diff --git a/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md index 1aec74f927..9184f6da42 100644 --- a/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md @@ -1,12 +1,7 @@ # The underlying trees of elements of coalgebras of polynomial endofunctors ```agda -open import foundation.function-extensionality-axiom - -module - trees.underlying-trees-elements-coalgebras-polynomial-endofunctors - (funext : function-extensionality) - where +module trees.underlying-trees-elements-coalgebras-polynomial-endofunctors where ```
Imports @@ -14,37 +9,37 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.binary-transport -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.empty-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.isolated-elements funext -open import foundation.negated-equality funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.isolated-elements +open import foundation.negated-equality +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.walks-directed-graphs funext - -open import trees.coalgebras-polynomial-endofunctors funext -open import trees.combinator-directed-trees funext -open import trees.combinator-enriched-directed-trees funext -open import trees.directed-trees funext -open import trees.elementhood-relation-coalgebras-polynomial-endofunctors funext -open import trees.enriched-directed-trees funext -open import trees.equivalences-directed-trees funext -open import trees.equivalences-enriched-directed-trees funext +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.walks-directed-graphs + +open import trees.coalgebras-polynomial-endofunctors +open import trees.combinator-directed-trees +open import trees.combinator-enriched-directed-trees +open import trees.directed-trees +open import trees.elementhood-relation-coalgebras-polynomial-endofunctors +open import trees.enriched-directed-trees +open import trees.equivalences-directed-trees +open import trees.equivalences-enriched-directed-trees ```
diff --git a/src/trees/underlying-trees-of-elements-of-w-types.lagda.md b/src/trees/underlying-trees-of-elements-of-w-types.lagda.md index d05a62ec35..bd9f754279 100644 --- a/src/trees/underlying-trees-of-elements-of-w-types.lagda.md +++ b/src/trees/underlying-trees-of-elements-of-w-types.lagda.md @@ -1,46 +1,41 @@ # The underlying trees of elements of W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.underlying-trees-of-elements-of-w-types - (funext : function-extensionality) - where +module trees.underlying-trees-of-elements-of-w-types where ```
Imports ```agda -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.isolated-elements funext -open import foundation.negated-equality funext -open import foundation.propositions funext -open import foundation.torsorial-type-families funext +open import foundation.empty-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.isolated-elements +open import foundation.negated-equality +open import foundation.propositions +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.directed-graphs funext -open import graph-theory.morphisms-directed-graphs funext -open import graph-theory.walks-directed-graphs funext - -open import trees.combinator-directed-trees funext -open import trees.combinator-enriched-directed-trees funext -open import trees.directed-trees funext -open import trees.elementhood-relation-w-types funext -open import trees.enriched-directed-trees funext -open import trees.equivalences-directed-trees funext -open import trees.equivalences-enriched-directed-trees funext -open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors funext -open import trees.w-types funext +open import graph-theory.directed-graphs +open import graph-theory.morphisms-directed-graphs +open import graph-theory.walks-directed-graphs + +open import trees.combinator-directed-trees +open import trees.combinator-enriched-directed-trees +open import trees.directed-trees +open import trees.elementhood-relation-w-types +open import trees.enriched-directed-trees +open import trees.equivalences-directed-trees +open import trees.equivalences-enriched-directed-trees +open import trees.underlying-trees-elements-coalgebras-polynomial-endofunctors +open import trees.w-types ```
diff --git a/src/trees/undirected-trees.lagda.md b/src/trees/undirected-trees.lagda.md index 2ac64dbb5b..f60cce11cf 100644 --- a/src/trees/undirected-trees.lagda.md +++ b/src/trees/undirected-trees.lagda.md @@ -1,12 +1,7 @@ # Undirected trees ```agda -open import foundation.function-extensionality-axiom - -module - trees.undirected-trees - (funext : function-extensionality) - where +module trees.undirected-trees where ```
Imports @@ -15,23 +10,23 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.contractible-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.transport-along-identifications open import foundation.universe-levels -open import graph-theory.paths-undirected-graphs funext -open import graph-theory.trails-undirected-graphs funext -open import graph-theory.undirected-graphs funext -open import graph-theory.walks-undirected-graphs funext +open import graph-theory.paths-undirected-graphs +open import graph-theory.trails-undirected-graphs +open import graph-theory.undirected-graphs +open import graph-theory.walks-undirected-graphs ```
diff --git a/src/trees/universal-multiset.lagda.md b/src/trees/universal-multiset.lagda.md index ec8b278cd7..954321d15a 100644 --- a/src/trees/universal-multiset.lagda.md +++ b/src/trees/universal-multiset.lagda.md @@ -1,30 +1,25 @@ # The universal multiset ```agda -open import foundation.function-extensionality-axiom - -module - trees.universal-multiset - (funext : function-extensionality) - where +module trees.universal-multiset where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.raising-universe-levels funext -open import foundation.small-types funext -open import foundation.small-universes funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.raising-universe-levels +open import foundation.small-types +open import foundation.small-universes open import foundation.transport-along-identifications open import foundation.universe-levels -open import trees.functoriality-w-types funext -open import trees.multisets funext -open import trees.small-multisets funext -open import trees.w-types funext +open import trees.functoriality-w-types +open import trees.multisets +open import trees.small-multisets +open import trees.w-types ```
diff --git a/src/trees/w-type-of-natural-numbers.lagda.md b/src/trees/w-type-of-natural-numbers.lagda.md index f394e72e1e..0d61f98e88 100644 --- a/src/trees/w-type-of-natural-numbers.lagda.md +++ b/src/trees/w-type-of-natural-numbers.lagda.md @@ -1,12 +1,7 @@ # The W-type of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - trees.w-type-of-natural-numbers - (funext : function-extensionality) - where +module trees.w-type-of-natural-numbers where ```
Imports @@ -15,20 +10,19 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.booleans funext -open import foundation.contractible-types funext +open import foundation.booleans +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.unit-type -open import foundation.universal-property-empty-type funext +open import foundation.universal-property-empty-type open import foundation.universe-levels -open import trees.w-types funext +open import trees.w-types ```
diff --git a/src/trees/w-type-of-propositions.lagda.md b/src/trees/w-type-of-propositions.lagda.md index 81bf34c4c9..8b460d8d29 100644 --- a/src/trees/w-type-of-propositions.lagda.md +++ b/src/trees/w-type-of-propositions.lagda.md @@ -1,29 +1,24 @@ # The W-type of the type of propositions ```agda -open import foundation.function-extensionality-axiom - -module - trees.w-type-of-propositions - (funext : function-extensionality) - where +module trees.w-type-of-propositions where ```
Imports ```agda -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.propositional-extensionality funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.propositional-extensionality +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import trees.extensional-w-types funext -open import trees.w-types funext +open import trees.extensional-w-types +open import trees.w-types ```
diff --git a/src/trees/w-types.lagda.md b/src/trees/w-types.lagda.md index 58ae562716..9e3ae175b9 100644 --- a/src/trees/w-types.lagda.md +++ b/src/trees/w-types.lagda.md @@ -1,45 +1,39 @@ # W-types ```agda -open import foundation.function-extensionality-axiom - -module - trees.w-types - (funext : function-extensionality) - where +module trees.w-types where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.dependent-products-truncated-types funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext +open import foundation.dependent-products-truncated-types +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.homotopy-induction funext -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext -open import foundation.propositional-truncations funext -open import foundation.sets funext -open import foundation.torsorial-type-families funext +open import foundation.homotopies +open import foundation.homotopy-induction +open import foundation.identity-types +open import foundation.postcomposition-functions +open import foundation.propositional-truncations +open import foundation.sets +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.truncated-types funext +open import foundation.truncated-types open import foundation.truncation-levels -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import trees.algebras-polynomial-endofunctors funext -open import trees.coalgebras-polynomial-endofunctors funext -open import trees.morphisms-algebras-polynomial-endofunctors funext -open import trees.polynomial-endofunctors funext +open import trees.algebras-polynomial-endofunctors +open import trees.coalgebras-polynomial-endofunctors +open import trees.morphisms-algebras-polynomial-endofunctors +open import trees.polynomial-endofunctors ```
diff --git a/src/type-theories.lagda.md b/src/type-theories.lagda.md index ab4878964a..1255733d03 100644 --- a/src/type-theories.lagda.md +++ b/src/type-theories.lagda.md @@ -7,21 +7,16 @@ ## Modules in the type theories namespace ```agda -open import foundation.function-extensionality-axiom - -module - type-theories - (funext : function-extensionality) - where +module type-theories where open import type-theories.comprehension-type-theories public -open import type-theories.dependent-type-theories funext public -open import type-theories.fibered-dependent-type-theories funext public -open import type-theories.pi-types-precategories-with-attributes funext public -open import type-theories.pi-types-precategories-with-families funext public -open import type-theories.precategories-with-attributes funext public -open import type-theories.precategories-with-families funext public -open import type-theories.sections-dependent-type-theories funext public -open import type-theories.simple-type-theories funext public -open import type-theories.unityped-type-theories funext public +open import type-theories.dependent-type-theories public +open import type-theories.fibered-dependent-type-theories public +open import type-theories.pi-types-precategories-with-attributes public +open import type-theories.pi-types-precategories-with-families public +open import type-theories.precategories-with-attributes public +open import type-theories.precategories-with-families public +open import type-theories.sections-dependent-type-theories public +open import type-theories.simple-type-theories public +open import type-theories.unityped-type-theories public ``` diff --git a/src/type-theories/dependent-type-theories.lagda.md b/src/type-theories/dependent-type-theories.lagda.md index f7fd49336d..6f40eba0bc 100644 --- a/src/type-theories/dependent-type-theories.lagda.md +++ b/src/type-theories/dependent-type-theories.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - type-theories.dependent-type-theories - (funext : function-extensionality) - where +module type-theories.dependent-type-theories where ```
Imports @@ -17,14 +12,14 @@ module open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.universe-levels -open import foundation.whiskering-identifications-concatenation funext +open import foundation.whiskering-identifications-concatenation ```
diff --git a/src/type-theories/fibered-dependent-type-theories.lagda.md b/src/type-theories/fibered-dependent-type-theories.lagda.md index 7d0e7242ff..a5da36d53a 100644 --- a/src/type-theories/fibered-dependent-type-theories.lagda.md +++ b/src/type-theories/fibered-dependent-type-theories.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - type-theories.fibered-dependent-type-theories - (funext : function-extensionality) - where +module type-theories.fibered-dependent-type-theories where ```
Imports @@ -16,12 +11,12 @@ module ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.dependent-type-theories funext +open import type-theories.dependent-type-theories ```
diff --git a/src/type-theories/pi-types-precategories-with-attributes.lagda.md b/src/type-theories/pi-types-precategories-with-attributes.lagda.md index 4f8e70e49c..bb36bc9fc8 100644 --- a/src/type-theories/pi-types-precategories-with-attributes.lagda.md +++ b/src/type-theories/pi-types-precategories-with-attributes.lagda.md @@ -1,23 +1,18 @@ # `Π`-types in precategories with attributes ```agda -open import foundation.function-extensionality-axiom - -module - type-theories.pi-types-precategories-with-attributes - (funext : function-extensionality) - where +module type-theories.pi-types-precategories-with-attributes where ```
Imports ```agda -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.precategories-with-attributes funext +open import type-theories.precategories-with-attributes ```
diff --git a/src/type-theories/pi-types-precategories-with-families.lagda.md b/src/type-theories/pi-types-precategories-with-families.lagda.md index 30b3122287..95f6a2b8e2 100644 --- a/src/type-theories/pi-types-precategories-with-families.lagda.md +++ b/src/type-theories/pi-types-precategories-with-families.lagda.md @@ -1,23 +1,18 @@ # Π-types in precategories with families ```agda -open import foundation.function-extensionality-axiom - -module - type-theories.pi-types-precategories-with-families - (funext : function-extensionality) - where +module type-theories.pi-types-precategories-with-families where ```
Imports ```agda -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.precategories-with-families funext +open import type-theories.precategories-with-families ```
diff --git a/src/type-theories/precategories-with-attributes.lagda.md b/src/type-theories/precategories-with-attributes.lagda.md index c25248a51f..c092065934 100644 --- a/src/type-theories/precategories-with-attributes.lagda.md +++ b/src/type-theories/precategories-with-attributes.lagda.md @@ -1,31 +1,26 @@ # Precategories with attributes ```agda -open import foundation.function-extensionality-axiom - -module - type-theories.precategories-with-attributes - (funext : function-extensionality) - where +module type-theories.precategories-with-attributes where ```
Imports ```agda -open import category-theory.commuting-squares-of-morphisms-in-precategories funext -open import category-theory.functors-precategories funext -open import category-theory.natural-transformations-functors-precategories funext -open import category-theory.precategories funext -open import category-theory.precategory-of-elements-of-a-presheaf funext -open import category-theory.presheaf-categories funext -open import category-theory.pullbacks-in-precategories funext +open import category-theory.commuting-squares-of-morphisms-in-precategories +open import category-theory.functors-precategories +open import category-theory.natural-transformations-functors-precategories +open import category-theory.precategories +open import category-theory.precategory-of-elements-of-a-presheaf +open import category-theory.presheaf-categories +open import category-theory.pullbacks-in-precategories open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.sets +open import foundation.subtypes open import foundation.universe-levels ``` diff --git a/src/type-theories/precategories-with-families.lagda.md b/src/type-theories/precategories-with-families.lagda.md index a61e18f4bc..5a8bc8f46e 100644 --- a/src/type-theories/precategories-with-families.lagda.md +++ b/src/type-theories/precategories-with-families.lagda.md @@ -1,25 +1,20 @@ # Precategories with families ```agda -open import foundation.function-extensionality-axiom - -module - type-theories.precategories-with-families - (funext : function-extensionality) - where +module type-theories.precategories-with-families where ```
Imports ```agda -open import category-theory.functors-precategories funext -open import category-theory.precategories funext -open import category-theory.precategory-of-elements-of-a-presheaf funext -open import category-theory.presheaf-categories funext +open import category-theory.functors-precategories +open import category-theory.precategories +open import category-theory.precategory-of-elements-of-a-presheaf +open import category-theory.presheaf-categories open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels ``` diff --git a/src/type-theories/sections-dependent-type-theories.lagda.md b/src/type-theories/sections-dependent-type-theories.lagda.md index 5fa8018c95..339dc4c6e7 100644 --- a/src/type-theories/sections-dependent-type-theories.lagda.md +++ b/src/type-theories/sections-dependent-type-theories.lagda.md @@ -3,23 +3,18 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - type-theories.sections-dependent-type-theories - (funext : function-extensionality) - where +module type-theories.sections-dependent-type-theories where ```
Imports ```agda -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels -open import type-theories.dependent-type-theories funext -open import type-theories.fibered-dependent-type-theories funext +open import type-theories.dependent-type-theories +open import type-theories.fibered-dependent-type-theories ```
diff --git a/src/type-theories/simple-type-theories.lagda.md b/src/type-theories/simple-type-theories.lagda.md index e975f9cf07..b8e45f3112 100644 --- a/src/type-theories/simple-type-theories.lagda.md +++ b/src/type-theories/simple-type-theories.lagda.md @@ -3,21 +3,16 @@ ```agda {-# OPTIONS --guardedness --allow-unsolved-metas #-} -open import foundation.function-extensionality-axiom - -module - type-theories.simple-type-theories - (funext : function-extensionality) - where +module type-theories.simple-type-theories where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.transport-along-identifications open import foundation.universe-levels ``` @@ -544,8 +539,8 @@ We specialize the above definitions to nonhomogenous homotopies. module dependent-simple where - open import type-theories.dependent-type-theories funext - open import type-theories.fibered-dependent-type-theories funext + open import type-theories.dependent-type-theories + open import type-theories.fibered-dependent-type-theories system : {l1 l2 : Level} {T : UU l1} → simple.system l2 T → dependent.system l1 l2 diff --git a/src/type-theories/unityped-type-theories.lagda.md b/src/type-theories/unityped-type-theories.lagda.md index 19b64300a5..99c7fb918f 100644 --- a/src/type-theories/unityped-type-theories.lagda.md +++ b/src/type-theories/unityped-type-theories.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness --allow-unsolved-metas #-} -open import foundation.function-extensionality-axiom - -module - type-theories.unityped-type-theories - (funext : function-extensionality) - where +module type-theories.unityped-type-theories where ```
Imports @@ -17,10 +12,10 @@ module open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sets funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics.lagda.md b/src/univalent-combinatorics.lagda.md index 8a2804e99e..96025ac714 100644 --- a/src/univalent-combinatorics.lagda.md +++ b/src/univalent-combinatorics.lagda.md @@ -23,106 +23,101 @@ and closedness under Π under a mild condition {{#cite Anel24}}. ## Modules in the univalent combinatorics namespace ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics where -module - univalent-combinatorics - (funext : function-extensionality) - where - -open import univalent-combinatorics.2-element-decidable-subtypes funext public -open import univalent-combinatorics.2-element-subtypes funext public -open import univalent-combinatorics.2-element-types funext public -open import univalent-combinatorics.binomial-types funext public -open import univalent-combinatorics.bracelets funext public -open import univalent-combinatorics.cartesian-product-types funext public -open import univalent-combinatorics.classical-finite-types funext public -open import univalent-combinatorics.complements-isolated-elements funext public -open import univalent-combinatorics.coproduct-types funext public -open import univalent-combinatorics.counting funext public -open import univalent-combinatorics.counting-decidable-subtypes funext public -open import univalent-combinatorics.counting-dependent-pair-types funext public +open import univalent-combinatorics.2-element-decidable-subtypes public +open import univalent-combinatorics.2-element-subtypes public +open import univalent-combinatorics.2-element-types public +open import univalent-combinatorics.binomial-types public +open import univalent-combinatorics.bracelets public +open import univalent-combinatorics.cartesian-product-types public +open import univalent-combinatorics.classical-finite-types public +open import univalent-combinatorics.complements-isolated-elements public +open import univalent-combinatorics.coproduct-types public +open import univalent-combinatorics.counting public +open import univalent-combinatorics.counting-decidable-subtypes public +open import univalent-combinatorics.counting-dependent-pair-types public open import univalent-combinatorics.counting-fibers-of-maps public -open import univalent-combinatorics.counting-maybe funext public -open import univalent-combinatorics.cubes funext public -open import univalent-combinatorics.cycle-partitions funext public -open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers funext public -open import univalent-combinatorics.cyclic-finite-types funext public -open import univalent-combinatorics.de-morgans-law funext public -open import univalent-combinatorics.decidable-dependent-function-types funext public -open import univalent-combinatorics.decidable-dependent-pair-types funext public -open import univalent-combinatorics.decidable-equivalence-relations funext public -open import univalent-combinatorics.decidable-propositions funext public -open import univalent-combinatorics.decidable-subtypes funext public -open import univalent-combinatorics.dedekind-finite-sets funext public -open import univalent-combinatorics.dependent-function-types funext public -open import univalent-combinatorics.dependent-pair-types funext public -open import univalent-combinatorics.discrete-sigma-decompositions funext public -open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products funext public -open import univalent-combinatorics.double-counting funext public -open import univalent-combinatorics.embeddings funext public -open import univalent-combinatorics.embeddings-standard-finite-types funext public -open import univalent-combinatorics.equality-finite-types funext public -open import univalent-combinatorics.equality-standard-finite-types funext public -open import univalent-combinatorics.equivalences funext public -open import univalent-combinatorics.equivalences-cubes funext public -open import univalent-combinatorics.equivalences-standard-finite-types funext public -open import univalent-combinatorics.ferrers-diagrams funext public -open import univalent-combinatorics.fibers-of-maps funext public -open import univalent-combinatorics.finite-choice funext public +open import univalent-combinatorics.counting-maybe public +open import univalent-combinatorics.cubes public +open import univalent-combinatorics.cycle-partitions public +open import univalent-combinatorics.cycle-prime-decomposition-natural-numbers public +open import univalent-combinatorics.cyclic-finite-types public +open import univalent-combinatorics.de-morgans-law public +open import univalent-combinatorics.decidable-dependent-function-types public +open import univalent-combinatorics.decidable-dependent-pair-types public +open import univalent-combinatorics.decidable-equivalence-relations public +open import univalent-combinatorics.decidable-propositions public +open import univalent-combinatorics.decidable-subtypes public +open import univalent-combinatorics.dedekind-finite-sets public +open import univalent-combinatorics.dependent-function-types public +open import univalent-combinatorics.dependent-pair-types public +open import univalent-combinatorics.discrete-sigma-decompositions public +open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products public +open import univalent-combinatorics.double-counting public +open import univalent-combinatorics.embeddings public +open import univalent-combinatorics.embeddings-standard-finite-types public +open import univalent-combinatorics.equality-finite-types public +open import univalent-combinatorics.equality-standard-finite-types public +open import univalent-combinatorics.equivalences public +open import univalent-combinatorics.equivalences-cubes public +open import univalent-combinatorics.equivalences-standard-finite-types public +open import univalent-combinatorics.ferrers-diagrams public +open import univalent-combinatorics.fibers-of-maps public +open import univalent-combinatorics.finite-choice public open import univalent-combinatorics.finite-presentations public -open import univalent-combinatorics.finite-types funext public -open import univalent-combinatorics.finitely-many-connected-components funext public -open import univalent-combinatorics.finitely-presented-types funext public -open import univalent-combinatorics.function-types funext public -open import univalent-combinatorics.image-of-maps funext public -open import univalent-combinatorics.inequality-types-with-counting funext public -open import univalent-combinatorics.inhabited-finite-types funext public -open import univalent-combinatorics.injective-maps funext public -open import univalent-combinatorics.involution-standard-finite-types funext public -open import univalent-combinatorics.isotopies-latin-squares funext public -open import univalent-combinatorics.kuratowski-finite-sets funext public -open import univalent-combinatorics.latin-squares funext public -open import univalent-combinatorics.locally-finite-types funext public -open import univalent-combinatorics.main-classes-of-latin-hypercubes funext public -open import univalent-combinatorics.main-classes-of-latin-squares funext public -open import univalent-combinatorics.maybe funext public -open import univalent-combinatorics.necklaces funext public -open import univalent-combinatorics.orientations-complete-undirected-graph funext public -open import univalent-combinatorics.orientations-cubes funext public -open import univalent-combinatorics.partitions funext public -open import univalent-combinatorics.petri-nets funext public -open import univalent-combinatorics.pi-finite-types funext public -open import univalent-combinatorics.pigeonhole-principle funext public +open import univalent-combinatorics.finite-types public +open import univalent-combinatorics.finitely-many-connected-components public +open import univalent-combinatorics.finitely-presented-types public +open import univalent-combinatorics.function-types public +open import univalent-combinatorics.image-of-maps public +open import univalent-combinatorics.inequality-types-with-counting public +open import univalent-combinatorics.inhabited-finite-types public +open import univalent-combinatorics.injective-maps public +open import univalent-combinatorics.involution-standard-finite-types public +open import univalent-combinatorics.isotopies-latin-squares public +open import univalent-combinatorics.kuratowski-finite-sets public +open import univalent-combinatorics.latin-squares public +open import univalent-combinatorics.locally-finite-types public +open import univalent-combinatorics.main-classes-of-latin-hypercubes public +open import univalent-combinatorics.main-classes-of-latin-squares public +open import univalent-combinatorics.maybe public +open import univalent-combinatorics.necklaces public +open import univalent-combinatorics.orientations-complete-undirected-graph public +open import univalent-combinatorics.orientations-cubes public +open import univalent-combinatorics.partitions public +open import univalent-combinatorics.petri-nets public +open import univalent-combinatorics.pi-finite-types public +open import univalent-combinatorics.pigeonhole-principle public open import univalent-combinatorics.presented-pi-finite-types public -open import univalent-combinatorics.quotients-finite-types funext public -open import univalent-combinatorics.ramsey-theory funext public -open import univalent-combinatorics.repetitions-of-values funext public +open import univalent-combinatorics.quotients-finite-types public +open import univalent-combinatorics.ramsey-theory public +open import univalent-combinatorics.repetitions-of-values public open import univalent-combinatorics.repetitions-of-values-sequences public -open import univalent-combinatorics.retracts-of-finite-types funext public -open import univalent-combinatorics.riffle-shuffles funext public -open import univalent-combinatorics.sequences-finite-types funext public -open import univalent-combinatorics.set-quotients-of-index-two funext public -open import univalent-combinatorics.sigma-decompositions funext public -open import univalent-combinatorics.skipping-element-standard-finite-types funext public -open import univalent-combinatorics.small-types funext public -open import univalent-combinatorics.standard-finite-pruned-trees funext public -open import univalent-combinatorics.standard-finite-trees funext public -open import univalent-combinatorics.standard-finite-types funext public -open import univalent-combinatorics.steiner-systems funext public -open import univalent-combinatorics.steiner-triple-systems funext public -open import univalent-combinatorics.sums-of-natural-numbers funext public -open import univalent-combinatorics.surjective-maps funext public -open import univalent-combinatorics.symmetric-difference funext public -open import univalent-combinatorics.trivial-sigma-decompositions funext public -open import univalent-combinatorics.type-duality funext public -open import univalent-combinatorics.unbounded-pi-finite-types funext public -open import univalent-combinatorics.unions-subtypes funext public -open import univalent-combinatorics.universal-property-standard-finite-types funext public +open import univalent-combinatorics.retracts-of-finite-types public +open import univalent-combinatorics.riffle-shuffles public +open import univalent-combinatorics.sequences-finite-types public +open import univalent-combinatorics.set-quotients-of-index-two public +open import univalent-combinatorics.sigma-decompositions public +open import univalent-combinatorics.skipping-element-standard-finite-types public +open import univalent-combinatorics.small-types public +open import univalent-combinatorics.standard-finite-pruned-trees public +open import univalent-combinatorics.standard-finite-trees public +open import univalent-combinatorics.standard-finite-types public +open import univalent-combinatorics.steiner-systems public +open import univalent-combinatorics.steiner-triple-systems public +open import univalent-combinatorics.sums-of-natural-numbers public +open import univalent-combinatorics.surjective-maps public +open import univalent-combinatorics.symmetric-difference public +open import univalent-combinatorics.trivial-sigma-decompositions public +open import univalent-combinatorics.type-duality public +open import univalent-combinatorics.unbounded-pi-finite-types public +open import univalent-combinatorics.unions-subtypes public +open import univalent-combinatorics.universal-property-standard-finite-types public open import univalent-combinatorics.unlabeled-partitions public open import univalent-combinatorics.unlabeled-rooted-trees public open import univalent-combinatorics.unlabeled-trees public -open import univalent-combinatorics.untruncated-pi-finite-types funext public +open import univalent-combinatorics.untruncated-pi-finite-types public ``` ## References diff --git a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md index 3d43f3d67e..eec01ce47a 100644 --- a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md @@ -1,56 +1,50 @@ # `2`-element decidable subtypes ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.2-element-decidable-subtypes - (funext : function-extensionality) - where +module univalent-combinatorics.2-element-decidable-subtypes where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types funext +open import elementary-number-theory.well-ordering-principle-standard-finite-types -open import foundation.automorphisms funext -open import foundation.booleans funext -open import foundation.decidable-equality funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.automorphisms +open import foundation.booleans +open import foundation.decidable-equality +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.logical-equivalences funext -open import foundation.mere-equivalences funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext +open import foundation.embeddings +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-propositional-truncation +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.logical-equivalences +open import foundation.mere-equivalences +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types funext -open import foundation.univalence funext +open import foundation.type-arithmetic-coproduct-types +open import foundation.univalence open import foundation.universe-levels -open import univalent-combinatorics.2-element-subtypes funext -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.decidable-subtypes funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-subtypes +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.decidable-subtypes +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/2-element-subtypes.lagda.md b/src/univalent-combinatorics/2-element-subtypes.lagda.md index 1b72867410..9c1bd2707d 100644 --- a/src/univalent-combinatorics/2-element-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-subtypes.lagda.md @@ -1,42 +1,37 @@ # `2`-element subtypes ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.2-element-subtypes - (funext : function-extensionality) - where +module univalent-combinatorics.2-element-subtypes where ```
Imports ```agda -open import foundation.automorphisms funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.automorphisms +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.logical-equivalences funext -open import foundation.mere-equivalences funext -open import foundation.negated-equality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.logical-equivalences +open import foundation.mere-equivalences +open import foundation.negated-equality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/2-element-types.lagda.md b/src/univalent-combinatorics/2-element-types.lagda.md index caf8837393..b44650d1ca 100644 --- a/src/univalent-combinatorics/2-element-types.lagda.md +++ b/src/univalent-combinatorics/2-element-types.lagda.md @@ -1,63 +1,58 @@ # `2`-element types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.2-element-types - (funext : function-extensionality) - where +module univalent-combinatorics.2-element-types where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import foundation.action-on-identifications-functions -open import foundation.automorphisms funext -open import foundation.connected-components-universes funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.automorphisms +open import foundation.connected-components-universes +open import foundation.contractible-maps +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.double-negation funext -open import foundation.empty-types funext -open import foundation.equivalence-extensionality funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.double-negation +open import foundation.empty-types +open import foundation.equivalence-extensionality +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext +open import foundation.homotopies open import foundation.identity-systems -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.involutions funext -open import foundation.mere-equivalences funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.sets funext -open import foundation.subuniverses funext -open import foundation.torsorial-type-families funext +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.involutions +open import foundation.mere-equivalences +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.sets +open import foundation.subuniverses +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-identity-systems funext +open import foundation.universal-property-identity-systems open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.equivalences funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.equivalences +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index 2816b63702..7effe481d3 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -1,62 +1,57 @@ # The binomial types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.binomial-types - (funext : function-extensionality) - where +module univalent-combinatorics.binomial-types where ```
Imports ```agda -open import elementary-number-theory.binomial-coefficients funext +open import elementary-number-theory.binomial-coefficients open import elementary-number-theory.natural-numbers -open import foundation.booleans funext -open import foundation.connected-components-universes funext -open import foundation.contractible-maps funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-embeddings funext -open import foundation.decidable-propositions funext -open import foundation.decidable-subtypes funext +open import foundation.booleans +open import foundation.connected-components-universes +open import foundation.contractible-maps +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-embeddings +open import foundation.decidable-propositions +open import foundation.decidable-subtypes open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.equivalences funext-maybe -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.logical-equivalences funext -open import foundation.maybe funext -open import foundation.mere-equivalences funext -open import foundation.negation funext -open import foundation.postcomposition-functions funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equivalences +open import foundation.equivalences-maybe +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-propositional-truncation +open import foundation.logical-equivalences +open import foundation.maybe +open import foundation.mere-equivalences +open import foundation.negation +open import foundation.postcomposition-functions +open import foundation.propositional-extensionality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.type-arithmetic-unit-type open import foundation.unit-type -open import foundation.universal-property-empty-type funext -open import foundation.universal-property-equivalences funext -open import foundation.universal-property-maybe funext +open import foundation.universal-property-empty-type +open import foundation.universal-property-equivalences +open import foundation.universal-property-maybe open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/bracelets.lagda.md b/src/univalent-combinatorics/bracelets.lagda.md index 35a0f6098e..f2e65151d7 100644 --- a/src/univalent-combinatorics/bracelets.lagda.md +++ b/src/univalent-combinatorics/bracelets.lagda.md @@ -1,12 +1,7 @@ # Bracelets ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.bracelets - (funext : function-extensionality) - where +module univalent-combinatorics.bracelets where ```
Imports @@ -17,9 +12,9 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import graph-theory.polygons funext +open import graph-theory.polygons -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/cartesian-product-types.lagda.md b/src/univalent-combinatorics/cartesian-product-types.lagda.md index d2f8951a56..43dee54458 100644 --- a/src/univalent-combinatorics/cartesian-product-types.lagda.md +++ b/src/univalent-combinatorics/cartesian-product-types.lagda.md @@ -1,12 +1,7 @@ # Cartesian products of finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.cartesian-product-types - (funext : function-extensionality) - where +module univalent-combinatorics.cartesian-product-types where ```
Imports @@ -15,35 +10,35 @@ module open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.decidable-equality funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.decidable-equality open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.identity-types funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.torsorial-type-families funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-propositional-truncation +open import foundation.identity-types +open import foundation.mere-equivalences +open import foundation.propositional-truncations +open import foundation.torsorial-type-families open import foundation.type-arithmetic-cartesian-product-types -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-dependent-pair-types -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.double-counting funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-dependent-pair-types +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.double-counting +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/classical-finite-types.lagda.md b/src/univalent-combinatorics/classical-finite-types.lagda.md index ae4640280d..95091e94ec 100644 --- a/src/univalent-combinatorics/classical-finite-types.lagda.md +++ b/src/univalent-combinatorics/classical-finite-types.lagda.md @@ -1,27 +1,22 @@ # The classical definition of the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.classical-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.classical-finite-types where ```
Imports ```agda -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/complements-isolated-elements.lagda.md b/src/univalent-combinatorics/complements-isolated-elements.lagda.md index c1e8c0d982..add3d8ff3f 100644 --- a/src/univalent-combinatorics/complements-isolated-elements.lagda.md +++ b/src/univalent-combinatorics/complements-isolated-elements.lagda.md @@ -1,12 +1,7 @@ # Complements of isolated elements of finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.complements-isolated-elements - (funext : function-extensionality) - where +module univalent-combinatorics.complements-isolated-elements where ```
Imports @@ -15,16 +10,16 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.equivalences funext-maybe -open import foundation.identity-types funext -open import foundation.isolated-elements funext -open import foundation.maybe funext -open import foundation.propositional-truncations funext +open import foundation.equivalences +open import foundation.equivalences-maybe +open import foundation.identity-types +open import foundation.isolated-elements +open import foundation.maybe +open import foundation.propositional-truncations open import foundation.universe-levels -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/coproduct-types.lagda.md b/src/univalent-combinatorics/coproduct-types.lagda.md index c5627f13ec..03c7063c2b 100644 --- a/src/univalent-combinatorics/coproduct-types.lagda.md +++ b/src/univalent-combinatorics/coproduct-types.lagda.md @@ -1,12 +1,7 @@ # Coproducts of finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.coproduct-types - (funext : function-extensionality) - where +module univalent-combinatorics.coproduct-types where ```
Imports @@ -16,26 +11,27 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.type-arithmetic-coproduct-types funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-propositional-truncation +open import foundation.homotopies +open import foundation.identity-types +open import foundation.mere-equivalences +open import foundation.propositional-truncations +open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-empty-type open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-decidable-subtypes -open import univalent-combinatorics.double-counting funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-decidable-subtypes +open import univalent-combinatorics.double-counting +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md index b432300747..2dc4eea133 100644 --- a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md @@ -1,14 +1,9 @@ # Counting the elements of decidable subtypes ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.counting-decidable-subtypes where -module - univalent-combinatorics.counting-decidable-subtypes - (funext : function-extensionality) - where - -open import foundation.decidable-subtypes funext public +open import foundation.decidable-subtypes public ```
Imports @@ -16,31 +11,31 @@ open import foundation.decidable-subtypes funext public ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-embeddings funext -open import foundation.decidable-types funext +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-embeddings +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.propositional-maps funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.type-arithmetic-coproduct-types funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.propositional-maps +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.subtypes +open import foundation.type-arithmetic-coproduct-types +open import foundation.type-arithmetic-empty-type open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md index 833c714a44..ce45d38d86 100644 --- a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md @@ -1,49 +1,44 @@ # Counting the elements of dependent pair types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.counting-dependent-pair-types - (funext : function-extensionality) - where +module univalent-combinatorics.counting-dependent-pair-types where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.sums-of-natural-numbers funext +open import elementary-number-theory.sums-of-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.sections funext -open import foundation.torsorial-type-families funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.sections +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.double-counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.double-counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/counting-maybe.lagda.md b/src/univalent-combinatorics/counting-maybe.lagda.md index cda5aaa6fe..a69e71d84a 100644 --- a/src/univalent-combinatorics/counting-maybe.lagda.md +++ b/src/univalent-combinatorics/counting-maybe.lagda.md @@ -1,12 +1,7 @@ # Counting the elements in Maybe ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.counting-maybe - (funext : function-extensionality) - where +module univalent-combinatorics.counting-maybe where ```
Imports @@ -15,14 +10,14 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences-maybe funext +open import foundation.equivalences-maybe open import foundation.universe-levels open import foundation-core.identity-types open import foundation-core.maybe -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.counting funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.counting ```
diff --git a/src/univalent-combinatorics/counting.lagda.md b/src/univalent-combinatorics/counting.lagda.md index 2fb9d291fa..b9c4fa6d19 100644 --- a/src/univalent-combinatorics/counting.lagda.md +++ b/src/univalent-combinatorics/counting.lagda.md @@ -1,12 +1,7 @@ # Counting in type theory ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.counting - (funext : function-extensionality) - where +module univalent-combinatorics.counting where ```
Imports @@ -14,25 +9,25 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/cubes.lagda.md b/src/univalent-combinatorics/cubes.lagda.md index b9610c82ae..658ef99b5f 100644 --- a/src/univalent-combinatorics/cubes.lagda.md +++ b/src/univalent-combinatorics/cubes.lagda.md @@ -1,12 +1,7 @@ # Cubes ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.cubes - (funext : function-extensionality) - where +module univalent-combinatorics.cubes where ```
Imports @@ -17,8 +12,8 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.complements-isolated-elements funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.complements-isolated-elements +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/cycle-partitions.lagda.md b/src/univalent-combinatorics/cycle-partitions.lagda.md index 470d724f08..2b24b1903a 100644 --- a/src/univalent-combinatorics/cycle-partitions.lagda.md +++ b/src/univalent-combinatorics/cycle-partitions.lagda.md @@ -1,12 +1,7 @@ # Cycle partitions of finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.cycle-partitions - (funext : function-extensionality) - where +module univalent-combinatorics.cycle-partitions where ```
Imports @@ -15,11 +10,11 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext +open import foundation.equivalences open import foundation.universe-levels -open import univalent-combinatorics.cyclic-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.cyclic-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md b/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md index 58f05e8f3e..f1c5ab49c3 100644 --- a/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md +++ b/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md @@ -1,46 +1,41 @@ # Cycle prime decompositions of natural numbers ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.cycle-prime-decomposition-natural-numbers - (funext : function-extensionality) - where +module univalent-combinatorics.cycle-prime-decomposition-natural-numbers where ```
Imports ```agda -open import elementary-number-theory.decidable-total-order-natural-numbers funext -open import elementary-number-theory.fundamental-theorem-of-arithmetic funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.decidable-total-order-natural-numbers +open import elementary-number-theory.fundamental-theorem-of-arithmetic +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.permutations-standard-finite-types funext +open import finite-group-theory.permutations-standard-finite-types open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.iterated-cartesian-product-types funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.iterated-cartesian-product-types open import foundation.transport-along-identifications -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.iterated-cartesian-products-concrete-groups funext +open import group-theory.concrete-groups +open import group-theory.iterated-cartesian-products-concrete-groups -open import lists.arrays funext -open import lists.concatenation-lists funext -open import lists.functoriality-lists funext -open import lists.permutation-lists funext -open import lists.sort-by-insertion-lists funext +open import lists.arrays +open import lists.concatenation-lists +open import lists.functoriality-lists +open import lists.permutation-lists +open import lists.sort-by-insertion-lists -open import univalent-combinatorics.cyclic-finite-types funext +open import univalent-combinatorics.cyclic-finite-types ```
diff --git a/src/univalent-combinatorics/cyclic-finite-types.lagda.md b/src/univalent-combinatorics/cyclic-finite-types.lagda.md index 2ef8352d0f..da2741d64a 100644 --- a/src/univalent-combinatorics/cyclic-finite-types.lagda.md +++ b/src/univalent-combinatorics/cyclic-finite-types.lagda.md @@ -1,57 +1,52 @@ # Cyclic finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.cyclic-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.cyclic-finite-types where ```
Imports ```agda -open import elementary-number-theory.addition-integers funext +open import elementary-number-theory.addition-integers open import elementary-number-theory.integers -open import elementary-number-theory.modular-arithmetic funext -open import elementary-number-theory.modular-arithmetic funext-standard-finite-types +open import elementary-number-theory.modular-arithmetic +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.standard-cyclic-groups funext +open import elementary-number-theory.standard-cyclic-groups -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.mere-equality funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.homotopies +open import foundation.identity-types +open import foundation.mere-equality +open import foundation.propositional-truncations +open import foundation.sets open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import group-theory.concrete-groups funext -open import group-theory.groups funext -open import group-theory.isomorphisms-groups funext +open import group-theory.concrete-groups +open import group-theory.groups +open import group-theory.isomorphisms-groups -open import higher-group-theory.higher-groups funext +open import higher-group-theory.higher-groups -open import structured-types.equivalences-types-equipped-with-endomorphisms funext -open import structured-types.mere-equivalences-types-equipped-with-endomorphisms funext +open import structured-types.equivalences-types-equipped-with-endomorphisms +open import structured-types.mere-equivalences-types-equipped-with-endomorphisms open import structured-types.pointed-types -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms -open import synthetic-homotopy-theory.groups-of-loops-in-1-types funext -open import synthetic-homotopy-theory.loop-spaces funext +open import synthetic-homotopy-theory.groups-of-loops-in-1-types +open import synthetic-homotopy-theory.loop-spaces ```
diff --git a/src/univalent-combinatorics/de-morgans-law.lagda.md b/src/univalent-combinatorics/de-morgans-law.lagda.md index e473843725..bca666f108 100644 --- a/src/univalent-combinatorics/de-morgans-law.lagda.md +++ b/src/univalent-combinatorics/de-morgans-law.lagda.md @@ -1,12 +1,7 @@ # De Morgan's law for finite families of propositions ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.de-morgans-law - (funext : function-extensionality) - where +module univalent-combinatorics.de-morgans-law where ```
Imports @@ -14,24 +9,24 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext -open import foundation.decidable-dependent-pair-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-dependent-pair-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.existential-quantification funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.negation funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.existential-quantification +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.negation open import foundation.unit-type open import foundation.universe-levels -open import logic.de-morgan-propositions funext -open import logic.de-morgan-types funext +open import logic.de-morgan-propositions +open import logic.de-morgan-types -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md b/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md index 6f87159d65..5f6cfff00c 100644 --- a/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md +++ b/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md @@ -1,14 +1,9 @@ # Decidable dependent function types ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.decidable-dependent-function-types where -module - univalent-combinatorics.decidable-dependent-function-types - (funext : function-extensionality) - where - -open import elementary-number-theory.decidable-dependent-function-types funext public +open import elementary-number-theory.decidable-dependent-function-types public ```
Imports @@ -16,21 +11,21 @@ open import elementary-number-theory.decidable-dependent-function-types funext p ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.finite-choice funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.finite-choice +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md b/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md index 1a269b2a0b..9e48dbc5b3 100644 --- a/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/decidable-dependent-pair-types.lagda.md @@ -1,12 +1,7 @@ # Decidability of dependent pair types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.decidable-dependent-pair-types - (funext : function-extensionality) - where +module univalent-combinatorics.decidable-dependent-pair-types where ```
Imports @@ -14,18 +9,18 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext -open import foundation.decidable-dependent-pair-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-dependent-pair-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md index c2e6e2550b..46f0521430 100644 --- a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md +++ b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md @@ -1,12 +1,7 @@ # Decidable equivalence relations on finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.decidable-equivalence-relations - (funext : function-extensionality) - where +module univalent-combinatorics.decidable-equivalence-relations where ```
Imports @@ -14,32 +9,32 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-equivalence-relations funext -open import foundation.decidable-relations funext -open import foundation.decidable-types funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.binary-relations +open import foundation.cartesian-product-types +open import foundation.decidable-equality +open import foundation.decidable-equivalence-relations +open import foundation.decidable-relations +open import foundation.decidable-types +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-pair-types +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.function-types funext -open import univalent-combinatorics.standard-finite-types funext -open import univalent-combinatorics.surjective-maps funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.function-types +open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.surjective-maps ```
diff --git a/src/univalent-combinatorics/decidable-propositions.lagda.md b/src/univalent-combinatorics/decidable-propositions.lagda.md index 7ac0edffed..c825d693f8 100644 --- a/src/univalent-combinatorics/decidable-propositions.lagda.md +++ b/src/univalent-combinatorics/decidable-propositions.lagda.md @@ -1,14 +1,9 @@ # Decidable propositions ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.decidable-propositions where -module - univalent-combinatorics.decidable-propositions - (funext : function-extensionality) - where - -open import foundation.decidable-propositions funext public +open import foundation.decidable-propositions public ```
Imports @@ -16,17 +11,17 @@ open import foundation.decidable-propositions funext public ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/decidable-subtypes.lagda.md b/src/univalent-combinatorics/decidable-subtypes.lagda.md index 0a1f5e0f1a..d7b83a688c 100644 --- a/src/univalent-combinatorics/decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/decidable-subtypes.lagda.md @@ -1,42 +1,37 @@ # Decidable subtypes of finite types ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.decidable-subtypes where -module - univalent-combinatorics.decidable-subtypes - (funext : function-extensionality) - where - -open import foundation.decidable-subtypes funext public +open import foundation.decidable-subtypes public ```
Imports ```agda -open import elementary-number-theory.exponentiation-natural-numbers funext +open import elementary-number-theory.exponentiation-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.decidable-propositions funext -open import foundation.embeddings funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.subtypes funext +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.decidable-propositions +open import foundation.embeddings +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.decidable-dependent-pair-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.function-types funext +open import univalent-combinatorics.decidable-dependent-pair-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.function-types ```
diff --git a/src/univalent-combinatorics/dedekind-finite-sets.lagda.md b/src/univalent-combinatorics/dedekind-finite-sets.lagda.md index 6f39fb33a8..f3d73ff2db 100644 --- a/src/univalent-combinatorics/dedekind-finite-sets.lagda.md +++ b/src/univalent-combinatorics/dedekind-finite-sets.lagda.md @@ -1,22 +1,17 @@ # Dedekind finite sets ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.dedekind-finite-sets - (funext : function-extensionality) - where +module univalent-combinatorics.dedekind-finite-sets where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equivalences +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics/dependent-function-types.lagda.md b/src/univalent-combinatorics/dependent-function-types.lagda.md index 8f23e0cc17..f8354b654c 100644 --- a/src/univalent-combinatorics/dependent-function-types.lagda.md +++ b/src/univalent-combinatorics/dependent-function-types.lagda.md @@ -1,12 +1,7 @@ # Counting the elements of dependent function types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.dependent-function-types - (funext : function-extensionality) - where +module univalent-combinatorics.dependent-function-types where ```
Imports @@ -14,28 +9,28 @@ module ```agda open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.products-of-natural-numbers funext +open import elementary-number-theory.products-of-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.dependent-universal-property-equivalences +open import foundation.equivalences +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.unit-type -open import foundation.universal-property-coproduct-types funext -open import foundation.universal-property-empty-type funext -open import foundation.universal-property-unit-type funext +open import foundation.universal-property-coproduct-types +open import foundation.universal-property-empty-type +open import foundation.universal-property-unit-type open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.finite-choice funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.finite-choice +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/dependent-pair-types.lagda.md b/src/univalent-combinatorics/dependent-pair-types.lagda.md index b96958a432..ce7fef9510 100644 --- a/src/univalent-combinatorics/dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/dependent-pair-types.lagda.md @@ -1,12 +1,7 @@ # Dependent pair types of finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.dependent-pair-types - (funext : function-extensionality) - where +module univalent-combinatorics.dependent-pair-types where open import foundation.dependent-pair-types public ``` @@ -15,33 +10,33 @@ open import foundation.dependent-pair-types public ```agda open import foundation.complements -open import foundation.decidable-types funext -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sections funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.torsorial-type-families funext +open import foundation.decidable-types +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-propositional-truncation +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sections +open import foundation.sets +open import foundation.subtypes +open import foundation.torsorial-type-families open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-dependent-pair-types -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-choice funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-dependent-pair-types +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-choice +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md index 58fb7fa268..3eb65dbffb 100644 --- a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md @@ -1,29 +1,24 @@ # Finite discrete Σ-decompositions ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.discrete-sigma-decompositions where -module - univalent-combinatorics.discrete-sigma-decompositions - (funext : function-extensionality) - where - -open import foundation.discrete-sigma-decompositions funext public +open import foundation.discrete-sigma-decompositions public ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.sigma-decompositions funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.sigma-decompositions ```
diff --git a/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md b/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md index 2f692573f5..64609a61a2 100644 --- a/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md +++ b/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md @@ -1,12 +1,7 @@ # Distributivity of set truncation over finite products ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.distributivity-of-set-truncation-over-finite-products - (funext : function-extensionality) - where +module univalent-combinatorics.distributivity-of-set-truncation-over-finite-products where ```
Imports @@ -15,38 +10,37 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-function-types funext -open import foundation.functoriality-set-truncation funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.postcomposition-functions funext -open import foundation.precomposition-dependent-functions funext -open import foundation.precomposition-functions funext -open import foundation.propositional-truncations funext -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.dependent-universal-property-equivalences +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-function-types +open import foundation.functoriality-set-truncation +open import foundation.homotopies +open import foundation.identity-types +open import foundation.postcomposition-functions +open import foundation.precomposition-dependent-functions +open import foundation.precomposition-functions +open import foundation.propositional-truncations +open import foundation.set-truncations +open import foundation.sets open import foundation.unit-type -open import foundation.universal-property-dependent-pair-types funext -open import foundation.universal-property-empty-type funext -open import foundation.universal-property-equivalences funext -open import foundation.universal-property-maybe funext +open import foundation.universal-property-dependent-pair-types +open import foundation.universal-property-empty-type +open import foundation.universal-property-equivalences +open import foundation.universal-property-maybe open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/double-counting.lagda.md b/src/univalent-combinatorics/double-counting.lagda.md index 0796893310..a6a55dcc85 100644 --- a/src/univalent-combinatorics/double-counting.lagda.md +++ b/src/univalent-combinatorics/double-counting.lagda.md @@ -1,24 +1,19 @@ # Double counting ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.double-counting - (funext : function-extensionality) - where +module univalent-combinatorics.double-counting where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md b/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md index a01863918c..458ec1b433 100644 --- a/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/embeddings-standard-finite-types.lagda.md @@ -1,34 +1,29 @@ # Embeddings between standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.embeddings-standard-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.embeddings-standard-finite-types where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.repeating-element-standard-finite-type funext +open import elementary-number-theory.repeating-element-standard-finite-type open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.empty-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/embeddings.lagda.md b/src/univalent-combinatorics/embeddings.lagda.md index 6bb8b115df..e9776b2416 100644 --- a/src/univalent-combinatorics/embeddings.lagda.md +++ b/src/univalent-combinatorics/embeddings.lagda.md @@ -1,14 +1,9 @@ # Embeddings ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.embeddings where -module - univalent-combinatorics.embeddings - (funext : function-extensionality) - where - -open import foundation.embeddings funext public +open import foundation.embeddings public ```
Imports @@ -16,22 +11,22 @@ open import foundation.embeddings funext public ```agda open import elementary-number-theory.natural-numbers -open import foundation.coproduct-types funext -open import foundation.decidable-embeddings funext -open import foundation.decidable-types funext +open import foundation.coproduct-types +open import foundation.decidable-embeddings +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.injective-maps funext -open import univalent-combinatorics.retracts-of-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.injective-maps +open import univalent-combinatorics.retracts-of-finite-types ```
diff --git a/src/univalent-combinatorics/equality-finite-types.lagda.md b/src/univalent-combinatorics/equality-finite-types.lagda.md index 9c027320b0..220051d0d8 100644 --- a/src/univalent-combinatorics/equality-finite-types.lagda.md +++ b/src/univalent-combinatorics/equality-finite-types.lagda.md @@ -1,12 +1,7 @@ # Equality in finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.equality-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.equality-finite-types where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-equality funext +open import foundation.decidable-equality open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositional-truncations funext +open import foundation.identity-types +open import foundation.propositional-truncations open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/equality-standard-finite-types.lagda.md b/src/univalent-combinatorics/equality-standard-finite-types.lagda.md index 891c79f055..637b3cf66a 100644 --- a/src/univalent-combinatorics/equality-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/equality-standard-finite-types.lagda.md @@ -1,43 +1,38 @@ # Equality in the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.equality-standard-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.equality-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.apartness-relations funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.apartness-relations +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.discrete-types funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.functoriality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositions funext -open import foundation.set-truncations funext -open import foundation.tight-apartness-relations funext +open import foundation.discrete-types +open import foundation.empty-types +open import foundation.equivalences +open import foundation.functoriality-coproduct-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositions +open import foundation.set-truncations +open import foundation.tight-apartness-relations open import foundation.unit-type open import foundation.universe-levels -open import foundation-core.decidable-propositions funext +open import foundation-core.decidable-propositions -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/equivalences-cubes.lagda.md b/src/univalent-combinatorics/equivalences-cubes.lagda.md index 6263dcf25b..c4971042e6 100644 --- a/src/univalent-combinatorics/equivalences-cubes.lagda.md +++ b/src/univalent-combinatorics/equivalences-cubes.lagda.md @@ -1,12 +1,7 @@ # Equivalences of cubes ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.equivalences-cubes - (funext : function-extensionality) - where +module univalent-combinatorics.equivalences-cubes where ```
Imports @@ -15,20 +10,20 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equality-dependent-function-types +open import foundation.equivalence-extensionality +open import foundation.equivalences +open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.homotopies +open import foundation.identity-types open import foundation.structure-identity-principle -open import foundation.torsorial-type-families funext +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels -open import univalent-combinatorics.cubes funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.cubes +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md b/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md index 0cdceeda4d..b7044ed428 100644 --- a/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md @@ -1,31 +1,26 @@ # Equivalences between standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.equivalences-standard-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.equivalences-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.exponentiation-natural-numbers funext +open import elementary-number-theory.exponentiation-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.contractible-types funext -open import foundation.equivalences funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.type-arithmetic-empty-type funext +open import foundation.contractible-types +open import foundation.equivalences +open import foundation.functoriality-cartesian-product-types +open import foundation.type-arithmetic-empty-type open import foundation.unit-type -open import foundation.universal-property-coproduct-types funext -open import foundation.universal-property-empty-type funext -open import foundation.universal-property-unit-type funext +open import foundation.universal-property-coproduct-types +open import foundation.universal-property-empty-type +open import foundation.universal-property-unit-type -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/equivalences.lagda.md b/src/univalent-combinatorics/equivalences.lagda.md index 61d17ec54d..6b439ee5a4 100644 --- a/src/univalent-combinatorics/equivalences.lagda.md +++ b/src/univalent-combinatorics/equivalences.lagda.md @@ -1,26 +1,21 @@ # Equivalences between finite types ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.equivalences where -module - univalent-combinatorics.equivalences - (funext : function-extensionality) - where - -open import foundation.equivalences funext public +open import foundation.equivalences public ```
Imports ```agda -open import foundation.decidable-types funext +open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.embeddings funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.surjective-maps funext +open import univalent-combinatorics.embeddings +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.surjective-maps ```
diff --git a/src/univalent-combinatorics/ferrers-diagrams.lagda.md b/src/univalent-combinatorics/ferrers-diagrams.lagda.md index 24b5ad25ec..034b26e3ad 100644 --- a/src/univalent-combinatorics/ferrers-diagrams.lagda.md +++ b/src/univalent-combinatorics/ferrers-diagrams.lagda.md @@ -1,33 +1,28 @@ # Ferrers diagrams (unlabeled partitions) ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.ferrers-diagrams - (funext : function-extensionality) - where +module univalent-combinatorics.ferrers-diagrams where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equality-dependent-function-types funext -open import foundation.equivalences funext +open import foundation.equality-dependent-function-types +open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types -open import foundation.identity-types funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.identity-types +open import foundation.mere-equivalences +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.structure-identity-principle open import foundation.subtype-identity-principle -open import foundation.torsorial-type-families funext -open import foundation.univalence funext +open import foundation.torsorial-type-families +open import foundation.univalence open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/fibers-of-maps.lagda.md b/src/univalent-combinatorics/fibers-of-maps.lagda.md index 204431e7c5..31ba87543e 100644 --- a/src/univalent-combinatorics/fibers-of-maps.lagda.md +++ b/src/univalent-combinatorics/fibers-of-maps.lagda.md @@ -1,44 +1,39 @@ # Fibers of maps between finite types ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.fibers-of-maps where -module - univalent-combinatorics.fibers-of-maps - (funext : function-extensionality) - where - -open import foundation.fibers-of-maps funext public +open import foundation.fibers-of-maps public ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.sums-of-natural-numbers funext - -open import foundation.decidable-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sections funext -open import foundation.torsorial-type-families funext +open import elementary-number-theory.sums-of-natural-numbers + +open import foundation.decidable-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.functoriality-dependent-pair-types +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sections +open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-dependent-pair-types -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.double-counting funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-dependent-pair-types +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.double-counting +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/finite-choice.lagda.md b/src/univalent-combinatorics/finite-choice.lagda.md index 291f0f0366..9446a425cb 100644 --- a/src/univalent-combinatorics/finite-choice.lagda.md +++ b/src/univalent-combinatorics/finite-choice.lagda.md @@ -1,44 +1,39 @@ # Finite choice ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.finite-choice - (funext : function-extensionality) - where +module univalent-combinatorics.finite-choice where ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types funext +open import elementary-number-theory.well-ordering-principle-standard-finite-types -open import foundation.coproduct-types funext -open import foundation.decidable-embeddings funext +open import foundation.coproduct-types +open import foundation.decidable-embeddings open import foundation.dependent-pair-types -open import foundation.dependent-universal-property-equivalences funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.fiber-inclusions funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.hilberts-epsilon-operators funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.dependent-universal-property-equivalences +open import foundation.empty-types +open import foundation.equivalences +open import foundation.fiber-inclusions +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-propositional-truncation +open import foundation.hilberts-epsilon-operators +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.sets open import foundation.unit-type -open import foundation.universal-property-coproduct-types funext -open import foundation.universal-property-unit-type funext +open import foundation.universal-property-coproduct-types +open import foundation.universal-property-unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-decidable-subtypes -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-decidable-subtypes +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/finite-types.lagda.md b/src/univalent-combinatorics/finite-types.lagda.md index 339fa34cf1..ca162f16ce 100644 --- a/src/univalent-combinatorics/finite-types.lagda.md +++ b/src/univalent-combinatorics/finite-types.lagda.md @@ -1,55 +1,50 @@ # Finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.finite-types where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types funext -open import foundation.1-types funext +open import foundation.0-connected-types +open import foundation.1-types open import foundation.action-on-identifications-functions -open import foundation.connected-components-universes funext -open import foundation.contractible-types funext -open import foundation.decidable-types funext +open import foundation.connected-components-universes +open import foundation.contractible-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-coproduct-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.logical-equivalences funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels funext -open import foundation.raising-universe-levels funext-unit-type -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.subuniverses funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-coproduct-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-propositional-truncation +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.logical-equivalences +open import foundation.mere-equivalences +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels +open import foundation.raising-universe-levels-unit-type +open import foundation.sets +open import foundation.subtypes +open import foundation.subuniverses open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-arithmetic-empty-type funext +open import foundation.type-arithmetic-empty-type open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation-core.torsorial-type-families -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/finitely-many-connected-components.lagda.md b/src/univalent-combinatorics/finitely-many-connected-components.lagda.md index 28b1c1f582..b2d49dc3a5 100644 --- a/src/univalent-combinatorics/finitely-many-connected-components.lagda.md +++ b/src/univalent-combinatorics/finitely-many-connected-components.lagda.md @@ -1,12 +1,7 @@ # Finiteness of the type of connected components ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.finitely-many-connected-components - (funext : function-extensionality) - where +module univalent-combinatorics.finitely-many-connected-components where ```
Imports @@ -14,28 +9,28 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.0-connected-types +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-set-truncation funext -open import foundation.mere-equivalences funext -open import foundation.propositions funext -open import foundation.retracts-of-types funext -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-set-truncation +open import foundation.mere-equivalences +open import foundation.propositions +open import foundation.retracts-of-types +open import foundation.set-truncations +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.retracts-of-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.distributivity-of-set-truncation-over-finite-products +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.retracts-of-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/finitely-presented-types.lagda.md b/src/univalent-combinatorics/finitely-presented-types.lagda.md index 55119541dc..6cc22a250a 100644 --- a/src/univalent-combinatorics/finitely-presented-types.lagda.md +++ b/src/univalent-combinatorics/finitely-presented-types.lagda.md @@ -1,12 +1,7 @@ # Finitely presented types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.finitely-presented-types - (funext : function-extensionality) - where +module univalent-combinatorics.finitely-presented-types where ```
Imports @@ -15,20 +10,20 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.fibers-of-maps funext -open import foundation.function-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.set-presented-types funext -open import foundation.set-truncations funext -open import foundation.subtypes funext +open import foundation.equivalences +open import foundation.fibers-of-maps +open import foundation.function-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.set-presented-types +open import foundation.set-truncations +open import foundation.subtypes open import foundation.universe-levels -open import univalent-combinatorics.finite-choice funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.finitely-many-connected-components funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.finite-choice +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finitely-many-connected-components +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/function-types.lagda.md b/src/univalent-combinatorics/function-types.lagda.md index 58065ca575..f461d7df2d 100644 --- a/src/univalent-combinatorics/function-types.lagda.md +++ b/src/univalent-combinatorics/function-types.lagda.md @@ -1,33 +1,28 @@ # Finite function types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.function-types - (funext : function-extensionality) - where +module univalent-combinatorics.function-types where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.exponentiation-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.exponentiation-natural-numbers open import foundation.action-on-identifications-binary-functions -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.sets open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/image-of-maps.lagda.md b/src/univalent-combinatorics/image-of-maps.lagda.md index 29c4d08f51..db8cf058d7 100644 --- a/src/univalent-combinatorics/image-of-maps.lagda.md +++ b/src/univalent-combinatorics/image-of-maps.lagda.md @@ -1,30 +1,25 @@ # The image of a map ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.image-of-maps where -module - univalent-combinatorics.image-of-maps - (funext : function-extensionality) - where - -open import foundation.images funext public +open import foundation.images public ```
Imports ```agda -open import foundation.decidable-equality funext -open import foundation.decidable-types funext -open import foundation.fibers-of-maps funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.decidable-equality +open import foundation.decidable-types +open import foundation.fibers-of-maps +open import foundation.propositional-truncations +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.universe-levels -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/inequality-types-with-counting.lagda.md b/src/univalent-combinatorics/inequality-types-with-counting.lagda.md index 8d41ab02c3..137bb6bd70 100644 --- a/src/univalent-combinatorics/inequality-types-with-counting.lagda.md +++ b/src/univalent-combinatorics/inequality-types-with-counting.lagda.md @@ -1,28 +1,23 @@ # Inequality on types equipped with a counting ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.inequality-types-with-counting - (funext : function-extensionality) - where +module univalent-combinatorics.inequality-types-with-counting where ```
Imports ```agda -open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.inequality-standard-finite-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.sets funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.sets open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/inhabited-finite-types.lagda.md b/src/univalent-combinatorics/inhabited-finite-types.lagda.md index 9a5a1370bb..f6ad56cab3 100644 --- a/src/univalent-combinatorics/inhabited-finite-types.lagda.md +++ b/src/univalent-combinatorics/inhabited-finite-types.lagda.md @@ -1,12 +1,7 @@ # Inhabited finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.inhabited-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.inhabited-finite-types where ```
Imports @@ -14,20 +9,20 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.propositions funext -open import foundation.subtypes funext -open import foundation.subuniverses funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-function-types +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.propositions +open import foundation.subtypes +open import foundation.subuniverses open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/injective-maps.lagda.md b/src/univalent-combinatorics/injective-maps.lagda.md index 5484df2631..b848851cf0 100644 --- a/src/univalent-combinatorics/injective-maps.lagda.md +++ b/src/univalent-combinatorics/injective-maps.lagda.md @@ -1,26 +1,21 @@ # Injective maps between finite types ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.injective-maps where -module - univalent-combinatorics.injective-maps - (funext : function-extensionality) - where - -open import foundation.injective-maps funext public +open import foundation.injective-maps public ```
Imports ```agda -open import foundation.decidable-types funext -open import foundation.identity-types funext +open import foundation.decidable-types +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.decidable-dependent-function-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.decidable-dependent-function-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/involution-standard-finite-types.lagda.md b/src/univalent-combinatorics/involution-standard-finite-types.lagda.md index da1786dca0..72c2a01a68 100644 --- a/src/univalent-combinatorics/involution-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/involution-standard-finite-types.lagda.md @@ -1,25 +1,20 @@ # An involution on the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.involution-standard-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.involution-standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.identity-types funext -open import foundation.involutions funext +open import foundation.identity-types +open import foundation.involutions -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/isotopies-latin-squares.lagda.md b/src/univalent-combinatorics/isotopies-latin-squares.lagda.md index 0669cddad2..58d4aa23c2 100644 --- a/src/univalent-combinatorics/isotopies-latin-squares.lagda.md +++ b/src/univalent-combinatorics/isotopies-latin-squares.lagda.md @@ -1,23 +1,18 @@ # Isotopies of Latin squares ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.isotopies-latin-squares - (funext : function-extensionality) - where +module univalent-combinatorics.isotopies-latin-squares where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.identity-types open import foundation.universe-levels -open import univalent-combinatorics.latin-squares funext +open import univalent-combinatorics.latin-squares ```
diff --git a/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md b/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md index be407d4dd4..7de999ba15 100644 --- a/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md +++ b/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md @@ -1,12 +1,7 @@ # Kuratowski finite sets ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.kuratowski-finite-sets - (funext : function-extensionality) - where +module univalent-combinatorics.kuratowski-finite-sets where ```
Imports @@ -14,19 +9,19 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-equality funext +open import foundation.decidable-equality open import foundation.dependent-pair-types -open import foundation.existential-quantification funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext -open import foundation.surjective-maps funext +open import foundation.existential-quantification +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets +open import foundation.surjective-maps open import foundation.universe-levels -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.image-of-maps funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.image-of-maps +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/latin-squares.lagda.md b/src/univalent-combinatorics/latin-squares.lagda.md index 036fc113ef..228092c29d 100644 --- a/src/univalent-combinatorics/latin-squares.lagda.md +++ b/src/univalent-combinatorics/latin-squares.lagda.md @@ -1,12 +1,7 @@ # Latin squares ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.latin-squares - (funext : function-extensionality) - where +module univalent-combinatorics.latin-squares where ```
Imports @@ -14,7 +9,7 @@ module ```agda open import foundation.binary-equivalences open import foundation.dependent-pair-types -open import foundation.inhabited-types funext +open import foundation.inhabited-types open import foundation.universe-levels ``` diff --git a/src/univalent-combinatorics/locally-finite-types.lagda.md b/src/univalent-combinatorics/locally-finite-types.lagda.md index 38d067338a..273e1cd35b 100644 --- a/src/univalent-combinatorics/locally-finite-types.lagda.md +++ b/src/univalent-combinatorics/locally-finite-types.lagda.md @@ -1,12 +1,7 @@ # Locally finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.locally-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.locally-finite-types where ```
Imports @@ -14,33 +9,33 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types funext -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-equality funext -open import foundation.dependent-universal-property-equivalences funext -open import foundation.empty-types funext +open import foundation.1-types +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-equality +open import foundation.dependent-universal-property-equivalences +open import foundation.empty-types open import foundation.equality-cartesian-product-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.transport-along-identifications open import foundation.unit-type -open import foundation.universal-property-coproduct-types funext -open import foundation.universal-property-empty-type funext -open import foundation.universal-property-unit-type funext +open import foundation.universal-property-coproduct-types +open import foundation.universal-property-empty-type +open import foundation.universal-property-unit-type open import foundation.universe-levels -open import univalent-combinatorics.cartesian-product-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.cartesian-product-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md b/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md index 7b2a53d9e4..f88ff5969a 100644 --- a/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md +++ b/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md @@ -1,12 +1,7 @@ # The groupoid of main classes of Latin hypercubes ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.main-classes-of-latin-hypercubes - (funext : function-extensionality) - where +module univalent-combinatorics.main-classes-of-latin-hypercubes where ```
Imports @@ -14,24 +9,24 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types funext -open import foundation.contractible-types funext -open import foundation.decidable-propositions funext +open import foundation.1-types +open import foundation.contractible-types +open import foundation.decidable-propositions open import foundation.dependent-pair-types -open import foundation.inhabited-types funext -open import foundation.mere-equivalences funext -open import foundation.products-unordered-tuples-of-types funext -open import foundation.set-truncations funext +open import foundation.inhabited-types +open import foundation.mere-equivalences +open import foundation.products-unordered-tuples-of-types +open import foundation.set-truncations open import foundation.universe-levels -open import foundation.unordered-tuples funext - -open import univalent-combinatorics.complements-isolated-elements funext -open import univalent-combinatorics.decidable-subtypes funext -open import univalent-combinatorics.dependent-function-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.pi-finite-types funext -open import univalent-combinatorics.standard-finite-types funext -open import univalent-combinatorics.untruncated-pi-finite-types funext +open import foundation.unordered-tuples + +open import univalent-combinatorics.complements-isolated-elements +open import univalent-combinatorics.decidable-subtypes +open import univalent-combinatorics.dependent-function-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.pi-finite-types +open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.untruncated-pi-finite-types ```
diff --git a/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md b/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md index 6ed8beda4a..0f3d9410e3 100644 --- a/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md +++ b/src/univalent-combinatorics/main-classes-of-latin-squares.lagda.md @@ -1,12 +1,7 @@ # The groupoid of main classes of Latin squares ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.main-classes-of-latin-squares - (funext : function-extensionality) - where +module univalent-combinatorics.main-classes-of-latin-squares where ```
Imports @@ -14,15 +9,15 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.1-types funext -open import foundation.mere-equivalences funext -open import foundation.set-truncations funext +open import foundation.1-types +open import foundation.mere-equivalences +open import foundation.set-truncations open import foundation.universe-levels -open import univalent-combinatorics.main-classes-of-latin-hypercubes funext -open import univalent-combinatorics.pi-finite-types funext -open import univalent-combinatorics.standard-finite-types funext -open import univalent-combinatorics.untruncated-pi-finite-types funext +open import univalent-combinatorics.main-classes-of-latin-hypercubes +open import univalent-combinatorics.pi-finite-types +open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.untruncated-pi-finite-types ```
diff --git a/src/univalent-combinatorics/maybe.lagda.md b/src/univalent-combinatorics/maybe.lagda.md index 2d15938771..7ba870c33e 100644 --- a/src/univalent-combinatorics/maybe.lagda.md +++ b/src/univalent-combinatorics/maybe.lagda.md @@ -1,12 +1,7 @@ # The maybe monad on finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.maybe - (funext : function-extensionality) - where +module univalent-combinatorics.maybe where open import foundation-core.maybe public ``` @@ -18,8 +13,8 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/necklaces.lagda.md b/src/univalent-combinatorics/necklaces.lagda.md index e0e6cf6141..49abdc1f29 100644 --- a/src/univalent-combinatorics/necklaces.lagda.md +++ b/src/univalent-combinatorics/necklaces.lagda.md @@ -1,12 +1,7 @@ # Necklaces ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.necklaces - (funext : function-extensionality) - where +module univalent-combinatorics.necklaces where ```
Imports @@ -15,20 +10,19 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types open import foundation.structure-identity-principle open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms -open import univalent-combinatorics.cyclic-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.cyclic-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md index fdc2717588..bd5ea5ce14 100644 --- a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md +++ b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md @@ -3,71 +3,66 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.orientations-complete-undirected-graph - (funext : function-extensionality) - where +module univalent-combinatorics.orientations-complete-undirected-graph where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.congruence-natural-numbers funext -open import elementary-number-theory.distance-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext -open import elementary-number-theory.modular-arithmetic-standard-finite-types funext +open import elementary-number-theory.congruence-natural-numbers +open import elementary-number-theory.distance-natural-numbers +open import elementary-number-theory.inequality-natural-numbers +open import elementary-number-theory.modular-arithmetic-standard-finite-types open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers -open import finite-group-theory.transpositions funext +open import finite-group-theory.transpositions open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-equivalence-relations funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.coproduct-types +open import foundation.decidable-equivalence-relations +open import foundation.decidable-propositions +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalence-classes funext -open import foundation.equivalence-extensionality funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.intersections-subtypes funext -open import foundation.involutions funext -open import foundation.logical-equivalences funext -open import foundation.mere-equivalences funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalence-classes +open import foundation.equivalence-extensionality +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-extensionality-axiom +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-propositional-truncation +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.intersections-subtypes +open import foundation.involutions +open import foundation.logical-equivalences +open import foundation.mere-equivalences +open import foundation.negated-equality +open import foundation.negation +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.2-element-decidable-subtypes funext -open import univalent-combinatorics.2-element-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.decidable-subtypes funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext -open import univalent-combinatorics.symmetric-difference funext +open import univalent-combinatorics.2-element-decidable-subtypes +open import univalent-combinatorics.2-element-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.decidable-subtypes +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.symmetric-difference ```
diff --git a/src/univalent-combinatorics/orientations-cubes.lagda.md b/src/univalent-combinatorics/orientations-cubes.lagda.md index 86bcf7a0ee..9d6c029313 100644 --- a/src/univalent-combinatorics/orientations-cubes.lagda.md +++ b/src/univalent-combinatorics/orientations-cubes.lagda.md @@ -1,12 +1,7 @@ # Orientations of cubes ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.orientations-cubes - (funext : function-extensionality) - where +module univalent-combinatorics.orientations-cubes where ```
Imports @@ -14,16 +9,16 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.identity-types funext -open import foundation.iterating-functions funext +open import foundation.identity-types +open import foundation.iterating-functions open import foundation.universe-levels -open import univalent-combinatorics.cubes funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.function-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.cubes +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.function-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/partitions.lagda.md b/src/univalent-combinatorics/partitions.lagda.md index 582d042732..1d697a9f42 100644 --- a/src/univalent-combinatorics/partitions.lagda.md +++ b/src/univalent-combinatorics/partitions.lagda.md @@ -1,12 +1,7 @@ # Partitions of finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.partitions - (funext : function-extensionality) - where +module univalent-combinatorics.partitions where ```
Imports @@ -14,25 +9,25 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.binary-relations funext -open import foundation.cartesian-product-types funext +open import foundation.binary-relations +open import foundation.cartesian-product-types open import foundation.equality-cartesian-product-types -open import foundation.equivalence-extensionality funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.equivalence-extensionality +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.structure-identity-principle open import foundation.type-arithmetic-cartesian-product-types open import foundation.universe-levels -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/petri-nets.lagda.md b/src/univalent-combinatorics/petri-nets.lagda.md index ff80e0f343..0c3f656649 100644 --- a/src/univalent-combinatorics/petri-nets.lagda.md +++ b/src/univalent-combinatorics/petri-nets.lagda.md @@ -1,22 +1,17 @@ # Petri-nets ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.petri-nets - (funext : function-extensionality) - where +module univalent-combinatorics.petri-nets where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/pi-finite-types.lagda.md b/src/univalent-combinatorics/pi-finite-types.lagda.md index 7a5dad66d3..5632fede24 100644 --- a/src/univalent-combinatorics/pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/pi-finite-types.lagda.md @@ -1,12 +1,7 @@ # π-finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.pi-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.pi-finite-types where ```
Imports @@ -15,16 +10,16 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.set-truncations funext -open import foundation.truncated-types funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.set-truncations +open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.finitely-many-connected-components funext -open import univalent-combinatorics.untruncated-pi-finite-types funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finitely-many-connected-components +open import univalent-combinatorics.untruncated-pi-finite-types ```
diff --git a/src/univalent-combinatorics/pigeonhole-principle.lagda.md b/src/univalent-combinatorics/pigeonhole-principle.lagda.md index 4a2db4566c..8c52386070 100644 --- a/src/univalent-combinatorics/pigeonhole-principle.lagda.md +++ b/src/univalent-combinatorics/pigeonhole-principle.lagda.md @@ -1,44 +1,39 @@ # The pigeonhole principle ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.pigeonhole-principle - (funext : function-extensionality) - where +module univalent-combinatorics.pigeonhole-principle where ```
Imports ```agda -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.pairs-of-distinct-elements funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation +open import foundation.pairs-of-distinct-elements +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.embeddings-standard-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.repetitions-of-values funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.embeddings-standard-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.repetitions-of-values +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/quotients-finite-types.lagda.md b/src/univalent-combinatorics/quotients-finite-types.lagda.md index 9e537936a7..0566bd152d 100644 --- a/src/univalent-combinatorics/quotients-finite-types.lagda.md +++ b/src/univalent-combinatorics/quotients-finite-types.lagda.md @@ -1,12 +1,7 @@ # Quotients of finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.quotients-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.quotients-finite-types where ```
Imports @@ -15,10 +10,10 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.decidable-equivalence-relations funext -open import univalent-combinatorics.decidable-subtypes funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.image-of-maps funext +open import univalent-combinatorics.decidable-equivalence-relations +open import univalent-combinatorics.decidable-subtypes +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.image-of-maps ```
diff --git a/src/univalent-combinatorics/ramsey-theory.lagda.md b/src/univalent-combinatorics/ramsey-theory.lagda.md index 5bd7e24cab..c5e0cc22ff 100644 --- a/src/univalent-combinatorics/ramsey-theory.lagda.md +++ b/src/univalent-combinatorics/ramsey-theory.lagda.md @@ -1,12 +1,7 @@ # Ramsey theory ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.ramsey-theory - (funext : function-extensionality) - where +module univalent-combinatorics.ramsey-theory where ```
Imports @@ -15,14 +10,14 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.function-types +open import foundation.identity-types +open import foundation.propositions open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/repetitions-of-values.lagda.md b/src/univalent-combinatorics/repetitions-of-values.lagda.md index 4d8eaeb72a..49862e4292 100644 --- a/src/univalent-combinatorics/repetitions-of-values.lagda.md +++ b/src/univalent-combinatorics/repetitions-of-values.lagda.md @@ -1,34 +1,29 @@ # Repetitions of values ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.repetitions-of-values where -module - univalent-combinatorics.repetitions-of-values - (funext : function-extensionality) - where - -open import foundation.repetitions-of-values funext public +open import foundation.repetitions-of-values public ```
Imports ```agda open import elementary-number-theory.natural-numbers -open import elementary-number-theory.well-ordering-principle-standard-finite-types funext - -open import foundation.cartesian-product-types funext -open import foundation.decidable-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext - -open import univalent-combinatorics.decidable-dependent-function-types funext -open import univalent-combinatorics.decidable-propositions funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import elementary-number-theory.well-ordering-principle-standard-finite-types + +open import foundation.cartesian-product-types +open import foundation.decidable-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation + +open import univalent-combinatorics.decidable-dependent-function-types +open import univalent-combinatorics.decidable-propositions +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/retracts-of-finite-types.lagda.md b/src/univalent-combinatorics/retracts-of-finite-types.lagda.md index 9325219a95..d7b3d888e4 100644 --- a/src/univalent-combinatorics/retracts-of-finite-types.lagda.md +++ b/src/univalent-combinatorics/retracts-of-finite-types.lagda.md @@ -1,12 +1,7 @@ # Retracts of finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.retracts-of-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.retracts-of-finite-types where ```
Imports @@ -14,23 +9,23 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.decidable-embeddings funext -open import foundation.decidable-maps funext +open import foundation.decidable-embeddings +open import foundation.decidable-maps open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.fibers-of-maps funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.injective-maps funext -open import foundation.retractions funext -open import foundation.retracts-of-types funext +open import foundation.embeddings +open import foundation.fibers-of-maps +open import foundation.functoriality-propositional-truncation +open import foundation.injective-maps +open import foundation.retractions +open import foundation.retracts-of-types open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-decidable-subtypes -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-decidable-subtypes +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/riffle-shuffles.lagda.md b/src/univalent-combinatorics/riffle-shuffles.lagda.md index d90a493132..f4c76c4499 100644 --- a/src/univalent-combinatorics/riffle-shuffles.lagda.md +++ b/src/univalent-combinatorics/riffle-shuffles.lagda.md @@ -1,35 +1,30 @@ # Riffle shuffles ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.riffle-shuffles - (funext : function-extensionality) - where +module univalent-combinatorics.riffle-shuffles where ```
Imports ```agda open import elementary-number-theory.addition-natural-numbers -open import elementary-number-theory.inequality-standard-finite-types funext +open import elementary-number-theory.inequality-standard-finite-types open import elementary-number-theory.natural-numbers -open import foundation.automorphisms funext -open import foundation.conjunction funext +open import foundation.automorphisms +open import foundation.conjunction open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext +open import foundation.equivalences +open import foundation.function-types open import foundation.universe-levels open import foundation-core.coproduct-types open import foundation-core.propositions -open import order-theory.order-preserving-maps-posets funext -open import order-theory.posets funext +open import order-theory.order-preserving-maps-posets +open import order-theory.posets -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/sequences-finite-types.lagda.md b/src/univalent-combinatorics/sequences-finite-types.lagda.md index adf47ad2d2..e9cd8106af 100644 --- a/src/univalent-combinatorics/sequences-finite-types.lagda.md +++ b/src/univalent-combinatorics/sequences-finite-types.lagda.md @@ -1,41 +1,36 @@ # Sequences of elements in finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.sequences-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.sequences-finite-types where ```
Imports ```agda -open import elementary-number-theory.decidable-types funext +open import elementary-number-theory.decidable-types open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext -open import elementary-number-theory.well-ordering-principle-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers +open import elementary-number-theory.well-ordering-principle-natural-numbers open import foundation.action-on-identifications-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.pairs-of-distinct-elements funext -open import foundation.repetitions-of-values funext -open import foundation.repetitions-sequences funext +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.pairs-of-distinct-elements +open import foundation.repetitions-of-values +open import foundation.repetitions-sequences open import foundation.sequences -open import foundation.sets funext +open import foundation.sets open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.equality-standard-finite-types funext -open import univalent-combinatorics.pigeonhole-principle funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.equality-standard-finite-types +open import univalent-combinatorics.pigeonhole-principle +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md b/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md index 3f1c446949..afd05cac1d 100644 --- a/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md +++ b/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md @@ -3,37 +3,32 @@ ```agda {-# OPTIONS --lossy-unification #-} -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.set-quotients-of-index-two - (funext : function-extensionality) - where +module univalent-combinatorics.set-quotients-of-index-two where ```
Imports ```agda open import foundation.action-on-identifications-functions -open import foundation.commuting-squares-of-maps funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.commuting-squares-of-maps +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.functoriality-set-quotients funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.logical-equivalences funext -open import foundation.reflecting-maps-equivalence-relations funext -open import foundation.sets funext -open import foundation.universal-property-set-quotients funext +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.function-types +open import foundation.functoriality-set-quotients +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.logical-equivalences +open import foundation.reflecting-maps-equivalence-relations +open import foundation.sets +open import foundation.universal-property-set-quotients open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/sigma-decompositions.lagda.md b/src/univalent-combinatorics/sigma-decompositions.lagda.md index c66bdbea12..3fe2f92b9c 100644 --- a/src/univalent-combinatorics/sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/sigma-decompositions.lagda.md @@ -1,42 +1,37 @@ # Finite Σ-decompositions of finite types ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.sigma-decompositions where -module - univalent-combinatorics.sigma-decompositions - (funext : function-extensionality) - where - -open import foundation.sigma-decompositions funext public +open import foundation.sigma-decompositions public ```
Imports ```agda -open import foundation.cartesian-product-types funext -open import foundation.dependent-universal-property-equivalences funext -open import foundation.embeddings funext -open import foundation.equivalences funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.logical-equivalences funext -open import foundation.propositions funext -open import foundation.relaxed-sigma-decompositions funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.cartesian-product-types +open import foundation.dependent-universal-property-equivalences +open import foundation.embeddings +open import foundation.equivalences +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.logical-equivalences +open import foundation.propositions +open import foundation.relaxed-sigma-decompositions +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels -open import univalent-combinatorics.decidable-equivalence-relations funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.inhabited-finite-types funext -open import univalent-combinatorics.type-duality funext +open import univalent-combinatorics.decidable-equivalence-relations +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.inhabited-finite-types +open import univalent-combinatorics.type-duality ```
diff --git a/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md b/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md index ed8b0ed481..9cadf867c1 100644 --- a/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/skipping-element-standard-finite-types.lagda.md @@ -1,12 +1,7 @@ # Skipping elements in standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.skipping-element-standard-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.skipping-element-standard-finite-types where ```
Imports @@ -15,16 +10,16 @@ module open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.equality-coproduct-types funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.equality-coproduct-types +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.sets open import foundation.unit-type -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/small-types.lagda.md b/src/univalent-combinatorics/small-types.lagda.md index bc7632d841..3a8347ad4a 100644 --- a/src/univalent-combinatorics/small-types.lagda.md +++ b/src/univalent-combinatorics/small-types.lagda.md @@ -1,14 +1,9 @@ # Small types ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.small-types where -module - univalent-combinatorics.small-types - (funext : function-extensionality) - where - -open import foundation.small-types funext public +open import foundation.small-types public ```
Imports @@ -17,11 +12,11 @@ open import foundation.small-types funext public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.propositional-truncations funext +open import foundation.propositional-truncations open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md b/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md index 7dc802a3d5..b310a181ee 100644 --- a/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md +++ b/src/univalent-combinatorics/standard-finite-pruned-trees.lagda.md @@ -1,12 +1,7 @@ # Standard finite pruned trees ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.standard-finite-pruned-trees - (funext : function-extensionality) - where +module univalent-combinatorics.standard-finite-pruned-trees where ```
Imports @@ -16,7 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/standard-finite-trees.lagda.md b/src/univalent-combinatorics/standard-finite-trees.lagda.md index 30c5fc220a..9ef39e079f 100644 --- a/src/univalent-combinatorics/standard-finite-trees.lagda.md +++ b/src/univalent-combinatorics/standard-finite-trees.lagda.md @@ -1,28 +1,23 @@ # Standard finite trees ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.standard-finite-trees - (funext : function-extensionality) - where +module univalent-combinatorics.standard-finite-trees where ```
Imports ```agda -open import elementary-number-theory.maximum-natural-numbers funext +open import elementary-number-theory.maximum-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.sums-of-natural-numbers funext +open import elementary-number-theory.sums-of-natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.empty-types funext -open import foundation.identity-types funext +open import foundation.cartesian-product-types +open import foundation.empty-types +open import foundation.identity-types open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/standard-finite-types.lagda.md b/src/univalent-combinatorics/standard-finite-types.lagda.md index 830dbb9253..31d90d106c 100644 --- a/src/univalent-combinatorics/standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/standard-finite-types.lagda.md @@ -1,50 +1,45 @@ # The standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.standard-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.standard-finite-types where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext -open import elementary-number-theory.inequality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers +open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers -open import elementary-number-theory.strict-inequality-natural-numbers funext +open import elementary-number-theory.strict-inequality-natural-numbers -open import foundation.action-on-higher-identifications-functions funext +open import foundation.action-on-higher-identifications-functions open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-types funext +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equality-coproduct-types funext -open import foundation.equivalence-injective-type-families funext -open import foundation.equivalences funext -open import foundation.equivalences funext-maybe -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.injective-maps funext -open import foundation.negated-equality funext -open import foundation.negation funext -open import foundation.noncontractible-types funext -open import foundation.preunivalent-type-families funext -open import foundation.raising-universe-levels funext -open import foundation.retractions funext -open import foundation.sets funext +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equality-coproduct-types +open import foundation.equivalence-injective-type-families +open import foundation.equivalences +open import foundation.equivalences-maybe +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.injective-maps +open import foundation.negated-equality +open import foundation.negation +open import foundation.noncontractible-types +open import foundation.preunivalent-type-families +open import foundation.raising-universe-levels +open import foundation.retractions +open import foundation.sets open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import structured-types.types-equipped-with-endomorphisms funext +open import structured-types.types-equipped-with-endomorphisms ```
diff --git a/src/univalent-combinatorics/steiner-systems.lagda.md b/src/univalent-combinatorics/steiner-systems.lagda.md index 750c1417a8..5c3a9d87d2 100644 --- a/src/univalent-combinatorics/steiner-systems.lagda.md +++ b/src/univalent-combinatorics/steiner-systems.lagda.md @@ -1,12 +1,7 @@ # Steiner systems ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.steiner-systems - (funext : function-extensionality) - where +module univalent-combinatorics.steiner-systems where ```
Imports @@ -14,12 +9,12 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.contractible-types funext -open import foundation.decidable-subtypes funext +open import foundation.contractible-types +open import foundation.decidable-subtypes open import foundation.dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/steiner-triple-systems.lagda.md b/src/univalent-combinatorics/steiner-triple-systems.lagda.md index f49d924235..2ac3dd0658 100644 --- a/src/univalent-combinatorics/steiner-triple-systems.lagda.md +++ b/src/univalent-combinatorics/steiner-triple-systems.lagda.md @@ -1,12 +1,7 @@ # Steiner triple systems ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.steiner-triple-systems - (funext : function-extensionality) - where +module univalent-combinatorics.steiner-triple-systems where ```
Imports @@ -16,7 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.universe-levels -open import univalent-combinatorics.steiner-systems funext +open import univalent-combinatorics.steiner-systems ```
diff --git a/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md b/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md index 7808ac541f..6fff4532d6 100644 --- a/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md +++ b/src/univalent-combinatorics/sums-of-natural-numbers.lagda.md @@ -1,14 +1,9 @@ # Combinatorial identities of sums of natural numbers ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.sums-of-natural-numbers where -module - univalent-combinatorics.sums-of-natural-numbers - (funext : function-extensionality) - where - -open import elementary-number-theory.sums-of-natural-numbers funext public +open import elementary-number-theory.sums-of-natural-numbers public ```
Imports @@ -17,14 +12,14 @@ open import elementary-number-theory.sums-of-natural-numbers funext public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-dependent-pair-types -open import univalent-combinatorics.double-counting funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-dependent-pair-types +open import univalent-combinatorics.double-counting +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/surjective-maps.lagda.md b/src/univalent-combinatorics/surjective-maps.lagda.md index 2ccd55ee6c..2ebd5851c5 100644 --- a/src/univalent-combinatorics/surjective-maps.lagda.md +++ b/src/univalent-combinatorics/surjective-maps.lagda.md @@ -1,14 +1,9 @@ # Surjective maps between finite types ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.surjective-maps where -module - univalent-combinatorics.surjective-maps - (funext : function-extensionality) - where - -open import foundation.surjective-maps funext public +open import foundation.surjective-maps public ```
Imports @@ -16,26 +11,26 @@ open import foundation.surjective-maps funext public ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.decidable-embeddings funext -open import foundation.decidable-equality funext -open import foundation.decidable-types funext +open import foundation.cartesian-product-types +open import foundation.decidable-embeddings +open import foundation.decidable-equality +open import foundation.decidable-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.logical-equivalences funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext +open import foundation.equivalences +open import foundation.logical-equivalences +open import foundation.propositional-truncations +open import foundation.propositions open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-decidable-subtypes -open import univalent-combinatorics.counting-dependent-pair-types funext -open import univalent-combinatorics.decidable-dependent-function-types funext -open import univalent-combinatorics.embeddings funext -open import univalent-combinatorics.fibers-of-maps funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-decidable-subtypes +open import univalent-combinatorics.counting-dependent-pair-types +open import univalent-combinatorics.decidable-dependent-function-types +open import univalent-combinatorics.embeddings +open import univalent-combinatorics.fibers-of-maps +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/symmetric-difference.lagda.md b/src/univalent-combinatorics/symmetric-difference.lagda.md index 668a97902e..1a75f29a9a 100644 --- a/src/univalent-combinatorics/symmetric-difference.lagda.md +++ b/src/univalent-combinatorics/symmetric-difference.lagda.md @@ -1,14 +1,9 @@ # Symmetric difference of finite subtypes ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.symmetric-difference where -module - univalent-combinatorics.symmetric-difference - (funext : function-extensionality) - where - -open import foundation.symmetric-difference funext public +open import foundation.symmetric-difference public ```
Imports @@ -19,18 +14,18 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.identity-types funext -open import foundation.intersections-subtypes funext -open import foundation.mere-equivalences funext -open import foundation.propositional-truncations funext +open import foundation.equivalences +open import foundation.identity-types +open import foundation.intersections-subtypes +open import foundation.mere-equivalences +open import foundation.propositional-truncations open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.decidable-subtypes funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.decidable-subtypes +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md index 7be0c392ba..5816c35f0e 100644 --- a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md @@ -1,30 +1,25 @@ # Finite trivial Σ-decompositions ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.trivial-sigma-decompositions where -module - univalent-combinatorics.trivial-sigma-decompositions - (funext : function-extensionality) - where - -open import foundation.trivial-sigma-decompositions funext public +open import foundation.trivial-sigma-decompositions public ```
Imports ```agda -open import foundation.contractible-types funext +open import foundation.contractible-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.inhabited-types funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.subtypes funext +open import foundation.identity-types +open import foundation.inhabited-types +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.subtypes open import foundation.universe-levels -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.sigma-decompositions funext +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.sigma-decompositions ```
diff --git a/src/univalent-combinatorics/type-duality.lagda.md b/src/univalent-combinatorics/type-duality.lagda.md index 2caecdc9f2..fc008806c9 100644 --- a/src/univalent-combinatorics/type-duality.lagda.md +++ b/src/univalent-combinatorics/type-duality.lagda.md @@ -1,39 +1,34 @@ # Type duality of finite types ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.type-duality where -module - univalent-combinatorics.type-duality - (funext : function-extensionality) - where - -open import foundation.type-duality funext public +open import foundation.type-duality public ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.full-subtypes funext -open import foundation.functoriality-dependent-function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.inhabited-types funext -open import foundation.postcomposition-functions funext -open import foundation.propositions funext -open import foundation.structure funext -open import foundation.structure funextd-type-duality -open import foundation.surjective-maps funext +open import foundation.equivalences +open import foundation.full-subtypes +open import foundation.functoriality-dependent-function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.inhabited-types +open import foundation.postcomposition-functions +open import foundation.propositions +open import foundation.structure +open import foundation.structured-type-duality +open import foundation.surjective-maps open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-dependent-pair-types -open import foundation.type-theoretic-principle-of-choice funext +open import foundation.type-theoretic-principle-of-choice open import foundation.universe-levels -open import univalent-combinatorics.fibers-of-maps funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.inhabited-finite-types funext +open import univalent-combinatorics.fibers-of-maps +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.inhabited-finite-types ```
diff --git a/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md b/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md index 9df90df19e..f4335a963a 100644 --- a/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.unbounded-pi-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.unbounded-pi-finite-types where ```
Imports @@ -16,30 +11,30 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.empty-types funext -open import foundation.equality-coproduct-types funext -open import foundation.equivalences funext -open import foundation.function-types funext -open import foundation.identity-types funext -open import foundation.maybe funext -open import foundation.retracts-of-types funext -open import foundation.set-truncations funext -open import foundation.sets funext +open import foundation.empty-types +open import foundation.equality-coproduct-types +open import foundation.equivalences +open import foundation.function-types +open import foundation.identity-types +open import foundation.maybe +open import foundation.retracts-of-types +open import foundation.set-truncations +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.finitely-many-connected-components funext -open import univalent-combinatorics.function-types funext -open import univalent-combinatorics.pi-finite-types funext -open import univalent-combinatorics.standard-finite-types funext -open import univalent-combinatorics.untruncated-pi-finite-types funext +open import univalent-combinatorics.counting +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finitely-many-connected-components +open import univalent-combinatorics.function-types +open import univalent-combinatorics.pi-finite-types +open import univalent-combinatorics.standard-finite-types +open import univalent-combinatorics.untruncated-pi-finite-types ```
diff --git a/src/univalent-combinatorics/unions-subtypes.lagda.md b/src/univalent-combinatorics/unions-subtypes.lagda.md index 7a655035e7..9649925534 100644 --- a/src/univalent-combinatorics/unions-subtypes.lagda.md +++ b/src/univalent-combinatorics/unions-subtypes.lagda.md @@ -1,30 +1,25 @@ # Unions of finite subtypes ```agda -open import foundation.function-extensionality-axiom +module univalent-combinatorics.unions-subtypes where -module - univalent-combinatorics.unions-subtypes - (funext : function-extensionality) - where - -open import foundation.unions-subtypes funext public +open import foundation.unions-subtypes public ```
Imports ```agda -open import foundation.decidable-equality funext -open import foundation.propositional-truncations funext -open import foundation.subtypes funext +open import foundation.decidable-equality +open import foundation.propositional-truncations +open import foundation.subtypes open import foundation.universe-levels -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.counting funext-decidable-subtypes -open import univalent-combinatorics.counting-dependent-pair-types funext -open import univalent-combinatorics.embeddings funext -open import univalent-combinatorics.finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.counting-decidable-subtypes +open import univalent-combinatorics.counting-dependent-pair-types +open import univalent-combinatorics.embeddings +open import univalent-combinatorics.finite-types ```
diff --git a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md index 84710f4720..707c60a123 100644 --- a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md @@ -1,12 +1,7 @@ # The universal property of the standard finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.universal-property-standard-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.universal-property-standard-finite-types where ```
Imports @@ -14,25 +9,24 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext -open import foundation.contractible-types funext -open import foundation.coproduct-types funext +open import foundation.cartesian-product-types +open import foundation.contractible-types +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-cartesian-product-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-cartesian-product-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type -open import foundation.universal-property-contractible-types funext -open import foundation.universal-property-empty-type funext -open import foundation.universal-property-maybe funext +open import foundation.universal-property-contractible-types +open import foundation.universal-property-empty-type +open import foundation.universal-property-maybe open import foundation.universe-levels -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md index 5bf89ff1f4..63f9ba773a 100644 --- a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md @@ -1,12 +1,7 @@ # Untruncated π-finite types ```agda -open import foundation.function-extensionality-axiom - -module - univalent-combinatorics.untruncated-pi-finite-types - (funext : function-extensionality) - where +module univalent-combinatorics.untruncated-pi-finite-types where ```
Imports @@ -14,55 +9,54 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.0-connected-types funext +open import foundation.0-connected-types open import foundation.action-on-identifications-functions -open import foundation.contractible-types funext -open import foundation.coproduct-types funext -open import foundation.decidable-propositions funext -open import foundation.decidable-types funext -open import foundation.dependent-identifications funext -open import foundation.embeddings funext -open import foundation.empty-types funext -open import foundation.equality-coproduct-types funext -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.fiber-inclusions funext -open import foundation.function-extensionality funext - -open import foundation.function-types funext -open import foundation.functoriality-dependent-pair-types funext -open import foundation.functoriality-set-truncation funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.logical-equivalences funext -open import foundation.maybe funext -open import foundation.mere-equality funext -open import foundation.propositional-extensionality funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.retracts-of-types funext -open import foundation.set-presented-types funext -open import foundation.set-truncations funext -open import foundation.sets funext -open import foundation.subtypes funext -open import foundation.surjective-maps funext +open import foundation.contractible-types +open import foundation.coproduct-types +open import foundation.decidable-propositions +open import foundation.decidable-types +open import foundation.dependent-identifications +open import foundation.embeddings +open import foundation.empty-types +open import foundation.equality-coproduct-types +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.fiber-inclusions +open import foundation.function-extensionality +open import foundation.function-types +open import foundation.functoriality-dependent-pair-types +open import foundation.functoriality-set-truncation +open import foundation.homotopies +open import foundation.identity-types +open import foundation.logical-equivalences +open import foundation.maybe +open import foundation.mere-equality +open import foundation.propositional-extensionality +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.retracts-of-types +open import foundation.set-presented-types +open import foundation.set-truncations +open import foundation.sets +open import foundation.subtypes +open import foundation.surjective-maps open import foundation.transport-along-identifications -open import foundation.type-arithmetic-coproduct-types funext +open import foundation.type-arithmetic-coproduct-types open import foundation.unit-type -open import foundation.univalence funext +open import foundation.univalence open import foundation.universe-levels open import foundation.whiskering-homotopies-composition -open import univalent-combinatorics.coproduct-types funext -open import univalent-combinatorics.counting funext -open import univalent-combinatorics.dependent-pair-types funext -open import univalent-combinatorics.equality-finite-types funext -open import univalent-combinatorics.finite-types funext -open import univalent-combinatorics.finitely-many-connected-components funext -open import univalent-combinatorics.finitely-presented-types funext -open import univalent-combinatorics.function-types funext -open import univalent-combinatorics.image-of-maps funext -open import univalent-combinatorics.standard-finite-types funext +open import univalent-combinatorics.coproduct-types +open import univalent-combinatorics.counting +open import univalent-combinatorics.dependent-pair-types +open import univalent-combinatorics.equality-finite-types +open import univalent-combinatorics.finite-types +open import univalent-combinatorics.finitely-many-connected-components +open import univalent-combinatorics.finitely-presented-types +open import univalent-combinatorics.function-types +open import univalent-combinatorics.image-of-maps +open import univalent-combinatorics.standard-finite-types ```
diff --git a/src/universal-algebra.lagda.md b/src/universal-algebra.lagda.md index 7cebf27d63..183927520e 100644 --- a/src/universal-algebra.lagda.md +++ b/src/universal-algebra.lagda.md @@ -3,22 +3,17 @@ ## Modules in the universal algebra namespace ```agda -open import foundation.function-extensionality-axiom +module universal-algebra where -module - universal-algebra - (funext : function-extensionality) - where - -open import universal-algebra.abstract-equations-over-signatures funext public -open import universal-algebra.algebraic-theories funext public -open import universal-algebra.algebraic-theory-of-groups funext public -open import universal-algebra.algebras-of-theories funext public -open import universal-algebra.congruences funext public -open import universal-algebra.homomorphisms-of-algebras funext public -open import universal-algebra.kernels funext public -open import universal-algebra.models-of-signatures funext public -open import universal-algebra.quotient-algebras funext public -open import universal-algebra.signatures funext public -open import universal-algebra.terms-over-signatures funext public +open import universal-algebra.abstract-equations-over-signatures public +open import universal-algebra.algebraic-theories public +open import universal-algebra.algebraic-theory-of-groups public +open import universal-algebra.algebras-of-theories public +open import universal-algebra.congruences public +open import universal-algebra.homomorphisms-of-algebras public +open import universal-algebra.kernels public +open import universal-algebra.models-of-signatures public +open import universal-algebra.quotient-algebras public +open import universal-algebra.signatures public +open import universal-algebra.terms-over-signatures public ``` diff --git a/src/universal-algebra/abstract-equations-over-signatures.lagda.md b/src/universal-algebra/abstract-equations-over-signatures.lagda.md index 770bb41412..836403a525 100644 --- a/src/universal-algebra/abstract-equations-over-signatures.lagda.md +++ b/src/universal-algebra/abstract-equations-over-signatures.lagda.md @@ -1,23 +1,18 @@ # Abstract equations over signatures ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.abstract-equations-over-signatures - (funext : function-extensionality) - where +module universal-algebra.abstract-equations-over-signatures where ```
Imports ```agda -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types open import foundation.universe-levels -open import universal-algebra.signatures funext -open import universal-algebra.terms-over-signatures funext +open import universal-algebra.signatures +open import universal-algebra.terms-over-signatures ```
diff --git a/src/universal-algebra/algebraic-theories.lagda.md b/src/universal-algebra/algebraic-theories.lagda.md index 4b2d3d6ee8..bff4ee1bee 100644 --- a/src/universal-algebra/algebraic-theories.lagda.md +++ b/src/universal-algebra/algebraic-theories.lagda.md @@ -1,12 +1,7 @@ # Algebraic theories ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.algebraic-theories - (funext : function-extensionality) - where +module universal-algebra.algebraic-theories where ```
Imports @@ -15,8 +10,8 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import universal-algebra.abstract-equations-over-signatures funext -open import universal-algebra.signatures funext +open import universal-algebra.abstract-equations-over-signatures +open import universal-algebra.signatures ```
diff --git a/src/universal-algebra/algebraic-theory-of-groups.lagda.md b/src/universal-algebra/algebraic-theory-of-groups.lagda.md index 72922812fe..719d008255 100644 --- a/src/universal-algebra/algebraic-theory-of-groups.lagda.md +++ b/src/universal-algebra/algebraic-theory-of-groups.lagda.md @@ -1,12 +1,7 @@ # Algebraic theory of groups ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.algebraic-theory-of-groups - (funext : function-extensionality) - where +module universal-algebra.algebraic-theory-of-groups where ```
Imports @@ -15,22 +10,21 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equality-dependent-pair-types funext -open import foundation.equivalences funext -open import foundation.function-extensionality funext - -open import foundation.identity-types funext -open import foundation.propositions funext +open import foundation.equality-dependent-pair-types +open import foundation.equivalences +open import foundation.function-extensionality +open import foundation.identity-types +open import foundation.propositions open import foundation.universe-levels -open import group-theory.groups funext +open import group-theory.groups -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import universal-algebra.algebraic-theories funext -open import universal-algebra.algebras-of-theories funext -open import universal-algebra.signatures funext -open import universal-algebra.terms-over-signatures funext +open import universal-algebra.algebraic-theories +open import universal-algebra.algebras-of-theories +open import universal-algebra.signatures +open import universal-algebra.terms-over-signatures ```
diff --git a/src/universal-algebra/algebras-of-theories.lagda.md b/src/universal-algebra/algebras-of-theories.lagda.md index 26d2ae744a..3ae5fa65d3 100644 --- a/src/universal-algebra/algebras-of-theories.lagda.md +++ b/src/universal-algebra/algebras-of-theories.lagda.md @@ -1,28 +1,23 @@ # Algebras ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.algebras-of-theories - (funext : function-extensionality) - where +module universal-algebra.algebras-of-theories where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.propositions funext -open import foundation.sets funext +open import foundation.identity-types +open import foundation.propositions +open import foundation.sets open import foundation.universe-levels -open import universal-algebra.abstract-equations-over-signatures funext -open import universal-algebra.algebraic-theories funext -open import universal-algebra.models-of-signatures funext -open import universal-algebra.signatures funext -open import universal-algebra.terms-over-signatures funext +open import universal-algebra.abstract-equations-over-signatures +open import universal-algebra.algebraic-theories +open import universal-algebra.models-of-signatures +open import universal-algebra.signatures +open import universal-algebra.terms-over-signatures ```
diff --git a/src/universal-algebra/congruences.lagda.md b/src/universal-algebra/congruences.lagda.md index 3c4752f535..d8951087da 100644 --- a/src/universal-algebra/congruences.lagda.md +++ b/src/universal-algebra/congruences.lagda.md @@ -1,12 +1,7 @@ # Congruences ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.congruences - (funext : function-extensionality) - where +module universal-algebra.congruences where ```
Imports @@ -14,19 +9,19 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.equivalence-relations +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import universal-algebra.algebraic-theories funext -open import universal-algebra.algebras-of-theories funext -open import universal-algebra.signatures funext +open import universal-algebra.algebraic-theories +open import universal-algebra.algebras-of-theories +open import universal-algebra.signatures ```
diff --git a/src/universal-algebra/homomorphisms-of-algebras.lagda.md b/src/universal-algebra/homomorphisms-of-algebras.lagda.md index 5022e0770a..f8c7ad948a 100644 --- a/src/universal-algebra/homomorphisms-of-algebras.lagda.md +++ b/src/universal-algebra/homomorphisms-of-algebras.lagda.md @@ -1,27 +1,22 @@ # Homomorphisms of algebras ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.homomorphisms-of-algebras - (funext : function-extensionality) - where +module universal-algebra.homomorphisms-of-algebras where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.identity-types funext +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors -open import universal-algebra.algebraic-theories funext -open import universal-algebra.algebras-of-theories funext -open import universal-algebra.signatures funext +open import universal-algebra.algebraic-theories +open import universal-algebra.algebras-of-theories +open import universal-algebra.signatures ```
diff --git a/src/universal-algebra/kernels.lagda.md b/src/universal-algebra/kernels.lagda.md index 1244c039df..e8c0fe6128 100644 --- a/src/universal-algebra/kernels.lagda.md +++ b/src/universal-algebra/kernels.lagda.md @@ -1,12 +1,7 @@ # Kernels of homomorphisms of algebras ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.kernels - (funext : function-extensionality) - where +module universal-algebra.kernels where ```
Imports @@ -16,20 +11,20 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions -open import foundation.binary-relations funext +open import foundation.binary-relations open import foundation.dependent-pair-types -open import foundation.equivalence-relations funext -open import foundation.identity-types funext +open import foundation.equivalence-relations +open import foundation.identity-types open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors -open import universal-algebra.algebraic-theories funext -open import universal-algebra.algebras-of-theories funext -open import universal-algebra.congruences funext -open import universal-algebra.homomorphisms-of-algebras funext -open import universal-algebra.signatures funext +open import universal-algebra.algebraic-theories +open import universal-algebra.algebras-of-theories +open import universal-algebra.congruences +open import universal-algebra.homomorphisms-of-algebras +open import universal-algebra.signatures ```
diff --git a/src/universal-algebra/models-of-signatures.lagda.md b/src/universal-algebra/models-of-signatures.lagda.md index 913e6b9245..18b796de52 100644 --- a/src/universal-algebra/models-of-signatures.lagda.md +++ b/src/universal-algebra/models-of-signatures.lagda.md @@ -1,24 +1,19 @@ # Models of signatures ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.models-of-signatures - (funext : function-extensionality) - where +module universal-algebra.models-of-signatures where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.sets funext +open import foundation.sets open import foundation.universe-levels -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import universal-algebra.signatures funext +open import universal-algebra.signatures ```
diff --git a/src/universal-algebra/quotient-algebras.lagda.md b/src/universal-algebra/quotient-algebras.lagda.md index 80538a4370..94bfede7ee 100644 --- a/src/universal-algebra/quotient-algebras.lagda.md +++ b/src/universal-algebra/quotient-algebras.lagda.md @@ -1,12 +1,7 @@ # Quotient algebras ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.quotient-algebras - (funext : function-extensionality) - where +module universal-algebra.quotient-algebras where ```
Imports @@ -15,28 +10,28 @@ module open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types -open import foundation.equivalence-classes funext -open import foundation.equivalence-relations funext -open import foundation.equivalences funext -open import foundation.functoriality-propositional-truncation funext -open import foundation.multivariable-functoriality-set-quotients funext -open import foundation.multivariable-operations funext -open import foundation.propositional-truncations funext -open import foundation.propositions funext -open import foundation.raising-universe-levels-unit-type funext -open import foundation.set-quotients funext -open import foundation.sets funext +open import foundation.equivalence-classes +open import foundation.equivalence-relations +open import foundation.equivalences +open import foundation.functoriality-propositional-truncation +open import foundation.multivariable-functoriality-set-quotients +open import foundation.multivariable-operations +open import foundation.propositional-truncations +open import foundation.propositions +open import foundation.raising-universe-levels-unit-type +open import foundation.set-quotients +open import foundation.sets open import foundation.unit-type open import foundation.universe-levels -open import foundation.vectors-set-quotients funext +open import foundation.vectors-set-quotients -open import linear-algebra.vectors funext +open import linear-algebra.vectors -open import universal-algebra.algebraic-theories funext -open import universal-algebra.algebras-of-theories funext -open import universal-algebra.congruences funext -open import universal-algebra.models-of-signatures funext -open import universal-algebra.signatures funext +open import universal-algebra.algebraic-theories +open import universal-algebra.algebras-of-theories +open import universal-algebra.congruences +open import universal-algebra.models-of-signatures +open import universal-algebra.signatures ```
diff --git a/src/universal-algebra/signatures.lagda.md b/src/universal-algebra/signatures.lagda.md index b8ab455575..e5b118ac6b 100644 --- a/src/universal-algebra/signatures.lagda.md +++ b/src/universal-algebra/signatures.lagda.md @@ -1,12 +1,7 @@ # Signatures ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.signatures - (funext : function-extensionality) - where +module universal-algebra.signatures where ```
Imports @@ -14,10 +9,10 @@ module ```agda open import elementary-number-theory.natural-numbers -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.embeddings funext -open import foundation.identity-types funext +open import foundation.embeddings +open import foundation.identity-types open import foundation.universe-levels ``` diff --git a/src/universal-algebra/terms-over-signatures.lagda.md b/src/universal-algebra/terms-over-signatures.lagda.md index eb6177ad78..6ecf7d9351 100644 --- a/src/universal-algebra/terms-over-signatures.lagda.md +++ b/src/universal-algebra/terms-over-signatures.lagda.md @@ -1,37 +1,32 @@ # Terms over signatures ```agda -open import foundation.function-extensionality-axiom - -module - universal-algebra.terms-over-signatures - (funext : function-extensionality) - where +module universal-algebra.terms-over-signatures where ```
Imports ```agda -open import elementary-number-theory.equality-natural-numbers funext +open import elementary-number-theory.equality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions -open import foundation.coproduct-types funext +open import foundation.coproduct-types open import foundation.dependent-pair-types -open import foundation.identity-types funext -open import foundation.raising-universe-levels-unit-type funext +open import foundation.identity-types +open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels -open import linear-algebra.functoriality-vectors funext -open import linear-algebra.vectors funext +open import linear-algebra.functoriality-vectors +open import linear-algebra.vectors open import lists.lists -open import lists.lists-discrete-types funext +open import lists.lists-discrete-types -open import universal-algebra.models-of-signatures funext -open import universal-algebra.signatures funext +open import universal-algebra.models-of-signatures +open import universal-algebra.signatures ```
diff --git a/src/wild-category-theory.lagda.md b/src/wild-category-theory.lagda.md index f1ba794c86..72cf1254d2 100644 --- a/src/wild-category-theory.lagda.md +++ b/src/wild-category-theory.lagda.md @@ -11,19 +11,14 @@ ## Modules in the wild category theory namespace ```agda -open import foundation.function-extensionality-axiom +module wild-category-theory where -module - wild-category-theory - (funext : function-extensionality) - where - -open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories funext public -open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories funext public -open import wild-category-theory.colax-functors-noncoherent-large-omega-precategories funext public -open import wild-category-theory.colax-functors-noncoherent-omega-precategories funext public -open import wild-category-theory.maps-noncoherent-large-omega-precategories funext public -open import wild-category-theory.maps-noncoherent-omega-precategories funext public -open import wild-category-theory.noncoherent-large-omega-precategories funext public -open import wild-category-theory.noncoherent-omega-precategories funext public +open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories public +open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories public +open import wild-category-theory.colax-functors-noncoherent-large-omega-precategories public +open import wild-category-theory.colax-functors-noncoherent-omega-precategories public +open import wild-category-theory.maps-noncoherent-large-omega-precategories public +open import wild-category-theory.maps-noncoherent-omega-precategories public +open import wild-category-theory.noncoherent-large-omega-precategories public +open import wild-category-theory.noncoherent-omega-precategories public ``` diff --git a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md index fa0ef4498c..303c5653ac 100644 --- a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-large-omega-precategories.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories - (funext : function-extensionality) - where +module wild-category-theory.coinductive-isomorphisms-in-noncoherent-large-omega-precategories where ```
Imports @@ -17,8 +12,8 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories funext -open import wild-category-theory.noncoherent-large-omega-precategories funext +open import wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories +open import wild-category-theory.noncoherent-large-omega-precategories ```
diff --git a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md index bb5d2d6d5d..c2494822ea 100644 --- a/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/coinductive-isomorphisms-in-noncoherent-omega-precategories.lagda.md @@ -3,12 +3,7 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories - (funext : function-extensionality) - where +module wild-category-theory.coinductive-isomorphisms-in-noncoherent-omega-precategories where ```
Imports @@ -17,7 +12,7 @@ module open import foundation.dependent-pair-types open import foundation.universe-levels -open import wild-category-theory.noncoherent-omega-precategories funext +open import wild-category-theory.noncoherent-omega-precategories ```
diff --git a/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md index ffa76f6cfd..714375f4a2 100644 --- a/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/colax-functors-noncoherent-large-omega-precategories.lagda.md @@ -3,33 +3,28 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - wild-category-theory.colax-functors-noncoherent-large-omega-precategories - (funext : function-extensionality) - where +module wild-category-theory.colax-functors-noncoherent-large-omega-precategories where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types -open import globular-types.large-colax-reflexive-globular-maps funext -open import globular-types.large-colax-transitive-globular-maps funext -open import globular-types.large-globular-maps funext - -open import wild-category-theory.colax-functors-noncoherent-omega-precategories funext -open import wild-category-theory.maps-noncoherent-large-omega-precategories funext -open import wild-category-theory.maps-noncoherent-omega-precategories funext -open import wild-category-theory.noncoherent-large-omega-precategories funext -open import wild-category-theory.noncoherent-omega-precategories funext +open import globular-types.large-colax-reflexive-globular-maps +open import globular-types.large-colax-transitive-globular-maps +open import globular-types.large-globular-maps + +open import wild-category-theory.colax-functors-noncoherent-omega-precategories +open import wild-category-theory.maps-noncoherent-large-omega-precategories +open import wild-category-theory.maps-noncoherent-omega-precategories +open import wild-category-theory.noncoherent-large-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories ```
diff --git a/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md index 8f8081b6d4..8bb9dc1251 100644 --- a/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/colax-functors-noncoherent-omega-precategories.lagda.md @@ -3,30 +3,25 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - wild-category-theory.colax-functors-noncoherent-omega-precategories - (funext : function-extensionality) - where +module wild-category-theory.colax-functors-noncoherent-omega-precategories where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.colax-reflexive-globular-maps funext -open import globular-types.colax-transitive-globular-maps funext -open import globular-types.globular-maps funext +open import globular-types.colax-reflexive-globular-maps +open import globular-types.colax-transitive-globular-maps +open import globular-types.globular-maps open import globular-types.globular-types -open import globular-types.reflexive-globular-types funext +open import globular-types.reflexive-globular-types -open import wild-category-theory.maps-noncoherent-omega-precategories funext -open import wild-category-theory.noncoherent-omega-precategories funext +open import wild-category-theory.maps-noncoherent-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories ```
diff --git a/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md index 780d53ef40..e7adea0a47 100644 --- a/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/maps-noncoherent-large-omega-precategories.lagda.md @@ -3,30 +3,25 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - wild-category-theory.maps-noncoherent-large-omega-precategories - (funext : function-extensionality) - where +module wild-category-theory.maps-noncoherent-large-omega-precategories where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types -open import globular-types.large-globular-maps funext +open import globular-types.large-globular-maps open import globular-types.large-globular-types -open import wild-category-theory.maps-noncoherent-omega-precategories funext -open import wild-category-theory.noncoherent-large-omega-precategories funext -open import wild-category-theory.noncoherent-omega-precategories funext +open import wild-category-theory.maps-noncoherent-omega-precategories +open import wild-category-theory.noncoherent-large-omega-precategories +open import wild-category-theory.noncoherent-omega-precategories ```
diff --git a/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md index 7a97c32298..2573be3c1a 100644 --- a/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/maps-noncoherent-omega-precategories.lagda.md @@ -3,26 +3,21 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - wild-category-theory.maps-noncoherent-omega-precategories - (funext : function-extensionality) - where +module wild-category-theory.maps-noncoherent-omega-precategories where ```
Imports ```agda open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.identity-types funext +open import foundation.function-types +open import foundation.identity-types open import foundation.universe-levels -open import globular-types.globular-maps funext +open import globular-types.globular-maps open import globular-types.globular-types -open import wild-category-theory.noncoherent-omega-precategories funext +open import wild-category-theory.noncoherent-omega-precategories ```
diff --git a/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md b/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md index 931351bc8d..d40fa26fd8 100644 --- a/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md +++ b/src/wild-category-theory/noncoherent-large-omega-precategories.lagda.md @@ -3,36 +3,31 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - wild-category-theory.noncoherent-large-omega-precategories - (funext : function-extensionality) - where +module wild-category-theory.noncoherent-large-omega-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.action-on-identifications-binary-functions open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels open import globular-types.globular-types open import globular-types.large-globular-types -open import globular-types.large-reflexive-globular-types funext -open import globular-types.large-transitive-globular-types funext -open import globular-types.reflexive-globular-types funext -open import globular-types.transitive-globular-types funext +open import globular-types.large-reflexive-globular-types +open import globular-types.large-transitive-globular-types +open import globular-types.reflexive-globular-types +open import globular-types.transitive-globular-types -open import wild-category-theory.noncoherent-omega-precategories funext +open import wild-category-theory.noncoherent-omega-precategories ```
diff --git a/src/wild-category-theory/noncoherent-omega-precategories.lagda.md b/src/wild-category-theory/noncoherent-omega-precategories.lagda.md index 3546a35dc9..648d1f464f 100644 --- a/src/wild-category-theory/noncoherent-omega-precategories.lagda.md +++ b/src/wild-category-theory/noncoherent-omega-precategories.lagda.md @@ -3,32 +3,27 @@ ```agda {-# OPTIONS --guardedness #-} -open import foundation.function-extensionality-axiom - -module - wild-category-theory.noncoherent-omega-precategories - (funext : function-extensionality) - where +module wild-category-theory.noncoherent-omega-precategories where ```
Imports ```agda -open import category-theory.precategories funext +open import category-theory.precategories open import foundation.action-on-identifications-binary-functions -open import foundation.cartesian-product-types funext +open import foundation.cartesian-product-types open import foundation.dependent-pair-types -open import foundation.function-types funext -open import foundation.homotopies funext -open import foundation.identity-types funext -open import foundation.sets funext -open import foundation.strictly-involutive-identity-types funext +open import foundation.function-types +open import foundation.homotopies +open import foundation.identity-types +open import foundation.sets +open import foundation.strictly-involutive-identity-types open import foundation.universe-levels open import globular-types.globular-types -open import globular-types.reflexive-globular-types funext -open import globular-types.transitive-globular-types funext +open import globular-types.reflexive-globular-types +open import globular-types.transitive-globular-types ```
From 77f4142c58e493717ea6760065f8bbce575cbe4e Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Fri, 21 Mar 2025 11:55:24 +0000 Subject: [PATCH 30/39] fix line length --- .../divisibility-natural-numbers.lagda.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md index a7879e5365..9687ed176c 100644 --- a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md +++ b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md @@ -117,7 +117,9 @@ eq-quotient-div-eq-div-ℕ x y z n e H I = ```agda is-prop-div-ℕ : (k x : ℕ) → is-nonzero-ℕ k → is-prop (div-ℕ k x) is-prop-div-ℕ k x f = - is-prop-map-is-emb (is-emb-is-injective is-set-ℕ (is-injective-right-mul-ℕ k f)) x + is-prop-map-is-emb + ( is-emb-is-injective is-set-ℕ (is-injective-right-mul-ℕ k f)) + ( x) ``` ### The divisibility relation is a partial order on the natural numbers From 566e00c31854e1fe7427114440cd760bcdacccf7 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Fri, 21 Mar 2025 13:51:52 +0000 Subject: [PATCH 31/39] fix dependencies public imports --- src/category-theory/categories.lagda.md | 1 + .../composition-operations-on-binary-families-of-sets.lagda.md | 1 + src/category-theory/cones-precategories.lagda.md | 2 ++ .../conservative-functors-precategories.lagda.md | 1 + src/category-theory/constant-functors.lagda.md | 1 + src/category-theory/copresheaf-categories.lagda.md | 1 + src/category-theory/coproducts-in-precategories.lagda.md | 2 ++ src/category-theory/cores-precategories.lagda.md | 1 + ...ependent-composition-operations-over-precategories.lagda.md | 2 ++ .../dependent-products-of-large-precategories.lagda.md | 1 + .../dependent-products-of-precategories.lagda.md | 1 + src/category-theory/displayed-precategories.lagda.md | 2 ++ src/category-theory/embedding-maps-precategories.lagda.md | 1 + src/category-theory/embeddings-precategories.lagda.md | 1 + .../epimorphisms-in-large-precategories.lagda.md | 1 + .../essentially-surjective-functors-precategories.lagda.md | 1 + src/category-theory/faithful-functors-precategories.lagda.md | 1 + src/category-theory/faithful-maps-precategories.lagda.md | 1 + src/category-theory/full-functors-precategories.lagda.md | 1 + src/category-theory/full-large-subcategories.lagda.md | 1 + src/category-theory/full-large-subprecategories.lagda.md | 1 + src/category-theory/full-maps-precategories.lagda.md | 1 + src/category-theory/full-subcategories.lagda.md | 1 + src/category-theory/full-subprecategories.lagda.md | 1 + .../fully-faithful-functors-precategories.lagda.md | 1 + src/category-theory/fully-faithful-maps-precategories.lagda.md | 1 + src/category-theory/functors-categories.lagda.md | 1 + src/category-theory/functors-precategories.lagda.md | 1 + src/category-theory/functors-set-magmoids.lagda.md | 1 + src/category-theory/gaunt-categories.lagda.md | 1 + src/category-theory/groupoids.lagda.md | 2 ++ src/category-theory/indiscrete-precategories.lagda.md | 2 ++ src/category-theory/initial-category.lagda.md | 1 + .../initial-objects-large-precategories.lagda.md | 1 + src/category-theory/initial-objects-precategories.lagda.md | 2 ++ src/category-theory/isomorphisms-in-categories.lagda.md | 2 ++ src/category-theory/isomorphisms-in-large-categories.lagda.md | 2 ++ .../isomorphisms-in-large-precategories.lagda.md | 1 + src/category-theory/isomorphisms-in-precategories.lagda.md | 1 + src/category-theory/isomorphisms-in-subprecategories.lagda.md | 1 + src/category-theory/limits-precategories.lagda.md | 1 + src/category-theory/maps-precategories.lagda.md | 1 + .../monomorphisms-in-large-precategories.lagda.md | 1 + .../natural-isomorphisms-functors-categories.lagda.md | 1 + .../natural-isomorphisms-functors-precategories.lagda.md | 1 + .../natural-isomorphisms-maps-categories.lagda.md | 1 + .../natural-isomorphisms-maps-precategories.lagda.md | 1 + .../natural-transformations-functors-categories.lagda.md | 1 + ...formations-functors-from-small-to-large-categories.lagda.md | 1 + ...mations-functors-from-small-to-large-precategories.lagda.md | 1 + .../natural-transformations-functors-precategories.lagda.md | 1 + .../natural-transformations-maps-categories.lagda.md | 1 + ...sformations-maps-from-small-to-large-precategories.lagda.md | 1 + .../natural-transformations-maps-precategories.lagda.md | 1 + src/category-theory/nonunital-precategories.lagda.md | 2 ++ src/category-theory/one-object-precategories.lagda.md | 2 ++ src/category-theory/precategories.lagda.md | 2 ++ src/category-theory/pregroupoids.lagda.md | 1 + src/category-theory/preunivalent-categories.lagda.md | 1 + src/category-theory/products-in-precategories.lagda.md | 2 ++ .../pseudomonic-functors-precategories.lagda.md | 1 + src/category-theory/pullbacks-in-precategories.lagda.md | 2 ++ src/category-theory/replete-subprecategories.lagda.md | 1 + src/category-theory/representing-arrow-category.lagda.md | 1 + src/category-theory/right-extensions-precategories.lagda.md | 2 ++ src/category-theory/rigid-objects-categories.lagda.md | 1 + src/category-theory/rigid-objects-precategories.lagda.md | 2 ++ src/category-theory/set-magmoids.lagda.md | 2 ++ src/category-theory/sieves-in-categories.lagda.md | 1 + src/category-theory/slice-precategories.lagda.md | 2 ++ ...plit-essentially-surjective-functors-precategories.lagda.md | 2 ++ src/category-theory/strict-categories.lagda.md | 1 + src/category-theory/strongly-preunivalent-categories.lagda.md | 1 + .../structure-equivalences-set-magmoids.lagda.md | 1 + src/category-theory/subcategories.lagda.md | 2 ++ src/category-theory/subprecategories.lagda.md | 1 + src/category-theory/subterminal-precategories.lagda.md | 2 ++ src/category-theory/terminal-category.lagda.md | 2 ++ src/category-theory/terminal-objects-precategories.lagda.md | 1 + src/category-theory/wide-subcategories.lagda.md | 2 ++ src/category-theory/wide-subprecategories.lagda.md | 1 + src/commutative-algebra/commutative-rings.lagda.md | 1 + src/commutative-algebra/commutative-semirings.lagda.md | 1 + src/commutative-algebra/euclidean-domains.lagda.md | 1 + src/commutative-algebra/full-ideals-commutative-rings.lagda.md | 1 + .../groups-of-units-commutative-rings.lagda.md | 1 + .../homomorphisms-commutative-rings.lagda.md | 1 + src/commutative-algebra/ideals-commutative-rings.lagda.md | 1 + src/commutative-algebra/ideals-commutative-semirings.lagda.md | 1 + src/commutative-algebra/integral-domains.lagda.md | 1 + .../invertible-elements-commutative-rings.lagda.md | 2 ++ .../isomorphisms-commutative-rings.lagda.md | 1 + src/commutative-algebra/local-commutative-rings.lagda.md | 1 + .../poset-of-ideals-commutative-rings.lagda.md | 1 + .../poset-of-radical-ideals-commutative-rings.lagda.md | 1 + .../prime-ideals-commutative-rings.lagda.md | 1 + .../radical-ideals-commutative-rings.lagda.md | 1 + .../radicals-of-ideals-commutative-rings.lagda.md | 1 + src/commutative-algebra/subsets-commutative-rings.lagda.md | 1 + src/commutative-algebra/subsets-commutative-semirings.lagda.md | 1 + src/commutative-algebra/trivial-commutative-rings.lagda.md | 2 ++ src/commutative-algebra/zariski-topology.lagda.md | 1 + src/domain-theory/directed-complete-posets.lagda.md | 1 + src/domain-theory/directed-families-posets.lagda.md | 1 + src/domain-theory/omega-complete-posets.lagda.md | 1 + .../omega-continuous-maps-omega-complete-posets.lagda.md | 1 + src/domain-theory/omega-continuous-maps-posets.lagda.md | 1 + src/domain-theory/reindexing-directed-families-posets.lagda.md | 1 + src/domain-theory/scott-continuous-maps-posets.lagda.md | 1 + .../based-strong-induction-natural-numbers.lagda.md | 1 + .../cross-multiplication-difference-integer-fractions.lagda.md | 1 + src/elementary-number-theory/divisibility-integers.lagda.md | 1 + .../divisibility-natural-numbers.lagda.md | 1 + src/elementary-number-theory/equality-integers.lagda.md | 1 + src/elementary-number-theory/equality-natural-numbers.lagda.md | 1 + .../equality-rational-numbers.lagda.md | 1 + .../fundamental-theorem-of-arithmetic.lagda.md | 2 ++ .../inequality-conatural-numbers.lagda.md | 1 + .../inequality-integer-fractions.lagda.md | 1 + src/elementary-number-theory/inequality-integers.lagda.md | 1 + .../inequality-natural-numbers.lagda.md | 1 + .../inequality-rational-numbers.lagda.md | 1 + .../inequality-standard-finite-types.lagda.md | 1 + .../initial-segments-natural-numbers.lagda.md | 1 + src/elementary-number-theory/integer-fractions.lagda.md | 1 + .../lower-bounds-natural-numbers.lagda.md | 1 + src/elementary-number-theory/negative-integers.lagda.md | 1 + src/elementary-number-theory/nonnegative-integers.lagda.md | 1 + src/elementary-number-theory/nonpositive-integers.lagda.md | 1 + src/elementary-number-theory/nonzero-integers.lagda.md | 1 + src/elementary-number-theory/nonzero-rational-numbers.lagda.md | 1 + src/elementary-number-theory/peano-arithmetic.lagda.md | 1 + .../poset-of-natural-numbers-ordered-by-divisibility.lagda.md | 1 + .../positive-integer-fractions.lagda.md | 1 + src/elementary-number-theory/positive-integers.lagda.md | 1 + .../positive-rational-numbers.lagda.md | 1 + src/elementary-number-theory/prime-numbers.lagda.md | 2 ++ .../proper-divisors-natural-numbers.lagda.md | 1 + src/elementary-number-theory/rational-numbers.lagda.md | 1 + .../reduced-integer-fractions.lagda.md | 1 + .../relatively-prime-integers.lagda.md | 1 + .../relatively-prime-natural-numbers.lagda.md | 1 + .../strict-inequality-integer-fractions.lagda.md | 1 + .../strict-inequality-integers.lagda.md | 1 + .../strict-inequality-natural-numbers.lagda.md | 1 + .../strict-inequality-rational-numbers.lagda.md | 1 + .../strict-inequality-standard-finite-types.lagda.md | 1 + .../strong-induction-natural-numbers.lagda.md | 1 + .../universal-property-conatural-numbers.lagda.md | 1 + .../universal-property-integers.lagda.md | 2 ++ .../universal-property-natural-numbers.lagda.md | 1 + .../well-ordering-principle-natural-numbers.lagda.md | 1 + .../well-ordering-principle-standard-finite-types.lagda.md | 1 + src/finite-algebra/commutative-finite-rings.lagda.md | 1 + src/finite-algebra/finite-fields.lagda.md | 1 + src/finite-algebra/finite-rings.lagda.md | 1 + .../homomorphisms-commutative-finite-rings.lagda.md | 1 + src/finite-algebra/homomorphisms-finite-rings.lagda.md | 1 + .../cartier-delooping-sign-homomorphism.lagda.md | 1 + src/finite-group-theory/delooping-sign-homomorphism.lagda.md | 3 +++ src/finite-group-theory/finite-abelian-groups.lagda.md | 1 + src/finite-group-theory/finite-groups.lagda.md | 1 + src/finite-group-theory/finite-monoids.lagda.md | 1 + src/finite-group-theory/finite-semigroups.lagda.md | 1 + src/finite-group-theory/finite-type-groups.lagda.md | 2 ++ 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.../orthogonal-factorization-systems.lagda.md | 2 ++ src/orthogonal-factorization-systems/orthogonal-maps.lagda.md | 2 ++ .../reflective-global-subuniverses.lagda.md | 2 ++ .../types-colocal-at-maps.lagda.md | 2 ++ .../types-local-at-maps.lagda.md | 2 ++ .../uniquely-eliminating-modalities.lagda.md | 2 ++ ...rsal-property-localizations-at-global-subuniverses.lagda.md | 2 ++ .../wide-function-classes.lagda.md | 1 + .../wide-global-function-classes.lagda.md | 1 + src/polytopes/abstract-polytopes.lagda.md | 2 ++ src/real-numbers/apartness-real-numbers.lagda.md | 1 + src/real-numbers/dedekind-real-numbers.lagda.md | 1 + .../inequality-lower-dedekind-real-numbers.lagda.md | 1 + src/real-numbers/inequality-real-numbers.lagda.md | 1 + .../inequality-upper-dedekind-real-numbers.lagda.md | 1 + src/real-numbers/lower-dedekind-real-numbers.lagda.md | 2 ++ src/real-numbers/metric-space-of-real-numbers.lagda.md | 1 + src/real-numbers/rational-real-numbers.lagda.md | 1 + src/real-numbers/similarity-real-numbers.lagda.md | 1 + src/real-numbers/strict-inequality-real-numbers.lagda.md | 1 + src/real-numbers/upper-dedekind-real-numbers.lagda.md | 2 ++ src/ring-theory/central-elements-rings.lagda.md | 1 + src/ring-theory/central-elements-semirings.lagda.md | 1 + src/ring-theory/commuting-elements-rings.lagda.md | 1 + src/ring-theory/congruence-relations-rings.lagda.md | 1 + src/ring-theory/congruence-relations-semirings.lagda.md | 1 + src/ring-theory/cyclic-rings.lagda.md | 1 + src/ring-theory/full-ideals-rings.lagda.md | 1 + src/ring-theory/generating-elements-rings.lagda.md | 1 + src/ring-theory/groups-of-units-rings.lagda.md | 1 + src/ring-theory/homomorphisms-cyclic-rings.lagda.md | 1 + src/ring-theory/homomorphisms-rings.lagda.md | 1 + src/ring-theory/homomorphisms-semirings.lagda.md | 1 + src/ring-theory/ideals-rings.lagda.md | 1 + src/ring-theory/ideals-semirings.lagda.md | 1 + src/ring-theory/idempotent-elements-rings.lagda.md | 1 + src/ring-theory/integer-multiples-of-elements-rings.lagda.md | 1 + src/ring-theory/invertible-elements-rings.lagda.md | 2 ++ src/ring-theory/isomorphisms-rings.lagda.md | 2 ++ .../left-ideals-generated-by-subsets-rings.lagda.md | 1 + src/ring-theory/left-ideals-rings.lagda.md | 1 + src/ring-theory/local-rings.lagda.md | 1 + src/ring-theory/localizations-rings.lagda.md | 2 ++ src/ring-theory/multiples-of-elements-rings.lagda.md | 1 + src/ring-theory/nil-ideals-rings.lagda.md | 1 + src/ring-theory/nilpotent-elements-rings.lagda.md | 1 + src/ring-theory/nilpotent-elements-semirings.lagda.md | 1 + src/ring-theory/poset-of-ideals-rings.lagda.md | 1 + src/ring-theory/poset-of-left-ideals-rings.lagda.md | 1 + src/ring-theory/poset-of-right-ideals-rings.lagda.md | 1 + src/ring-theory/radical-ideals-rings.lagda.md | 1 + .../right-ideals-generated-by-subsets-rings.lagda.md | 1 + src/ring-theory/right-ideals-rings.lagda.md | 1 + src/ring-theory/rings.lagda.md | 1 + src/ring-theory/semirings.lagda.md | 1 + src/ring-theory/subsets-rings.lagda.md | 1 + src/ring-theory/subsets-semirings.lagda.md | 1 + src/ring-theory/trivial-rings.lagda.md | 2 ++ src/set-theory/cardinalities.lagda.md | 1 + src/set-theory/countable-sets.lagda.md | 1 + src/set-theory/cumulative-hierarchy.lagda.md | 2 ++ src/set-theory/infinite-sets.lagda.md | 1 + src/set-theory/uncountable-sets.lagda.md | 1 + ...auchy-composition-species-of-types-in-subuniverses.lagda.md | 2 ++ src/species/cauchy-composition-species-of-types.lagda.md | 1 + ...uchy-exponentials-species-of-types-in-subuniverses.lagda.md | 1 + .../cauchy-products-species-of-types-in-subuniverses.lagda.md | 1 + .../cauchy-series-species-of-types-in-subuniverses.lagda.md | 1 + ...hlet-exponentials-species-of-types-in-subuniverses.lagda.md | 1 + ...irichlet-products-species-of-types-in-subuniverses.lagda.md | 2 ++ src/species/morphisms-finite-species.lagda.md | 1 + ...uchy-composition-species-of-finite-inhabited-types.lagda.md | 2 ++ ...auchy-composition-species-of-types-in-subuniverses.lagda.md | 2 ++ src/species/species-of-types-in-subuniverses.lagda.md | 1 + ...auchy-composition-species-of-types-in-subuniverses.lagda.md | 1 + src/species/unit-cauchy-composition-species-of-types.lagda.md | 1 + src/structured-types/contractible-pointed-types.lagda.md | 2 ++ src/structured-types/cyclic-types.lagda.md | 1 + .../equivalences-types-equipped-with-endomorphisms.lagda.md | 1 + .../initial-pointed-type-equipped-with-automorphism.lagda.md | 1 + .../involutive-type-of-h-space-structures.lagda.md | 1 + ...ere-equivalences-types-equipped-with-endomorphisms.lagda.md | 1 + src/structured-types/morphisms-pointed-arrows.lagda.md | 1 + .../morphisms-types-equipped-with-endomorphisms.lagda.md | 1 + src/structured-types/pointed-2-homotopies.lagda.md | 1 + src/structured-types/pointed-equivalences.lagda.md | 1 + src/structured-types/pointed-isomorphisms.lagda.md | 2 ++ .../pointed-types-equipped-with-automorphisms.lagda.md | 1 + .../pointed-universal-property-contractible-types.lagda.md | 1 + src/structured-types/small-pointed-types.lagda.md | 2 ++ src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md | 1 + src/synthetic-homotopy-theory/0-acyclic-types.lagda.md | 2 ++ src/synthetic-homotopy-theory/1-acyclic-types.lagda.md | 3 +++ src/synthetic-homotopy-theory/acyclic-maps.lagda.md | 2 ++ src/synthetic-homotopy-theory/acyclic-types.lagda.md | 2 ++ src/synthetic-homotopy-theory/circle.lagda.md | 2 ++ .../cocartesian-morphisms-arrows.lagda.md | 1 + src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md | 1 + src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md | 1 + src/synthetic-homotopy-theory/coforks.lagda.md | 1 + .../connected-set-bundles-circle.lagda.md | 1 + src/synthetic-homotopy-theory/connective-prespectra.lagda.md | 1 + src/synthetic-homotopy-theory/connective-spectra.lagda.md | 1 + .../dependent-cocones-under-spans.lagda.md | 1 + .../dependent-descent-circle.lagda.md | 1 + .../dependent-pushout-products.lagda.md | 1 + .../dependent-universal-property-coequalizers.lagda.md | 1 + .../dependent-universal-property-pushouts.lagda.md | 1 + .../dependent-universal-property-sequential-colimits.lagda.md | 1 + .../descent-circle-equivalence-types.lagda.md | 1 + src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md | 1 + src/synthetic-homotopy-theory/descent-circle.lagda.md | 1 + .../descent-data-equivalence-types-over-pushouts.lagda.md | 1 + .../descent-data-function-types-over-pushouts.lagda.md | 1 + .../descent-property-pushouts.lagda.md | 1 + src/synthetic-homotopy-theory/free-loops.lagda.md | 1 + src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md | 1 + .../identity-systems-descent-data-pushouts.lagda.md | 1 + src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md | 2 ++ src/synthetic-homotopy-theory/interval-type.lagda.md | 1 + src/synthetic-homotopy-theory/joins-of-maps.lagda.md | 1 + src/synthetic-homotopy-theory/joins-of-types.lagda.md | 2 ++ src/synthetic-homotopy-theory/mere-spheres.lagda.md | 1 + src/synthetic-homotopy-theory/plus-principle.lagda.md | 1 + src/synthetic-homotopy-theory/pushout-products.lagda.md | 1 + src/synthetic-homotopy-theory/pushouts.lagda.md | 1 + src/synthetic-homotopy-theory/sections-descent-circle.lagda.md | 1 + .../sections-descent-data-pushouts.lagda.md | 1 + src/synthetic-homotopy-theory/sequential-colimits.lagda.md | 1 + src/synthetic-homotopy-theory/sequential-diagrams.lagda.md | 1 + .../sequentially-compact-types.lagda.md | 1 + .../shifts-sequential-diagrams.lagda.md | 1 + src/synthetic-homotopy-theory/spectra.lagda.md | 1 + src/synthetic-homotopy-theory/suspension-structures.lagda.md | 1 + .../suspensions-of-propositions.lagda.md | 2 ++ src/synthetic-homotopy-theory/suspensions-of-types.lagda.md | 3 +++ src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md | 2 ++ src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md | 2 ++ src/synthetic-homotopy-theory/universal-cover-circle.lagda.md | 1 + .../universal-property-circle.lagda.md | 2 ++ .../universal-property-coequalizers.lagda.md | 1 + .../universal-property-pushouts.lagda.md | 1 + .../universal-property-sequential-colimits.lagda.md | 1 + .../universal-property-suspensions-of-pointed-types.lagda.md | 1 + src/trees/bases-directed-trees.lagda.md | 2 ++ src/trees/bases-enriched-directed-trees.lagda.md | 1 + src/trees/bounded-multisets.lagda.md | 1 + src/trees/combinator-directed-trees.lagda.md | 2 ++ src/trees/directed-trees.lagda.md | 2 ++ src/trees/empty-multisets.lagda.md | 1 + src/trees/enriched-directed-trees.lagda.md | 2 ++ src/trees/equivalences-directed-trees.lagda.md | 1 + src/trees/equivalences-enriched-directed-trees.lagda.md | 1 + src/trees/extensional-w-types.lagda.md | 2 ++ src/trees/fibers-enriched-directed-trees.lagda.md | 1 + src/trees/functoriality-combinator-directed-trees.lagda.md | 1 + src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md | 1 + .../morphisms-coalgebras-polynomial-endofunctors.lagda.md | 1 + src/trees/morphisms-directed-trees.lagda.md | 1 + src/trees/polynomial-endofunctors.lagda.md | 1 + src/trees/raising-universe-levels-directed-trees.lagda.md | 1 + src/trees/ranks-of-elements-w-types.lagda.md | 1 + src/trees/rooted-morphisms-directed-trees.lagda.md | 2 ++ src/trees/rooted-morphisms-enriched-directed-trees.lagda.md | 1 + src/trees/rooted-quasitrees.lagda.md | 1 + src/trees/small-multisets.lagda.md | 1 + ...-trees-elements-coalgebras-polynomial-endofunctors.lagda.md | 2 ++ src/trees/underlying-trees-of-elements-of-w-types.lagda.md | 2 ++ src/trees/undirected-trees.lagda.md | 2 ++ src/trees/w-type-of-natural-numbers.lagda.md | 1 + src/trees/w-type-of-propositions.lagda.md | 1 + src/trees/w-types.lagda.md | 1 + src/type-theories/dependent-type-theories.lagda.md | 1 + .../2-element-decidable-subtypes.lagda.md | 1 + src/univalent-combinatorics/2-element-subtypes.lagda.md | 2 ++ src/univalent-combinatorics/2-element-types.lagda.md | 2 ++ src/univalent-combinatorics/binomial-types.lagda.md | 2 ++ src/univalent-combinatorics/cartesian-product-types.lagda.md | 1 + .../counting-decidable-subtypes.lagda.md | 2 ++ .../counting-dependent-pair-types.lagda.md | 1 + src/univalent-combinatorics/counting.lagda.md | 2 ++ .../cycle-prime-decomposition-natural-numbers.lagda.md | 1 + src/univalent-combinatorics/cyclic-finite-types.lagda.md | 1 + .../decidable-dependent-function-types.lagda.md | 1 + .../decidable-equivalence-relations.lagda.md | 1 + src/univalent-combinatorics/decidable-propositions.lagda.md | 1 + src/univalent-combinatorics/decidable-subtypes.lagda.md | 1 + src/univalent-combinatorics/dedekind-finite-sets.lagda.md | 1 + src/univalent-combinatorics/dependent-pair-types.lagda.md | 1 + .../discrete-sigma-decompositions.lagda.md | 2 ++ ...tributivity-of-set-truncation-over-finite-products.lagda.md | 1 + src/univalent-combinatorics/embeddings.lagda.md | 1 + .../equality-standard-finite-types.lagda.md | 2 ++ .../equivalences-standard-finite-types.lagda.md | 1 + src/univalent-combinatorics/ferrers-diagrams.lagda.md | 1 + src/univalent-combinatorics/fibers-of-maps.lagda.md | 1 + src/univalent-combinatorics/finite-types.lagda.md | 2 ++ .../finitely-many-connected-components.lagda.md | 2 ++ src/univalent-combinatorics/finitely-presented-types.lagda.md | 1 + src/univalent-combinatorics/inhabited-finite-types.lagda.md | 1 + src/univalent-combinatorics/kuratowski-finite-sets.lagda.md | 1 + src/univalent-combinatorics/locally-finite-types.lagda.md | 2 ++ .../main-classes-of-latin-hypercubes.lagda.md | 1 + .../orientations-complete-undirected-graph.lagda.md | 1 + src/univalent-combinatorics/partitions.lagda.md | 1 + src/univalent-combinatorics/pi-finite-types.lagda.md | 2 ++ src/univalent-combinatorics/pigeonhole-principle.lagda.md | 1 + src/univalent-combinatorics/ramsey-theory.lagda.md | 1 + .../set-quotients-of-index-two.lagda.md | 1 + src/univalent-combinatorics/sigma-decompositions.lagda.md | 1 + src/univalent-combinatorics/standard-finite-types.lagda.md | 1 + src/univalent-combinatorics/steiner-systems.lagda.md | 1 + src/univalent-combinatorics/surjective-maps.lagda.md | 1 + .../trivial-sigma-decompositions.lagda.md | 2 ++ src/univalent-combinatorics/type-duality.lagda.md | 1 + src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md | 1 + .../universal-property-standard-finite-types.lagda.md | 1 + .../untruncated-pi-finite-types.lagda.md | 2 ++ src/universal-algebra/algebraic-theory-of-groups.lagda.md | 1 + src/universal-algebra/algebras-of-theories.lagda.md | 1 + src/universal-algebra/congruences.lagda.md | 1 + src/universal-algebra/quotient-algebras.lagda.md | 1 + 722 files changed, 857 insertions(+), 5 deletions(-) diff --git a/src/category-theory/categories.lagda.md b/src/category-theory/categories.lagda.md index 42f12c7076..ba25122493 100644 --- a/src/category-theory/categories.lagda.md +++ b/src/category-theory/categories.lagda.md @@ -17,6 +17,7 @@ open import category-theory.strongly-preunivalent-categories open import foundation.1-types open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md index 49fbe79018..7c19f3c49b 100644 --- a/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md +++ b/src/category-theory/composition-operations-on-binary-families-of-sets.lagda.md @@ -9,6 +9,7 @@ module category-theory.composition-operations-on-binary-families-of-sets where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-extensionality open import foundation.identity-types open import foundation.iterated-dependent-product-types diff --git a/src/category-theory/cones-precategories.lagda.md b/src/category-theory/cones-precategories.lagda.md index 12df81dc10..1db29c5648 100644 --- a/src/category-theory/cones-precategories.lagda.md +++ b/src/category-theory/cones-precategories.lagda.md @@ -22,6 +22,8 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/category-theory/conservative-functors-precategories.lagda.md b/src/category-theory/conservative-functors-precategories.lagda.md index e3b24903e9..6ff77c4d09 100644 --- a/src/category-theory/conservative-functors-precategories.lagda.md +++ b/src/category-theory/conservative-functors-precategories.lagda.md @@ -12,6 +12,7 @@ open import category-theory.isomorphisms-in-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.iterated-dependent-product-types open import foundation.propositions open import foundation.telescopes diff --git a/src/category-theory/constant-functors.lagda.md b/src/category-theory/constant-functors.lagda.md index a07c37b14b..a62d103b31 100644 --- a/src/category-theory/constant-functors.lagda.md +++ b/src/category-theory/constant-functors.lagda.md @@ -19,6 +19,7 @@ open import category-theory.precategories open import category-theory.precategory-of-functors open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/category-theory/copresheaf-categories.lagda.md b/src/category-theory/copresheaf-categories.lagda.md index 71e72eff00..dcce328cf6 100644 --- a/src/category-theory/copresheaf-categories.lagda.md +++ b/src/category-theory/copresheaf-categories.lagda.md @@ -24,6 +24,7 @@ open import category-theory.terminal-objects-precategories open import foundation.category-of-sets open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-cartesian-product-types open import foundation.function-extensionality diff --git a/src/category-theory/coproducts-in-precategories.lagda.md b/src/category-theory/coproducts-in-precategories.lagda.md index 89a697bd01..1466eea066 100644 --- a/src/category-theory/coproducts-in-precategories.lagda.md +++ b/src/category-theory/coproducts-in-precategories.lagda.md @@ -13,6 +13,8 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions diff --git a/src/category-theory/cores-precategories.lagda.md b/src/category-theory/cores-precategories.lagda.md index 210c08f99c..21392dbbe2 100644 --- a/src/category-theory/cores-precategories.lagda.md +++ b/src/category-theory/cores-precategories.lagda.md @@ -18,6 +18,7 @@ open import category-theory.wide-subprecategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md index cd698e7403..b6607a0b34 100644 --- a/src/category-theory/dependent-composition-operations-over-precategories.lagda.md +++ b/src/category-theory/dependent-composition-operations-over-precategories.lagda.md @@ -15,6 +15,8 @@ open import category-theory.set-magmoids open import foundation.cartesian-product-types open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.function-types open import foundation.identity-types open import foundation.iterated-dependent-product-types diff --git a/src/category-theory/dependent-products-of-large-precategories.lagda.md b/src/category-theory/dependent-products-of-large-precategories.lagda.md index 4eacbea052..d4e599864d 100644 --- a/src/category-theory/dependent-products-of-large-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-large-precategories.lagda.md @@ -11,6 +11,7 @@ open import category-theory.isomorphisms-in-large-precategories open import category-theory.large-precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-extensionality-axiom diff --git a/src/category-theory/dependent-products-of-precategories.lagda.md b/src/category-theory/dependent-products-of-precategories.lagda.md index e4f7e693fb..9005ab9e0c 100644 --- a/src/category-theory/dependent-products-of-precategories.lagda.md +++ b/src/category-theory/dependent-products-of-precategories.lagda.md @@ -12,6 +12,7 @@ open import category-theory.isomorphisms-in-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-extensionality-axiom diff --git a/src/category-theory/displayed-precategories.lagda.md b/src/category-theory/displayed-precategories.lagda.md index 959ce0871a..fb310fd7de 100644 --- a/src/category-theory/displayed-precategories.lagda.md +++ b/src/category-theory/displayed-precategories.lagda.md @@ -16,6 +16,8 @@ open import category-theory.set-magmoids open import foundation.cartesian-product-types open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.equality-dependent-pair-types open import foundation.function-types open import foundation.identity-types diff --git a/src/category-theory/embedding-maps-precategories.lagda.md b/src/category-theory/embedding-maps-precategories.lagda.md index 469ee2913d..1705026d5f 100644 --- a/src/category-theory/embedding-maps-precategories.lagda.md +++ b/src/category-theory/embedding-maps-precategories.lagda.md @@ -12,6 +12,7 @@ open import category-theory.maps-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.propositions open import foundation.universe-levels diff --git a/src/category-theory/embeddings-precategories.lagda.md b/src/category-theory/embeddings-precategories.lagda.md index 39ffe2e71f..16ae6dbcdf 100644 --- a/src/category-theory/embeddings-precategories.lagda.md +++ b/src/category-theory/embeddings-precategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.maps-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/epimorphisms-in-large-precategories.lagda.md b/src/category-theory/epimorphisms-in-large-precategories.lagda.md index d03cd93b4a..4256fc3e47 100644 --- a/src/category-theory/epimorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/epimorphisms-in-large-precategories.lagda.md @@ -10,6 +10,7 @@ module category-theory.epimorphisms-in-large-precategories where open import category-theory.isomorphisms-in-large-precategories open import category-theory.large-precategories +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.propositions diff --git a/src/category-theory/essentially-surjective-functors-precategories.lagda.md b/src/category-theory/essentially-surjective-functors-precategories.lagda.md index da79c73d46..226adf4c31 100644 --- a/src/category-theory/essentially-surjective-functors-precategories.lagda.md +++ b/src/category-theory/essentially-surjective-functors-precategories.lagda.md @@ -12,6 +12,7 @@ open import category-theory.isomorphisms-in-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.propositions open import foundation.universe-levels diff --git a/src/category-theory/faithful-functors-precategories.lagda.md b/src/category-theory/faithful-functors-precategories.lagda.md index 8c6ea55099..13be09da49 100644 --- a/src/category-theory/faithful-functors-precategories.lagda.md +++ b/src/category-theory/faithful-functors-precategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.isomorphisms-in-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.propositions diff --git a/src/category-theory/faithful-maps-precategories.lagda.md b/src/category-theory/faithful-maps-precategories.lagda.md index 092f8cb396..79875fbf05 100644 --- a/src/category-theory/faithful-maps-precategories.lagda.md +++ b/src/category-theory/faithful-maps-precategories.lagda.md @@ -11,6 +11,7 @@ open import category-theory.maps-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/category-theory/full-functors-precategories.lagda.md b/src/category-theory/full-functors-precategories.lagda.md index 6fcd4a2690..7da94b4e18 100644 --- a/src/category-theory/full-functors-precategories.lagda.md +++ b/src/category-theory/full-functors-precategories.lagda.md @@ -12,6 +12,7 @@ open import category-theory.functors-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/category-theory/full-large-subcategories.lagda.md b/src/category-theory/full-large-subcategories.lagda.md index 4b96c679d6..957f6c5321 100644 --- a/src/category-theory/full-large-subcategories.lagda.md +++ b/src/category-theory/full-large-subcategories.lagda.md @@ -12,6 +12,7 @@ open import category-theory.functors-large-categories open import category-theory.large-categories open import category-theory.large-precategories +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/category-theory/full-large-subprecategories.lagda.md b/src/category-theory/full-large-subprecategories.lagda.md index a3789dd83e..dc78220daa 100644 --- a/src/category-theory/full-large-subprecategories.lagda.md +++ b/src/category-theory/full-large-subprecategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.isomorphisms-in-large-precategories open import category-theory.large-categories open import category-theory.large-precategories +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/category-theory/full-maps-precategories.lagda.md b/src/category-theory/full-maps-precategories.lagda.md index 0e88643319..dc4b187cb0 100644 --- a/src/category-theory/full-maps-precategories.lagda.md +++ b/src/category-theory/full-maps-precategories.lagda.md @@ -11,6 +11,7 @@ open import category-theory.maps-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.iterated-dependent-product-types open import foundation.propositions diff --git a/src/category-theory/full-subcategories.lagda.md b/src/category-theory/full-subcategories.lagda.md index a1921d9182..97428aef3a 100644 --- a/src/category-theory/full-subcategories.lagda.md +++ b/src/category-theory/full-subcategories.lagda.md @@ -17,6 +17,7 @@ open import category-theory.maps-categories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.identity-types open import foundation.propositions diff --git a/src/category-theory/full-subprecategories.lagda.md b/src/category-theory/full-subprecategories.lagda.md index 7d2faeebad..6da738aa7b 100644 --- a/src/category-theory/full-subprecategories.lagda.md +++ b/src/category-theory/full-subprecategories.lagda.md @@ -18,6 +18,7 @@ open import category-theory.maps-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/category-theory/fully-faithful-functors-precategories.lagda.md b/src/category-theory/fully-faithful-functors-precategories.lagda.md index a0de4952c0..4189761b36 100644 --- a/src/category-theory/fully-faithful-functors-precategories.lagda.md +++ b/src/category-theory/fully-faithful-functors-precategories.lagda.md @@ -20,6 +20,7 @@ open import category-theory.pseudomonic-functors-precategories open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/category-theory/fully-faithful-maps-precategories.lagda.md b/src/category-theory/fully-faithful-maps-precategories.lagda.md index 2317e1536a..485e66e356 100644 --- a/src/category-theory/fully-faithful-maps-precategories.lagda.md +++ b/src/category-theory/fully-faithful-maps-precategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.maps-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.iterated-dependent-product-types diff --git a/src/category-theory/functors-categories.lagda.md b/src/category-theory/functors-categories.lagda.md index 8b751210a5..b1bcad6e77 100644 --- a/src/category-theory/functors-categories.lagda.md +++ b/src/category-theory/functors-categories.lagda.md @@ -12,6 +12,7 @@ open import category-theory.functors-precategories open import category-theory.isomorphisms-in-categories open import category-theory.maps-categories +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/category-theory/functors-precategories.lagda.md b/src/category-theory/functors-precategories.lagda.md index 0a9c7a225e..02bfd9cb86 100644 --- a/src/category-theory/functors-precategories.lagda.md +++ b/src/category-theory/functors-precategories.lagda.md @@ -15,6 +15,7 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/category-theory/functors-set-magmoids.lagda.md b/src/category-theory/functors-set-magmoids.lagda.md index 340252ac73..df7aebf6bd 100644 --- a/src/category-theory/functors-set-magmoids.lagda.md +++ b/src/category-theory/functors-set-magmoids.lagda.md @@ -12,6 +12,7 @@ open import category-theory.set-magmoids open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/category-theory/gaunt-categories.lagda.md b/src/category-theory/gaunt-categories.lagda.md index 01853cf160..23fb5c5809 100644 --- a/src/category-theory/gaunt-categories.lagda.md +++ b/src/category-theory/gaunt-categories.lagda.md @@ -20,6 +20,7 @@ open import category-theory.strongly-preunivalent-categories open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/category-theory/groupoids.lagda.md b/src/category-theory/groupoids.lagda.md index b137946933..95f6b91f8e 100644 --- a/src/category-theory/groupoids.lagda.md +++ b/src/category-theory/groupoids.lagda.md @@ -17,6 +17,8 @@ open import category-theory.pregroupoids open import foundation.1-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/category-theory/indiscrete-precategories.lagda.md b/src/category-theory/indiscrete-precategories.lagda.md index 7692b84a17..7ee7d27892 100644 --- a/src/category-theory/indiscrete-precategories.lagda.md +++ b/src/category-theory/indiscrete-precategories.lagda.md @@ -16,6 +16,8 @@ open import category-theory.subterminal-precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/category-theory/initial-category.lagda.md b/src/category-theory/initial-category.lagda.md index c24a71c44d..27fc2c6415 100644 --- a/src/category-theory/initial-category.lagda.md +++ b/src/category-theory/initial-category.lagda.md @@ -17,6 +17,7 @@ open import category-theory.strongly-preunivalent-categories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.empty-types open import foundation.identity-types open import foundation.sets diff --git a/src/category-theory/initial-objects-large-precategories.lagda.md b/src/category-theory/initial-objects-large-precategories.lagda.md index c49900291d..847975f970 100644 --- a/src/category-theory/initial-objects-large-precategories.lagda.md +++ b/src/category-theory/initial-objects-large-precategories.lagda.md @@ -10,6 +10,7 @@ module category-theory.initial-objects-large-precategories where open import category-theory.large-precategories open import foundation.contractible-types +open import foundation.dependent-products-contractible-types open import foundation.universe-levels ``` diff --git a/src/category-theory/initial-objects-precategories.lagda.md b/src/category-theory/initial-objects-precategories.lagda.md index dac1af8fa9..47a868e0ef 100644 --- a/src/category-theory/initial-objects-precategories.lagda.md +++ b/src/category-theory/initial-objects-precategories.lagda.md @@ -11,6 +11,8 @@ open import category-theory.precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/category-theory/isomorphisms-in-categories.lagda.md b/src/category-theory/isomorphisms-in-categories.lagda.md index a0f12490f9..c93de6bf79 100644 --- a/src/category-theory/isomorphisms-in-categories.lagda.md +++ b/src/category-theory/isomorphisms-in-categories.lagda.md @@ -14,6 +14,8 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/category-theory/isomorphisms-in-large-categories.lagda.md b/src/category-theory/isomorphisms-in-large-categories.lagda.md index e6f13cb68a..6faa569aba 100644 --- a/src/category-theory/isomorphisms-in-large-categories.lagda.md +++ b/src/category-theory/isomorphisms-in-large-categories.lagda.md @@ -13,6 +13,8 @@ open import category-theory.large-categories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/category-theory/isomorphisms-in-large-precategories.lagda.md b/src/category-theory/isomorphisms-in-large-precategories.lagda.md index 065f4abe1e..568778af3d 100644 --- a/src/category-theory/isomorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/isomorphisms-in-large-precategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.large-precategories open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/category-theory/isomorphisms-in-precategories.lagda.md b/src/category-theory/isomorphisms-in-precategories.lagda.md index 31a63e5d4f..d7c0db40da 100644 --- a/src/category-theory/isomorphisms-in-precategories.lagda.md +++ b/src/category-theory/isomorphisms-in-precategories.lagda.md @@ -12,6 +12,7 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/category-theory/isomorphisms-in-subprecategories.lagda.md b/src/category-theory/isomorphisms-in-subprecategories.lagda.md index e0d8560de0..0425d467b3 100644 --- a/src/category-theory/isomorphisms-in-subprecategories.lagda.md +++ b/src/category-theory/isomorphisms-in-subprecategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.subprecategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.sets open import foundation.subtypes diff --git a/src/category-theory/limits-precategories.lagda.md b/src/category-theory/limits-precategories.lagda.md index 60015d9a58..2f2eb60d1e 100644 --- a/src/category-theory/limits-precategories.lagda.md +++ b/src/category-theory/limits-precategories.lagda.md @@ -17,6 +17,7 @@ open import category-theory.right-kan-extensions-precategories open import category-theory.terminal-category open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-types diff --git a/src/category-theory/maps-precategories.lagda.md b/src/category-theory/maps-precategories.lagda.md index ba08c41d5c..38d45cdbc5 100644 --- a/src/category-theory/maps-precategories.lagda.md +++ b/src/category-theory/maps-precategories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.precategories open import foundation.binary-transport open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-function-types open import foundation.equivalences open import foundation.function-types diff --git a/src/category-theory/monomorphisms-in-large-precategories.lagda.md b/src/category-theory/monomorphisms-in-large-precategories.lagda.md index 73ce9e3886..cc61348885 100644 --- a/src/category-theory/monomorphisms-in-large-precategories.lagda.md +++ b/src/category-theory/monomorphisms-in-large-precategories.lagda.md @@ -10,6 +10,7 @@ module category-theory.monomorphisms-in-large-precategories where open import category-theory.isomorphisms-in-large-precategories open import category-theory.large-precategories +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.propositions diff --git a/src/category-theory/natural-isomorphisms-functors-categories.lagda.md b/src/category-theory/natural-isomorphisms-functors-categories.lagda.md index f8f8894aea..651250fb8d 100644 --- a/src/category-theory/natural-isomorphisms-functors-categories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-categories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.natural-isomorphisms-functors-precategories open import category-theory.natural-transformations-functors-categories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md b/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md index 35a1b71552..59afbc0d42 100644 --- a/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-functors-precategories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.natural-transformations-functors-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/category-theory/natural-isomorphisms-maps-categories.lagda.md b/src/category-theory/natural-isomorphisms-maps-categories.lagda.md index 571c2723dc..d2e2f3adff 100644 --- a/src/category-theory/natural-isomorphisms-maps-categories.lagda.md +++ b/src/category-theory/natural-isomorphisms-maps-categories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.natural-isomorphisms-maps-precategories open import category-theory.natural-transformations-maps-categories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md b/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md index 1e2ff1ccc6..85bca1f958 100644 --- a/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md +++ b/src/category-theory/natural-isomorphisms-maps-precategories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/category-theory/natural-transformations-functors-categories.lagda.md b/src/category-theory/natural-transformations-functors-categories.lagda.md index 31ddf1de0b..f7f8fd73eb 100644 --- a/src/category-theory/natural-transformations-functors-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-categories.lagda.md @@ -11,6 +11,7 @@ open import category-theory.categories open import category-theory.functors-categories open import category-theory.natural-transformations-functors-precategories +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.homotopies diff --git a/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md b/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md index 229103a8d2..3b0daba4fb 100644 --- a/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md +++ b/src/category-theory/natural-transformations-functors-from-small-to-large-categories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.large-categories open import category-theory.natural-transformations-functors-from-small-to-large-precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.homotopies diff --git a/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md b/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md index bde1b382d5..6c8c95bac7 100644 --- a/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-from-small-to-large-precategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.natural-transformations-maps-from-small-to-large-pre open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.homotopies diff --git a/src/category-theory/natural-transformations-functors-precategories.lagda.md b/src/category-theory/natural-transformations-functors-precategories.lagda.md index 7076ad1387..ccec9dc1c3 100644 --- a/src/category-theory/natural-transformations-functors-precategories.lagda.md +++ b/src/category-theory/natural-transformations-functors-precategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/category-theory/natural-transformations-maps-categories.lagda.md b/src/category-theory/natural-transformations-maps-categories.lagda.md index 04e78aa05e..7d6b507f60 100644 --- a/src/category-theory/natural-transformations-maps-categories.lagda.md +++ b/src/category-theory/natural-transformations-maps-categories.lagda.md @@ -11,6 +11,7 @@ open import category-theory.categories open import category-theory.maps-categories open import category-theory.natural-transformations-maps-precategories +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.homotopies diff --git a/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md b/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md index 3158288d63..f0a45b7698 100644 --- a/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md +++ b/src/category-theory/natural-transformations-maps-from-small-to-large-precategories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/category-theory/natural-transformations-maps-precategories.lagda.md b/src/category-theory/natural-transformations-maps-precategories.lagda.md index 57b61936ce..e0cfe963da 100644 --- a/src/category-theory/natural-transformations-maps-precategories.lagda.md +++ b/src/category-theory/natural-transformations-maps-precategories.lagda.md @@ -13,6 +13,7 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/category-theory/nonunital-precategories.lagda.md b/src/category-theory/nonunital-precategories.lagda.md index 32f4782eab..ab15a28dff 100644 --- a/src/category-theory/nonunital-precategories.lagda.md +++ b/src/category-theory/nonunital-precategories.lagda.md @@ -12,6 +12,8 @@ open import category-theory.set-magmoids open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/category-theory/one-object-precategories.lagda.md b/src/category-theory/one-object-precategories.lagda.md index 76dbd98741..d5b1bffc2b 100644 --- a/src/category-theory/one-object-precategories.lagda.md +++ b/src/category-theory/one-object-precategories.lagda.md @@ -12,6 +12,8 @@ open import category-theory.precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/category-theory/precategories.lagda.md b/src/category-theory/precategories.lagda.md index 1eb71cad75..ec94bb864a 100644 --- a/src/category-theory/precategories.lagda.md +++ b/src/category-theory/precategories.lagda.md @@ -14,6 +14,8 @@ open import category-theory.set-magmoids open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/category-theory/pregroupoids.lagda.md b/src/category-theory/pregroupoids.lagda.md index 6acee12a3c..31faaee0ea 100644 --- a/src/category-theory/pregroupoids.lagda.md +++ b/src/category-theory/pregroupoids.lagda.md @@ -11,6 +11,7 @@ open import category-theory.isomorphisms-in-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.iterated-dependent-product-types diff --git a/src/category-theory/preunivalent-categories.lagda.md b/src/category-theory/preunivalent-categories.lagda.md index 15f683b862..8af49cfa55 100644 --- a/src/category-theory/preunivalent-categories.lagda.md +++ b/src/category-theory/preunivalent-categories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.precategories open import foundation.1-types open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.identity-types open import foundation.propositions diff --git a/src/category-theory/products-in-precategories.lagda.md b/src/category-theory/products-in-precategories.lagda.md index 69fc1f4b93..6be00105d2 100644 --- a/src/category-theory/products-in-precategories.lagda.md +++ b/src/category-theory/products-in-precategories.lagda.md @@ -13,6 +13,8 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions diff --git a/src/category-theory/pseudomonic-functors-precategories.lagda.md b/src/category-theory/pseudomonic-functors-precategories.lagda.md index f5127417ad..6b9c25b75c 100644 --- a/src/category-theory/pseudomonic-functors-precategories.lagda.md +++ b/src/category-theory/pseudomonic-functors-precategories.lagda.md @@ -15,6 +15,7 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.injective-maps diff --git a/src/category-theory/pullbacks-in-precategories.lagda.md b/src/category-theory/pullbacks-in-precategories.lagda.md index 2ade1aec32..bd171f40d3 100644 --- a/src/category-theory/pullbacks-in-precategories.lagda.md +++ b/src/category-theory/pullbacks-in-precategories.lagda.md @@ -13,6 +13,8 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions diff --git a/src/category-theory/replete-subprecategories.lagda.md b/src/category-theory/replete-subprecategories.lagda.md index 4f15777ab4..1195c37cbd 100644 --- a/src/category-theory/replete-subprecategories.lagda.md +++ b/src/category-theory/replete-subprecategories.lagda.md @@ -15,6 +15,7 @@ open import category-theory.precategories open import category-theory.subprecategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.iterated-dependent-product-types diff --git a/src/category-theory/representing-arrow-category.lagda.md b/src/category-theory/representing-arrow-category.lagda.md index a4259a4611..5479ab8e27 100644 --- a/src/category-theory/representing-arrow-category.lagda.md +++ b/src/category-theory/representing-arrow-category.lagda.md @@ -12,6 +12,7 @@ open import category-theory.isomorphisms-in-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/category-theory/right-extensions-precategories.lagda.md b/src/category-theory/right-extensions-precategories.lagda.md index 4c3828347f..906f2c76c0 100644 --- a/src/category-theory/right-extensions-precategories.lagda.md +++ b/src/category-theory/right-extensions-precategories.lagda.md @@ -16,6 +16,8 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/category-theory/rigid-objects-categories.lagda.md b/src/category-theory/rigid-objects-categories.lagda.md index ed69843f56..a9bc67e00a 100644 --- a/src/category-theory/rigid-objects-categories.lagda.md +++ b/src/category-theory/rigid-objects-categories.lagda.md @@ -10,6 +10,7 @@ module category-theory.rigid-objects-categories where open import category-theory.categories open import category-theory.rigid-objects-precategories +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/rigid-objects-precategories.lagda.md b/src/category-theory/rigid-objects-precategories.lagda.md index 356a7f517a..fc8de57c9a 100644 --- a/src/category-theory/rigid-objects-precategories.lagda.md +++ b/src/category-theory/rigid-objects-precategories.lagda.md @@ -12,6 +12,8 @@ open import category-theory.precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/category-theory/set-magmoids.lagda.md b/src/category-theory/set-magmoids.lagda.md index ec501dc223..f517c0d622 100644 --- a/src/category-theory/set-magmoids.lagda.md +++ b/src/category-theory/set-magmoids.lagda.md @@ -11,6 +11,8 @@ open import category-theory.composition-operations-on-binary-families-of-sets open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.propositions open import foundation.sets open import foundation.truncated-types diff --git a/src/category-theory/sieves-in-categories.lagda.md b/src/category-theory/sieves-in-categories.lagda.md index 1bab198afa..cc9661ed16 100644 --- a/src/category-theory/sieves-in-categories.lagda.md +++ b/src/category-theory/sieves-in-categories.lagda.md @@ -9,6 +9,7 @@ module category-theory.sieves-in-categories where ```agda open import category-theory.categories +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/category-theory/slice-precategories.lagda.md b/src/category-theory/slice-precategories.lagda.md index 9443a721e1..cefbbc2c33 100644 --- a/src/category-theory/slice-precategories.lagda.md +++ b/src/category-theory/slice-precategories.lagda.md @@ -17,6 +17,8 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-types diff --git a/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md b/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md index d62ed8e8fe..f3a3c71068 100644 --- a/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md +++ b/src/category-theory/split-essentially-surjective-functors-precategories.lagda.md @@ -20,6 +20,8 @@ open import category-theory.pseudomonic-functors-precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/category-theory/strict-categories.lagda.md b/src/category-theory/strict-categories.lagda.md index 549eed68e0..46ebed1dc3 100644 --- a/src/category-theory/strict-categories.lagda.md +++ b/src/category-theory/strict-categories.lagda.md @@ -16,6 +16,7 @@ open import category-theory.strongly-preunivalent-categories open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.injective-maps open import foundation.propositions diff --git a/src/category-theory/strongly-preunivalent-categories.lagda.md b/src/category-theory/strongly-preunivalent-categories.lagda.md index 8ba02ef3ba..bc122f1df3 100644 --- a/src/category-theory/strongly-preunivalent-categories.lagda.md +++ b/src/category-theory/strongly-preunivalent-categories.lagda.md @@ -15,6 +15,7 @@ open import category-theory.preunivalent-categories open import foundation.1-types open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/category-theory/structure-equivalences-set-magmoids.lagda.md b/src/category-theory/structure-equivalences-set-magmoids.lagda.md index 38be07d265..eae60f47a9 100644 --- a/src/category-theory/structure-equivalences-set-magmoids.lagda.md +++ b/src/category-theory/structure-equivalences-set-magmoids.lagda.md @@ -12,6 +12,7 @@ open import category-theory.set-magmoids open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-dependent-function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/category-theory/subcategories.lagda.md b/src/category-theory/subcategories.lagda.md index cb8cf062cf..ce29fcc2c6 100644 --- a/src/category-theory/subcategories.lagda.md +++ b/src/category-theory/subcategories.lagda.md @@ -21,6 +21,8 @@ open import category-theory.subprecategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.functoriality-dependent-pair-types diff --git a/src/category-theory/subprecategories.lagda.md b/src/category-theory/subprecategories.lagda.md index 9d2ff28504..a10cb9c981 100644 --- a/src/category-theory/subprecategories.lagda.md +++ b/src/category-theory/subprecategories.lagda.md @@ -14,6 +14,7 @@ open import category-theory.maps-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.identity-types open import foundation.iterated-dependent-product-types diff --git a/src/category-theory/subterminal-precategories.lagda.md b/src/category-theory/subterminal-precategories.lagda.md index a85c94a746..2d12c25898 100644 --- a/src/category-theory/subterminal-precategories.lagda.md +++ b/src/category-theory/subterminal-precategories.lagda.md @@ -18,6 +18,8 @@ open import category-theory.terminal-category open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/category-theory/terminal-category.lagda.md b/src/category-theory/terminal-category.lagda.md index a8a8284077..320b686372 100644 --- a/src/category-theory/terminal-category.lagda.md +++ b/src/category-theory/terminal-category.lagda.md @@ -22,6 +22,8 @@ open import category-theory.strongly-preunivalent-categories open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.homotopies open import foundation.identity-types diff --git a/src/category-theory/terminal-objects-precategories.lagda.md b/src/category-theory/terminal-objects-precategories.lagda.md index 5a1fcb7d9c..37e2165f92 100644 --- a/src/category-theory/terminal-objects-precategories.lagda.md +++ b/src/category-theory/terminal-objects-precategories.lagda.md @@ -11,6 +11,7 @@ open import category-theory.precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-types open import foundation.identity-types open import foundation.universe-levels diff --git a/src/category-theory/wide-subcategories.lagda.md b/src/category-theory/wide-subcategories.lagda.md index 7c10b8b282..3d9a2d8ef2 100644 --- a/src/category-theory/wide-subcategories.lagda.md +++ b/src/category-theory/wide-subcategories.lagda.md @@ -20,6 +20,8 @@ open import category-theory.wide-subprecategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/category-theory/wide-subprecategories.lagda.md b/src/category-theory/wide-subprecategories.lagda.md index 9c22aab29a..d821251802 100644 --- a/src/category-theory/wide-subprecategories.lagda.md +++ b/src/category-theory/wide-subprecategories.lagda.md @@ -15,6 +15,7 @@ open import category-theory.precategories open import category-theory.subprecategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/commutative-algebra/commutative-rings.lagda.md b/src/commutative-algebra/commutative-rings.lagda.md index 06b3e5d600..d72ad24f82 100644 --- a/src/commutative-algebra/commutative-rings.lagda.md +++ b/src/commutative-algebra/commutative-rings.lagda.md @@ -17,6 +17,7 @@ open import foundation.action-on-identifications-functions open import foundation.binary-embeddings open import foundation.binary-equivalences open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/commutative-algebra/commutative-semirings.lagda.md b/src/commutative-algebra/commutative-semirings.lagda.md index 9f261db26a..58ade31e34 100644 --- a/src/commutative-algebra/commutative-semirings.lagda.md +++ b/src/commutative-algebra/commutative-semirings.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.iterated-dependent-product-types open import foundation.propositions diff --git a/src/commutative-algebra/euclidean-domains.lagda.md b/src/commutative-algebra/euclidean-domains.lagda.md index abd586d5ef..b17fa2dca0 100644 --- a/src/commutative-algebra/euclidean-domains.lagda.md +++ b/src/commutative-algebra/euclidean-domains.lagda.md @@ -23,6 +23,7 @@ open import foundation.binary-equivalences open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.identity-types diff --git a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md index 762bbd4709..1bd4b8a1eb 100644 --- a/src/commutative-algebra/full-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/full-ideals-commutative-rings.lagda.md @@ -15,6 +15,7 @@ open import commutative-algebra.radical-ideals-commutative-rings open import commutative-algebra.subsets-commutative-rings open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.raising-universe-levels-unit-type open import foundation.unit-type diff --git a/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md b/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md index f3fcd5aac1..b72b0d3223 100644 --- a/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md +++ b/src/commutative-algebra/groups-of-units-commutative-rings.lagda.md @@ -14,6 +14,7 @@ open import commutative-algebra.homomorphisms-commutative-rings open import commutative-algebra.precategory-of-commutative-rings open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.subtypes diff --git a/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md b/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md index 284d752ce5..e3af821a5e 100644 --- a/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md +++ b/src/commutative-algebra/homomorphisms-commutative-rings.lagda.md @@ -11,6 +11,7 @@ open import commutative-algebra.commutative-rings open import commutative-algebra.homomorphisms-commutative-semirings open import commutative-algebra.invertible-elements-commutative-rings +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.propositions diff --git a/src/commutative-algebra/ideals-commutative-rings.lagda.md b/src/commutative-algebra/ideals-commutative-rings.lagda.md index 90f082cc86..1548093147 100644 --- a/src/commutative-algebra/ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/ideals-commutative-rings.lagda.md @@ -14,6 +14,7 @@ open import commutative-algebra.subsets-commutative-rings open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.propositions diff --git a/src/commutative-algebra/ideals-commutative-semirings.lagda.md b/src/commutative-algebra/ideals-commutative-semirings.lagda.md index 8fb7d4a127..1fb77114ff 100644 --- a/src/commutative-algebra/ideals-commutative-semirings.lagda.md +++ b/src/commutative-algebra/ideals-commutative-semirings.lagda.md @@ -11,6 +11,7 @@ open import commutative-algebra.commutative-semirings open import commutative-algebra.subsets-commutative-semirings open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/commutative-algebra/integral-domains.lagda.md b/src/commutative-algebra/integral-domains.lagda.md index d960d94053..19c0a7d0be 100644 --- a/src/commutative-algebra/integral-domains.lagda.md +++ b/src/commutative-algebra/integral-domains.lagda.md @@ -20,6 +20,7 @@ open import foundation.binary-embeddings open import foundation.binary-equivalences open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.identity-types diff --git a/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md b/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md index ebc4116027..66b95ec448 100644 --- a/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md +++ b/src/commutative-algebra/invertible-elements-commutative-rings.lagda.md @@ -11,6 +11,8 @@ open import commutative-algebra.commutative-rings open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md b/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md index 663583921f..d14d1ebeef 100644 --- a/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md +++ b/src/commutative-algebra/isomorphisms-commutative-rings.lagda.md @@ -15,6 +15,7 @@ open import commutative-algebra.invertible-elements-commutative-rings open import commutative-algebra.precategory-of-commutative-rings open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/commutative-algebra/local-commutative-rings.lagda.md b/src/commutative-algebra/local-commutative-rings.lagda.md index 9de71b60fc..606fb3b7dd 100644 --- a/src/commutative-algebra/local-commutative-rings.lagda.md +++ b/src/commutative-algebra/local-commutative-rings.lagda.md @@ -10,6 +10,7 @@ module commutative-algebra.local-commutative-rings where open import commutative-algebra.commutative-rings open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.sets open import foundation.universe-levels diff --git a/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md b/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md index 4b5b4c589f..08b9737c72 100644 --- a/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/poset-of-ideals-commutative-rings.lagda.md @@ -10,6 +10,7 @@ module commutative-algebra.poset-of-ideals-commutative-rings where open import commutative-algebra.commutative-rings open import commutative-algebra.ideals-commutative-rings +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md index 79e6803732..c8feb2c1f7 100644 --- a/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/poset-of-radical-ideals-commutative-rings.lagda.md @@ -11,6 +11,7 @@ open import commutative-algebra.commutative-rings open import commutative-algebra.poset-of-ideals-commutative-rings open import commutative-algebra.radical-ideals-commutative-rings +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.subtypes diff --git a/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md b/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md index de9a327c13..5d639db2e8 100644 --- a/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/prime-ideals-commutative-rings.lagda.md @@ -17,6 +17,7 @@ open import commutative-algebra.subsets-commutative-rings open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.function-types open import foundation.identity-types diff --git a/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md b/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md index f087226bc9..f7c1a4a31e 100644 --- a/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/radical-ideals-commutative-rings.lagda.md @@ -15,6 +15,7 @@ open import commutative-algebra.subsets-commutative-rings open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md b/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md index 13a2f12ae2..63c25f6b87 100644 --- a/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md +++ b/src/commutative-algebra/radicals-of-ideals-commutative-rings.lagda.md @@ -21,6 +21,7 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.logical-equivalences open import foundation.propositional-truncations diff --git a/src/commutative-algebra/subsets-commutative-rings.lagda.md b/src/commutative-algebra/subsets-commutative-rings.lagda.md index fd7c2d204e..5dbde46d23 100644 --- a/src/commutative-algebra/subsets-commutative-rings.lagda.md +++ b/src/commutative-algebra/subsets-commutative-rings.lagda.md @@ -9,6 +9,7 @@ module commutative-algebra.subsets-commutative-rings where ```agda open import commutative-algebra.commutative-rings +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositional-extensionality open import foundation.propositions diff --git a/src/commutative-algebra/subsets-commutative-semirings.lagda.md b/src/commutative-algebra/subsets-commutative-semirings.lagda.md index 73f9932341..adfb7d3db5 100644 --- a/src/commutative-algebra/subsets-commutative-semirings.lagda.md +++ b/src/commutative-algebra/subsets-commutative-semirings.lagda.md @@ -9,6 +9,7 @@ module commutative-algebra.subsets-commutative-semirings where ```agda open import commutative-algebra.commutative-semirings +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/commutative-algebra/trivial-commutative-rings.lagda.md b/src/commutative-algebra/trivial-commutative-rings.lagda.md index 8aa4781e63..49a35c6218 100644 --- a/src/commutative-algebra/trivial-commutative-rings.lagda.md +++ b/src/commutative-algebra/trivial-commutative-rings.lagda.md @@ -12,6 +12,8 @@ open import commutative-algebra.isomorphisms-commutative-rings open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.negation open import foundation.propositions open import foundation.sets diff --git a/src/commutative-algebra/zariski-topology.lagda.md b/src/commutative-algebra/zariski-topology.lagda.md index b3bbbec25c..d552a8e8c8 100644 --- a/src/commutative-algebra/zariski-topology.lagda.md +++ b/src/commutative-algebra/zariski-topology.lagda.md @@ -10,6 +10,7 @@ module commutative-algebra.zariski-topology where open import commutative-algebra.commutative-rings open import commutative-algebra.prime-ideals-commutative-rings +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.identity-types open import foundation.propositions diff --git a/src/domain-theory/directed-complete-posets.lagda.md b/src/domain-theory/directed-complete-posets.lagda.md index 2225aeff51..f47310a178 100644 --- a/src/domain-theory/directed-complete-posets.lagda.md +++ b/src/domain-theory/directed-complete-posets.lagda.md @@ -11,6 +11,7 @@ open import domain-theory.directed-families-posets open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.logical-equivalences diff --git a/src/domain-theory/directed-families-posets.lagda.md b/src/domain-theory/directed-families-posets.lagda.md index 0b192c1b84..bb4acdfb54 100644 --- a/src/domain-theory/directed-families-posets.lagda.md +++ b/src/domain-theory/directed-families-posets.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.existential-quantification open import foundation.function-types diff --git a/src/domain-theory/omega-complete-posets.lagda.md b/src/domain-theory/omega-complete-posets.lagda.md index 612e60affb..d3c02e74d6 100644 --- a/src/domain-theory/omega-complete-posets.lagda.md +++ b/src/domain-theory/omega-complete-posets.lagda.md @@ -13,6 +13,7 @@ open import elementary-number-theory.natural-numbers open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.logical-equivalences diff --git a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md index 60ce16827f..c53ceea500 100644 --- a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md @@ -17,6 +17,7 @@ open import elementary-number-theory.natural-numbers open import foundation.booleans open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.evaluation-functions open import foundation.existential-quantification diff --git a/src/domain-theory/omega-continuous-maps-posets.lagda.md b/src/domain-theory/omega-continuous-maps-posets.lagda.md index 3781ac426b..43b73432ad 100644 --- a/src/domain-theory/omega-continuous-maps-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-posets.lagda.md @@ -15,6 +15,7 @@ open import elementary-number-theory.natural-numbers open import foundation.booleans open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.evaluation-functions open import foundation.existential-quantification diff --git a/src/domain-theory/reindexing-directed-families-posets.lagda.md b/src/domain-theory/reindexing-directed-families-posets.lagda.md index 28396bf30a..8609ed61a0 100644 --- a/src/domain-theory/reindexing-directed-families-posets.lagda.md +++ b/src/domain-theory/reindexing-directed-families-posets.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.existential-quantification open import foundation.function-types diff --git a/src/domain-theory/scott-continuous-maps-posets.lagda.md b/src/domain-theory/scott-continuous-maps-posets.lagda.md index bd50ff479e..f405401866 100644 --- a/src/domain-theory/scott-continuous-maps-posets.lagda.md +++ b/src/domain-theory/scott-continuous-maps-posets.lagda.md @@ -12,6 +12,7 @@ open import domain-theory.reindexing-directed-families-posets open import foundation.booleans open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.evaluation-functions open import foundation.existential-quantification diff --git a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md index d355c01418..16c501a45f 100644 --- a/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/based-strong-induction-natural-numbers.lagda.md @@ -15,6 +15,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.coproduct-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.function-extensionality open import foundation.function-extensionality-axiom diff --git a/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md b/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md index 38bca51942..83e6a7643f 100644 --- a/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md +++ b/src/elementary-number-theory/cross-multiplication-difference-integer-fractions.lagda.md @@ -15,6 +15,7 @@ open import elementary-number-theory.multiplication-integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.negation open import foundation.propositions diff --git a/src/elementary-number-theory/divisibility-integers.lagda.md b/src/elementary-number-theory/divisibility-integers.lagda.md index bed59408c3..e2606d37e3 100644 --- a/src/elementary-number-theory/divisibility-integers.lagda.md +++ b/src/elementary-number-theory/divisibility-integers.lagda.md @@ -26,6 +26,7 @@ open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.function-types open import foundation.identity-types diff --git a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md index 9687ed176c..934d40a703 100644 --- a/src/elementary-number-theory/divisibility-natural-numbers.lagda.md +++ b/src/elementary-number-theory/divisibility-natural-numbers.lagda.md @@ -18,6 +18,7 @@ open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.injective-maps diff --git a/src/elementary-number-theory/equality-integers.lagda.md b/src/elementary-number-theory/equality-integers.lagda.md index 0ff7538a18..52d59d9990 100644 --- a/src/elementary-number-theory/equality-integers.lagda.md +++ b/src/elementary-number-theory/equality-integers.lagda.md @@ -15,6 +15,7 @@ open import foundation.coproduct-types open import foundation.decidable-equality open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.discrete-types open import foundation.empty-types open import foundation.equality-coproduct-types diff --git a/src/elementary-number-theory/equality-natural-numbers.lagda.md b/src/elementary-number-theory/equality-natural-numbers.lagda.md index bb335e5e58..92db29b0ec 100644 --- a/src/elementary-number-theory/equality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/equality-natural-numbers.lagda.md @@ -14,6 +14,7 @@ open import foundation.coproduct-types open import foundation.decidable-equality open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/elementary-number-theory/equality-rational-numbers.lagda.md b/src/elementary-number-theory/equality-rational-numbers.lagda.md index aaf8ae64f0..45b202c9e5 100644 --- a/src/elementary-number-theory/equality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/equality-rational-numbers.lagda.md @@ -13,6 +13,7 @@ open import elementary-number-theory.reduced-integer-fractions open import foundation.decidable-equality open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types diff --git a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md index 770e230cd9..051d844339 100644 --- a/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md +++ b/src/elementary-number-theory/fundamental-theorem-of-arithmetic.lagda.md @@ -31,6 +31,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.propositions diff --git a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md index 5a90091ea9..af621eefb3 100644 --- a/src/elementary-number-theory/inequality-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-conatural-numbers.lagda.md @@ -17,6 +17,7 @@ open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.function-types open import foundation.functoriality-coproduct-types diff --git a/src/elementary-number-theory/inequality-integer-fractions.lagda.md b/src/elementary-number-theory/inequality-integer-fractions.lagda.md index e87b85c1c3..b44c165204 100644 --- a/src/elementary-number-theory/inequality-integer-fractions.lagda.md +++ b/src/elementary-number-theory/inequality-integer-fractions.lagda.md @@ -28,6 +28,7 @@ open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.negation diff --git a/src/elementary-number-theory/inequality-integers.lagda.md b/src/elementary-number-theory/inequality-integers.lagda.md index 1e9c9063f6..421f304fdc 100644 --- a/src/elementary-number-theory/inequality-integers.lagda.md +++ b/src/elementary-number-theory/inequality-integers.lagda.md @@ -23,6 +23,7 @@ open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.functoriality-coproduct-types open import foundation.identity-types diff --git a/src/elementary-number-theory/inequality-natural-numbers.lagda.md b/src/elementary-number-theory/inequality-natural-numbers.lagda.md index a31c50691d..b0b0880abe 100644 --- a/src/elementary-number-theory/inequality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-natural-numbers.lagda.md @@ -19,6 +19,7 @@ open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.function-types open import foundation.functoriality-coproduct-types diff --git a/src/elementary-number-theory/inequality-rational-numbers.lagda.md b/src/elementary-number-theory/inequality-rational-numbers.lagda.md index c8956f0ff1..b11a5dbc2f 100644 --- a/src/elementary-number-theory/inequality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/inequality-rational-numbers.lagda.md @@ -25,6 +25,7 @@ open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.functoriality-coproduct-types open import foundation.identity-types diff --git a/src/elementary-number-theory/inequality-standard-finite-types.lagda.md b/src/elementary-number-theory/inequality-standard-finite-types.lagda.md index d21985ad6f..b1c93bc90d 100644 --- a/src/elementary-number-theory/inequality-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/inequality-standard-finite-types.lagda.md @@ -17,6 +17,7 @@ open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.propositions diff --git a/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md b/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md index 9823b2c9a1..0c8c7fbfb9 100644 --- a/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md +++ b/src/elementary-number-theory/initial-segments-natural-numbers.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.maximum-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/elementary-number-theory/integer-fractions.lagda.md b/src/elementary-number-theory/integer-fractions.lagda.md index c2bc0db1a8..04864113d9 100644 --- a/src/elementary-number-theory/integer-fractions.lagda.md +++ b/src/elementary-number-theory/integer-fractions.lagda.md @@ -19,6 +19,7 @@ open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.decidable-equality open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.identity-types open import foundation.negation diff --git a/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md b/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md index 1a84c70750..366f100b58 100644 --- a/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md +++ b/src/elementary-number-theory/lower-bounds-natural-numbers.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.inequality-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/negative-integers.lagda.md b/src/elementary-number-theory/negative-integers.lagda.md index 86dd90ed11..a5f64cc4f7 100644 --- a/src/elementary-number-theory/negative-integers.lagda.md +++ b/src/elementary-number-theory/negative-integers.lagda.md @@ -17,6 +17,7 @@ open import foundation.coproduct-types open import foundation.decidable-subtypes open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/elementary-number-theory/nonnegative-integers.lagda.md b/src/elementary-number-theory/nonnegative-integers.lagda.md index d9c2b50561..85a0720b09 100644 --- a/src/elementary-number-theory/nonnegative-integers.lagda.md +++ b/src/elementary-number-theory/nonnegative-integers.lagda.md @@ -16,6 +16,7 @@ open import foundation.coproduct-types open import foundation.decidable-subtypes open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/elementary-number-theory/nonpositive-integers.lagda.md b/src/elementary-number-theory/nonpositive-integers.lagda.md index e5a31ad753..431ca888ea 100644 --- a/src/elementary-number-theory/nonpositive-integers.lagda.md +++ b/src/elementary-number-theory/nonpositive-integers.lagda.md @@ -16,6 +16,7 @@ open import foundation.coproduct-types open import foundation.decidable-subtypes open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/elementary-number-theory/nonzero-integers.lagda.md b/src/elementary-number-theory/nonzero-integers.lagda.md index 2d7dd2e4a9..5986d0c520 100644 --- a/src/elementary-number-theory/nonzero-integers.lagda.md +++ b/src/elementary-number-theory/nonzero-integers.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.negation open import foundation.propositions diff --git a/src/elementary-number-theory/nonzero-rational-numbers.lagda.md b/src/elementary-number-theory/nonzero-rational-numbers.lagda.md index 29defc2276..3881bd004b 100644 --- a/src/elementary-number-theory/nonzero-rational-numbers.lagda.md +++ b/src/elementary-number-theory/nonzero-rational-numbers.lagda.md @@ -21,6 +21,7 @@ open import elementary-number-theory.reduced-integer-fractions open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.function-types open import foundation.functoriality-coproduct-types diff --git a/src/elementary-number-theory/peano-arithmetic.lagda.md b/src/elementary-number-theory/peano-arithmetic.lagda.md index 97139b2a63..a9258f1f5f 100644 --- a/src/elementary-number-theory/peano-arithmetic.lagda.md +++ b/src/elementary-number-theory/peano-arithmetic.lagda.md @@ -10,6 +10,7 @@ module elementary-number-theory.peano-arithmetic where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md b/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md index 4977a5e18b..985af13295 100644 --- a/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md +++ b/src/elementary-number-theory/poset-of-natural-numbers-ordered-by-divisibility.lagda.md @@ -15,6 +15,7 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.propositional-truncations diff --git a/src/elementary-number-theory/positive-integer-fractions.lagda.md b/src/elementary-number-theory/positive-integer-fractions.lagda.md index 7e92ff3e65..b419f808b3 100644 --- a/src/elementary-number-theory/positive-integer-fractions.lagda.md +++ b/src/elementary-number-theory/positive-integer-fractions.lagda.md @@ -16,6 +16,7 @@ open import elementary-number-theory.multiplication-positive-and-negative-intege open import elementary-number-theory.positive-integers open import elementary-number-theory.reduced-integer-fractions +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/elementary-number-theory/positive-integers.lagda.md b/src/elementary-number-theory/positive-integers.lagda.md index 9070e78e0c..e06deadc44 100644 --- a/src/elementary-number-theory/positive-integers.lagda.md +++ b/src/elementary-number-theory/positive-integers.lagda.md @@ -18,6 +18,7 @@ open import foundation.coproduct-types open import foundation.decidable-subtypes open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.existential-quantification diff --git a/src/elementary-number-theory/positive-rational-numbers.lagda.md b/src/elementary-number-theory/positive-rational-numbers.lagda.md index 439940ac49..003fa82ca9 100644 --- a/src/elementary-number-theory/positive-rational-numbers.lagda.md +++ b/src/elementary-number-theory/positive-rational-numbers.lagda.md @@ -37,6 +37,7 @@ open import foundation.binary-transport open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.existential-quantification diff --git a/src/elementary-number-theory/prime-numbers.lagda.md b/src/elementary-number-theory/prime-numbers.lagda.md index 930d240933..e3b44e74f0 100644 --- a/src/elementary-number-theory/prime-numbers.lagda.md +++ b/src/elementary-number-theory/prime-numbers.lagda.md @@ -22,6 +22,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md b/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md index 0f35339378..269b16ea3a 100644 --- a/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md +++ b/src/elementary-number-theory/proper-divisors-natural-numbers.lagda.md @@ -18,6 +18,7 @@ open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.cartesian-product-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.negated-equality diff --git a/src/elementary-number-theory/rational-numbers.lagda.md b/src/elementary-number-theory/rational-numbers.lagda.md index 732f9bb66f..dd28e9697d 100644 --- a/src/elementary-number-theory/rational-numbers.lagda.md +++ b/src/elementary-number-theory/rational-numbers.lagda.md @@ -18,6 +18,7 @@ open import elementary-number-theory.reduced-integer-fractions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-cartesian-product-types open import foundation.equality-dependent-pair-types open import foundation.identity-types diff --git a/src/elementary-number-theory/reduced-integer-fractions.lagda.md b/src/elementary-number-theory/reduced-integer-fractions.lagda.md index b74d316dd3..084afcbad4 100644 --- a/src/elementary-number-theory/reduced-integer-fractions.lagda.md +++ b/src/elementary-number-theory/reduced-integer-fractions.lagda.md @@ -23,6 +23,7 @@ open import elementary-number-theory.relatively-prime-integers open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-cartesian-product-types open import foundation.equality-dependent-pair-types diff --git a/src/elementary-number-theory/relatively-prime-integers.lagda.md b/src/elementary-number-theory/relatively-prime-integers.lagda.md index a3719203ab..517be019de 100644 --- a/src/elementary-number-theory/relatively-prime-integers.lagda.md +++ b/src/elementary-number-theory/relatively-prime-integers.lagda.md @@ -14,6 +14,7 @@ open import elementary-number-theory.integers open import elementary-number-theory.relatively-prime-natural-numbers open import foundation.action-on-identifications-functions +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md b/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md index 01f59c2f4b..b8859eaf45 100644 --- a/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md +++ b/src/elementary-number-theory/relatively-prime-natural-numbers.lagda.md @@ -17,6 +17,7 @@ open import elementary-number-theory.prime-numbers open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.negated-equality open import foundation.propositions diff --git a/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md b/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md index d58fbf1f4c..b8b78413dd 100644 --- a/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md +++ b/src/elementary-number-theory/strict-inequality-integer-fractions.lagda.md @@ -32,6 +32,7 @@ open import foundation.conjunction open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.existential-quantification open import foundation.function-types diff --git a/src/elementary-number-theory/strict-inequality-integers.lagda.md b/src/elementary-number-theory/strict-inequality-integers.lagda.md index 107592ee5c..60b45e669f 100644 --- a/src/elementary-number-theory/strict-inequality-integers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-integers.lagda.md @@ -26,6 +26,7 @@ open import foundation.binary-transport open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.functoriality-coproduct-types open import foundation.identity-types diff --git a/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md b/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md index 623bc26c65..ea79df0494 100644 --- a/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-natural-numbers.lagda.md @@ -19,6 +19,7 @@ open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.function-types open import foundation.functoriality-coproduct-types diff --git a/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md b/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md index 99d4619055..cf0c24d8e0 100644 --- a/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md +++ b/src/elementary-number-theory/strict-inequality-rational-numbers.lagda.md @@ -35,6 +35,7 @@ open import foundation.conjunction open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.existential-quantification open import foundation.function-types diff --git a/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md b/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md index 5083034a1f..6768d75116 100644 --- a/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/strict-inequality-standard-finite-types.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.coproduct-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.function-types open import foundation.identity-types diff --git a/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md b/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md index 6a0bf777c5..6a176168b7 100644 --- a/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md +++ b/src/elementary-number-theory/strong-induction-natural-numbers.lagda.md @@ -15,6 +15,7 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.function-extensionality open import foundation.function-types diff --git a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md index 54e612e108..1f524c4ab7 100644 --- a/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md +++ b/src/elementary-number-theory/universal-property-conatural-numbers.lagda.md @@ -9,6 +9,7 @@ module elementary-number-theory.universal-property-conatural-numbers where ```agda open import foundation.coalgebras-maybe open import foundation.contractible-types +open import foundation.dependent-products-contractible-types open import foundation.morphisms-coalgebras-maybe open import foundation.universe-levels ``` diff --git a/src/elementary-number-theory/universal-property-integers.lagda.md b/src/elementary-number-theory/universal-property-integers.lagda.md index 2d36403b4e..47bb00e8c2 100644 --- a/src/elementary-number-theory/universal-property-integers.lagda.md +++ b/src/elementary-number-theory/universal-property-integers.lagda.md @@ -14,6 +14,8 @@ open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/elementary-number-theory/universal-property-natural-numbers.lagda.md b/src/elementary-number-theory/universal-property-natural-numbers.lagda.md index 69460d3015..cfc45bdee2 100644 --- a/src/elementary-number-theory/universal-property-natural-numbers.lagda.md +++ b/src/elementary-number-theory/universal-property-natural-numbers.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md b/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md index a72905645f..6ff60ea7a3 100644 --- a/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md +++ b/src/elementary-number-theory/well-ordering-principle-natural-numbers.lagda.md @@ -15,6 +15,7 @@ open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.functoriality-dependent-pair-types open import foundation.hilberts-epsilon-operators diff --git a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md index a422c722f0..f8ab98a1db 100644 --- a/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md +++ b/src/elementary-number-theory/well-ordering-principle-standard-finite-types.lagda.md @@ -17,6 +17,7 @@ open import foundation.coproduct-types open import foundation.decidable-subtypes open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/finite-algebra/commutative-finite-rings.lagda.md b/src/finite-algebra/commutative-finite-rings.lagda.md index 035aeea3e7..1519eeccc0 100644 --- a/src/finite-algebra/commutative-finite-rings.lagda.md +++ b/src/finite-algebra/commutative-finite-rings.lagda.md @@ -19,6 +19,7 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.binary-embeddings open import foundation.binary-equivalences +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.identity-types diff --git a/src/finite-algebra/finite-fields.lagda.md b/src/finite-algebra/finite-fields.lagda.md index 27425b25c9..d0389c1e39 100644 --- a/src/finite-algebra/finite-fields.lagda.md +++ b/src/finite-algebra/finite-fields.lagda.md @@ -20,6 +20,7 @@ open import foundation.action-on-identifications-binary-functions open import foundation.binary-embeddings open import foundation.binary-equivalences open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.identity-types diff --git a/src/finite-algebra/finite-rings.lagda.md b/src/finite-algebra/finite-rings.lagda.md index e78ca56b4d..5c640f913e 100644 --- a/src/finite-algebra/finite-rings.lagda.md +++ b/src/finite-algebra/finite-rings.lagda.md @@ -16,6 +16,7 @@ open import finite-group-theory.finite-monoids open import foundation.binary-embeddings open import foundation.binary-equivalences +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.identity-types diff --git a/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md b/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md index 21ac9504c6..65ba21ad6b 100644 --- a/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md +++ b/src/finite-algebra/homomorphisms-commutative-finite-rings.lagda.md @@ -12,6 +12,7 @@ open import commutative-algebra.homomorphisms-commutative-semirings open import finite-algebra.commutative-finite-rings +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.propositions diff --git a/src/finite-algebra/homomorphisms-finite-rings.lagda.md b/src/finite-algebra/homomorphisms-finite-rings.lagda.md index 9cc03a1249..5d6a8219c7 100644 --- a/src/finite-algebra/homomorphisms-finite-rings.lagda.md +++ b/src/finite-algebra/homomorphisms-finite-rings.lagda.md @@ -9,6 +9,7 @@ module finite-algebra.homomorphisms-finite-rings where ```agda open import finite-algebra.finite-rings +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.propositions diff --git a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md index bf4f606cc2..e60eb8b932 100644 --- a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md @@ -21,6 +21,7 @@ open import foundation.action-on-equivalences-type-families-over-subuniverses open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalence-relations open import foundation.equivalences open import foundation.identity-types diff --git a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md index 4cc333bf45..96b95761fd 100644 --- a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md @@ -27,6 +27,9 @@ open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.embeddings open import foundation.empty-types open import foundation.equality-dependent-pair-types diff --git a/src/finite-group-theory/finite-abelian-groups.lagda.md b/src/finite-group-theory/finite-abelian-groups.lagda.md index 51bc616d82..f944d3248b 100644 --- a/src/finite-group-theory/finite-abelian-groups.lagda.md +++ b/src/finite-group-theory/finite-abelian-groups.lagda.md @@ -9,6 +9,7 @@ module finite-group-theory.finite-abelian-groups where ```agda open import finite-group-theory.finite-groups +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.interchange-law diff --git a/src/finite-group-theory/finite-groups.lagda.md b/src/finite-group-theory/finite-groups.lagda.md index b52469f559..1ba2e32f92 100644 --- a/src/finite-group-theory/finite-groups.lagda.md +++ b/src/finite-group-theory/finite-groups.lagda.md @@ -17,6 +17,7 @@ open import foundation.binary-embeddings open import foundation.binary-equivalences open import foundation.decidable-equality open import foundation.decidable-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/finite-group-theory/finite-monoids.lagda.md b/src/finite-group-theory/finite-monoids.lagda.md index 36b3f1e29b..db50be0278 100644 --- a/src/finite-group-theory/finite-monoids.lagda.md +++ b/src/finite-group-theory/finite-monoids.lagda.md @@ -15,6 +15,7 @@ open import foundation.1-types open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.mere-equivalences diff --git a/src/finite-group-theory/finite-semigroups.lagda.md b/src/finite-group-theory/finite-semigroups.lagda.md index 40f90172d9..659ad674db 100644 --- a/src/finite-group-theory/finite-semigroups.lagda.md +++ b/src/finite-group-theory/finite-semigroups.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.1-types open import foundation.decidable-propositions +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/finite-group-theory/finite-type-groups.lagda.md b/src/finite-group-theory/finite-type-groups.lagda.md index 4b7783f027..b4e0df3adb 100644 --- a/src/finite-group-theory/finite-type-groups.lagda.md +++ b/src/finite-group-theory/finite-type-groups.lagda.md @@ -14,6 +14,8 @@ open import elementary-number-theory.natural-numbers open import foundation.0-connected-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.equality-dependent-pair-types open import foundation.function-extensionality open import foundation.function-types diff --git a/src/finite-group-theory/orbits-permutations.lagda.md b/src/finite-group-theory/orbits-permutations.lagda.md index 06919a3b39..150b518f55 100644 --- a/src/finite-group-theory/orbits-permutations.lagda.md +++ b/src/finite-group-theory/orbits-permutations.lagda.md @@ -31,6 +31,7 @@ open import foundation.decidable-equivalence-relations open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.empty-types open import foundation.equality-dependent-pair-types diff --git a/src/finite-group-theory/permutations-standard-finite-types.lagda.md b/src/finite-group-theory/permutations-standard-finite-types.lagda.md index 0be0d3314d..28535a7fe5 100644 --- a/src/finite-group-theory/permutations-standard-finite-types.lagda.md +++ b/src/finite-group-theory/permutations-standard-finite-types.lagda.md @@ -19,6 +19,7 @@ open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalence-extensionality diff --git a/src/finite-group-theory/permutations.lagda.md b/src/finite-group-theory/permutations.lagda.md index 02097ffebf..22915dcf89 100644 --- a/src/finite-group-theory/permutations.lagda.md +++ b/src/finite-group-theory/permutations.lagda.md @@ -22,6 +22,9 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalence-extensionality diff --git a/src/finite-group-theory/sign-homomorphism.lagda.md b/src/finite-group-theory/sign-homomorphism.lagda.md index 877705c2d4..e888295882 100644 --- a/src/finite-group-theory/sign-homomorphism.lagda.md +++ b/src/finite-group-theory/sign-homomorphism.lagda.md @@ -19,6 +19,7 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.function-types diff --git a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md index b416cd96b6..8fb9e6fd97 100644 --- a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md @@ -28,6 +28,7 @@ open import foundation.coproduct-types open import foundation.decidable-equivalence-relations open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.empty-types open import foundation.equivalence-classes open import foundation.equivalence-extensionality diff --git a/src/finite-group-theory/subgroups-finite-groups.lagda.md b/src/finite-group-theory/subgroups-finite-groups.lagda.md index e693dcaa67..83c1e6247d 100644 --- a/src/finite-group-theory/subgroups-finite-groups.lagda.md +++ b/src/finite-group-theory/subgroups-finite-groups.lagda.md @@ -12,6 +12,7 @@ open import finite-group-theory.finite-semigroups open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalence-relations open import foundation.equivalences diff --git a/src/finite-group-theory/transpositions-standard-finite-types.lagda.md b/src/finite-group-theory/transpositions-standard-finite-types.lagda.md index bd345f2692..23923436c8 100644 --- a/src/finite-group-theory/transpositions-standard-finite-types.lagda.md +++ b/src/finite-group-theory/transpositions-standard-finite-types.lagda.md @@ -17,6 +17,7 @@ open import finite-group-theory.transpositions open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/finite-group-theory/transpositions.lagda.md b/src/finite-group-theory/transpositions.lagda.md index ad26d6e6af..477adf32dd 100644 --- a/src/finite-group-theory/transpositions.lagda.md +++ b/src/finite-group-theory/transpositions.lagda.md @@ -20,6 +20,7 @@ open import foundation.decidable-propositions open import foundation.decidable-subtypes open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalence-extensionality diff --git a/src/foundation-core/1-types.lagda.md b/src/foundation-core/1-types.lagda.md index 79ac7bd491..e77e1f77a1 100644 --- a/src/foundation-core/1-types.lagda.md +++ b/src/foundation-core/1-types.lagda.md @@ -9,6 +9,8 @@ module foundation-core.1-types where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-truncated-types open import foundation.truncated-types open import foundation.universe-levels diff --git a/src/foundation/0-connected-types.lagda.md b/src/foundation/0-connected-types.lagda.md index d2bdc9203d..6ddc4d196a 100644 --- a/src/foundation/0-connected-types.lagda.md +++ b/src/foundation/0-connected-types.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.constant-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.fiber-inclusions open import foundation.functoriality-set-truncation open import foundation.images diff --git a/src/foundation/connected-components.lagda.md b/src/foundation/connected-components.lagda.md index 9de3f80bbc..b4518a4ce1 100644 --- a/src/foundation/connected-components.lagda.md +++ b/src/foundation/connected-components.lagda.md @@ -9,6 +9,7 @@ module foundation.connected-components where ```agda open import foundation.0-connected-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.logical-equivalences open import foundation.mere-equality open import foundation.propositional-truncations diff --git a/src/foundation/connected-maps.lagda.md b/src/foundation/connected-maps.lagda.md index 74bc45c267..45bfc39a86 100644 --- a/src/foundation/connected-maps.lagda.md +++ b/src/foundation/connected-maps.lagda.md @@ -10,6 +10,7 @@ module foundation.connected-maps where open import foundation.connected-types open import foundation.dependent-pair-types open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.function-extensionality-axiom open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction diff --git a/src/foundation/connected-types.lagda.md b/src/foundation/connected-types.lagda.md index 433b38821f..c6a72c99b6 100644 --- a/src/foundation/connected-types.lagda.md +++ b/src/foundation/connected-types.lagda.md @@ -9,6 +9,8 @@ module foundation.connected-types where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.function-extensionality-axiom open import foundation.functoriality-truncation open import foundation.inhabited-types diff --git a/src/foundation/contractible-types.lagda.md b/src/foundation/contractible-types.lagda.md index 0a1a3f297f..d335c28e74 100644 --- a/src/foundation/contractible-types.lagda.md +++ b/src/foundation/contractible-types.lagda.md @@ -4,7 +4,6 @@ module foundation.contractible-types where open import foundation-core.contractible-types public -open import foundation.dependent-products-contractible-types public ```
Imports @@ -12,6 +11,7 @@ open import foundation.dependent-products-contractible-types public ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.logical-equivalences diff --git a/src/foundation/copartial-functions.lagda.md b/src/foundation/copartial-functions.lagda.md index 6b5c611c47..f205b74049 100644 --- a/src/foundation/copartial-functions.lagda.md +++ b/src/foundation/copartial-functions.lagda.md @@ -8,6 +8,7 @@ module foundation.copartial-functions where ```agda open import foundation.copartial-elements +open import foundation.dependent-products-propositions open import foundation.partial-functions open import foundation.propositions open import foundation.universe-levels diff --git a/src/foundation/decidable-propositions.lagda.md b/src/foundation/decidable-propositions.lagda.md index 5a6cc27816..d2425e4573 100644 --- a/src/foundation/decidable-propositions.lagda.md +++ b/src/foundation/decidable-propositions.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-functions open import foundation.booleans open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.empty-types open import foundation.equivalences diff --git a/src/foundation/dependent-binomial-theorem.lagda.md b/src/foundation/dependent-binomial-theorem.lagda.md index d86a4ac378..8be54bea03 100644 --- a/src/foundation/dependent-binomial-theorem.lagda.md +++ b/src/foundation/dependent-binomial-theorem.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.coproduct-decompositions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.functoriality-cartesian-product-types open import foundation.functoriality-dependent-function-types diff --git a/src/foundation/diaconescus-theorem.lagda.md b/src/foundation/diaconescus-theorem.lagda.md index 246899fdd2..0a0e266a2a 100644 --- a/src/foundation/diaconescus-theorem.lagda.md +++ b/src/foundation/diaconescus-theorem.lagda.md @@ -13,6 +13,7 @@ open import foundation.booleans open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.law-of-excluded-middle open import foundation.logical-equivalences open import foundation.propositional-truncations diff --git a/src/foundation/discrete-reflexive-relations.lagda.md b/src/foundation/discrete-reflexive-relations.lagda.md index 2bb6edc906..38a8f6f96c 100644 --- a/src/foundation/discrete-reflexive-relations.lagda.md +++ b/src/foundation/discrete-reflexive-relations.lagda.md @@ -10,6 +10,7 @@ module foundation.discrete-reflexive-relations where open import foundation.binary-relations open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.reflexive-relations open import foundation.torsorial-type-families diff --git a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md index 5c88106f31..334f37a62f 100644 --- a/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-relaxed-sigma-decompositions.lagda.md @@ -10,6 +10,7 @@ module foundation.discrete-relaxed-sigma-decompositions where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.raising-universe-levels-unit-type diff --git a/src/foundation/discrete-sigma-decompositions.lagda.md b/src/foundation/discrete-sigma-decompositions.lagda.md index 4f46918e5b..7527dd92bd 100644 --- a/src/foundation/discrete-sigma-decompositions.lagda.md +++ b/src/foundation/discrete-sigma-decompositions.lagda.md @@ -10,6 +10,7 @@ module foundation.discrete-sigma-decompositions where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.propositional-truncations diff --git a/src/foundation/double-negation-modality.lagda.md b/src/foundation/double-negation-modality.lagda.md index 89f91c3ee0..fb98a826a1 100644 --- a/src/foundation/double-negation-modality.lagda.md +++ b/src/foundation/double-negation-modality.lagda.md @@ -8,6 +8,7 @@ module foundation.double-negation-modality where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.empty-types open import foundation.logical-equivalences diff --git a/src/foundation/equivalences-span-diagrams.lagda.md b/src/foundation/equivalences-span-diagrams.lagda.md index 92238d6cff..d758f29cdf 100644 --- a/src/foundation/equivalences-span-diagrams.lagda.md +++ b/src/foundation/equivalences-span-diagrams.lagda.md @@ -9,6 +9,7 @@ module foundation.equivalences-span-diagrams where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.equivalences-arrows open import foundation.equivalences-spans diff --git a/src/foundation/extensions-types-global-subuniverses.lagda.md b/src/foundation/extensions-types-global-subuniverses.lagda.md index a75184e2aa..2465e402f9 100644 --- a/src/foundation/extensions-types-global-subuniverses.lagda.md +++ b/src/foundation/extensions-types-global-subuniverses.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-triangles-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.extensions-types diff --git a/src/foundation/extensions-types-subuniverses.lagda.md b/src/foundation/extensions-types-subuniverses.lagda.md index b76a1afee1..602d1706eb 100644 --- a/src/foundation/extensions-types-subuniverses.lagda.md +++ b/src/foundation/extensions-types-subuniverses.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-triangles-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.extensions-types diff --git a/src/foundation/functional-correspondences.lagda.md b/src/foundation/functional-correspondences.lagda.md index d2a98ae2fe..50d3e16e47 100644 --- a/src/foundation/functional-correspondences.lagda.md +++ b/src/foundation/functional-correspondences.lagda.md @@ -10,6 +10,7 @@ module foundation.functional-correspondences where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.function-extensionality diff --git a/src/foundation/homotopy-preorder-of-types.lagda.md b/src/foundation/homotopy-preorder-of-types.lagda.md index c6c1e1902e..751faa0f5c 100644 --- a/src/foundation/homotopy-preorder-of-types.lagda.md +++ b/src/foundation/homotopy-preorder-of-types.lagda.md @@ -10,6 +10,7 @@ module ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.mere-functions diff --git a/src/foundation/infinitely-coherent-equivalences.lagda.md b/src/foundation/infinitely-coherent-equivalences.lagda.md index a650beffa9..0e9ecb5fd4 100644 --- a/src/foundation/infinitely-coherent-equivalences.lagda.md +++ b/src/foundation/infinitely-coherent-equivalences.lagda.md @@ -11,6 +11,7 @@ module foundation.infinitely-coherent-equivalences where ```agda open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/foundation/inhabited-types.lagda.md b/src/foundation/inhabited-types.lagda.md index ff290bc467..06ef1fb332 100644 --- a/src/foundation/inhabited-types.lagda.md +++ b/src/foundation/inhabited-types.lagda.md @@ -9,6 +9,7 @@ module foundation.inhabited-types where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-function-types open import foundation.functoriality-propositional-truncation open import foundation.fundamental-theorem-of-identity-types diff --git a/src/foundation/irrefutable-propositions.lagda.md b/src/foundation/irrefutable-propositions.lagda.md index d89ec3fd7b..99ba2702aa 100644 --- a/src/foundation/irrefutable-propositions.lagda.md +++ b/src/foundation/irrefutable-propositions.lagda.md @@ -13,6 +13,7 @@ open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.empty-types diff --git a/src/foundation/large-apartness-relations.lagda.md b/src/foundation/large-apartness-relations.lagda.md index b87c9a5b09..ca04529c9e 100644 --- a/src/foundation/large-apartness-relations.lagda.md +++ b/src/foundation/large-apartness-relations.lagda.md @@ -7,6 +7,7 @@ module foundation.large-apartness-relations where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.large-binary-relations open import foundation.negated-equality diff --git a/src/foundation/null-homotopic-maps.lagda.md b/src/foundation/null-homotopic-maps.lagda.md index 2500c019f4..6cc34e69b3 100644 --- a/src/foundation/null-homotopic-maps.lagda.md +++ b/src/foundation/null-homotopic-maps.lagda.md @@ -10,6 +10,7 @@ module foundation.null-homotopic-maps where open import foundation.commuting-triangles-of-identifications open import foundation.constant-maps open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/foundation/partitions.lagda.md b/src/foundation/partitions.lagda.md index b46f3f5c10..ec8c78a019 100644 --- a/src/foundation/partitions.lagda.md +++ b/src/foundation/partitions.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.conjunction open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences diff --git a/src/foundation/powersets.lagda.md b/src/foundation/powersets.lagda.md index e195cf37f9..0823ad893f 100644 --- a/src/foundation/powersets.lagda.md +++ b/src/foundation/powersets.lagda.md @@ -8,6 +8,7 @@ module foundation.powersets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.large-locale-of-propositions diff --git a/src/foundation/propositions.lagda.md b/src/foundation/propositions.lagda.md index 75b2a12684..35cb7fef2d 100644 --- a/src/foundation/propositions.lagda.md +++ b/src/foundation/propositions.lagda.md @@ -4,7 +4,6 @@ module foundation.propositions where open import foundation-core.propositions public -open import foundation.dependent-products-propositions public ```
Imports @@ -12,6 +11,8 @@ open import foundation.dependent-products-propositions public ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.fibers-of-maps open import foundation.logical-equivalences open import foundation.retracts-of-types diff --git a/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md b/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md index c830446ce5..0c385b41dd 100644 --- a/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md +++ b/src/foundation/regensburg-extension-fundamental-theorem-of-identity-types.lagda.md @@ -13,6 +13,7 @@ open import foundation.0-connected-types open import foundation.connected-maps open import foundation.connected-types open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.equivalences open import foundation.fiber-inclusions open import foundation.fibers-of-maps diff --git a/src/foundation/sets.lagda.md b/src/foundation/sets.lagda.md index f486be35a9..a60440cc1b 100644 --- a/src/foundation/sets.lagda.md +++ b/src/foundation/sets.lagda.md @@ -11,6 +11,7 @@ open import foundation-core.sets public ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-truncated-types open import foundation.logical-equivalences open import foundation.subuniverses diff --git a/src/foundation/singleton-subtypes.lagda.md b/src/foundation/singleton-subtypes.lagda.md index b624eca1cc..d9ed363927 100644 --- a/src/foundation/singleton-subtypes.lagda.md +++ b/src/foundation/singleton-subtypes.lagda.md @@ -10,6 +10,7 @@ module foundation.singleton-subtypes where open import foundation.connected-components open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.functoriality-propositional-truncation open import foundation.images-subtypes open import foundation.inhabited-subtypes diff --git a/src/foundation/strong-preunivalence.lagda.md b/src/foundation/strong-preunivalence.lagda.md index 051e55fa52..dff170a8bb 100644 --- a/src/foundation/strong-preunivalence.lagda.md +++ b/src/foundation/strong-preunivalence.lagda.md @@ -9,6 +9,8 @@ module foundation.strong-preunivalence where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.preunivalence diff --git a/src/foundation/surjective-maps.lagda.md b/src/foundation/surjective-maps.lagda.md index 6296eb39df..02bdc034ba 100644 --- a/src/foundation/surjective-maps.lagda.md +++ b/src/foundation/surjective-maps.lagda.md @@ -11,7 +11,9 @@ open import foundation.action-on-identifications-functions open import foundation.connected-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.embeddings open import foundation.equality-cartesian-product-types open import foundation.functoriality-cartesian-product-types diff --git a/src/foundation/torsorial-type-families.lagda.md b/src/foundation/torsorial-type-families.lagda.md index 0929568e83..4be6dce2f6 100644 --- a/src/foundation/torsorial-type-families.lagda.md +++ b/src/foundation/torsorial-type-families.lagda.md @@ -11,6 +11,7 @@ open import foundation-core.torsorial-type-families public ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.fundamental-theorem-of-identity-types open import foundation.logical-equivalences open import foundation.universal-property-identity-types diff --git a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md index 905d56a633..a2e1fbb690 100644 --- a/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-relaxed-sigma-decompositions.lagda.md @@ -9,6 +9,7 @@ module foundation.trivial-relaxed-sigma-decompositions where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.raising-universe-levels-unit-type open import foundation.relaxed-sigma-decompositions open import foundation.transposition-identifications-along-equivalences diff --git a/src/foundation/trivial-sigma-decompositions.lagda.md b/src/foundation/trivial-sigma-decompositions.lagda.md index d7a099583f..5d5b4f17c5 100644 --- a/src/foundation/trivial-sigma-decompositions.lagda.md +++ b/src/foundation/trivial-sigma-decompositions.lagda.md @@ -9,6 +9,7 @@ module foundation.trivial-sigma-decompositions where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.functoriality-propositional-truncation open import foundation.inhabited-types open import foundation.raising-universe-levels-unit-type diff --git a/src/foundation/truncated-types.lagda.md b/src/foundation/truncated-types.lagda.md index 4233ee729d..11bc7eb2b1 100644 --- a/src/foundation/truncated-types.lagda.md +++ b/src/foundation/truncated-types.lagda.md @@ -4,7 +4,6 @@ module foundation.truncated-types where open import foundation-core.truncated-types public -open import foundation.dependent-products-truncated-types public ```
Imports @@ -13,6 +12,7 @@ open import foundation.dependent-products-truncated-types public open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.equivalences open import foundation.logical-equivalences open import foundation.subtype-identity-principle diff --git a/src/foundation/truncation-equivalences.lagda.md b/src/foundation/truncation-equivalences.lagda.md index 95d6169280..6bb861e192 100644 --- a/src/foundation/truncation-equivalences.lagda.md +++ b/src/foundation/truncation-equivalences.lagda.md @@ -12,6 +12,7 @@ open import foundation.connected-maps open import foundation.connected-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-truncated-types open import foundation.functoriality-truncation open import foundation.identity-types diff --git a/src/foundation/truncations.lagda.md b/src/foundation/truncations.lagda.md index d7bed98e65..d757a7284c 100644 --- a/src/foundation/truncations.lagda.md +++ b/src/foundation/truncations.lagda.md @@ -10,6 +10,8 @@ module foundation.truncations where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-truncated-types open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-function-types diff --git a/src/foundation/type-arithmetic-dependent-function-types.lagda.md b/src/foundation/type-arithmetic-dependent-function-types.lagda.md index 27533716f7..bd861661a8 100644 --- a/src/foundation/type-arithmetic-dependent-function-types.lagda.md +++ b/src/foundation/type-arithmetic-dependent-function-types.lagda.md @@ -9,6 +9,7 @@ module foundation.type-arithmetic-dependent-function-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.functoriality-dependent-function-types open import foundation.type-arithmetic-unit-type open import foundation.unit-type diff --git a/src/foundation/type-arithmetic-unit-type.lagda.md b/src/foundation/type-arithmetic-unit-type.lagda.md index 92febc1ec5..03ca87584d 100644 --- a/src/foundation/type-arithmetic-unit-type.lagda.md +++ b/src/foundation/type-arithmetic-unit-type.lagda.md @@ -8,6 +8,7 @@ module foundation.type-arithmetic-unit-type where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.unit-type open import foundation.universe-levels diff --git a/src/foundation/uniformly-decidable-type-families.lagda.md b/src/foundation/uniformly-decidable-type-families.lagda.md index 9beb5f6b51..a2ad2965ac 100644 --- a/src/foundation/uniformly-decidable-type-families.lagda.md +++ b/src/foundation/uniformly-decidable-type-families.lagda.md @@ -12,6 +12,7 @@ open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.dependent-products-truncated-types open import foundation.equality-coproduct-types open import foundation.inhabited-types diff --git a/src/foundation/univalent-type-families.lagda.md b/src/foundation/univalent-type-families.lagda.md index 0a3999846c..e471866e10 100644 --- a/src/foundation/univalent-type-families.lagda.md +++ b/src/foundation/univalent-type-families.lagda.md @@ -9,6 +9,7 @@ module foundation.univalent-type-families where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types diff --git a/src/foundation/unordered-pairs.lagda.md b/src/foundation/unordered-pairs.lagda.md index 764054eed8..96e88ff402 100644 --- a/src/foundation/unordered-pairs.lagda.md +++ b/src/foundation/unordered-pairs.lagda.md @@ -12,6 +12,7 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-types open import foundation.decidable-equality open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-universal-property-equivalences open import foundation.existential-quantification open import foundation.function-extensionality diff --git a/src/globular-types/discrete-globular-types.lagda.md b/src/globular-types/discrete-globular-types.lagda.md index 77b4dd1141..c6b65c31f3 100644 --- a/src/globular-types/discrete-globular-types.lagda.md +++ b/src/globular-types/discrete-globular-types.lagda.md @@ -10,6 +10,7 @@ module globular-types.discrete-globular-types where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.discrete-binary-relations open import foundation.propositions open import foundation.universe-levels diff --git a/src/globular-types/terminal-globular-types.lagda.md b/src/globular-types/terminal-globular-types.lagda.md index b9007c4347..c5630e58c7 100644 --- a/src/globular-types/terminal-globular-types.lagda.md +++ b/src/globular-types/terminal-globular-types.lagda.md @@ -10,6 +10,7 @@ module globular-types.terminal-globular-types where ```agda open import foundation.contractible-types +open import foundation.dependent-products-contractible-types open import foundation.universe-levels open import globular-types.globular-maps diff --git a/src/graph-theory/connected-undirected-graphs.lagda.md b/src/graph-theory/connected-undirected-graphs.lagda.md index fafe80a55b..e9109e3c7e 100644 --- a/src/graph-theory/connected-undirected-graphs.lagda.md +++ b/src/graph-theory/connected-undirected-graphs.lagda.md @@ -7,6 +7,7 @@ module graph-theory.connected-undirected-graphs where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositional-truncations open import foundation.propositions open import foundation.universe-levels diff --git a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md index 562665d1c4..06387e3440 100644 --- a/src/graph-theory/dependent-products-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-products-reflexive-graphs.lagda.md @@ -12,6 +12,7 @@ open import foundation.binary-transport open import foundation.commuting-squares-of-identifications open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-function-types open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md b/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md index f8b5131441..b8884d3c86 100644 --- a/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md +++ b/src/graph-theory/dependent-sums-reflexive-graphs.lagda.md @@ -9,6 +9,7 @@ module graph-theory.dependent-sums-reflexive-graphs where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.identity-types open import foundation.structure-identity-principle diff --git a/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md b/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md index 9d43af0730..1dfd511684 100644 --- a/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md +++ b/src/graph-theory/discrete-dependent-reflexive-graphs.lagda.md @@ -7,6 +7,7 @@ module graph-theory.discrete-dependent-reflexive-graphs where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/graph-theory/discrete-directed-graphs.lagda.md b/src/graph-theory/discrete-directed-graphs.lagda.md index c3ff8a436b..1653db7780 100644 --- a/src/graph-theory/discrete-directed-graphs.lagda.md +++ b/src/graph-theory/discrete-directed-graphs.lagda.md @@ -9,6 +9,7 @@ module graph-theory.discrete-directed-graphs where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.discrete-binary-relations open import foundation.empty-types open import foundation.equivalences diff --git a/src/graph-theory/discrete-reflexive-graphs.lagda.md b/src/graph-theory/discrete-reflexive-graphs.lagda.md index e750402ea7..504ae19cd1 100644 --- a/src/graph-theory/discrete-reflexive-graphs.lagda.md +++ b/src/graph-theory/discrete-reflexive-graphs.lagda.md @@ -9,6 +9,7 @@ module graph-theory.discrete-reflexive-graphs where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.discrete-reflexive-relations open import foundation.universe-levels diff --git a/src/graph-theory/embeddings-directed-graphs.lagda.md b/src/graph-theory/embeddings-directed-graphs.lagda.md index e483f06dc2..eab04e7cd2 100644 --- a/src/graph-theory/embeddings-directed-graphs.lagda.md +++ b/src/graph-theory/embeddings-directed-graphs.lagda.md @@ -8,6 +8,7 @@ module graph-theory.embeddings-directed-graphs where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.propositions open import foundation.universe-levels diff --git a/src/graph-theory/embeddings-undirected-graphs.lagda.md b/src/graph-theory/embeddings-undirected-graphs.lagda.md index db07969f1c..441fb3adc5 100644 --- a/src/graph-theory/embeddings-undirected-graphs.lagda.md +++ b/src/graph-theory/embeddings-undirected-graphs.lagda.md @@ -8,6 +8,7 @@ module graph-theory.embeddings-undirected-graphs where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.propositions open import foundation.universe-levels diff --git a/src/graph-theory/equivalences-directed-graphs.lagda.md b/src/graph-theory/equivalences-directed-graphs.lagda.md index a95e1ea270..8e303f1034 100644 --- a/src/graph-theory/equivalences-directed-graphs.lagda.md +++ b/src/graph-theory/equivalences-directed-graphs.lagda.md @@ -13,6 +13,7 @@ open import foundation.binary-transport open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-function-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/graph-theory/equivalences-undirected-graphs.lagda.md b/src/graph-theory/equivalences-undirected-graphs.lagda.md index 4b98ef0d5e..90d8cf3284 100644 --- a/src/graph-theory/equivalences-undirected-graphs.lagda.md +++ b/src/graph-theory/equivalences-undirected-graphs.lagda.md @@ -10,6 +10,7 @@ module graph-theory.equivalences-undirected-graphs where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-function-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md b/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md index 685ec29151..d720c8e403 100644 --- a/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/faithful-morphisms-undirected-graphs.lagda.md @@ -8,6 +8,7 @@ module graph-theory.faithful-morphisms-undirected-graphs where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.propositions open import foundation.universe-levels diff --git a/src/graph-theory/fibers-directed-graphs.lagda.md b/src/graph-theory/fibers-directed-graphs.lagda.md index ed82be7273..9e1605ac1d 100644 --- a/src/graph-theory/fibers-directed-graphs.lagda.md +++ b/src/graph-theory/fibers-directed-graphs.lagda.md @@ -10,6 +10,7 @@ module graph-theory.fibers-directed-graphs where open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.homotopies diff --git a/src/graph-theory/matchings.lagda.md b/src/graph-theory/matchings.lagda.md index 66d2d1cc2c..4d333e4239 100644 --- a/src/graph-theory/matchings.lagda.md +++ b/src/graph-theory/matchings.lagda.md @@ -10,6 +10,8 @@ module graph-theory.matchings where open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.unit-type diff --git a/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md b/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md index 9376ae4058..aef2eeb88b 100644 --- a/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md +++ b/src/graph-theory/mere-equivalences-undirected-graphs.lagda.md @@ -7,6 +7,7 @@ module graph-theory.mere-equivalences-undirected-graphs where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositional-truncations open import foundation.propositions open import foundation.universe-levels diff --git a/src/graph-theory/morphisms-undirected-graphs.lagda.md b/src/graph-theory/morphisms-undirected-graphs.lagda.md index aa80fba80a..52ff7182b9 100644 --- a/src/graph-theory/morphisms-undirected-graphs.lagda.md +++ b/src/graph-theory/morphisms-undirected-graphs.lagda.md @@ -10,6 +10,7 @@ module graph-theory.morphisms-undirected-graphs where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-function-types open import foundation.equivalences open import foundation.function-types diff --git a/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md b/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md index 5be62477ee..0c6365722e 100644 --- a/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md +++ b/src/graph-theory/reflecting-maps-undirected-graphs.lagda.md @@ -9,6 +9,7 @@ module graph-theory.reflecting-maps-undirected-graphs where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.symmetric-identity-types open import foundation.unit-type open import foundation.universe-levels diff --git a/src/graph-theory/regular-undirected-graphs.lagda.md b/src/graph-theory/regular-undirected-graphs.lagda.md index 295ec95081..815b1a9373 100644 --- a/src/graph-theory/regular-undirected-graphs.lagda.md +++ b/src/graph-theory/regular-undirected-graphs.lagda.md @@ -7,6 +7,7 @@ module graph-theory.regular-undirected-graphs where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.mere-equivalences open import foundation.propositions open import foundation.universe-levels diff --git a/src/graph-theory/simple-undirected-graphs.lagda.md b/src/graph-theory/simple-undirected-graphs.lagda.md index b81f7668e6..3621105d64 100644 --- a/src/graph-theory/simple-undirected-graphs.lagda.md +++ b/src/graph-theory/simple-undirected-graphs.lagda.md @@ -8,6 +8,7 @@ module graph-theory.simple-undirected-graphs where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.negation open import foundation.propositions diff --git a/src/graph-theory/terminal-directed-graphs.lagda.md b/src/graph-theory/terminal-directed-graphs.lagda.md index d49804435a..95903aeffc 100644 --- a/src/graph-theory/terminal-directed-graphs.lagda.md +++ b/src/graph-theory/terminal-directed-graphs.lagda.md @@ -8,8 +8,10 @@ module graph-theory.terminal-directed-graphs where ```agda open import foundation.contractible-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-pair-types open import foundation.propositions +open import foundation.dependent-products-propositions open import foundation.unit-type open import foundation.universe-levels diff --git a/src/graph-theory/terminal-reflexive-graphs.lagda.md b/src/graph-theory/terminal-reflexive-graphs.lagda.md index 31ff8ae60a..a387b24b43 100644 --- a/src/graph-theory/terminal-reflexive-graphs.lagda.md +++ b/src/graph-theory/terminal-reflexive-graphs.lagda.md @@ -8,8 +8,10 @@ module graph-theory.terminal-reflexive-graphs where ```agda open import foundation.contractible-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-pair-types open import foundation.propositions +open import foundation.dependent-products-propositions open import foundation.unit-type open import foundation.universe-levels diff --git a/src/graph-theory/trails-undirected-graphs.lagda.md b/src/graph-theory/trails-undirected-graphs.lagda.md index 3aaaa397cc..88b42411b0 100644 --- a/src/graph-theory/trails-undirected-graphs.lagda.md +++ b/src/graph-theory/trails-undirected-graphs.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.injective-maps open import foundation.propositions open import foundation.universe-levels diff --git a/src/graph-theory/walks-directed-graphs.lagda.md b/src/graph-theory/walks-directed-graphs.lagda.md index b7e9537b73..62dbd71950 100644 --- a/src/graph-theory/walks-directed-graphs.lagda.md +++ b/src/graph-theory/walks-directed-graphs.lagda.md @@ -15,6 +15,7 @@ open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-cartesian-product-types diff --git a/src/graph-theory/walks-undirected-graphs.lagda.md b/src/graph-theory/walks-undirected-graphs.lagda.md index b73510b8b4..f17e3b7de3 100644 --- a/src/graph-theory/walks-undirected-graphs.lagda.md +++ b/src/graph-theory/walks-undirected-graphs.lagda.md @@ -15,6 +15,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/group-theory/abelian-groups.lagda.md b/src/group-theory/abelian-groups.lagda.md index 6023e6276d..7873001c85 100644 --- a/src/group-theory/abelian-groups.lagda.md +++ b/src/group-theory/abelian-groups.lagda.md @@ -13,6 +13,7 @@ open import foundation.binary-embeddings open import foundation.binary-equivalences open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.full-subtypes diff --git a/src/group-theory/cartesian-products-concrete-groups.lagda.md b/src/group-theory/cartesian-products-concrete-groups.lagda.md index a60202281c..141a833888 100644 --- a/src/group-theory/cartesian-products-concrete-groups.lagda.md +++ b/src/group-theory/cartesian-products-concrete-groups.lagda.md @@ -11,6 +11,8 @@ open import foundation.0-connected-types open import foundation.1-types open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.equivalences open import foundation.identity-types open import foundation.mere-equality diff --git a/src/group-theory/centers-groups.lagda.md b/src/group-theory/centers-groups.lagda.md index a92e3af960..4ba199be39 100644 --- a/src/group-theory/centers-groups.lagda.md +++ b/src/group-theory/centers-groups.lagda.md @@ -8,6 +8,7 @@ module group-theory.centers-groups where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/centers-monoids.lagda.md b/src/group-theory/centers-monoids.lagda.md index 39deb28916..f3c3800be2 100644 --- a/src/group-theory/centers-monoids.lagda.md +++ b/src/group-theory/centers-monoids.lagda.md @@ -8,6 +8,7 @@ module group-theory.centers-monoids where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/centers-semigroups.lagda.md b/src/group-theory/centers-semigroups.lagda.md index 9997e96a0c..e38711f784 100644 --- a/src/group-theory/centers-semigroups.lagda.md +++ b/src/group-theory/centers-semigroups.lagda.md @@ -8,6 +8,7 @@ module group-theory.centers-semigroups where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/central-elements-groups.lagda.md b/src/group-theory/central-elements-groups.lagda.md index 21cd4b9353..f451b3cbb1 100644 --- a/src/group-theory/central-elements-groups.lagda.md +++ b/src/group-theory/central-elements-groups.lagda.md @@ -8,6 +8,7 @@ module group-theory.central-elements-groups where ```agda open import foundation.action-on-identifications-functions +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.subtypes diff --git a/src/group-theory/central-elements-monoids.lagda.md b/src/group-theory/central-elements-monoids.lagda.md index bece727ced..6dbc1ae5bc 100644 --- a/src/group-theory/central-elements-monoids.lagda.md +++ b/src/group-theory/central-elements-monoids.lagda.md @@ -7,6 +7,7 @@ module group-theory.central-elements-monoids where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/central-elements-semigroups.lagda.md b/src/group-theory/central-elements-semigroups.lagda.md index cedeca3a11..78bc8a03ce 100644 --- a/src/group-theory/central-elements-semigroups.lagda.md +++ b/src/group-theory/central-elements-semigroups.lagda.md @@ -8,6 +8,7 @@ module group-theory.central-elements-semigroups where ```agda open import foundation.action-on-identifications-functions +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/group-theory/centralizer-subgroups.lagda.md b/src/group-theory/centralizer-subgroups.lagda.md index 9e44de697c..134a316218 100644 --- a/src/group-theory/centralizer-subgroups.lagda.md +++ b/src/group-theory/centralizer-subgroups.lagda.md @@ -9,6 +9,7 @@ module group-theory.centralizer-subgroups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/group-theory/characteristic-subgroups.lagda.md b/src/group-theory/characteristic-subgroups.lagda.md index 023e2b5cee..18ab7fc99e 100644 --- a/src/group-theory/characteristic-subgroups.lagda.md +++ b/src/group-theory/characteristic-subgroups.lagda.md @@ -7,6 +7,7 @@ module group-theory.characteristic-subgroups where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/commutative-monoids.lagda.md b/src/group-theory/commutative-monoids.lagda.md index ad42cb9e4f..c2131fbee7 100644 --- a/src/group-theory/commutative-monoids.lagda.md +++ b/src/group-theory/commutative-monoids.lagda.md @@ -9,6 +9,7 @@ module group-theory.commutative-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.interchange-law open import foundation.iterated-dependent-product-types diff --git a/src/group-theory/commuting-elements-groups.lagda.md b/src/group-theory/commuting-elements-groups.lagda.md index 9e76af7d68..871a118e81 100644 --- a/src/group-theory/commuting-elements-groups.lagda.md +++ b/src/group-theory/commuting-elements-groups.lagda.md @@ -7,6 +7,7 @@ module group-theory.commuting-elements-groups where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/commuting-elements-monoids.lagda.md b/src/group-theory/commuting-elements-monoids.lagda.md index 3f74bcc1d1..5456c02853 100644 --- a/src/group-theory/commuting-elements-monoids.lagda.md +++ b/src/group-theory/commuting-elements-monoids.lagda.md @@ -7,6 +7,7 @@ module group-theory.commuting-elements-monoids where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/commuting-elements-semigroups.lagda.md b/src/group-theory/commuting-elements-semigroups.lagda.md index 4c5d7998e8..66bb856c8c 100644 --- a/src/group-theory/commuting-elements-semigroups.lagda.md +++ b/src/group-theory/commuting-elements-semigroups.lagda.md @@ -8,6 +8,7 @@ module group-theory.commuting-elements-semigroups where ```agda open import foundation.action-on-identifications-functions +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/group-theory/concrete-groups.lagda.md b/src/group-theory/concrete-groups.lagda.md index 17b5b67ad6..a106030349 100644 --- a/src/group-theory/concrete-groups.lagda.md +++ b/src/group-theory/concrete-groups.lagda.md @@ -10,6 +10,8 @@ module group-theory.concrete-groups where open import foundation.0-connected-types open import foundation.1-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.identity-types open import foundation.mere-equality open import foundation.propositional-truncations diff --git a/src/group-theory/congruence-relations-abelian-groups.lagda.md b/src/group-theory/congruence-relations-abelian-groups.lagda.md index f9f130587d..47871118c9 100644 --- a/src/group-theory/congruence-relations-abelian-groups.lagda.md +++ b/src/group-theory/congruence-relations-abelian-groups.lagda.md @@ -8,6 +8,7 @@ module group-theory.congruence-relations-abelian-groups where ```agda open import foundation.binary-relations +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.identity-types diff --git a/src/group-theory/congruence-relations-commutative-monoids.lagda.md b/src/group-theory/congruence-relations-commutative-monoids.lagda.md index 2b79291e89..a4168fb70e 100644 --- a/src/group-theory/congruence-relations-commutative-monoids.lagda.md +++ b/src/group-theory/congruence-relations-commutative-monoids.lagda.md @@ -8,6 +8,7 @@ module group-theory.congruence-relations-commutative-monoids where ```agda open import foundation.binary-relations +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.identity-types diff --git a/src/group-theory/congruence-relations-groups.lagda.md b/src/group-theory/congruence-relations-groups.lagda.md index ca3018bb5d..02d32c1eb3 100644 --- a/src/group-theory/congruence-relations-groups.lagda.md +++ b/src/group-theory/congruence-relations-groups.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.binary-transport open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.identity-types diff --git a/src/group-theory/congruence-relations-monoids.lagda.md b/src/group-theory/congruence-relations-monoids.lagda.md index ce5778b509..db4d6461b2 100644 --- a/src/group-theory/congruence-relations-monoids.lagda.md +++ b/src/group-theory/congruence-relations-monoids.lagda.md @@ -9,6 +9,7 @@ module group-theory.congruence-relations-monoids where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.identity-types diff --git a/src/group-theory/congruence-relations-semigroups.lagda.md b/src/group-theory/congruence-relations-semigroups.lagda.md index 5ebc48e734..12821950c3 100644 --- a/src/group-theory/congruence-relations-semigroups.lagda.md +++ b/src/group-theory/congruence-relations-semigroups.lagda.md @@ -9,6 +9,7 @@ module group-theory.congruence-relations-semigroups where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types diff --git a/src/group-theory/cores-monoids.lagda.md b/src/group-theory/cores-monoids.lagda.md index 50328b33a1..47c236e1d6 100644 --- a/src/group-theory/cores-monoids.lagda.md +++ b/src/group-theory/cores-monoids.lagda.md @@ -10,6 +10,7 @@ module group-theory.cores-monoids where open import category-theory.functors-large-precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.subtypes diff --git a/src/group-theory/cyclic-groups.lagda.md b/src/group-theory/cyclic-groups.lagda.md index 08c862b1fc..e49680a1be 100644 --- a/src/group-theory/cyclic-groups.lagda.md +++ b/src/group-theory/cyclic-groups.lagda.md @@ -8,6 +8,7 @@ module group-theory.cyclic-groups where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.identity-types open import foundation.inhabited-subtypes diff --git a/src/group-theory/decidable-subgroups.lagda.md b/src/group-theory/decidable-subgroups.lagda.md index e523eb23cb..e8595a07e5 100644 --- a/src/group-theory/decidable-subgroups.lagda.md +++ b/src/group-theory/decidable-subgroups.lagda.md @@ -10,6 +10,7 @@ module group-theory.decidable-subgroups where open import foundation.binary-relations open import foundation.decidable-subtypes open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalence-relations open import foundation.equivalences diff --git a/src/group-theory/elements-of-finite-order-groups.lagda.md b/src/group-theory/elements-of-finite-order-groups.lagda.md index de05cf476b..c63a8048fa 100644 --- a/src/group-theory/elements-of-finite-order-groups.lagda.md +++ b/src/group-theory/elements-of-finite-order-groups.lagda.md @@ -10,6 +10,7 @@ module group-theory.elements-of-finite-order-groups where open import elementary-number-theory.group-of-integers open import elementary-number-theory.nonzero-integers +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/epimorphisms-groups.lagda.md b/src/group-theory/epimorphisms-groups.lagda.md index be41b90450..6084d2e524 100644 --- a/src/group-theory/epimorphisms-groups.lagda.md +++ b/src/group-theory/epimorphisms-groups.lagda.md @@ -9,6 +9,7 @@ module group-theory.epimorphisms-groups where ```agda open import category-theory.epimorphisms-in-large-precategories +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/equivalences-concrete-group-actions.lagda.md b/src/group-theory/equivalences-concrete-group-actions.lagda.md index 27c37431a5..22e1e7eb49 100644 --- a/src/group-theory/equivalences-concrete-group-actions.lagda.md +++ b/src/group-theory/equivalences-concrete-group-actions.lagda.md @@ -9,6 +9,7 @@ module group-theory.equivalences-concrete-group-actions where ```agda open import foundation.1-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equality-dependent-function-types open import foundation.equivalences diff --git a/src/group-theory/equivalences-group-actions.lagda.md b/src/group-theory/equivalences-group-actions.lagda.md index cabae428b7..07ddf148ab 100644 --- a/src/group-theory/equivalences-group-actions.lagda.md +++ b/src/group-theory/equivalences-group-actions.lagda.md @@ -10,6 +10,7 @@ module group-theory.equivalences-group-actions where open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.functoriality-dependent-function-types diff --git a/src/group-theory/equivalences-semigroups.lagda.md b/src/group-theory/equivalences-semigroups.lagda.md index b0ec4a907d..ff96b5f518 100644 --- a/src/group-theory/equivalences-semigroups.lagda.md +++ b/src/group-theory/equivalences-semigroups.lagda.md @@ -8,6 +8,7 @@ module group-theory.equivalences-semigroups where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-types diff --git a/src/group-theory/free-concrete-group-actions.lagda.md b/src/group-theory/free-concrete-group-actions.lagda.md index 7eb0462d9f..eb72881ae8 100644 --- a/src/group-theory/free-concrete-group-actions.lagda.md +++ b/src/group-theory/free-concrete-group-actions.lagda.md @@ -8,6 +8,7 @@ module group-theory.free-concrete-group-actions where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.propositions open import foundation.sets diff --git a/src/group-theory/full-subgroups.lagda.md b/src/group-theory/full-subgroups.lagda.md index 5200efc0f3..61f7e6dc6c 100644 --- a/src/group-theory/full-subgroups.lagda.md +++ b/src/group-theory/full-subgroups.lagda.md @@ -8,6 +8,7 @@ module group-theory.full-subgroups where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.full-subtypes open import foundation.propositions diff --git a/src/group-theory/full-subsemigroups.lagda.md b/src/group-theory/full-subsemigroups.lagda.md index 507941cd28..68b33a7da1 100644 --- a/src/group-theory/full-subsemigroups.lagda.md +++ b/src/group-theory/full-subsemigroups.lagda.md @@ -8,6 +8,7 @@ module group-theory.full-subsemigroups where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.full-subtypes open import foundation.propositions diff --git a/src/group-theory/functoriality-quotient-groups.lagda.md b/src/group-theory/functoriality-quotient-groups.lagda.md index 6b48fc225f..cbc8a0fe85 100644 --- a/src/group-theory/functoriality-quotient-groups.lagda.md +++ b/src/group-theory/functoriality-quotient-groups.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.homotopies open import foundation.identity-types open import foundation.universe-levels diff --git a/src/group-theory/generating-elements-groups.lagda.md b/src/group-theory/generating-elements-groups.lagda.md index f0b26019b2..d4016e3ff4 100644 --- a/src/group-theory/generating-elements-groups.lagda.md +++ b/src/group-theory/generating-elements-groups.lagda.md @@ -13,6 +13,7 @@ open import elementary-number-theory.integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.identity-types diff --git a/src/group-theory/groups.lagda.md b/src/group-theory/groups.lagda.md index ae04f5eb0d..28a107f53d 100644 --- a/src/group-theory/groups.lagda.md +++ b/src/group-theory/groups.lagda.md @@ -13,6 +13,7 @@ open import foundation.binary-embeddings open import foundation.binary-equivalences open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/group-theory/homomorphisms-concrete-group-actions.lagda.md b/src/group-theory/homomorphisms-concrete-group-actions.lagda.md index 62057b8e87..43e9df8f97 100644 --- a/src/group-theory/homomorphisms-concrete-group-actions.lagda.md +++ b/src/group-theory/homomorphisms-concrete-group-actions.lagda.md @@ -8,6 +8,7 @@ module group-theory.homomorphisms-concrete-group-actions where ```agda open import foundation.0-connected-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/group-theory/homomorphisms-generated-subgroups.lagda.md b/src/group-theory/homomorphisms-generated-subgroups.lagda.md index 4f2f8359a6..efa058ae23 100644 --- a/src/group-theory/homomorphisms-generated-subgroups.lagda.md +++ b/src/group-theory/homomorphisms-generated-subgroups.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.dependent-products-truncated-types open import foundation.embeddings open import foundation.equality-dependent-pair-types diff --git a/src/group-theory/homomorphisms-group-actions.lagda.md b/src/group-theory/homomorphisms-group-actions.lagda.md index 7c488f7072..400664e0db 100644 --- a/src/group-theory/homomorphisms-group-actions.lagda.md +++ b/src/group-theory/homomorphisms-group-actions.lagda.md @@ -9,6 +9,7 @@ module group-theory.homomorphisms-group-actions where ```agda open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/group-theory/homomorphisms-groups.lagda.md b/src/group-theory/homomorphisms-groups.lagda.md index a4e286a07f..e9cf7bc4e7 100644 --- a/src/group-theory/homomorphisms-groups.lagda.md +++ b/src/group-theory/homomorphisms-groups.lagda.md @@ -10,6 +10,7 @@ module group-theory.homomorphisms-groups where open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.propositions diff --git a/src/group-theory/homomorphisms-monoids.lagda.md b/src/group-theory/homomorphisms-monoids.lagda.md index f8c37265bd..1ca45a0924 100644 --- a/src/group-theory/homomorphisms-monoids.lagda.md +++ b/src/group-theory/homomorphisms-monoids.lagda.md @@ -9,6 +9,7 @@ module group-theory.homomorphisms-monoids where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies diff --git a/src/group-theory/homomorphisms-semigroups.lagda.md b/src/group-theory/homomorphisms-semigroups.lagda.md index b00a30a3fa..17714303a0 100644 --- a/src/group-theory/homomorphisms-semigroups.lagda.md +++ b/src/group-theory/homomorphisms-semigroups.lagda.md @@ -9,6 +9,7 @@ module group-theory.homomorphisms-semigroups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md b/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md index e592961eb4..fad057642a 100644 --- a/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md +++ b/src/group-theory/integer-multiples-of-elements-abelian-groups.lagda.md @@ -14,6 +14,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/integer-powers-of-elements-groups.lagda.md b/src/group-theory/integer-powers-of-elements-groups.lagda.md index 47de6edf13..5444c8d915 100644 --- a/src/group-theory/integer-powers-of-elements-groups.lagda.md +++ b/src/group-theory/integer-powers-of-elements-groups.lagda.md @@ -14,6 +14,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.coproduct-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.identity-types open import foundation.iterating-automorphisms diff --git a/src/group-theory/inverse-semigroups.lagda.md b/src/group-theory/inverse-semigroups.lagda.md index 983cf5a04e..4cc34b00c4 100644 --- a/src/group-theory/inverse-semigroups.lagda.md +++ b/src/group-theory/inverse-semigroups.lagda.md @@ -10,6 +10,7 @@ module group-theory.inverse-semigroups where open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.identity-types open import foundation.sets open import foundation.universe-levels diff --git a/src/group-theory/invertible-elements-monoids.lagda.md b/src/group-theory/invertible-elements-monoids.lagda.md index c50cf77558..88529335b8 100644 --- a/src/group-theory/invertible-elements-monoids.lagda.md +++ b/src/group-theory/invertible-elements-monoids.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/group-theory/isomorphisms-abelian-groups.lagda.md b/src/group-theory/isomorphisms-abelian-groups.lagda.md index 9d7b07d36e..5f503f17f1 100644 --- a/src/group-theory/isomorphisms-abelian-groups.lagda.md +++ b/src/group-theory/isomorphisms-abelian-groups.lagda.md @@ -10,6 +10,8 @@ module group-theory.isomorphisms-abelian-groups where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/group-theory/isomorphisms-group-actions.lagda.md b/src/group-theory/isomorphisms-group-actions.lagda.md index 49635eee09..c3edfaaebf 100644 --- a/src/group-theory/isomorphisms-group-actions.lagda.md +++ b/src/group-theory/isomorphisms-group-actions.lagda.md @@ -12,6 +12,8 @@ open import category-theory.isomorphisms-in-large-precategories open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.functoriality-dependent-pair-types diff --git a/src/group-theory/isomorphisms-groups.lagda.md b/src/group-theory/isomorphisms-groups.lagda.md index 0ab46ae767..e833547233 100644 --- a/src/group-theory/isomorphisms-groups.lagda.md +++ b/src/group-theory/isomorphisms-groups.lagda.md @@ -11,6 +11,8 @@ open import category-theory.isomorphisms-in-large-precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/group-theory/isomorphisms-monoids.lagda.md b/src/group-theory/isomorphisms-monoids.lagda.md index 5ed4766a19..458ffa98b5 100644 --- a/src/group-theory/isomorphisms-monoids.lagda.md +++ b/src/group-theory/isomorphisms-monoids.lagda.md @@ -9,6 +9,7 @@ module group-theory.isomorphisms-monoids where ```agda open import category-theory.isomorphisms-in-large-precategories +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/group-theory/isomorphisms-semigroups.lagda.md b/src/group-theory/isomorphisms-semigroups.lagda.md index c6f29143b3..4eae2f318e 100644 --- a/src/group-theory/isomorphisms-semigroups.lagda.md +++ b/src/group-theory/isomorphisms-semigroups.lagda.md @@ -12,6 +12,8 @@ open import category-theory.isomorphisms-in-large-precategories open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality-axiom open import foundation.function-types diff --git a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md index d189124e89..5776ced209 100644 --- a/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md +++ b/src/group-theory/iterated-cartesian-products-concrete-groups.lagda.md @@ -14,6 +14,9 @@ open import foundation.1-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-cartesian-product-types diff --git a/src/group-theory/kernels-homomorphisms-groups.lagda.md b/src/group-theory/kernels-homomorphisms-groups.lagda.md index ba177596f8..76c29d2c74 100644 --- a/src/group-theory/kernels-homomorphisms-groups.lagda.md +++ b/src/group-theory/kernels-homomorphisms-groups.lagda.md @@ -9,6 +9,7 @@ module group-theory.kernels-homomorphisms-groups where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-cartesian-product-types open import foundation.identity-types open import foundation.propositions diff --git a/src/group-theory/loop-groups-sets.lagda.md b/src/group-theory/loop-groups-sets.lagda.md index 15fdf92516..2968e00b2e 100644 --- a/src/group-theory/loop-groups-sets.lagda.md +++ b/src/group-theory/loop-groups-sets.lagda.md @@ -9,6 +9,8 @@ module group-theory.loop-groups-sets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md b/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md index 5e895381eb..5cda13063d 100644 --- a/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md +++ b/src/group-theory/mere-equivalences-concrete-group-actions.lagda.md @@ -7,6 +7,7 @@ module group-theory.mere-equivalences-concrete-group-actions where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.functoriality-propositional-truncation open import foundation.mere-equality open import foundation.propositional-truncations diff --git a/src/group-theory/mere-equivalences-group-actions.lagda.md b/src/group-theory/mere-equivalences-group-actions.lagda.md index 72c1412d12..e850631561 100644 --- a/src/group-theory/mere-equivalences-group-actions.lagda.md +++ b/src/group-theory/mere-equivalences-group-actions.lagda.md @@ -7,6 +7,7 @@ module group-theory.mere-equivalences-group-actions where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositional-truncations open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/monoids.lagda.md b/src/group-theory/monoids.lagda.md index 6a0c542cfc..2ba334187b 100644 --- a/src/group-theory/monoids.lagda.md +++ b/src/group-theory/monoids.lagda.md @@ -8,6 +8,7 @@ module group-theory.monoids where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/group-theory/monomorphisms-concrete-groups.lagda.md b/src/group-theory/monomorphisms-concrete-groups.lagda.md index 243579c974..b113383308 100644 --- a/src/group-theory/monomorphisms-concrete-groups.lagda.md +++ b/src/group-theory/monomorphisms-concrete-groups.lagda.md @@ -8,6 +8,7 @@ module group-theory.monomorphisms-concrete-groups where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/monomorphisms-groups.lagda.md b/src/group-theory/monomorphisms-groups.lagda.md index eeebe4fb6c..df3d857208 100644 --- a/src/group-theory/monomorphisms-groups.lagda.md +++ b/src/group-theory/monomorphisms-groups.lagda.md @@ -9,6 +9,7 @@ module group-theory.monomorphisms-groups where ```agda open import category-theory.monomorphisms-in-large-precategories +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/multiples-of-elements-abelian-groups.lagda.md b/src/group-theory/multiples-of-elements-abelian-groups.lagda.md index 475f609270..7a17f4b99e 100644 --- a/src/group-theory/multiples-of-elements-abelian-groups.lagda.md +++ b/src/group-theory/multiples-of-elements-abelian-groups.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/nontrivial-groups.lagda.md b/src/group-theory/nontrivial-groups.lagda.md index 725296c895..b1381777e7 100644 --- a/src/group-theory/nontrivial-groups.lagda.md +++ b/src/group-theory/nontrivial-groups.lagda.md @@ -10,6 +10,8 @@ module group-theory.nontrivial-groups where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.embeddings open import foundation.empty-types diff --git a/src/group-theory/normal-subgroups.lagda.md b/src/group-theory/normal-subgroups.lagda.md index 1691141439..afbb14efed 100644 --- a/src/group-theory/normal-subgroups.lagda.md +++ b/src/group-theory/normal-subgroups.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.binary-transport open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalence-relations open import foundation.equivalences diff --git a/src/group-theory/normal-submonoids-commutative-monoids.lagda.md b/src/group-theory/normal-submonoids-commutative-monoids.lagda.md index 64d971f8b0..247678b483 100644 --- a/src/group-theory/normal-submonoids-commutative-monoids.lagda.md +++ b/src/group-theory/normal-submonoids-commutative-monoids.lagda.md @@ -9,6 +9,7 @@ module group-theory.normal-submonoids-commutative-monoids where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.function-types diff --git a/src/group-theory/normal-submonoids.lagda.md b/src/group-theory/normal-submonoids.lagda.md index 45aaa58a2c..0bb3c046bb 100644 --- a/src/group-theory/normal-submonoids.lagda.md +++ b/src/group-theory/normal-submonoids.lagda.md @@ -10,6 +10,7 @@ module group-theory.normal-submonoids where open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.function-types diff --git a/src/group-theory/normalizer-subgroups.lagda.md b/src/group-theory/normalizer-subgroups.lagda.md index dfdbbcae1a..4b08a72415 100644 --- a/src/group-theory/normalizer-subgroups.lagda.md +++ b/src/group-theory/normalizer-subgroups.lagda.md @@ -8,6 +8,7 @@ module group-theory.normalizer-subgroups where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/group-theory/nullifying-group-homomorphisms.lagda.md b/src/group-theory/nullifying-group-homomorphisms.lagda.md index 92dfe9bbae..60c5d661a4 100644 --- a/src/group-theory/nullifying-group-homomorphisms.lagda.md +++ b/src/group-theory/nullifying-group-homomorphisms.lagda.md @@ -8,6 +8,7 @@ module group-theory.nullifying-group-homomorphisms where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.propositions diff --git a/src/group-theory/perfect-groups.lagda.md b/src/group-theory/perfect-groups.lagda.md index 830d29efab..1c60b806f0 100644 --- a/src/group-theory/perfect-groups.lagda.md +++ b/src/group-theory/perfect-groups.lagda.md @@ -7,6 +7,7 @@ module group-theory.perfect-groups where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/perfect-subgroups.lagda.md b/src/group-theory/perfect-subgroups.lagda.md index 9e4dac3fc1..0dc3e06e9d 100644 --- a/src/group-theory/perfect-subgroups.lagda.md +++ b/src/group-theory/perfect-subgroups.lagda.md @@ -7,6 +7,7 @@ module group-theory.perfect-subgroups where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/powers-of-elements-commutative-monoids.lagda.md b/src/group-theory/powers-of-elements-commutative-monoids.lagda.md index 344471dcb0..7640487f6b 100644 --- a/src/group-theory/powers-of-elements-commutative-monoids.lagda.md +++ b/src/group-theory/powers-of-elements-commutative-monoids.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/powers-of-elements-groups.lagda.md b/src/group-theory/powers-of-elements-groups.lagda.md index 745ee9159a..13accba5b2 100644 --- a/src/group-theory/powers-of-elements-groups.lagda.md +++ b/src/group-theory/powers-of-elements-groups.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/group-theory/powers-of-elements-monoids.lagda.md b/src/group-theory/powers-of-elements-monoids.lagda.md index 66c4e4f41b..fbba7c5858 100644 --- a/src/group-theory/powers-of-elements-monoids.lagda.md +++ b/src/group-theory/powers-of-elements-monoids.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.identity-types open import foundation.propositions diff --git a/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md b/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md index 5a51488a0e..8676fc98f3 100644 --- a/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md +++ b/src/group-theory/precategory-of-orbits-monoid-actions.lagda.md @@ -11,6 +11,8 @@ open import category-theory.precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/group-theory/quotient-groups.lagda.md b/src/group-theory/quotient-groups.lagda.md index d109a8292d..c4f5369b5c 100644 --- a/src/group-theory/quotient-groups.lagda.md +++ b/src/group-theory/quotient-groups.lagda.md @@ -13,6 +13,8 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.effective-maps-equivalence-relations open import foundation.equivalences open import foundation.function-types diff --git a/src/group-theory/quotients-abelian-groups.lagda.md b/src/group-theory/quotients-abelian-groups.lagda.md index 51ce7f9b4a..d152823310 100644 --- a/src/group-theory/quotients-abelian-groups.lagda.md +++ b/src/group-theory/quotients-abelian-groups.lagda.md @@ -12,6 +12,7 @@ module group-theory.quotients-abelian-groups where open import foundation.action-on-identifications-functions open import foundation.binary-functoriality-set-quotients open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.effective-maps-equivalence-relations open import foundation.equivalences open import foundation.functoriality-set-quotients diff --git a/src/group-theory/rational-commutative-monoids.lagda.md b/src/group-theory/rational-commutative-monoids.lagda.md index 2c036f47fe..53f821cbd9 100644 --- a/src/group-theory/rational-commutative-monoids.lagda.md +++ b/src/group-theory/rational-commutative-monoids.lagda.md @@ -10,6 +10,7 @@ module group-theory.rational-commutative-monoids where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.propositions diff --git a/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md b/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md index 52a270e3cb..007f2931e1 100644 --- a/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md +++ b/src/group-theory/saturated-congruence-relations-commutative-monoids.lagda.md @@ -9,6 +9,7 @@ module group-theory.saturated-congruence-relations-commutative-monoids where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types diff --git a/src/group-theory/saturated-congruence-relations-monoids.lagda.md b/src/group-theory/saturated-congruence-relations-monoids.lagda.md index fe77217ff6..fc411179cc 100644 --- a/src/group-theory/saturated-congruence-relations-monoids.lagda.md +++ b/src/group-theory/saturated-congruence-relations-monoids.lagda.md @@ -9,6 +9,7 @@ module group-theory.saturated-congruence-relations-monoids where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types diff --git a/src/group-theory/subgroups-abelian-groups.lagda.md b/src/group-theory/subgroups-abelian-groups.lagda.md index 61238aa5c7..c656fa6f70 100644 --- a/src/group-theory/subgroups-abelian-groups.lagda.md +++ b/src/group-theory/subgroups-abelian-groups.lagda.md @@ -9,6 +9,7 @@ module group-theory.subgroups-abelian-groups where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalence-relations open import foundation.equivalences diff --git a/src/group-theory/subgroups-concrete-groups.lagda.md b/src/group-theory/subgroups-concrete-groups.lagda.md index eb86e36730..e7a205424c 100644 --- a/src/group-theory/subgroups-concrete-groups.lagda.md +++ b/src/group-theory/subgroups-concrete-groups.lagda.md @@ -10,6 +10,7 @@ module group-theory.subgroups-concrete-groups where open import foundation.0-connected-types open import foundation.0-maps open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.existential-quantification open import foundation.faithful-maps diff --git a/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md b/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md index bdcb3c854f..504e2dc37b 100644 --- a/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md +++ b/src/group-theory/subgroups-generated-by-subsets-groups.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.fibers-of-maps open import foundation.function-types open import foundation.identity-types diff --git a/src/group-theory/subgroups.lagda.md b/src/group-theory/subgroups.lagda.md index 98631e94e6..bd70dd89d0 100644 --- a/src/group-theory/subgroups.lagda.md +++ b/src/group-theory/subgroups.lagda.md @@ -13,6 +13,7 @@ open import elementary-number-theory.natural-numbers open import foundation.binary-relations open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.embeddings open import foundation.equivalence-relations diff --git a/src/group-theory/submonoids-commutative-monoids.lagda.md b/src/group-theory/submonoids-commutative-monoids.lagda.md index 1b93a31af2..0f00172c30 100644 --- a/src/group-theory/submonoids-commutative-monoids.lagda.md +++ b/src/group-theory/submonoids-commutative-monoids.lagda.md @@ -8,6 +8,7 @@ module group-theory.submonoids-commutative-monoids where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.propositions diff --git a/src/group-theory/submonoids.lagda.md b/src/group-theory/submonoids.lagda.md index 4245b22e10..24c023825b 100644 --- a/src/group-theory/submonoids.lagda.md +++ b/src/group-theory/submonoids.lagda.md @@ -8,6 +8,7 @@ module group-theory.submonoids where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/group-theory/subsemigroups.lagda.md b/src/group-theory/subsemigroups.lagda.md index f283a68db3..055eff9b3b 100644 --- a/src/group-theory/subsemigroups.lagda.md +++ b/src/group-theory/subsemigroups.lagda.md @@ -8,6 +8,7 @@ module group-theory.subsemigroups where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/group-theory/subsets-commutative-monoids.lagda.md b/src/group-theory/subsets-commutative-monoids.lagda.md index be1275afe2..c45cd504d0 100644 --- a/src/group-theory/subsets-commutative-monoids.lagda.md +++ b/src/group-theory/subsets-commutative-monoids.lagda.md @@ -7,6 +7,7 @@ module group-theory.subsets-commutative-monoids where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/group-theory/subsets-monoids.lagda.md b/src/group-theory/subsets-monoids.lagda.md index 97bb8b9059..1c084d3db8 100644 --- a/src/group-theory/subsets-monoids.lagda.md +++ b/src/group-theory/subsets-monoids.lagda.md @@ -7,6 +7,7 @@ module group-theory.subsets-monoids where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/group-theory/subsets-semigroups.lagda.md b/src/group-theory/subsets-semigroups.lagda.md index ddfdf50d40..cd67fda8ca 100644 --- a/src/group-theory/subsets-semigroups.lagda.md +++ b/src/group-theory/subsets-semigroups.lagda.md @@ -7,6 +7,7 @@ module group-theory.subsets-semigroups where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.large-locale-of-subtypes open import foundation.powersets diff --git a/src/group-theory/surjective-group-homomorphisms.lagda.md b/src/group-theory/surjective-group-homomorphisms.lagda.md index c482bc5e50..150767a0ea 100644 --- a/src/group-theory/surjective-group-homomorphisms.lagda.md +++ b/src/group-theory/surjective-group-homomorphisms.lagda.md @@ -7,6 +7,7 @@ module group-theory.surjective-group-homomorphisms where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.surjective-maps open import foundation.universe-levels diff --git a/src/group-theory/surjective-semigroup-homomorphisms.lagda.md b/src/group-theory/surjective-semigroup-homomorphisms.lagda.md index e112844df8..95cb6e1a97 100644 --- a/src/group-theory/surjective-semigroup-homomorphisms.lagda.md +++ b/src/group-theory/surjective-semigroup-homomorphisms.lagda.md @@ -7,6 +7,7 @@ module group-theory.surjective-semigroup-homomorphisms where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.surjective-maps open import foundation.universe-levels diff --git a/src/group-theory/torsion-elements-groups.lagda.md b/src/group-theory/torsion-elements-groups.lagda.md index 9b7a129185..33e8c8f764 100644 --- a/src/group-theory/torsion-elements-groups.lagda.md +++ b/src/group-theory/torsion-elements-groups.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.integers open import elementary-number-theory.nonzero-integers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.identity-types open import foundation.propositions diff --git a/src/group-theory/torsion-free-groups.lagda.md b/src/group-theory/torsion-free-groups.lagda.md index d7e4ed6170..3233660097 100644 --- a/src/group-theory/torsion-free-groups.lagda.md +++ b/src/group-theory/torsion-free-groups.lagda.md @@ -13,6 +13,8 @@ open import elementary-number-theory.nonzero-integers open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.existential-quantification open import foundation.fundamental-theorem-of-identity-types diff --git a/src/group-theory/torsors.lagda.md b/src/group-theory/torsors.lagda.md index 0e1b1d1375..a52c66041f 100644 --- a/src/group-theory/torsors.lagda.md +++ b/src/group-theory/torsors.lagda.md @@ -10,6 +10,7 @@ module group-theory.torsors where open import foundation.0-connected-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/group-theory/transitive-concrete-group-actions.lagda.md b/src/group-theory/transitive-concrete-group-actions.lagda.md index f6af5d47b3..dda4b0852a 100644 --- a/src/group-theory/transitive-concrete-group-actions.lagda.md +++ b/src/group-theory/transitive-concrete-group-actions.lagda.md @@ -10,6 +10,7 @@ module group-theory.transitive-concrete-group-actions where open import foundation.1-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.existential-quantification open import foundation.function-types diff --git a/src/group-theory/transitive-group-actions.lagda.md b/src/group-theory/transitive-group-actions.lagda.md index c8513a1bf5..4c48f2957f 100644 --- a/src/group-theory/transitive-group-actions.lagda.md +++ b/src/group-theory/transitive-group-actions.lagda.md @@ -7,6 +7,7 @@ module group-theory.transitive-group-actions where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.identity-types open import foundation.propositions diff --git a/src/group-theory/trivial-concrete-groups.lagda.md b/src/group-theory/trivial-concrete-groups.lagda.md index 5c20a531f4..9cf2993303 100644 --- a/src/group-theory/trivial-concrete-groups.lagda.md +++ b/src/group-theory/trivial-concrete-groups.lagda.md @@ -9,6 +9,8 @@ module group-theory.trivial-concrete-groups where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.raising-universe-levels-unit-type open import foundation.truncation-levels diff --git a/src/group-theory/trivial-group-homomorphisms.lagda.md b/src/group-theory/trivial-group-homomorphisms.lagda.md index 3cc3b50278..b2a9a97de2 100644 --- a/src/group-theory/trivial-group-homomorphisms.lagda.md +++ b/src/group-theory/trivial-group-homomorphisms.lagda.md @@ -8,6 +8,7 @@ module group-theory.trivial-group-homomorphisms where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/group-theory/trivial-groups.lagda.md b/src/group-theory/trivial-groups.lagda.md index a018e83b69..b1a2bb41ae 100644 --- a/src/group-theory/trivial-groups.lagda.md +++ b/src/group-theory/trivial-groups.lagda.md @@ -9,6 +9,8 @@ module group-theory.trivial-groups where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/higher-group-theory/automorphism-groups.lagda.md b/src/higher-group-theory/automorphism-groups.lagda.md index 3c2e64a205..b4df79ff2c 100644 --- a/src/higher-group-theory/automorphism-groups.lagda.md +++ b/src/higher-group-theory/automorphism-groups.lagda.md @@ -11,6 +11,7 @@ open import foundation.0-connected-types open import foundation.connected-components open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/higher-group-theory/cartesian-products-higher-groups.lagda.md b/src/higher-group-theory/cartesian-products-higher-groups.lagda.md index 2183bb2862..c4a09bac5f 100644 --- a/src/higher-group-theory/cartesian-products-higher-groups.lagda.md +++ b/src/higher-group-theory/cartesian-products-higher-groups.lagda.md @@ -10,6 +10,7 @@ module higher-group-theory.cartesian-products-higher-groups where open import foundation.0-connected-types open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-cartesian-product-types open import foundation.equivalences open import foundation.identity-types diff --git a/src/higher-group-theory/cyclic-higher-groups.lagda.md b/src/higher-group-theory/cyclic-higher-groups.lagda.md index d9067fb971..8172f67bbb 100644 --- a/src/higher-group-theory/cyclic-higher-groups.lagda.md +++ b/src/higher-group-theory/cyclic-higher-groups.lagda.md @@ -7,6 +7,7 @@ module higher-group-theory.cyclic-higher-groups where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.existential-quantification open import foundation.propositions diff --git a/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md b/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md index 13a8cf9fab..8656c20304 100644 --- a/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md +++ b/src/higher-group-theory/eilenberg-mac-lane-spaces.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.0-connected-types open import foundation.cartesian-product-types open import foundation.connected-types +open import foundation.dependent-products-truncated-types open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/higher-group-theory/free-higher-group-actions.lagda.md b/src/higher-group-theory/free-higher-group-actions.lagda.md index ea43e3e1b2..b59055afb3 100644 --- a/src/higher-group-theory/free-higher-group-actions.lagda.md +++ b/src/higher-group-theory/free-higher-group-actions.lagda.md @@ -7,6 +7,7 @@ module higher-group-theory.free-higher-group-actions where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.identity-types open import foundation.propositional-maps diff --git a/src/higher-group-theory/higher-groups.lagda.md b/src/higher-group-theory/higher-groups.lagda.md index 6102d85536..e6b22e3502 100644 --- a/src/higher-group-theory/higher-groups.lagda.md +++ b/src/higher-group-theory/higher-groups.lagda.md @@ -9,6 +9,7 @@ module higher-group-theory.higher-groups where ```agda open import foundation.0-connected-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.full-subtypes open import foundation.identity-types diff --git a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md index d8ae507260..80d9e4c011 100644 --- a/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md +++ b/src/higher-group-theory/iterated-cartesian-products-higher-groups.lagda.md @@ -13,6 +13,8 @@ open import foundation.0-connected-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-cartesian-product-types diff --git a/src/higher-group-theory/small-higher-groups.lagda.md b/src/higher-group-theory/small-higher-groups.lagda.md index 0252d1093d..f420be4c06 100644 --- a/src/higher-group-theory/small-higher-groups.lagda.md +++ b/src/higher-group-theory/small-higher-groups.lagda.md @@ -9,6 +9,7 @@ module higher-group-theory.small-higher-groups where ```agda open import foundation.0-connected-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.images diff --git a/src/higher-group-theory/transitive-higher-group-actions.lagda.md b/src/higher-group-theory/transitive-higher-group-actions.lagda.md index a6a4b3f711..d6cbb0ff78 100644 --- a/src/higher-group-theory/transitive-higher-group-actions.lagda.md +++ b/src/higher-group-theory/transitive-higher-group-actions.lagda.md @@ -9,6 +9,7 @@ module higher-group-theory.transitive-higher-group-actions where ```agda open import foundation.0-connected-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.inhabited-types open import foundation.propositional-truncations diff --git a/src/higher-group-theory/trivial-higher-groups.lagda.md b/src/higher-group-theory/trivial-higher-groups.lagda.md index 32e453fac8..fc7df20983 100644 --- a/src/higher-group-theory/trivial-higher-groups.lagda.md +++ b/src/higher-group-theory/trivial-higher-groups.lagda.md @@ -10,6 +10,8 @@ module higher-group-theory.trivial-higher-groups where open import foundation.0-connected-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.raising-universe-levels-unit-type open import foundation.unit-type diff --git a/src/linear-algebra/matrices.lagda.md b/src/linear-algebra/matrices.lagda.md index f95efc19d8..463b640234 100644 --- a/src/linear-algebra/matrices.lagda.md +++ b/src/linear-algebra/matrices.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-binary-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.identity-types open import foundation.universe-levels diff --git a/src/linear-algebra/vectors.lagda.md b/src/linear-algebra/vectors.lagda.md index 4a6be035b9..c4ad918758 100644 --- a/src/linear-algebra/vectors.lagda.md +++ b/src/linear-algebra/vectors.lagda.md @@ -14,6 +14,7 @@ open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-truncated-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/lists/arrays.lagda.md b/src/lists/arrays.lagda.md index 054ea39af4..2d570996e7 100644 --- a/src/lists/arrays.lagda.md +++ b/src/lists/arrays.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/lists/equality-lists.lagda.md b/src/lists/equality-lists.lagda.md index b2345f4801..ddfac7ade4 100644 --- a/src/lists/equality-lists.lagda.md +++ b/src/lists/equality-lists.lagda.md @@ -15,6 +15,8 @@ open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-truncated-types open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/lists/functoriality-lists.lagda.md b/src/lists/functoriality-lists.lagda.md index 233992c6a0..1b331db03a 100644 --- a/src/lists/functoriality-lists.lagda.md +++ b/src/lists/functoriality-lists.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.function-types open import foundation.homotopies diff --git a/src/lists/permutation-lists.lagda.md b/src/lists/permutation-lists.lagda.md index 26ca630086..19401994e1 100644 --- a/src/lists/permutation-lists.lagda.md +++ b/src/lists/permutation-lists.lagda.md @@ -14,6 +14,7 @@ open import finite-group-theory.permutations-standard-finite-types open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.identity-types open import foundation.propositions diff --git a/src/lists/predicates-on-lists.lagda.md b/src/lists/predicates-on-lists.lagda.md index 69fb45c9a5..4df17390d6 100644 --- a/src/lists/predicates-on-lists.lagda.md +++ b/src/lists/predicates-on-lists.lagda.md @@ -7,6 +7,7 @@ module lists.predicates-on-lists where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.raising-universe-levels-unit-type open import foundation.unit-type diff --git a/src/lists/sorted-lists.lagda.md b/src/lists/sorted-lists.lagda.md index fb82aebedd..c3b6d88f3e 100644 --- a/src/lists/sorted-lists.lagda.md +++ b/src/lists/sorted-lists.lagda.md @@ -10,6 +10,7 @@ module lists.sorted-lists where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.raising-universe-levels-unit-type open import foundation.unit-type diff --git a/src/lists/sorted-vectors.lagda.md b/src/lists/sorted-vectors.lagda.md index 0aeb41d303..babd8a2568 100644 --- a/src/lists/sorted-vectors.lagda.md +++ b/src/lists/sorted-vectors.lagda.md @@ -13,6 +13,7 @@ open import finite-group-theory.permutations-standard-finite-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.propositions diff --git a/src/literature/introduction-to-homotopy-type-theory.lagda.md b/src/literature/introduction-to-homotopy-type-theory.lagda.md index 73694d20ac..39b75e92c2 100644 --- a/src/literature/introduction-to-homotopy-type-theory.lagda.md +++ b/src/literature/introduction-to-homotopy-type-theory.lagda.md @@ -556,7 +556,8 @@ open import foundation.action-on-identifications-dependent-functions using ```agda open import foundation.torsorial-type-families using ( is-torsorial-Id) -open import foundation.contractible-types using +open import foundation.contractible-types +open import foundation.dependent-products-contractible-types using ( eq-is-contr') _ : {l : Level} {A : UU l} (a : A) (y : Σ A (λ x → a ＝ x)) → (a , refl) ＝ y diff --git a/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md b/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md index 34e5e2e86f..e53d2f2c92 100644 --- a/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md +++ b/src/literature/sequential-colimits-in-homotopy-type-theory.lagda.md @@ -48,7 +48,8 @@ open import foundation.transport-along-identifications using open import foundation.action-on-identifications-dependent-functions using ( apd -- "dependent functions respect paths" ) -open import foundation.truncated-types using +open import foundation.truncated-types +open import foundation.dependent-products-truncated-types using ( is-trunc -- "`n`-truncated types" ) open import foundation.truncations using diff --git a/src/logic/de-morgan-embeddings.lagda.md b/src/logic/de-morgan-embeddings.lagda.md index 3391dea43b..9c8a430b2c 100644 --- a/src/logic/de-morgan-embeddings.lagda.md +++ b/src/logic/de-morgan-embeddings.lagda.md @@ -14,6 +14,7 @@ open import foundation.decidable-maps open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.fibers-of-maps open import foundation.functoriality-cartesian-product-types diff --git a/src/logic/de-morgan-maps.lagda.md b/src/logic/de-morgan-maps.lagda.md index 17b5a68d6e..db5efbdcd9 100644 --- a/src/logic/de-morgan-maps.lagda.md +++ b/src/logic/de-morgan-maps.lagda.md @@ -16,6 +16,7 @@ open import foundation.decidable-equality open import foundation.decidable-maps open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.embeddings open import foundation.empty-types diff --git a/src/logic/de-morgan-propositions.lagda.md b/src/logic/de-morgan-propositions.lagda.md index 5ca81ba117..eed1c74835 100644 --- a/src/logic/de-morgan-propositions.lagda.md +++ b/src/logic/de-morgan-propositions.lagda.md @@ -13,6 +13,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.double-negation open import foundation.embeddings diff --git a/src/logic/de-morgan-types.lagda.md b/src/logic/de-morgan-types.lagda.md index 749e83645f..37f15937b1 100644 --- a/src/logic/de-morgan-types.lagda.md +++ b/src/logic/de-morgan-types.lagda.md @@ -13,6 +13,7 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.double-negation diff --git a/src/logic/double-negation-stable-embeddings.lagda.md b/src/logic/double-negation-stable-embeddings.lagda.md index 4e6a207085..368f477270 100644 --- a/src/logic/double-negation-stable-embeddings.lagda.md +++ b/src/logic/double-negation-stable-embeddings.lagda.md @@ -14,6 +14,7 @@ open import foundation.decidable-maps open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.double-negation-stable-propositions open import foundation.embeddings open import foundation.fibers-of-maps diff --git a/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md b/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md index 33740c7c95..c4f646f0c2 100644 --- a/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md +++ b/src/metric-spaces/category-of-metric-spaces-and-isometries.lagda.md @@ -12,6 +12,7 @@ open import category-theory.isomorphisms-in-precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.torsorial-type-families diff --git a/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md index 64d510500c..7ef7fce894 100644 --- a/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/category-of-metric-spaces-and-short-functions.lagda.md @@ -12,6 +12,7 @@ open import category-theory.isomorphisms-in-precategories open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.torsorial-type-families diff --git a/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md index 1b5a1f41c2..683c45dfbb 100644 --- a/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-metric-spaces.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md index 55627ce6e3..3a742499a3 100644 --- a/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md +++ b/src/metric-spaces/cauchy-approximations-premetric-spaces.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.cauchy-approximations-premetric-spaces where open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/metric-spaces/closed-premetric-structures.lagda.md b/src/metric-spaces/closed-premetric-structures.lagda.md index 8bf46dea34..e63794b18b 100644 --- a/src/metric-spaces/closed-premetric-structures.lagda.md +++ b/src/metric-spaces/closed-premetric-structures.lagda.md @@ -14,6 +14,7 @@ open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-types diff --git a/src/metric-spaces/complete-metric-spaces.lagda.md b/src/metric-spaces/complete-metric-spaces.lagda.md index 1cb1c38a3a..0bab35d2ce 100644 --- a/src/metric-spaces/complete-metric-spaces.lagda.md +++ b/src/metric-spaces/complete-metric-spaces.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.complete-metric-spaces where open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md b/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md index f8ade7ad4b..f3b09e4550 100644 --- a/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md +++ b/src/metric-spaces/convergent-cauchy-approximations-metric-spaces.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.convergent-cauchy-approximations-metric-spaces where open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/metric-spaces/dependent-products-metric-spaces.lagda.md b/src/metric-spaces/dependent-products-metric-spaces.lagda.md index 9114877759..aa8ba7ab1b 100644 --- a/src/metric-spaces/dependent-products-metric-spaces.lagda.md +++ b/src/metric-spaces/dependent-products-metric-spaces.lagda.md @@ -8,6 +8,7 @@ module metric-spaces.dependent-products-metric-spaces where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-extensionality open import foundation.propositions open import foundation.sets diff --git a/src/metric-spaces/discrete-premetric-structures.lagda.md b/src/metric-spaces/discrete-premetric-structures.lagda.md index 7dfae22799..4985db00fc 100644 --- a/src/metric-spaces/discrete-premetric-structures.lagda.md +++ b/src/metric-spaces/discrete-premetric-structures.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.discrete-premetric-structures where open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/metric-spaces/equality-of-metric-spaces.lagda.md b/src/metric-spaces/equality-of-metric-spaces.lagda.md index 9e6b49a73c..77b130efae 100644 --- a/src/metric-spaces/equality-of-metric-spaces.lagda.md +++ b/src/metric-spaces/equality-of-metric-spaces.lagda.md @@ -9,6 +9,8 @@ module metric-spaces.equality-of-metric-spaces where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/metric-spaces/equality-of-premetric-spaces.lagda.md b/src/metric-spaces/equality-of-premetric-spaces.lagda.md index bf75c6dad0..d2ca4bee50 100644 --- a/src/metric-spaces/equality-of-premetric-spaces.lagda.md +++ b/src/metric-spaces/equality-of-premetric-spaces.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types diff --git a/src/metric-spaces/extensional-premetric-structures.lagda.md b/src/metric-spaces/extensional-premetric-structures.lagda.md index 0e614ca440..15254e0299 100644 --- a/src/metric-spaces/extensional-premetric-structures.lagda.md +++ b/src/metric-spaces/extensional-premetric-structures.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.extensional-premetric-structures where open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md b/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md index 34c143ce20..334409f70c 100644 --- a/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md +++ b/src/metric-spaces/isometric-equivalences-premetric-spaces.lagda.md @@ -10,6 +10,8 @@ module metric-spaces.isometric-equivalences-premetric-spaces where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-types diff --git a/src/metric-spaces/isometries-metric-spaces.lagda.md b/src/metric-spaces/isometries-metric-spaces.lagda.md index 5078244b1f..1608ab87a2 100644 --- a/src/metric-spaces/isometries-metric-spaces.lagda.md +++ b/src/metric-spaces/isometries-metric-spaces.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.binary-transport open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.existential-quantification diff --git a/src/metric-spaces/isometries-premetric-spaces.lagda.md b/src/metric-spaces/isometries-premetric-spaces.lagda.md index 6b3812351b..1dd88b7b6b 100644 --- a/src/metric-spaces/isometries-premetric-spaces.lagda.md +++ b/src/metric-spaces/isometries-premetric-spaces.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.binary-transport open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md index a3390d3a52..c192300802 100644 --- a/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md +++ b/src/metric-spaces/limits-of-cauchy-approximations-in-premetric-spaces.lagda.md @@ -9,6 +9,7 @@ module metric-spaces.limits-of-cauchy-approximations-in-premetric-spaces where ```agda open import elementary-number-theory.positive-rational-numbers +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.transport-along-identifications diff --git a/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md b/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md index 5f2525fef2..4ac301af80 100644 --- a/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md +++ b/src/metric-spaces/metric-space-of-rational-numbers-with-open-neighborhoods.lagda.md @@ -19,6 +19,7 @@ open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/metric-spaces/metric-space-of-rational-numbers.lagda.md b/src/metric-spaces/metric-space-of-rational-numbers.lagda.md index 8ad75841c4..b72bbbb83c 100644 --- a/src/metric-spaces/metric-space-of-rational-numbers.lagda.md +++ b/src/metric-spaces/metric-space-of-rational-numbers.lagda.md @@ -20,6 +20,7 @@ open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.diagonal-maps-cartesian-products-of-types open import foundation.empty-types open import foundation.equivalences diff --git a/src/metric-spaces/metric-spaces.lagda.md b/src/metric-spaces/metric-spaces.lagda.md index 27701dbe35..081cbdc597 100644 --- a/src/metric-spaces/metric-spaces.lagda.md +++ b/src/metric-spaces/metric-spaces.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/metric-spaces/metric-structures.lagda.md b/src/metric-spaces/metric-structures.lagda.md index 0839f2efae..0bcd23b2f6 100644 --- a/src/metric-spaces/metric-structures.lagda.md +++ b/src/metric-spaces/metric-structures.lagda.md @@ -8,6 +8,7 @@ module metric-spaces.metric-structures where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/metric-spaces/monotonic-premetric-structures.lagda.md b/src/metric-spaces/monotonic-premetric-structures.lagda.md index d495f3087d..e227aa311e 100644 --- a/src/metric-spaces/monotonic-premetric-structures.lagda.md +++ b/src/metric-spaces/monotonic-premetric-structures.lagda.md @@ -9,6 +9,7 @@ module metric-spaces.monotonic-premetric-structures where ```agda open import elementary-number-theory.positive-rational-numbers +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/metric-spaces/ordering-premetric-structures.lagda.md b/src/metric-spaces/ordering-premetric-structures.lagda.md index 9d31996995..62968ce140 100644 --- a/src/metric-spaces/ordering-premetric-structures.lagda.md +++ b/src/metric-spaces/ordering-premetric-structures.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md index bc3ca88ffe..64311a3194 100644 --- a/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md +++ b/src/metric-spaces/precategory-of-metric-spaces-and-short-functions.lagda.md @@ -13,6 +13,7 @@ open import category-theory.precategories open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality-axiom open import foundation.functoriality-dependent-pair-types diff --git a/src/metric-spaces/premetric-spaces.lagda.md b/src/metric-spaces/premetric-spaces.lagda.md index edc68f4a20..0c566bb4f5 100644 --- a/src/metric-spaces/premetric-spaces.lagda.md +++ b/src/metric-spaces/premetric-spaces.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.premetric-spaces where open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/metric-spaces/premetric-structures.lagda.md b/src/metric-spaces/premetric-structures.lagda.md index 1efac73fa8..3ce5087017 100644 --- a/src/metric-spaces/premetric-structures.lagda.md +++ b/src/metric-spaces/premetric-structures.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.existential-quantification diff --git a/src/metric-spaces/pseudometric-spaces.lagda.md b/src/metric-spaces/pseudometric-spaces.lagda.md index 1504bef0ae..7bc487fe68 100644 --- a/src/metric-spaces/pseudometric-spaces.lagda.md +++ b/src/metric-spaces/pseudometric-spaces.lagda.md @@ -9,6 +9,7 @@ module metric-spaces.pseudometric-spaces where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.identity-types open import foundation.propositions diff --git a/src/metric-spaces/pseudometric-structures.lagda.md b/src/metric-spaces/pseudometric-structures.lagda.md index fb0476457b..35db46355d 100644 --- a/src/metric-spaces/pseudometric-structures.lagda.md +++ b/src/metric-spaces/pseudometric-structures.lagda.md @@ -8,6 +8,7 @@ module metric-spaces.pseudometric-structures where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/metric-spaces/reflexive-premetric-structures.lagda.md b/src/metric-spaces/reflexive-premetric-structures.lagda.md index 5bb77664f7..ed3f6e7ca4 100644 --- a/src/metric-spaces/reflexive-premetric-structures.lagda.md +++ b/src/metric-spaces/reflexive-premetric-structures.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.existential-quantification diff --git a/src/metric-spaces/saturated-metric-spaces.lagda.md b/src/metric-spaces/saturated-metric-spaces.lagda.md index f4d759453b..6729ed80ae 100644 --- a/src/metric-spaces/saturated-metric-spaces.lagda.md +++ b/src/metric-spaces/saturated-metric-spaces.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.positive-rational-numbers open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/metric-spaces/short-functions-metric-spaces.lagda.md b/src/metric-spaces/short-functions-metric-spaces.lagda.md index bab344ebbb..328be7852d 100644 --- a/src/metric-spaces/short-functions-metric-spaces.lagda.md +++ b/src/metric-spaces/short-functions-metric-spaces.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.short-functions-metric-spaces where open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/metric-spaces/short-functions-premetric-spaces.lagda.md b/src/metric-spaces/short-functions-premetric-spaces.lagda.md index f719e1acfc..76177bd533 100644 --- a/src/metric-spaces/short-functions-premetric-spaces.lagda.md +++ b/src/metric-spaces/short-functions-premetric-spaces.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.short-functions-premetric-spaces where open import elementary-number-theory.positive-rational-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.existential-quantification open import foundation.function-extensionality diff --git a/src/metric-spaces/symmetric-premetric-structures.lagda.md b/src/metric-spaces/symmetric-premetric-structures.lagda.md index 86d360e6a2..975a179e1d 100644 --- a/src/metric-spaces/symmetric-premetric-structures.lagda.md +++ b/src/metric-spaces/symmetric-premetric-structures.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.symmetric-premetric-structures where open import elementary-number-theory.positive-rational-numbers open import foundation.binary-relations +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.function-types open import foundation.identity-types diff --git a/src/metric-spaces/triangular-premetric-structures.lagda.md b/src/metric-spaces/triangular-premetric-structures.lagda.md index 98b2b7c42a..aed5bffa0b 100644 --- a/src/metric-spaces/triangular-premetric-structures.lagda.md +++ b/src/metric-spaces/triangular-premetric-structures.lagda.md @@ -10,6 +10,7 @@ module metric-spaces.triangular-premetric-structures where open import elementary-number-theory.positive-rational-numbers open import foundation.binary-relations +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/modal-type-theory/flat-discrete-crisp-types.lagda.md b/src/modal-type-theory/flat-discrete-crisp-types.lagda.md index 5bf37687fc..286ac5f7bb 100644 --- a/src/modal-type-theory/flat-discrete-crisp-types.lagda.md +++ b/src/modal-type-theory/flat-discrete-crisp-types.lagda.md @@ -14,6 +14,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.booleans open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.empty-types open import foundation.equivalences diff --git a/src/modal-type-theory/sharp-codiscrete-maps.lagda.md b/src/modal-type-theory/sharp-codiscrete-maps.lagda.md index b6f62e6748..2575fc24e7 100644 --- a/src/modal-type-theory/sharp-codiscrete-maps.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-maps.lagda.md @@ -9,6 +9,7 @@ module modal-type-theory.sharp-codiscrete-maps where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.fibers-of-maps open import foundation.propositions open import foundation.universe-levels diff --git a/src/modal-type-theory/sharp-codiscrete-types.lagda.md b/src/modal-type-theory/sharp-codiscrete-types.lagda.md index 7b570a8aa2..c3d1167982 100644 --- a/src/modal-type-theory/sharp-codiscrete-types.lagda.md +++ b/src/modal-type-theory/sharp-codiscrete-types.lagda.md @@ -11,6 +11,7 @@ module modal-type-theory.sharp-codiscrete-types where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-extensionality-axiom diff --git a/src/order-theory/bottom-elements-posets.lagda.md b/src/order-theory/bottom-elements-posets.lagda.md index 19f835b65c..029c8d44d5 100644 --- a/src/order-theory/bottom-elements-posets.lagda.md +++ b/src/order-theory/bottom-elements-posets.lagda.md @@ -8,6 +8,7 @@ module order-theory.bottom-elements-posets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/bottom-elements-preorders.lagda.md b/src/order-theory/bottom-elements-preorders.lagda.md index 5d5c0f1b8b..8edcad7c38 100644 --- a/src/order-theory/bottom-elements-preorders.lagda.md +++ b/src/order-theory/bottom-elements-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.bottom-elements-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/chains-posets.lagda.md b/src/order-theory/chains-posets.lagda.md index 404b506ee9..26551a9ae4 100644 --- a/src/order-theory/chains-posets.lagda.md +++ b/src/order-theory/chains-posets.lagda.md @@ -9,6 +9,7 @@ module order-theory.chains-posets where ```agda open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.existential-quantification open import foundation.function-types diff --git a/src/order-theory/chains-preorders.lagda.md b/src/order-theory/chains-preorders.lagda.md index 65c1ad4c19..7e0da94eaa 100644 --- a/src/order-theory/chains-preorders.lagda.md +++ b/src/order-theory/chains-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.chains-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/closure-operators-large-locales.lagda.md b/src/order-theory/closure-operators-large-locales.lagda.md index 3bc839becd..297f55f1d8 100644 --- a/src/order-theory/closure-operators-large-locales.lagda.md +++ b/src/order-theory/closure-operators-large-locales.lagda.md @@ -9,6 +9,7 @@ module order-theory.closure-operators-large-locales where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.large-binary-relations diff --git a/src/order-theory/closure-operators-large-posets.lagda.md b/src/order-theory/closure-operators-large-posets.lagda.md index edc0a558e9..2df2794db3 100644 --- a/src/order-theory/closure-operators-large-posets.lagda.md +++ b/src/order-theory/closure-operators-large-posets.lagda.md @@ -7,6 +7,7 @@ module order-theory.closure-operators-large-posets where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.large-binary-relations open import foundation.propositions diff --git a/src/order-theory/decidable-posets.lagda.md b/src/order-theory/decidable-posets.lagda.md index b02c21afbf..70af21121f 100644 --- a/src/order-theory/decidable-posets.lagda.md +++ b/src/order-theory/decidable-posets.lagda.md @@ -10,6 +10,7 @@ module order-theory.decidable-posets where open import foundation.binary-relations open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/order-theory/decidable-preorders.lagda.md b/src/order-theory/decidable-preorders.lagda.md index b752e33a13..bc99e12dd3 100644 --- a/src/order-theory/decidable-preorders.lagda.md +++ b/src/order-theory/decidable-preorders.lagda.md @@ -10,6 +10,7 @@ module order-theory.decidable-preorders where open import foundation.binary-relations open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/decidable-subposets.lagda.md b/src/order-theory/decidable-subposets.lagda.md index d57463aa0b..f67d0ffa40 100644 --- a/src/order-theory/decidable-subposets.lagda.md +++ b/src/order-theory/decidable-subposets.lagda.md @@ -10,6 +10,7 @@ module order-theory.decidable-subposets where open import foundation.binary-relations open import foundation.decidable-subtypes open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/decidable-subpreorders.lagda.md b/src/order-theory/decidable-subpreorders.lagda.md index 57e290edc2..7e3c60057c 100644 --- a/src/order-theory/decidable-subpreorders.lagda.md +++ b/src/order-theory/decidable-subpreorders.lagda.md @@ -10,6 +10,7 @@ module order-theory.decidable-subpreorders where open import foundation.binary-relations open import foundation.decidable-subtypes open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/decidable-total-orders.lagda.md b/src/order-theory/decidable-total-orders.lagda.md index 1b3086e12d..95ab482346 100644 --- a/src/order-theory/decidable-total-orders.lagda.md +++ b/src/order-theory/decidable-total-orders.lagda.md @@ -11,6 +11,7 @@ open import foundation.binary-relations open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.propositions diff --git a/src/order-theory/decidable-total-preorders.lagda.md b/src/order-theory/decidable-total-preorders.lagda.md index c3385ce7ae..c3348f6e76 100644 --- a/src/order-theory/decidable-total-preorders.lagda.md +++ b/src/order-theory/decidable-total-preorders.lagda.md @@ -13,6 +13,7 @@ open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.function-types open import foundation.identity-types diff --git a/src/order-theory/deflationary-maps-posets.lagda.md b/src/order-theory/deflationary-maps-posets.lagda.md index ffeb8f4da5..8d23f53862 100644 --- a/src/order-theory/deflationary-maps-posets.lagda.md +++ b/src/order-theory/deflationary-maps-posets.lagda.md @@ -8,6 +8,7 @@ module order-theory.deflationary-maps-posets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/deflationary-maps-preorders.lagda.md b/src/order-theory/deflationary-maps-preorders.lagda.md index 508b702878..93d97e5fee 100644 --- a/src/order-theory/deflationary-maps-preorders.lagda.md +++ b/src/order-theory/deflationary-maps-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.deflationary-maps-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/dependent-products-large-preorders.lagda.md b/src/order-theory/dependent-products-large-preorders.lagda.md index fa7fafa61e..3ccd5f4aa8 100644 --- a/src/order-theory/dependent-products-large-preorders.lagda.md +++ b/src/order-theory/dependent-products-large-preorders.lagda.md @@ -7,6 +7,7 @@ module order-theory.dependent-products-large-preorders where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.large-binary-relations open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/distributive-lattices.lagda.md b/src/order-theory/distributive-lattices.lagda.md index e2dff425a0..44c794fe08 100644 --- a/src/order-theory/distributive-lattices.lagda.md +++ b/src/order-theory/distributive-lattices.lagda.md @@ -9,6 +9,7 @@ module order-theory.distributive-lattices where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/order-theory/finite-posets.lagda.md b/src/order-theory/finite-posets.lagda.md index 597af98d12..a5cd6bba36 100644 --- a/src/order-theory/finite-posets.lagda.md +++ b/src/order-theory/finite-posets.lagda.md @@ -9,6 +9,7 @@ module order-theory.finite-posets where ```agda open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/finite-preorders.lagda.md b/src/order-theory/finite-preorders.lagda.md index b7a2511b49..0a88cb275a 100644 --- a/src/order-theory/finite-preorders.lagda.md +++ b/src/order-theory/finite-preorders.lagda.md @@ -15,6 +15,7 @@ open import foundation.decidable-equality open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.mere-equivalences open import foundation.propositions diff --git a/src/order-theory/finite-total-orders.lagda.md b/src/order-theory/finite-total-orders.lagda.md index 4bfb6edcd4..c96500cd41 100644 --- a/src/order-theory/finite-total-orders.lagda.md +++ b/src/order-theory/finite-total-orders.lagda.md @@ -9,6 +9,7 @@ module order-theory.finite-total-orders where ```agda open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/finitely-graded-posets.lagda.md b/src/order-theory/finitely-graded-posets.lagda.md index b4fb4a404b..4c28ab1b16 100644 --- a/src/order-theory/finitely-graded-posets.lagda.md +++ b/src/order-theory/finitely-graded-posets.lagda.md @@ -14,6 +14,7 @@ open import elementary-number-theory.natural-numbers open import foundation.binary-relations open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.empty-types open import foundation.equality-dependent-pair-types diff --git a/src/order-theory/frames.lagda.md b/src/order-theory/frames.lagda.md index 96d2f47cec..cac85804bd 100644 --- a/src/order-theory/frames.lagda.md +++ b/src/order-theory/frames.lagda.md @@ -9,6 +9,7 @@ module order-theory.frames where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/order-theory/galois-connections.lagda.md b/src/order-theory/galois-connections.lagda.md index e0ac6170c7..5bc50f11d1 100644 --- a/src/order-theory/galois-connections.lagda.md +++ b/src/order-theory/galois-connections.lagda.md @@ -9,6 +9,7 @@ module order-theory.galois-connections where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/order-theory/greatest-lower-bounds-posets.lagda.md b/src/order-theory/greatest-lower-bounds-posets.lagda.md index 9a1430a0c4..9d759cfa95 100644 --- a/src/order-theory/greatest-lower-bounds-posets.lagda.md +++ b/src/order-theory/greatest-lower-bounds-posets.lagda.md @@ -9,6 +9,7 @@ module order-theory.greatest-lower-bounds-posets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/order-theory/homomorphisms-meet-semilattices.lagda.md b/src/order-theory/homomorphisms-meet-semilattices.lagda.md index d22b55a690..fdba09b6eb 100644 --- a/src/order-theory/homomorphisms-meet-semilattices.lagda.md +++ b/src/order-theory/homomorphisms-meet-semilattices.lagda.md @@ -9,6 +9,7 @@ module order-theory.homomorphisms-meet-semilattices where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/order-theory/inflationary-maps-posets.lagda.md b/src/order-theory/inflationary-maps-posets.lagda.md index 00c3374a3b..abfdb30246 100644 --- a/src/order-theory/inflationary-maps-posets.lagda.md +++ b/src/order-theory/inflationary-maps-posets.lagda.md @@ -8,6 +8,7 @@ module order-theory.inflationary-maps-posets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/inflationary-maps-preorders.lagda.md b/src/order-theory/inflationary-maps-preorders.lagda.md index aa2d482b97..8d8ebc9e9c 100644 --- a/src/order-theory/inflationary-maps-preorders.lagda.md +++ b/src/order-theory/inflationary-maps-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.inflationary-maps-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/inflattices.lagda.md b/src/order-theory/inflattices.lagda.md index 03b68b3db8..a9e5eb5929 100644 --- a/src/order-theory/inflattices.lagda.md +++ b/src/order-theory/inflattices.lagda.md @@ -9,6 +9,7 @@ module order-theory.inflattices where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.logical-equivalences open import foundation.propositions open import foundation.sets diff --git a/src/order-theory/inhabited-chains-posets.lagda.md b/src/order-theory/inhabited-chains-posets.lagda.md index 8274e4af2a..4ccb2e5e4c 100644 --- a/src/order-theory/inhabited-chains-posets.lagda.md +++ b/src/order-theory/inhabited-chains-posets.lagda.md @@ -11,6 +11,7 @@ open import domain-theory.directed-families-posets open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.existential-quantification open import foundation.inhabited-subtypes diff --git a/src/order-theory/inhabited-chains-preorders.lagda.md b/src/order-theory/inhabited-chains-preorders.lagda.md index 1722f40034..776f71377e 100644 --- a/src/order-theory/inhabited-chains-preorders.lagda.md +++ b/src/order-theory/inhabited-chains-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.inhabited-chains-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.inhabited-subtypes open import foundation.propositions open import foundation.subtypes diff --git a/src/order-theory/inhabited-finite-total-orders.lagda.md b/src/order-theory/inhabited-finite-total-orders.lagda.md index a7a49e6404..9d55fcffc0 100644 --- a/src/order-theory/inhabited-finite-total-orders.lagda.md +++ b/src/order-theory/inhabited-finite-total-orders.lagda.md @@ -7,6 +7,7 @@ module order-theory.inhabited-finite-total-orders where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.inhabited-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/interval-subposets.lagda.md b/src/order-theory/interval-subposets.lagda.md index 5f53725119..0a15914e62 100644 --- a/src/order-theory/interval-subposets.lagda.md +++ b/src/order-theory/interval-subposets.lagda.md @@ -8,6 +8,7 @@ module order-theory.interval-subposets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.inhabited-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/join-preserving-maps-posets.lagda.md b/src/order-theory/join-preserving-maps-posets.lagda.md index 1da7506fa2..11d5cc44fb 100644 --- a/src/order-theory/join-preserving-maps-posets.lagda.md +++ b/src/order-theory/join-preserving-maps-posets.lagda.md @@ -9,6 +9,7 @@ module order-theory.join-preserving-maps-posets where ```agda open import foundation.booleans open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.evaluation-functions open import foundation.function-types diff --git a/src/order-theory/join-semilattices.lagda.md b/src/order-theory/join-semilattices.lagda.md index fe7f25a8cc..90e7943ca7 100644 --- a/src/order-theory/join-semilattices.lagda.md +++ b/src/order-theory/join-semilattices.lagda.md @@ -10,6 +10,7 @@ module order-theory.join-semilattices where open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/order-theory/large-posets.lagda.md b/src/order-theory/large-posets.lagda.md index ebe0411daf..79d4f1a7a1 100644 --- a/src/order-theory/large-posets.lagda.md +++ b/src/order-theory/large-posets.lagda.md @@ -14,6 +14,7 @@ open import category-theory.large-precategories open import category-theory.precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.large-binary-relations open import foundation.logical-equivalences diff --git a/src/order-theory/large-preorders.lagda.md b/src/order-theory/large-preorders.lagda.md index 34c9170742..ffbf72698b 100644 --- a/src/order-theory/large-preorders.lagda.md +++ b/src/order-theory/large-preorders.lagda.md @@ -10,6 +10,7 @@ module order-theory.large-preorders where open import category-theory.large-precategories open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.large-binary-relations open import foundation.propositions diff --git a/src/order-theory/large-subpreorders.lagda.md b/src/order-theory/large-subpreorders.lagda.md index d69fca9bbe..63ab032254 100644 --- a/src/order-theory/large-subpreorders.lagda.md +++ b/src/order-theory/large-subpreorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.large-subpreorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.large-binary-relations open import foundation.propositions open import foundation.subtypes diff --git a/src/order-theory/large-suplattices.lagda.md b/src/order-theory/large-suplattices.lagda.md index 489330b18b..fa0e52b1a4 100644 --- a/src/order-theory/large-suplattices.lagda.md +++ b/src/order-theory/large-suplattices.lagda.md @@ -9,6 +9,7 @@ module order-theory.large-suplattices where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.large-binary-relations open import foundation.logical-equivalences diff --git a/src/order-theory/lattices.lagda.md b/src/order-theory/lattices.lagda.md index bc9d9bc466..fe00a398cd 100644 --- a/src/order-theory/lattices.lagda.md +++ b/src/order-theory/lattices.lagda.md @@ -9,6 +9,7 @@ module order-theory.lattices where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.sets open import foundation.universe-levels diff --git a/src/order-theory/least-upper-bounds-posets.lagda.md b/src/order-theory/least-upper-bounds-posets.lagda.md index d0a5e74b02..c78c2bdf4d 100644 --- a/src/order-theory/least-upper-bounds-posets.lagda.md +++ b/src/order-theory/least-upper-bounds-posets.lagda.md @@ -10,6 +10,7 @@ module order-theory.least-upper-bounds-posets where open import foundation.action-on-identifications-functions open import foundation.booleans open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/order-theory/locales.lagda.md b/src/order-theory/locales.lagda.md index 25983102a6..38b76cf287 100644 --- a/src/order-theory/locales.lagda.md +++ b/src/order-theory/locales.lagda.md @@ -8,6 +8,7 @@ module order-theory.locales where ```agda open import foundation.binary-relations +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/order-theory/locally-finite-posets.lagda.md b/src/order-theory/locally-finite-posets.lagda.md index 69a7c93beb..86b9b78730 100644 --- a/src/order-theory/locally-finite-posets.lagda.md +++ b/src/order-theory/locally-finite-posets.lagda.md @@ -7,6 +7,7 @@ module order-theory.locally-finite-posets where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/lower-bounds-large-posets.lagda.md b/src/order-theory/lower-bounds-large-posets.lagda.md index 3f527ccddc..02a90b1a0d 100644 --- a/src/order-theory/lower-bounds-large-posets.lagda.md +++ b/src/order-theory/lower-bounds-large-posets.lagda.md @@ -9,6 +9,7 @@ module order-theory.lower-bounds-large-posets where ```agda open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.logical-equivalences open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/lower-bounds-posets.lagda.md b/src/order-theory/lower-bounds-posets.lagda.md index 5ae8f55417..cb0ec3aa41 100644 --- a/src/order-theory/lower-bounds-posets.lagda.md +++ b/src/order-theory/lower-bounds-posets.lagda.md @@ -8,6 +8,7 @@ module order-theory.lower-bounds-posets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/maximal-chains-posets.lagda.md b/src/order-theory/maximal-chains-posets.lagda.md index e62dabcc6e..6d4963ddb0 100644 --- a/src/order-theory/maximal-chains-posets.lagda.md +++ b/src/order-theory/maximal-chains-posets.lagda.md @@ -7,6 +7,7 @@ module order-theory.maximal-chains-posets where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/maximal-chains-preorders.lagda.md b/src/order-theory/maximal-chains-preorders.lagda.md index 0cf6169f4f..eec1b8e7de 100644 --- a/src/order-theory/maximal-chains-preorders.lagda.md +++ b/src/order-theory/maximal-chains-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.maximal-chains-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/meet-semilattices.lagda.md b/src/order-theory/meet-semilattices.lagda.md index 4a01ec4db8..a95e2e6b81 100644 --- a/src/order-theory/meet-semilattices.lagda.md +++ b/src/order-theory/meet-semilattices.lagda.md @@ -10,6 +10,7 @@ module order-theory.meet-semilattices where open import foundation.action-on-identifications-functions open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/order-theory/meet-suplattices.lagda.md b/src/order-theory/meet-suplattices.lagda.md index 898eeb5f7a..9240896a94 100644 --- a/src/order-theory/meet-suplattices.lagda.md +++ b/src/order-theory/meet-suplattices.lagda.md @@ -9,6 +9,7 @@ module order-theory.meet-suplattices where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.sets open import foundation.universe-levels diff --git a/src/order-theory/nuclei-large-locales.lagda.md b/src/order-theory/nuclei-large-locales.lagda.md index b6d44973c9..f653909c65 100644 --- a/src/order-theory/nuclei-large-locales.lagda.md +++ b/src/order-theory/nuclei-large-locales.lagda.md @@ -9,6 +9,7 @@ module order-theory.nuclei-large-locales where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.large-binary-relations diff --git a/src/order-theory/opposite-large-posets.lagda.md b/src/order-theory/opposite-large-posets.lagda.md index cbb94d58f5..d3a3a57b4e 100644 --- a/src/order-theory/opposite-large-posets.lagda.md +++ b/src/order-theory/opposite-large-posets.lagda.md @@ -8,6 +8,7 @@ module order-theory.opposite-large-posets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.homotopies open import foundation.identity-types diff --git a/src/order-theory/opposite-large-preorders.lagda.md b/src/order-theory/opposite-large-preorders.lagda.md index 5ecbfef3d7..0b6c8df4d1 100644 --- a/src/order-theory/opposite-large-preorders.lagda.md +++ b/src/order-theory/opposite-large-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.opposite-large-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.homotopies open import foundation.identity-types diff --git a/src/order-theory/opposite-posets.lagda.md b/src/order-theory/opposite-posets.lagda.md index 45b842294c..21ae309bd9 100644 --- a/src/order-theory/opposite-posets.lagda.md +++ b/src/order-theory/opposite-posets.lagda.md @@ -8,6 +8,7 @@ module order-theory.opposite-posets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.homotopies open import foundation.identity-types diff --git a/src/order-theory/opposite-preorders.lagda.md b/src/order-theory/opposite-preorders.lagda.md index 2e6db98be2..1388072aa3 100644 --- a/src/order-theory/opposite-preorders.lagda.md +++ b/src/order-theory/opposite-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.opposite-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.homotopies open import foundation.identity-types diff --git a/src/order-theory/order-preserving-maps-posets.lagda.md b/src/order-theory/order-preserving-maps-posets.lagda.md index 163aee3f3f..2f408ebe4a 100644 --- a/src/order-theory/order-preserving-maps-posets.lagda.md +++ b/src/order-theory/order-preserving-maps-posets.lagda.md @@ -7,6 +7,7 @@ module order-theory.order-preserving-maps-posets where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/order-theory/order-preserving-maps-preorders.lagda.md b/src/order-theory/order-preserving-maps-preorders.lagda.md index a45df09656..c7e1403c37 100644 --- a/src/order-theory/order-preserving-maps-preorders.lagda.md +++ b/src/order-theory/order-preserving-maps-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.order-preserving-maps-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/order-theory/ordinals.lagda.md b/src/order-theory/ordinals.lagda.md index 7dc9994603..03868f9067 100644 --- a/src/order-theory/ordinals.lagda.md +++ b/src/order-theory/ordinals.lagda.md @@ -10,6 +10,7 @@ module order-theory.ordinals where open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/order-theory/posets.lagda.md b/src/order-theory/posets.lagda.md index f1875f86f2..aeba70c861 100644 --- a/src/order-theory/posets.lagda.md +++ b/src/order-theory/posets.lagda.md @@ -14,6 +14,7 @@ open import category-theory.precategories open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.injective-maps diff --git a/src/order-theory/preorders.lagda.md b/src/order-theory/preorders.lagda.md index 37293a7863..2a901a2b92 100644 --- a/src/order-theory/preorders.lagda.md +++ b/src/order-theory/preorders.lagda.md @@ -12,6 +12,7 @@ open import category-theory.precategories open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/order-theory/resizing-posets.lagda.md b/src/order-theory/resizing-posets.lagda.md index 4fcaf5e66f..ad22722865 100644 --- a/src/order-theory/resizing-posets.lagda.md +++ b/src/order-theory/resizing-posets.lagda.md @@ -12,6 +12,7 @@ open import category-theory.isomorphisms-in-large-precategories open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/order-theory/resizing-preorders.lagda.md b/src/order-theory/resizing-preorders.lagda.md index 26a17b7682..ac6fec8dbe 100644 --- a/src/order-theory/resizing-preorders.lagda.md +++ b/src/order-theory/resizing-preorders.lagda.md @@ -10,6 +10,7 @@ module order-theory.resizing-preorders where open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/order-theory/resizing-suplattices.lagda.md b/src/order-theory/resizing-suplattices.lagda.md index 6c0cdeede8..fa3a2a7c22 100644 --- a/src/order-theory/resizing-suplattices.lagda.md +++ b/src/order-theory/resizing-suplattices.lagda.md @@ -10,6 +10,7 @@ module order-theory.resizing-suplattices where open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/order-theory/similarity-of-elements-large-posets.lagda.md b/src/order-theory/similarity-of-elements-large-posets.lagda.md index 5e2d8199ea..5d4eb3a77c 100644 --- a/src/order-theory/similarity-of-elements-large-posets.lagda.md +++ b/src/order-theory/similarity-of-elements-large-posets.lagda.md @@ -8,6 +8,7 @@ module order-theory.similarity-of-elements-large-posets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/order-theory/similarity-of-elements-large-preorders.lagda.md b/src/order-theory/similarity-of-elements-large-preorders.lagda.md index c027bb56db..0bf0cad049 100644 --- a/src/order-theory/similarity-of-elements-large-preorders.lagda.md +++ b/src/order-theory/similarity-of-elements-large-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.similarity-of-elements-large-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.large-binary-relations open import foundation.propositions diff --git a/src/order-theory/strict-order-preserving-maps.lagda.md b/src/order-theory/strict-order-preserving-maps.lagda.md index 44b8225347..0676a0a13c 100644 --- a/src/order-theory/strict-order-preserving-maps.lagda.md +++ b/src/order-theory/strict-order-preserving-maps.lagda.md @@ -9,6 +9,7 @@ module order-theory.strict-order-preserving-maps where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/strict-preorders.lagda.md b/src/order-theory/strict-preorders.lagda.md index 071d017b3d..8481e8d98b 100644 --- a/src/order-theory/strict-preorders.lagda.md +++ b/src/order-theory/strict-preorders.lagda.md @@ -10,6 +10,7 @@ module order-theory.strict-preorders where open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.negation open import foundation.propositions diff --git a/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md b/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md index d8a4672caa..ed41fae943 100644 --- a/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md +++ b/src/order-theory/strictly-inflationary-maps-strict-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.strictly-inflationary-maps-strict-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/strictly-preordered-sets.lagda.md b/src/order-theory/strictly-preordered-sets.lagda.md index c639e6fe02..4c2842250d 100644 --- a/src/order-theory/strictly-preordered-sets.lagda.md +++ b/src/order-theory/strictly-preordered-sets.lagda.md @@ -10,6 +10,7 @@ module order-theory.strictly-preordered-sets where open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.negation open import foundation.propositions diff --git a/src/order-theory/subposets.lagda.md b/src/order-theory/subposets.lagda.md index d7cd52162e..59b03b0a3b 100644 --- a/src/order-theory/subposets.lagda.md +++ b/src/order-theory/subposets.lagda.md @@ -9,6 +9,7 @@ module order-theory.subposets where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/subpreorders.lagda.md b/src/order-theory/subpreorders.lagda.md index 8ac0925ccd..cc43ea0478 100644 --- a/src/order-theory/subpreorders.lagda.md +++ b/src/order-theory/subpreorders.lagda.md @@ -9,6 +9,7 @@ module order-theory.subpreorders where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/order-theory/suplattices.lagda.md b/src/order-theory/suplattices.lagda.md index e2cac7a583..c935dc1753 100644 --- a/src/order-theory/suplattices.lagda.md +++ b/src/order-theory/suplattices.lagda.md @@ -9,6 +9,7 @@ module order-theory.suplattices where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/order-theory/supremum-preserving-maps-posets.lagda.md b/src/order-theory/supremum-preserving-maps-posets.lagda.md index b5abca4ab4..eeda5fcfba 100644 --- a/src/order-theory/supremum-preserving-maps-posets.lagda.md +++ b/src/order-theory/supremum-preserving-maps-posets.lagda.md @@ -9,6 +9,7 @@ module order-theory.supremum-preserving-maps-posets where ```agda open import foundation.booleans open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.evaluation-functions open import foundation.function-types diff --git a/src/order-theory/top-elements-posets.lagda.md b/src/order-theory/top-elements-posets.lagda.md index 658fc977cc..7a1482419a 100644 --- a/src/order-theory/top-elements-posets.lagda.md +++ b/src/order-theory/top-elements-posets.lagda.md @@ -8,6 +8,7 @@ module order-theory.top-elements-posets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.subtypes open import foundation.universe-levels diff --git a/src/order-theory/top-elements-preorders.lagda.md b/src/order-theory/top-elements-preorders.lagda.md index 1c9655f1de..b10d59fd45 100644 --- a/src/order-theory/top-elements-preorders.lagda.md +++ b/src/order-theory/top-elements-preorders.lagda.md @@ -8,6 +8,7 @@ module order-theory.top-elements-preorders where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/total-orders.lagda.md b/src/order-theory/total-orders.lagda.md index 1f84d69e67..9f21938e09 100644 --- a/src/order-theory/total-orders.lagda.md +++ b/src/order-theory/total-orders.lagda.md @@ -9,6 +9,7 @@ module order-theory.total-orders where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/order-theory/total-preorders.lagda.md b/src/order-theory/total-preorders.lagda.md index facdaddbd8..46faf84189 100644 --- a/src/order-theory/total-preorders.lagda.md +++ b/src/order-theory/total-preorders.lagda.md @@ -9,6 +9,7 @@ module order-theory.total-preorders where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/upper-bounds-large-posets.lagda.md b/src/order-theory/upper-bounds-large-posets.lagda.md index bada6644c6..bf2dac888b 100644 --- a/src/order-theory/upper-bounds-large-posets.lagda.md +++ b/src/order-theory/upper-bounds-large-posets.lagda.md @@ -9,6 +9,7 @@ module order-theory.upper-bounds-large-posets where ```agda open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.logical-equivalences open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/upper-bounds-posets.lagda.md b/src/order-theory/upper-bounds-posets.lagda.md index 0193ab6052..27cae5bdad 100644 --- a/src/order-theory/upper-bounds-posets.lagda.md +++ b/src/order-theory/upper-bounds-posets.lagda.md @@ -8,6 +8,7 @@ module order-theory.upper-bounds-posets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/order-theory/well-founded-relations.lagda.md b/src/order-theory/well-founded-relations.lagda.md index 7ae600f45c..65a128d17e 100644 --- a/src/order-theory/well-founded-relations.lagda.md +++ b/src/order-theory/well-founded-relations.lagda.md @@ -9,6 +9,7 @@ module order-theory.well-founded-relations where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/organic-chemistry/ethane.lagda.md b/src/organic-chemistry/ethane.lagda.md index b20b3fe687..0d9bd03f7a 100644 --- a/src/organic-chemistry/ethane.lagda.md +++ b/src/organic-chemistry/ethane.lagda.md @@ -15,6 +15,7 @@ open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.empty-types open import foundation.equality-dependent-pair-types diff --git a/src/organic-chemistry/saturated-carbons.lagda.md b/src/organic-chemistry/saturated-carbons.lagda.md index f214d5aa80..0dc116fe04 100644 --- a/src/organic-chemistry/saturated-carbons.lagda.md +++ b/src/organic-chemistry/saturated-carbons.lagda.md @@ -8,6 +8,7 @@ module organic-chemistry.saturated-carbons where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.propositional-truncations open import foundation.propositions open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/cd-structures.lagda.md b/src/orthogonal-factorization-systems/cd-structures.lagda.md index d33d5a3d4a..ae4e3cf965 100644 --- a/src/orthogonal-factorization-systems/cd-structures.lagda.md +++ b/src/orthogonal-factorization-systems/cd-structures.lagda.md @@ -7,6 +7,7 @@ module orthogonal-factorization-systems.cd-structures where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.morphisms-arrows open import foundation.propositions open import foundation.subtypes diff --git a/src/orthogonal-factorization-systems/closed-modalities.lagda.md b/src/orthogonal-factorization-systems/closed-modalities.lagda.md index c42bfe9572..7684d22361 100644 --- a/src/orthogonal-factorization-systems/closed-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/closed-modalities.lagda.md @@ -10,6 +10,8 @@ module orthogonal-factorization-systems.closed-modalities where open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md index 37b7855617..9b021c89b9 100644 --- a/src/orthogonal-factorization-systems/continuation-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/continuation-modalities.lagda.md @@ -10,6 +10,7 @@ module orthogonal-factorization-systems.continuation-modalities where open import foundation.cartesian-product-types open import foundation.continuations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.logical-equivalences diff --git a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md index d48dc64cdd..b66a687bb0 100644 --- a/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md +++ b/src/orthogonal-factorization-systems/double-negation-sheaves.lagda.md @@ -9,6 +9,7 @@ module orthogonal-factorization-systems.double-negation-sheaves where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-propositions open import foundation.double-negation-stable-propositions open import foundation.empty-types diff --git a/src/orthogonal-factorization-systems/extensions-maps.lagda.md b/src/orthogonal-factorization-systems/extensions-maps.lagda.md index 1afb566035..26b3c67a77 100644 --- a/src/orthogonal-factorization-systems/extensions-maps.lagda.md +++ b/src/orthogonal-factorization-systems/extensions-maps.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.dependent-products-truncated-types open import foundation.embeddings open import foundation.equivalences diff --git a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md index 1d51743a99..ae45691f52 100644 --- a/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations-function-classes.lagda.md @@ -11,6 +11,8 @@ open import foundation.cartesian-product-types open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md index a372c14a56..31b0b8b7b7 100644 --- a/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorization-operations-global-function-classes.lagda.md @@ -7,6 +7,7 @@ module orthogonal-factorization-systems.factorization-operations-global-function
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md index f4eee03050..62a3e9aa80 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps-function-classes.lagda.md @@ -10,6 +10,8 @@ module orthogonal-factorization-systems.factorizations-of-maps-function-classes open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md index 9945116577..9489672cae 100644 --- a/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/factorizations-of-maps-global-function-classes.lagda.md @@ -10,6 +10,8 @@ module orthogonal-factorization-systems.factorizations-of-maps-global-function-c open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md index 0d79431a42..b4cc86fd30 100644 --- a/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/families-of-types-local-at-maps.lagda.md @@ -8,6 +8,7 @@ module orthogonal-factorization-systems.families-of-types-local-at-maps where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.precomposition-functions open import foundation.propositions diff --git a/src/orthogonal-factorization-systems/function-classes.lagda.md b/src/orthogonal-factorization-systems/function-classes.lagda.md index 821f6aa51e..632ac6ceff 100644 --- a/src/orthogonal-factorization-systems/function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/function-classes.lagda.md @@ -10,6 +10,7 @@ module orthogonal-factorization-systems.function-classes where open import foundation.action-on-identifications-functions open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalence-induction open import foundation.equivalences diff --git a/src/orthogonal-factorization-systems/global-function-classes.lagda.md b/src/orthogonal-factorization-systems/global-function-classes.lagda.md index b11fa84d13..4db20085ca 100644 --- a/src/orthogonal-factorization-systems/global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/global-function-classes.lagda.md @@ -9,6 +9,7 @@ module orthogonal-factorization-systems.global-function-classes where ```agda open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md b/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md index b6fd6cabc1..e9e54ab8b5 100644 --- a/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md +++ b/src/orthogonal-factorization-systems/large-lawvere-tierney-topologies.lagda.md @@ -10,6 +10,7 @@ module orthogonal-factorization-systems.large-lawvere-tierney-topologies where open import foundation.cartesian-product-types open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.logical-equivalences open import foundation.propositions diff --git a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md index 8976f0993e..d9982a9678 100644 --- a/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md +++ b/src/orthogonal-factorization-systems/lawvere-tierney-topologies.lagda.md @@ -10,6 +10,7 @@ module orthogonal-factorization-systems.lawvere-tierney-topologies where open import foundation.cartesian-product-types open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.logical-equivalences open import foundation.propositional-extensionality diff --git a/src/orthogonal-factorization-systems/lifts-maps.lagda.md b/src/orthogonal-factorization-systems/lifts-maps.lagda.md index 60cb9ba46c..c70f889795 100644 --- a/src/orthogonal-factorization-systems/lifts-maps.lagda.md +++ b/src/orthogonal-factorization-systems/lifts-maps.lagda.md @@ -10,6 +10,8 @@ module orthogonal-factorization-systems.lifts-maps where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.dependent-products-truncated-types open import foundation.equivalences open import foundation.function-types diff --git a/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md index f4ba57ae36..9e26136630 100644 --- a/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/localizations-at-global-subuniverses.lagda.md @@ -14,6 +14,7 @@ open import foundation.constant-maps open import foundation.contractible-types open import foundation.cospan-diagrams open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.equivalences-arrows open import foundation.extensions-types diff --git a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md index dd2128327c..c4b2bf31b6 100644 --- a/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/maps-local-at-maps.lagda.md @@ -8,6 +8,7 @@ module orthogonal-factorization-systems.maps-local-at-maps where ```agda open import foundation.cartesian-morphisms-arrows +open import foundation.dependent-products-propositions open import foundation.fibers-of-maps open import foundation.propositions open import foundation.retracts-of-maps diff --git a/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md b/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md index ffc220075a..916191e259 100644 --- a/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md +++ b/src/orthogonal-factorization-systems/mere-lifting-properties.lagda.md @@ -7,6 +7,7 @@ module orthogonal-factorization-systems.mere-lifting-properties where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.surjective-maps open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/modal-operators.lagda.md b/src/orthogonal-factorization-systems/modal-operators.lagda.md index 457aeddced..d216416033 100644 --- a/src/orthogonal-factorization-systems/modal-operators.lagda.md +++ b/src/orthogonal-factorization-systems/modal-operators.lagda.md @@ -8,6 +8,7 @@ module orthogonal-factorization-systems.modal-operators where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.propositions diff --git a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md index 1ea050536a..36b880a7ea 100644 --- a/src/orthogonal-factorization-systems/null-families-of-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-families-of-types.lagda.md @@ -8,6 +8,7 @@ module orthogonal-factorization-systems.null-families-of-types where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.precomposition-functions open import foundation.propositions diff --git a/src/orthogonal-factorization-systems/null-maps.lagda.md b/src/orthogonal-factorization-systems/null-maps.lagda.md index abce4f90c5..f7bed0e804 100644 --- a/src/orthogonal-factorization-systems/null-maps.lagda.md +++ b/src/orthogonal-factorization-systems/null-maps.lagda.md @@ -9,6 +9,7 @@ module orthogonal-factorization-systems.null-maps where ```agda open import foundation.cones-over-cospan-diagrams open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.equivalences-arrows open import foundation.families-of-equivalences diff --git a/src/orthogonal-factorization-systems/null-types.lagda.md b/src/orthogonal-factorization-systems/null-types.lagda.md index f6b07a4409..8b4b8345d8 100644 --- a/src/orthogonal-factorization-systems/null-types.lagda.md +++ b/src/orthogonal-factorization-systems/null-types.lagda.md @@ -10,6 +10,8 @@ module orthogonal-factorization-systems.null-types where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.diagonal-maps-of-types open import foundation.equivalences open import foundation.equivalences-arrows diff --git a/src/orthogonal-factorization-systems/open-modalities.lagda.md b/src/orthogonal-factorization-systems/open-modalities.lagda.md index 3de73e9582..141b9a2049 100644 --- a/src/orthogonal-factorization-systems/open-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/open-modalities.lagda.md @@ -9,6 +9,7 @@ module orthogonal-factorization-systems.open-modalities where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-extensionality-axiom diff --git a/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md b/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md index ccdba0c7e2..10226d4a45 100644 --- a/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md +++ b/src/orthogonal-factorization-systems/orthogonal-factorization-systems.lagda.md @@ -11,6 +11,8 @@ open import foundation.cartesian-product-types open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md index 0d98e6c2ea..035b6d5912 100644 --- a/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md +++ b/src/orthogonal-factorization-systems/orthogonal-maps.lagda.md @@ -16,6 +16,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.coproducts-pullbacks open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.dependent-products-pullbacks open import foundation.dependent-sums-pullbacks open import foundation.equivalences diff --git a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md index 440719b15d..7e88cab774 100644 --- a/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/reflective-global-subuniverses.lagda.md @@ -10,6 +10,8 @@ module orthogonal-factorization-systems.reflective-global-subuniverses where open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.cospan-diagrams +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.extensions-types-global-subuniverses open import foundation.global-subuniverses diff --git a/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md index 7292a82aa0..f23418a53f 100644 --- a/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-colocal-at-maps.lagda.md @@ -12,6 +12,8 @@ open import foundation.commuting-squares-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.equivalences-arrows diff --git a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md index 0e261e3ed9..02bf7179c8 100644 --- a/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md +++ b/src/orthogonal-factorization-systems/types-local-at-maps.lagda.md @@ -13,6 +13,8 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.dependent-universal-property-equivalences open import foundation.empty-types open import foundation.equivalences diff --git a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md index d0a891d833..0d388f758d 100644 --- a/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/uniquely-eliminating-modalities.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-extensionality-axiom diff --git a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md index 59815d7643..10b1e3d0b6 100644 --- a/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md +++ b/src/orthogonal-factorization-systems/universal-property-localizations-at-global-subuniverses.lagda.md @@ -10,6 +10,8 @@ module orthogonal-factorization-systems.universal-property-localizations-at-glob open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.extensions-types open import foundation.extensions-types-global-subuniverses diff --git a/src/orthogonal-factorization-systems/wide-function-classes.lagda.md b/src/orthogonal-factorization-systems/wide-function-classes.lagda.md index 7798c4379d..4a27892627 100644 --- a/src/orthogonal-factorization-systems/wide-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/wide-function-classes.lagda.md @@ -9,6 +9,7 @@ module orthogonal-factorization-systems.wide-function-classes where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md b/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md index e8ed36b96f..2743933179 100644 --- a/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md +++ b/src/orthogonal-factorization-systems/wide-global-function-classes.lagda.md @@ -9,6 +9,7 @@ module orthogonal-factorization-systems.wide-global-function-classes where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.function-types open import foundation.propositions diff --git a/src/polytopes/abstract-polytopes.lagda.md b/src/polytopes/abstract-polytopes.lagda.md index b2a62140af..8a7a476a69 100644 --- a/src/polytopes/abstract-polytopes.lagda.md +++ b/src/polytopes/abstract-polytopes.lagda.md @@ -14,6 +14,8 @@ open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.identity-types open import foundation.propositional-truncations diff --git a/src/real-numbers/apartness-real-numbers.lagda.md b/src/real-numbers/apartness-real-numbers.lagda.md index 610c8bcdbb..6bb86cda08 100644 --- a/src/real-numbers/apartness-real-numbers.lagda.md +++ b/src/real-numbers/apartness-real-numbers.lagda.md @@ -7,6 +7,7 @@ module real-numbers.apartness-real-numbers where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.empty-types open import foundation.function-types diff --git a/src/real-numbers/dedekind-real-numbers.lagda.md b/src/real-numbers/dedekind-real-numbers.lagda.md index 36f5e8e621..52af6c1c06 100644 --- a/src/real-numbers/dedekind-real-numbers.lagda.md +++ b/src/real-numbers/dedekind-real-numbers.lagda.md @@ -16,6 +16,7 @@ open import foundation.binary-transport open import foundation.conjunction open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjoint-subtypes open import foundation.disjunction open import foundation.embeddings diff --git a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md index 87a1154a7f..80f4236859 100644 --- a/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-lower-dedekind-real-numbers.lagda.md @@ -13,6 +13,7 @@ open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.existential-quantification open import foundation.logical-equivalences diff --git a/src/real-numbers/inequality-real-numbers.lagda.md b/src/real-numbers/inequality-real-numbers.lagda.md index 06313f63bb..d399fb5c0c 100644 --- a/src/real-numbers/inequality-real-numbers.lagda.md +++ b/src/real-numbers/inequality-real-numbers.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.rational-numbers open import foundation.complements-subtypes open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md index 1c124e2f50..6bdf9bf45d 100644 --- a/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/inequality-upper-dedekind-real-numbers.lagda.md @@ -13,6 +13,7 @@ open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.existential-quantification open import foundation.logical-equivalences diff --git a/src/real-numbers/lower-dedekind-real-numbers.lagda.md b/src/real-numbers/lower-dedekind-real-numbers.lagda.md index 2d9c8b829b..1d84df075d 100644 --- a/src/real-numbers/lower-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/lower-dedekind-real-numbers.lagda.md @@ -14,6 +14,8 @@ open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.conjunction open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.existential-quantification open import foundation.function-types open import foundation.identity-types diff --git a/src/real-numbers/metric-space-of-real-numbers.lagda.md b/src/real-numbers/metric-space-of-real-numbers.lagda.md index 7a4d12c506..2de240af64 100644 --- a/src/real-numbers/metric-space-of-real-numbers.lagda.md +++ b/src/real-numbers/metric-space-of-real-numbers.lagda.md @@ -16,6 +16,7 @@ open import elementary-number-theory.rational-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.diagonal-maps-cartesian-products-of-types open import foundation.existential-quantification open import foundation.function-types diff --git a/src/real-numbers/rational-real-numbers.lagda.md b/src/real-numbers/rational-real-numbers.lagda.md index c5dfe24fcc..df323423d5 100644 --- a/src/real-numbers/rational-real-numbers.lagda.md +++ b/src/real-numbers/rational-real-numbers.lagda.md @@ -15,6 +15,7 @@ open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.action-on-identifications-functions open import foundation.conjunction open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.empty-types open import foundation.equivalences diff --git a/src/real-numbers/similarity-real-numbers.lagda.md b/src/real-numbers/similarity-real-numbers.lagda.md index d7b13097d2..bcdcd5e004 100644 --- a/src/real-numbers/similarity-real-numbers.lagda.md +++ b/src/real-numbers/similarity-real-numbers.lagda.md @@ -8,6 +8,7 @@ module real-numbers.similarity-real-numbers where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.logical-equivalences open import foundation.powersets diff --git a/src/real-numbers/strict-inequality-real-numbers.lagda.md b/src/real-numbers/strict-inequality-real-numbers.lagda.md index 2b2ccc6a6b..9ab86939a0 100644 --- a/src/real-numbers/strict-inequality-real-numbers.lagda.md +++ b/src/real-numbers/strict-inequality-real-numbers.lagda.md @@ -15,6 +15,7 @@ open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.conjunction open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.empty-types open import foundation.existential-quantification diff --git a/src/real-numbers/upper-dedekind-real-numbers.lagda.md b/src/real-numbers/upper-dedekind-real-numbers.lagda.md index fa82905722..feca0e5359 100644 --- a/src/real-numbers/upper-dedekind-real-numbers.lagda.md +++ b/src/real-numbers/upper-dedekind-real-numbers.lagda.md @@ -14,6 +14,8 @@ open import elementary-number-theory.strict-inequality-rational-numbers open import foundation.conjunction open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.existential-quantification open import foundation.function-types open import foundation.identity-types diff --git a/src/ring-theory/central-elements-rings.lagda.md b/src/ring-theory/central-elements-rings.lagda.md index 7ecc9dc806..804f8f4928 100644 --- a/src/ring-theory/central-elements-rings.lagda.md +++ b/src/ring-theory/central-elements-rings.lagda.md @@ -8,6 +8,7 @@ module ring-theory.central-elements-rings where ```agda open import foundation.action-on-identifications-functions +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/ring-theory/central-elements-semirings.lagda.md b/src/ring-theory/central-elements-semirings.lagda.md index 41cb19f6ef..d2768fd24b 100644 --- a/src/ring-theory/central-elements-semirings.lagda.md +++ b/src/ring-theory/central-elements-semirings.lagda.md @@ -7,6 +7,7 @@ module ring-theory.central-elements-semirings where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/ring-theory/commuting-elements-rings.lagda.md b/src/ring-theory/commuting-elements-rings.lagda.md index 3d35949217..9a6ce88ca1 100644 --- a/src/ring-theory/commuting-elements-rings.lagda.md +++ b/src/ring-theory/commuting-elements-rings.lagda.md @@ -8,6 +8,7 @@ module ring-theory.commuting-elements-rings where ```agda open import foundation.action-on-identifications-functions +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/ring-theory/congruence-relations-rings.lagda.md b/src/ring-theory/congruence-relations-rings.lagda.md index 7b12139706..2ccaca9b2c 100644 --- a/src/ring-theory/congruence-relations-rings.lagda.md +++ b/src/ring-theory/congruence-relations-rings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.congruence-relations-rings where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.identity-types diff --git a/src/ring-theory/congruence-relations-semirings.lagda.md b/src/ring-theory/congruence-relations-semirings.lagda.md index 2a0089a148..49ce923a83 100644 --- a/src/ring-theory/congruence-relations-semirings.lagda.md +++ b/src/ring-theory/congruence-relations-semirings.lagda.md @@ -10,6 +10,7 @@ module ring-theory.congruence-relations-semirings where open import foundation.binary-relations open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types diff --git a/src/ring-theory/cyclic-rings.lagda.md b/src/ring-theory/cyclic-rings.lagda.md index e3b3ac6fca..6fef7dfdb3 100644 --- a/src/ring-theory/cyclic-rings.lagda.md +++ b/src/ring-theory/cyclic-rings.lagda.md @@ -15,6 +15,7 @@ open import elementary-number-theory.ring-of-integers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.identity-types diff --git a/src/ring-theory/full-ideals-rings.lagda.md b/src/ring-theory/full-ideals-rings.lagda.md index 145fc154fa..b65befc56b 100644 --- a/src/ring-theory/full-ideals-rings.lagda.md +++ b/src/ring-theory/full-ideals-rings.lagda.md @@ -8,6 +8,7 @@ module ring-theory.full-ideals-rings where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.full-subtypes open import foundation.propositions open import foundation.raising-universe-levels-unit-type diff --git a/src/ring-theory/generating-elements-rings.lagda.md b/src/ring-theory/generating-elements-rings.lagda.md index f143405f0f..dc8e940af5 100644 --- a/src/ring-theory/generating-elements-rings.lagda.md +++ b/src/ring-theory/generating-elements-rings.lagda.md @@ -7,6 +7,7 @@ module ring-theory.generating-elements-rings where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/ring-theory/groups-of-units-rings.lagda.md b/src/ring-theory/groups-of-units-rings.lagda.md index 16e293804e..cadb1844aa 100644 --- a/src/ring-theory/groups-of-units-rings.lagda.md +++ b/src/ring-theory/groups-of-units-rings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.groups-of-units-rings where ```agda open import category-theory.functors-large-precategories +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/ring-theory/homomorphisms-cyclic-rings.lagda.md b/src/ring-theory/homomorphisms-cyclic-rings.lagda.md index 8bdb6d76cf..74f843f3fd 100644 --- a/src/ring-theory/homomorphisms-cyclic-rings.lagda.md +++ b/src/ring-theory/homomorphisms-cyclic-rings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.homomorphisms-cyclic-rings where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositional-truncations open import foundation.propositions diff --git a/src/ring-theory/homomorphisms-rings.lagda.md b/src/ring-theory/homomorphisms-rings.lagda.md index 95f466ea7c..5a82b5efcb 100644 --- a/src/ring-theory/homomorphisms-rings.lagda.md +++ b/src/ring-theory/homomorphisms-rings.lagda.md @@ -8,6 +8,7 @@ module ring-theory.homomorphisms-rings where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies diff --git a/src/ring-theory/homomorphisms-semirings.lagda.md b/src/ring-theory/homomorphisms-semirings.lagda.md index 9bd4acad47..0d1ad17c62 100644 --- a/src/ring-theory/homomorphisms-semirings.lagda.md +++ b/src/ring-theory/homomorphisms-semirings.lagda.md @@ -8,6 +8,7 @@ module ring-theory.homomorphisms-semirings where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies diff --git a/src/ring-theory/ideals-rings.lagda.md b/src/ring-theory/ideals-rings.lagda.md index 74b99261c9..cbb03c2842 100644 --- a/src/ring-theory/ideals-rings.lagda.md +++ b/src/ring-theory/ideals-rings.lagda.md @@ -12,6 +12,7 @@ open import foundation.binary-relations open import foundation.binary-transport open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.function-types diff --git a/src/ring-theory/ideals-semirings.lagda.md b/src/ring-theory/ideals-semirings.lagda.md index 801c43f0b9..62c2831249 100644 --- a/src/ring-theory/ideals-semirings.lagda.md +++ b/src/ring-theory/ideals-semirings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.ideals-semirings where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/ring-theory/idempotent-elements-rings.lagda.md b/src/ring-theory/idempotent-elements-rings.lagda.md index 3d3369a849..2bfa9cb5aa 100644 --- a/src/ring-theory/idempotent-elements-rings.lagda.md +++ b/src/ring-theory/idempotent-elements-rings.lagda.md @@ -7,6 +7,7 @@ module ring-theory.idempotent-elements-rings where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.sets open import foundation.subtypes diff --git a/src/ring-theory/integer-multiples-of-elements-rings.lagda.md b/src/ring-theory/integer-multiples-of-elements-rings.lagda.md index 9f66654609..35c987f634 100644 --- a/src/ring-theory/integer-multiples-of-elements-rings.lagda.md +++ b/src/ring-theory/integer-multiples-of-elements-rings.lagda.md @@ -14,6 +14,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.coproduct-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.transport-along-identifications diff --git a/src/ring-theory/invertible-elements-rings.lagda.md b/src/ring-theory/invertible-elements-rings.lagda.md index 5066846791..614c3729df 100644 --- a/src/ring-theory/invertible-elements-rings.lagda.md +++ b/src/ring-theory/invertible-elements-rings.lagda.md @@ -9,6 +9,8 @@ module ring-theory.invertible-elements-rings where ```agda open import foundation.action-on-identifications-functions open import foundation.contractible-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-cartesian-product-types diff --git a/src/ring-theory/isomorphisms-rings.lagda.md b/src/ring-theory/isomorphisms-rings.lagda.md index 9ca0051cd9..ad3737a750 100644 --- a/src/ring-theory/isomorphisms-rings.lagda.md +++ b/src/ring-theory/isomorphisms-rings.lagda.md @@ -12,6 +12,8 @@ open import category-theory.isomorphisms-in-large-precategories open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.equivalences open import foundation.function-types diff --git a/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md index 45001b74cb..101243cf09 100644 --- a/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/left-ideals-generated-by-subsets-rings.lagda.md @@ -10,6 +10,7 @@ module ring-theory.left-ideals-generated-by-subsets-rings where open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.fibers-of-maps open import foundation.function-types open import foundation.identity-types diff --git a/src/ring-theory/left-ideals-rings.lagda.md b/src/ring-theory/left-ideals-rings.lagda.md index c0d2710a89..927c827ba6 100644 --- a/src/ring-theory/left-ideals-rings.lagda.md +++ b/src/ring-theory/left-ideals-rings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.left-ideals-rings where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/ring-theory/local-rings.lagda.md b/src/ring-theory/local-rings.lagda.md index 6ec65472c7..3553f43273 100644 --- a/src/ring-theory/local-rings.lagda.md +++ b/src/ring-theory/local-rings.lagda.md @@ -8,6 +8,7 @@ module ring-theory.local-rings where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.propositions open import foundation.sets diff --git a/src/ring-theory/localizations-rings.lagda.md b/src/ring-theory/localizations-rings.lagda.md index 0c3aeb511a..b4b1ca32ac 100644 --- a/src/ring-theory/localizations-rings.lagda.md +++ b/src/ring-theory/localizations-rings.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.functoriality-dependent-pair-types diff --git a/src/ring-theory/multiples-of-elements-rings.lagda.md b/src/ring-theory/multiples-of-elements-rings.lagda.md index f0bf36215a..d151f8fd60 100644 --- a/src/ring-theory/multiples-of-elements-rings.lagda.md +++ b/src/ring-theory/multiples-of-elements-rings.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.addition-natural-numbers open import elementary-number-theory.multiplication-natural-numbers open import elementary-number-theory.natural-numbers +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.universe-levels diff --git a/src/ring-theory/nil-ideals-rings.lagda.md b/src/ring-theory/nil-ideals-rings.lagda.md index 22688c8e4c..2c2d4afdfa 100644 --- a/src/ring-theory/nil-ideals-rings.lagda.md +++ b/src/ring-theory/nil-ideals-rings.lagda.md @@ -7,6 +7,7 @@ module ring-theory.nil-ideals-rings where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/ring-theory/nilpotent-elements-rings.lagda.md b/src/ring-theory/nilpotent-elements-rings.lagda.md index 96f8512935..e3cf9a9c72 100644 --- a/src/ring-theory/nilpotent-elements-rings.lagda.md +++ b/src/ring-theory/nilpotent-elements-rings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.nilpotent-elements-rings where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.identity-types open import foundation.propositional-truncations diff --git a/src/ring-theory/nilpotent-elements-semirings.lagda.md b/src/ring-theory/nilpotent-elements-semirings.lagda.md index 434bdf7fb8..94f93d8c1b 100644 --- a/src/ring-theory/nilpotent-elements-semirings.lagda.md +++ b/src/ring-theory/nilpotent-elements-semirings.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.identity-types open import foundation.propositional-truncations diff --git a/src/ring-theory/poset-of-ideals-rings.lagda.md b/src/ring-theory/poset-of-ideals-rings.lagda.md index 7ac68be10d..b31969cc7d 100644 --- a/src/ring-theory/poset-of-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-ideals-rings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.poset-of-ideals-rings where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.powersets open import foundation.propositions diff --git a/src/ring-theory/poset-of-left-ideals-rings.lagda.md b/src/ring-theory/poset-of-left-ideals-rings.lagda.md index a34d3bad4a..e9f10db6f1 100644 --- a/src/ring-theory/poset-of-left-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-left-ideals-rings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.poset-of-left-ideals-rings where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.powersets open import foundation.propositions diff --git a/src/ring-theory/poset-of-right-ideals-rings.lagda.md b/src/ring-theory/poset-of-right-ideals-rings.lagda.md index 9ddb7754b7..6c1fd89e20 100644 --- a/src/ring-theory/poset-of-right-ideals-rings.lagda.md +++ b/src/ring-theory/poset-of-right-ideals-rings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.poset-of-right-ideals-rings where ```agda open import foundation.binary-relations open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.powersets open import foundation.propositions diff --git a/src/ring-theory/radical-ideals-rings.lagda.md b/src/ring-theory/radical-ideals-rings.lagda.md index 964017ee37..2d2546accc 100644 --- a/src/ring-theory/radical-ideals-rings.lagda.md +++ b/src/ring-theory/radical-ideals-rings.lagda.md @@ -7,6 +7,7 @@ module ring-theory.radical-ideals-rings where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md b/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md index ec913d21e3..0bf8be447b 100644 --- a/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md +++ b/src/ring-theory/right-ideals-generated-by-subsets-rings.lagda.md @@ -10,6 +10,7 @@ module ring-theory.right-ideals-generated-by-subsets-rings where open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.fibers-of-maps open import foundation.function-types open import foundation.identity-types diff --git a/src/ring-theory/right-ideals-rings.lagda.md b/src/ring-theory/right-ideals-rings.lagda.md index 1da87674fc..470dc29bbc 100644 --- a/src/ring-theory/right-ideals-rings.lagda.md +++ b/src/ring-theory/right-ideals-rings.lagda.md @@ -9,6 +9,7 @@ module ring-theory.right-ideals-rings where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types diff --git a/src/ring-theory/rings.lagda.md b/src/ring-theory/rings.lagda.md index 757f7994ee..4d3d79af13 100644 --- a/src/ring-theory/rings.lagda.md +++ b/src/ring-theory/rings.lagda.md @@ -16,6 +16,7 @@ open import foundation.binary-embeddings open import foundation.binary-equivalences open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/ring-theory/semirings.lagda.md b/src/ring-theory/semirings.lagda.md index 982869d8d3..2545e267cb 100644 --- a/src/ring-theory/semirings.lagda.md +++ b/src/ring-theory/semirings.lagda.md @@ -14,6 +14,7 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.negation open import foundation.propositions diff --git a/src/ring-theory/subsets-rings.lagda.md b/src/ring-theory/subsets-rings.lagda.md index df9a3f2c84..e1b541fb5f 100644 --- a/src/ring-theory/subsets-rings.lagda.md +++ b/src/ring-theory/subsets-rings.lagda.md @@ -7,6 +7,7 @@ module ring-theory.subsets-rings where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositional-extensionality open import foundation.propositions diff --git a/src/ring-theory/subsets-semirings.lagda.md b/src/ring-theory/subsets-semirings.lagda.md index 0236a79809..cc21326980 100644 --- a/src/ring-theory/subsets-semirings.lagda.md +++ b/src/ring-theory/subsets-semirings.lagda.md @@ -7,6 +7,7 @@ module ring-theory.subsets-semirings where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositional-extensionality open import foundation.propositions diff --git a/src/ring-theory/trivial-rings.lagda.md b/src/ring-theory/trivial-rings.lagda.md index 4173514622..efd52982c6 100644 --- a/src/ring-theory/trivial-rings.lagda.md +++ b/src/ring-theory/trivial-rings.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.negated-equality open import foundation.negation diff --git a/src/set-theory/cardinalities.lagda.md b/src/set-theory/cardinalities.lagda.md index 27c781d4cc..25c331e2a9 100644 --- a/src/set-theory/cardinalities.lagda.md +++ b/src/set-theory/cardinalities.lagda.md @@ -8,6 +8,7 @@ module set-theory.cardinalities where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality-axiom open import foundation.functoriality-propositional-truncation diff --git a/src/set-theory/countable-sets.lagda.md b/src/set-theory/countable-sets.lagda.md index ab92a803d5..6b2a4cf4d7 100644 --- a/src/set-theory/countable-sets.lagda.md +++ b/src/set-theory/countable-sets.lagda.md @@ -19,6 +19,7 @@ open import foundation.decidable-propositions open import foundation.decidable-subtypes open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-coproduct-types open import foundation.equivalences diff --git a/src/set-theory/cumulative-hierarchy.lagda.md b/src/set-theory/cumulative-hierarchy.lagda.md index baa1ddad21..c4e25f4da1 100644 --- a/src/set-theory/cumulative-hierarchy.lagda.md +++ b/src/set-theory/cumulative-hierarchy.lagda.md @@ -15,6 +15,8 @@ open import foundation.cartesian-product-types open import foundation.constant-type-families open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.empty-types open import foundation.existential-quantification open import foundation.function-types diff --git a/src/set-theory/infinite-sets.lagda.md b/src/set-theory/infinite-sets.lagda.md index d94e6be82f..238613510a 100644 --- a/src/set-theory/infinite-sets.lagda.md +++ b/src/set-theory/infinite-sets.lagda.md @@ -10,6 +10,7 @@ module set-theory.infinite-sets where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.mere-embeddings open import foundation.propositions open import foundation.sets diff --git a/src/set-theory/uncountable-sets.lagda.md b/src/set-theory/uncountable-sets.lagda.md index f1cb306d08..d6380269ab 100644 --- a/src/set-theory/uncountable-sets.lagda.md +++ b/src/set-theory/uncountable-sets.lagda.md @@ -7,6 +7,7 @@ module set-theory.uncountable-sets where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.negation open import foundation.propositions open import foundation.sets diff --git a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md index d3642b399f..2d4bede8d6 100644 --- a/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -10,6 +10,8 @@ module species.cauchy-composition-species-of-types-in-subuniverses where open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equality-cartesian-product-types open import foundation.equivalences open import foundation.function-types diff --git a/src/species/cauchy-composition-species-of-types.lagda.md b/src/species/cauchy-composition-species-of-types.lagda.md index 05943435c9..680390a530 100644 --- a/src/species/cauchy-composition-species-of-types.lagda.md +++ b/src/species/cauchy-composition-species-of-types.lagda.md @@ -10,6 +10,7 @@ module species.cauchy-composition-species-of-types where open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-universal-property-equivalences open import foundation.discrete-relaxed-sigma-decompositions open import foundation.equivalences diff --git a/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md index a5d3b8b486..f8bd2bcd57 100644 --- a/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-exponentials-species-of-types-in-subuniverses.lagda.md @@ -11,6 +11,7 @@ open import foundation.cartesian-product-types open import foundation.coproduct-decompositions open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-cartesian-product-types diff --git a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md index dc5f62299c..99e82859bb 100644 --- a/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-products-species-of-types-in-subuniverses.lagda.md @@ -12,6 +12,7 @@ open import foundation.coproduct-decompositions open import foundation.coproduct-decompositions-subuniverse open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types diff --git a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md index 4e9a36c29a..a51d995740 100644 --- a/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md +++ b/src/species/cauchy-series-species-of-types-in-subuniverses.lagda.md @@ -9,6 +9,7 @@ module species.cauchy-series-species-of-types-in-subuniverses where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-cartesian-product-types open import foundation.functoriality-dependent-pair-types diff --git a/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md index caf7c99d4d..9615d3fe32 100644 --- a/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-exponentials-species-of-types-in-subuniverses.lagda.md @@ -9,6 +9,7 @@ module species.dirichlet-exponentials-species-of-types-in-subuniverses where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-cartesian-product-types diff --git a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md index b2e6b43e7c..2894650906 100644 --- a/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md +++ b/src/species/dirichlet-products-species-of-types-in-subuniverses.lagda.md @@ -10,6 +10,8 @@ module species.dirichlet-products-species-of-types-in-subuniverses where open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.global-subuniverses diff --git a/src/species/morphisms-finite-species.lagda.md b/src/species/morphisms-finite-species.lagda.md index 52f2991b25..7e39371d67 100644 --- a/src/species/morphisms-finite-species.lagda.md +++ b/src/species/morphisms-finite-species.lagda.md @@ -8,6 +8,7 @@ module species.morphisms-finite-species where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.equivalences open import foundation.function-types diff --git a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md index 2b7b0202fd..7e16576b00 100644 --- a/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md +++ b/src/species/small-cauchy-composition-species-of-finite-inhabited-types.lagda.md @@ -11,6 +11,8 @@ module species.small-cauchy-composition-species-of-finite-inhabited-types where ```agda open import foundation.contractible-types open import foundation.decidable-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-cartesian-product-types diff --git a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md index 22cb26f896..0fcbea9430 100644 --- a/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/small-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -10,6 +10,8 @@ module species.small-cauchy-composition-species-of-types-in-subuniverses where open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equality-cartesian-product-types open import foundation.equivalences open import foundation.functoriality-cartesian-product-types diff --git a/src/species/species-of-types-in-subuniverses.lagda.md b/src/species/species-of-types-in-subuniverses.lagda.md index 1ef1c85fec..9ce1790640 100644 --- a/src/species/species-of-types-in-subuniverses.lagda.md +++ b/src/species/species-of-types-in-subuniverses.lagda.md @@ -9,6 +9,7 @@ module species.species-of-types-in-subuniverses where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.propositions diff --git a/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md b/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md index 030f8440d0..722116577b 100644 --- a/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md +++ b/src/species/unit-cauchy-composition-species-of-types-in-subuniverses.lagda.md @@ -9,6 +9,7 @@ module species.unit-cauchy-composition-species-of-types-in-subuniverses where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.global-subuniverses open import foundation.subuniverses open import foundation.universe-levels diff --git a/src/species/unit-cauchy-composition-species-of-types.lagda.md b/src/species/unit-cauchy-composition-species-of-types.lagda.md index 15884d5b45..3b37fe26fe 100644 --- a/src/species/unit-cauchy-composition-species-of-types.lagda.md +++ b/src/species/unit-cauchy-composition-species-of-types.lagda.md @@ -8,6 +8,7 @@ module species.unit-cauchy-composition-species-of-types where ```agda open import foundation.contractible-types +open import foundation.dependent-products-contractible-types open import foundation.universe-levels open import species.species-of-types diff --git a/src/structured-types/contractible-pointed-types.lagda.md b/src/structured-types/contractible-pointed-types.lagda.md index 67d5b144e8..61d36e53ed 100644 --- a/src/structured-types/contractible-pointed-types.lagda.md +++ b/src/structured-types/contractible-pointed-types.lagda.md @@ -8,6 +8,8 @@ module structured-types.contractible-pointed-types where ```agda open import foundation.contractible-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/structured-types/cyclic-types.lagda.md b/src/structured-types/cyclic-types.lagda.md index dcd59c7116..5b84515fdc 100644 --- a/src/structured-types/cyclic-types.lagda.md +++ b/src/structured-types/cyclic-types.lagda.md @@ -9,6 +9,7 @@ module structured-types.cyclic-types where ```agda open import foundation.automorphisms open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.iterating-automorphisms open import foundation.propositional-truncations open import foundation.propositions diff --git a/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md index 3b8b45fb50..60a1a7d801 100644 --- a/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/equivalences-types-equipped-with-endomorphisms.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md b/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md index cab4124961..3a40c71c3d 100644 --- a/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md +++ b/src/structured-types/initial-pointed-type-equipped-with-automorphism.lagda.md @@ -14,6 +14,7 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.homotopies open import foundation.identity-types diff --git a/src/structured-types/involutive-type-of-h-space-structures.lagda.md b/src/structured-types/involutive-type-of-h-space-structures.lagda.md index a9109305c2..5166ab62e9 100644 --- a/src/structured-types/involutive-type-of-h-space-structures.lagda.md +++ b/src/structured-types/involutive-type-of-h-space-structures.lagda.md @@ -12,6 +12,7 @@ open import foundation.binary-transport open import foundation.constant-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-function-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types diff --git a/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md index 0d43b47932..a483e3fda1 100644 --- a/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/mere-equivalences-types-equipped-with-endomorphisms.lagda.md @@ -8,6 +8,7 @@ module structured-types.mere-equivalences-types-equipped-with-endomorphisms wher ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/structured-types/morphisms-pointed-arrows.lagda.md b/src/structured-types/morphisms-pointed-arrows.lagda.md index a7f8e2d3fe..5d912d0e00 100644 --- a/src/structured-types/morphisms-pointed-arrows.lagda.md +++ b/src/structured-types/morphisms-pointed-arrows.lagda.md @@ -13,6 +13,7 @@ open import foundation.commuting-squares-of-identifications open import foundation.commuting-triangles-of-identifications open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopy-induction diff --git a/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md b/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md index 3215246b06..2561449f2a 100644 --- a/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md +++ b/src/structured-types/morphisms-types-equipped-with-endomorphisms.lagda.md @@ -10,6 +10,7 @@ module structured-types.morphisms-types-equipped-with-endomorphisms where open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/structured-types/pointed-2-homotopies.lagda.md b/src/structured-types/pointed-2-homotopies.lagda.md index 7b40b04004..30d4757e3b 100644 --- a/src/structured-types/pointed-2-homotopies.lagda.md +++ b/src/structured-types/pointed-2-homotopies.lagda.md @@ -12,6 +12,7 @@ open import foundation.binary-equivalences open import foundation.commuting-triangles-of-identifications open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/structured-types/pointed-equivalences.lagda.md b/src/structured-types/pointed-equivalences.lagda.md index 0305b2134d..92fa16ad60 100644 --- a/src/structured-types/pointed-equivalences.lagda.md +++ b/src/structured-types/pointed-equivalences.lagda.md @@ -10,6 +10,7 @@ module structured-types.pointed-equivalences where open import foundation.action-on-identifications-functions open import foundation.binary-equivalences open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/structured-types/pointed-isomorphisms.lagda.md b/src/structured-types/pointed-isomorphisms.lagda.md index f38534a262..524e6b95ff 100644 --- a/src/structured-types/pointed-isomorphisms.lagda.md +++ b/src/structured-types/pointed-isomorphisms.lagda.md @@ -11,6 +11,8 @@ open import foundation.cartesian-product-types open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.logical-equivalences diff --git a/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md b/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md index b97e8e7ae3..fe219df3c9 100644 --- a/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md +++ b/src/structured-types/pointed-types-equipped-with-automorphisms.lagda.md @@ -12,6 +12,7 @@ open import foundation.automorphisms open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/structured-types/pointed-universal-property-contractible-types.lagda.md b/src/structured-types/pointed-universal-property-contractible-types.lagda.md index 296b91ee4b..0e2fbed5a9 100644 --- a/src/structured-types/pointed-universal-property-contractible-types.lagda.md +++ b/src/structured-types/pointed-universal-property-contractible-types.lagda.md @@ -10,6 +10,7 @@ module structured-types.pointed-universal-property-contractible-types where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/structured-types/small-pointed-types.lagda.md b/src/structured-types/small-pointed-types.lagda.md index c1ee5d36fa..ef6b80dadf 100644 --- a/src/structured-types/small-pointed-types.lagda.md +++ b/src/structured-types/small-pointed-types.lagda.md @@ -9,6 +9,8 @@ module structured-types.small-pointed-types where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md index aaa7ec0e76..d6c1f5c808 100644 --- a/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/0-acyclic-maps.lagda.md @@ -7,6 +7,7 @@ module synthetic-homotopy-theory.0-acyclic-maps where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.epimorphisms-with-respect-to-sets open import foundation.propositions open import foundation.surjective-maps diff --git a/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md index cdfaabba69..3091974200 100644 --- a/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/0-acyclic-types.lagda.md @@ -9,6 +9,8 @@ module synthetic-homotopy-theory.0-acyclic-types where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.functoriality-propositional-truncation open import foundation.inhabited-types open import foundation.propositional-truncations diff --git a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md index c7e47d89d0..762892288f 100644 --- a/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/1-acyclic-types.lagda.md @@ -11,6 +11,9 @@ open import foundation.0-connected-types open import foundation.binary-transport open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.diagonal-maps-of-types open import foundation.equivalences open import foundation.function-extensionality-axiom diff --git a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md index 3bf63f4ed1..da7eea3d78 100644 --- a/src/synthetic-homotopy-theory/acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/acyclic-maps.lagda.md @@ -15,6 +15,8 @@ open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-epimorphisms open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.dependent-universal-property-equivalences open import foundation.diagonal-maps-of-types open import foundation.embeddings diff --git a/src/synthetic-homotopy-theory/acyclic-types.lagda.md b/src/synthetic-homotopy-theory/acyclic-types.lagda.md index 35473b70bf..2c75fec76a 100644 --- a/src/synthetic-homotopy-theory/acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/acyclic-types.lagda.md @@ -8,6 +8,8 @@ module synthetic-homotopy-theory.acyclic-types where ```agda open import foundation.contractible-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.propositions open import foundation.retracts-of-types diff --git a/src/synthetic-homotopy-theory/circle.lagda.md b/src/synthetic-homotopy-theory/circle.lagda.md index 0340db0b69..c62cde65d3 100644 --- a/src/synthetic-homotopy-theory/circle.lagda.md +++ b/src/synthetic-homotopy-theory/circle.lagda.md @@ -15,6 +15,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md b/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md index 9e34713e9c..9d0c9111df 100644 --- a/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md +++ b/src/synthetic-homotopy-theory/cocartesian-morphisms-arrows.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.cocartesian-morphisms-arrows where ```agda open import foundation.commuting-squares-of-maps open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.morphisms-arrows open import foundation.propositions open import foundation.universe-levels diff --git a/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md b/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md index b483d3e9a8..d7cfb09edb 100644 --- a/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/codiagonals-of-maps.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.codiagonals-of-maps where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-types diff --git a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md index e14dce732d..133500a665 100644 --- a/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/cofibers-of-maps.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.cofibers-of-maps where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.unit-type open import foundation.universe-levels diff --git a/src/synthetic-homotopy-theory/coforks.lagda.md b/src/synthetic-homotopy-theory/coforks.lagda.md index fa5ea65e19..e28ffce6cf 100644 --- a/src/synthetic-homotopy-theory/coforks.lagda.md +++ b/src/synthetic-homotopy-theory/coforks.lagda.md @@ -13,6 +13,7 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.double-arrows open import foundation.equivalences open import foundation.equivalences-double-arrows diff --git a/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md b/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md index 46a02e248f..76120bc8ef 100644 --- a/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md +++ b/src/synthetic-homotopy-theory/connected-set-bundles-circle.lagda.md @@ -10,6 +10,7 @@ module synthetic-homotopy-theory.connected-set-bundles-circle where open import foundation.0-connected-types open import foundation.automorphisms open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/connective-prespectra.lagda.md b/src/synthetic-homotopy-theory/connective-prespectra.lagda.md index db0ebe5577..fa63fba4ad 100644 --- a/src/synthetic-homotopy-theory/connective-prespectra.lagda.md +++ b/src/synthetic-homotopy-theory/connective-prespectra.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.connected-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/connective-spectra.lagda.md b/src/synthetic-homotopy-theory/connective-spectra.lagda.md index 939ec9243c..00487ab199 100644 --- a/src/synthetic-homotopy-theory/connective-spectra.lagda.md +++ b/src/synthetic-homotopy-theory/connective-spectra.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.connected-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md b/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md index cfba684dd3..998a73b967 100644 --- a/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-cocones-under-spans.lagda.md @@ -16,6 +16,7 @@ open import foundation.contractible-types open import foundation.dependent-homotopies open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md b/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md index a847a0abfa..f5c185e626 100644 --- a/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-descent-circle.lagda.md @@ -10,6 +10,7 @@ module synthetic-homotopy-theory.dependent-descent-circle where open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-types diff --git a/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md b/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md index 265ce6a2c9..aa717c78ab 100644 --- a/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-pushout-products.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.dependent-pushout-products where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md index ba60811fcb..370b13e504 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-coequalizers.lagda.md @@ -10,6 +10,7 @@ module synthetic-homotopy-theory.dependent-universal-property-coequalizers where open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.double-arrows open import foundation.equivalences open import foundation.fibers-of-maps diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md index c0b9760150..7b5f4e6aba 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-pushouts.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-dependent-functions open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps diff --git a/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md index 449c744b8e..958bfea56f 100644 --- a/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/dependent-universal-property-sequential-colimits.lagda.md @@ -12,6 +12,7 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-types diff --git a/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md b/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md index cec4371a5e..2c323e24df 100644 --- a/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-equivalence-types.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.descent-circle-equivalence-types where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.universe-levels diff --git a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md index 8b2ed00fc2..d747a7a170 100644 --- a/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle-subtypes.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.descent-circle-subtypes where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/descent-circle.lagda.md b/src/synthetic-homotopy-theory/descent-circle.lagda.md index 26cb9592d3..32ae4d93c8 100644 --- a/src/synthetic-homotopy-theory/descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/descent-circle.lagda.md @@ -13,6 +13,7 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality-axiom diff --git a/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md index 7095433e23..7074a42649 100644 --- a/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-equivalence-types-over-pushouts.lagda.md @@ -14,6 +14,7 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalence-extensionality open import foundation.equivalences open import foundation.fibers-of-maps diff --git a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md index 35a5f3e58d..333f7520a2 100644 --- a/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-data-function-types-over-pushouts.lagda.md @@ -14,6 +14,7 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality diff --git a/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md index 6d1f56638f..354b3f347a 100644 --- a/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/descent-property-pushouts.lagda.md @@ -11,6 +11,7 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps diff --git a/src/synthetic-homotopy-theory/free-loops.lagda.md b/src/synthetic-homotopy-theory/free-loops.lagda.md index 2ca408cc36..06fa0b3416 100644 --- a/src/synthetic-homotopy-theory/free-loops.lagda.md +++ b/src/synthetic-homotopy-theory/free-loops.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.constant-type-families open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md index 10609483e0..8edd725590 100644 --- a/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md +++ b/src/synthetic-homotopy-theory/hatchers-acyclic-type.lagda.md @@ -13,6 +13,7 @@ open import foundation.cartesian-product-types open import foundation.commuting-squares-of-identifications open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.functoriality-cartesian-product-types open import foundation.functoriality-dependent-pair-types diff --git a/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md index ed4ca2232d..4e1a490d3c 100644 --- a/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/identity-systems-descent-data-pushouts.lagda.md @@ -12,6 +12,7 @@ module synthetic-homotopy-theory.identity-systems-descent-data-pushouts where open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md index c651ce59fa..3c499aa004 100644 --- a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md @@ -16,6 +16,8 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-extensionality-axiom open import foundation.function-types diff --git a/src/synthetic-homotopy-theory/interval-type.lagda.md b/src/synthetic-homotopy-theory/interval-type.lagda.md index eb421618ba..b918ea9cf6 100644 --- a/src/synthetic-homotopy-theory/interval-type.lagda.md +++ b/src/synthetic-homotopy-theory/interval-type.lagda.md @@ -13,6 +13,7 @@ open import foundation.commuting-squares-of-identifications open import foundation.contractible-types open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-extensionality open import foundation.homotopies diff --git a/src/synthetic-homotopy-theory/joins-of-maps.lagda.md b/src/synthetic-homotopy-theory/joins-of-maps.lagda.md index d31b23c331..d9aa3e0bb4 100644 --- a/src/synthetic-homotopy-theory/joins-of-maps.lagda.md +++ b/src/synthetic-homotopy-theory/joins-of-maps.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.joins-of-maps where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-types open import foundation.homotopies open import foundation.standard-pullbacks diff --git a/src/synthetic-homotopy-theory/joins-of-types.lagda.md b/src/synthetic-homotopy-theory/joins-of-types.lagda.md index 8b6ea38172..9bac4da444 100644 --- a/src/synthetic-homotopy-theory/joins-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/joins-of-types.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.disjunction open import foundation.empty-types open import foundation.equivalences diff --git a/src/synthetic-homotopy-theory/mere-spheres.lagda.md b/src/synthetic-homotopy-theory/mere-spheres.lagda.md index 70a895594b..4f85792d61 100644 --- a/src/synthetic-homotopy-theory/mere-spheres.lagda.md +++ b/src/synthetic-homotopy-theory/mere-spheres.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types open import foundation.mere-equivalences open import foundation.propositions +open import foundation.dependent-products-propositions open import foundation.universe-levels open import synthetic-homotopy-theory.spheres diff --git a/src/synthetic-homotopy-theory/plus-principle.lagda.md b/src/synthetic-homotopy-theory/plus-principle.lagda.md index 30af8ac24a..2f40459889 100644 --- a/src/synthetic-homotopy-theory/plus-principle.lagda.md +++ b/src/synthetic-homotopy-theory/plus-principle.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.plus-principle where ```agda open import foundation.connected-types open import foundation.contractible-types +open import foundation.dependent-products-contractible-types open import foundation.truncation-levels open import foundation.universe-levels diff --git a/src/synthetic-homotopy-theory/pushout-products.lagda.md b/src/synthetic-homotopy-theory/pushout-products.lagda.md index 5756497b68..f7d724635b 100644 --- a/src/synthetic-homotopy-theory/pushout-products.lagda.md +++ b/src/synthetic-homotopy-theory/pushout-products.lagda.md @@ -10,6 +10,7 @@ module synthetic-homotopy-theory.pushout-products where open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-types open import foundation.functoriality-cartesian-product-types open import foundation.homotopies diff --git a/src/synthetic-homotopy-theory/pushouts.lagda.md b/src/synthetic-homotopy-theory/pushouts.lagda.md index 1b5112681f..5404a80214 100644 --- a/src/synthetic-homotopy-theory/pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/pushouts.lagda.md @@ -12,6 +12,7 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-squares-of-maps open import foundation.constant-type-families open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-types diff --git a/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md b/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md index 77c8924b1c..3d4f95adb6 100644 --- a/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md +++ b/src/synthetic-homotopy-theory/sections-descent-circle.lagda.md @@ -16,6 +16,7 @@ open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-types diff --git a/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md b/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md index 583235db13..eea674b2a3 100644 --- a/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/sections-descent-data-pushouts.lagda.md @@ -14,6 +14,7 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.embeddings open import foundation.equivalences open import foundation.fibers-of-maps diff --git a/src/synthetic-homotopy-theory/sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/sequential-colimits.lagda.md index e0767413bd..5c95c77a2a 100644 --- a/src/synthetic-homotopy-theory/sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/sequential-colimits.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.commuting-triangles-of-maps open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-function-types diff --git a/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md index 44b7e094cb..fb32e15967 100644 --- a/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/sequential-diagrams.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.universe-levels ``` diff --git a/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md b/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md index bd20d04559..17d79d1bf5 100644 --- a/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md +++ b/src/synthetic-homotopy-theory/sequentially-compact-types.lagda.md @@ -7,6 +7,7 @@ module synthetic-homotopy-theory.sequentially-compact-types where
Imports ```agda +open import foundation.dependent-products-propositions open import foundation.propositions open import foundation.universe-levels diff --git a/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md b/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md index c7c6e22f6f..18c138e0d7 100644 --- a/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md +++ b/src/synthetic-homotopy-theory/shifts-sequential-diagrams.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.commuting-triangles-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/synthetic-homotopy-theory/spectra.lagda.md b/src/synthetic-homotopy-theory/spectra.lagda.md index ba8278a8ec..86a543ac45 100644 --- a/src/synthetic-homotopy-theory/spectra.lagda.md +++ b/src/synthetic-homotopy-theory/spectra.lagda.md @@ -10,6 +10,7 @@ module synthetic-homotopy-theory.spectra where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.identity-types diff --git a/src/synthetic-homotopy-theory/suspension-structures.lagda.md b/src/synthetic-homotopy-theory/suspension-structures.lagda.md index 7d579d350f..c12c083f52 100644 --- a/src/synthetic-homotopy-theory/suspension-structures.lagda.md +++ b/src/synthetic-homotopy-theory/suspension-structures.lagda.md @@ -12,6 +12,7 @@ open import foundation.commuting-squares-of-identifications open import foundation.constant-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-types diff --git a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md index 511ff1e9b6..1735e6f4c2 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-propositions.lagda.md @@ -10,6 +10,8 @@ module synthetic-homotopy-theory.suspensions-of-propositions where open import foundation.booleans open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.existential-quantification open import foundation.function-extensionality diff --git a/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md b/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md index b0d6084cbc..966ca3860e 100644 --- a/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md +++ b/src/synthetic-homotopy-theory/suspensions-of-types.lagda.md @@ -16,6 +16,9 @@ open import foundation.constant-maps open import foundation.contractible-types open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.diagonal-maps-of-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md index 95872ea9f7..952d0dff26 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-maps.lagda.md @@ -15,6 +15,8 @@ open import foundation.connected-types open import foundation.constant-maps open import foundation.dependent-epimorphisms-with-respect-to-truncated-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.dependent-universal-property-equivalences open import foundation.diagonal-maps-of-types open import foundation.embeddings diff --git a/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md b/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md index 6324c36e58..fcebd3d790 100644 --- a/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/truncated-acyclic-types.lagda.md @@ -9,6 +9,8 @@ module synthetic-homotopy-theory.truncated-acyclic-types where ```agda open import foundation.connected-types open import foundation.contractible-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.propositions open import foundation.retracts-of-types diff --git a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md index 55603d9eb5..0b7e16571f 100644 --- a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md @@ -19,6 +19,7 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-squares-of-maps open import foundation.dependent-identifications open import foundation.dependent-pair-types +open import foundation.dependent-products-truncated-types open import foundation.dependent-universal-property-equivalences open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/synthetic-homotopy-theory/universal-property-circle.lagda.md b/src/synthetic-homotopy-theory/universal-property-circle.lagda.md index 9698cb554f..1b32f484dd 100644 --- a/src/synthetic-homotopy-theory/universal-property-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-circle.lagda.md @@ -13,6 +13,8 @@ open import foundation.constant-type-families open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality diff --git a/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md b/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md index 14abaccfc2..e880269ee1 100644 --- a/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-coequalizers.lagda.md @@ -13,6 +13,7 @@ open import foundation.contractible-maps open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.double-arrows open import foundation.equivalences open import foundation.equivalences-double-arrows diff --git a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md index 171038972c..6ad1862827 100644 --- a/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-pushouts.lagda.md @@ -16,6 +16,7 @@ open import foundation.cones-over-cospan-diagrams open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps diff --git a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md index 7969ee8012..369e6dc327 100644 --- a/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-sequential-colimits.lagda.md @@ -15,6 +15,7 @@ open import foundation.commuting-triangles-of-maps open import foundation.contractible-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-extensionality-axiom diff --git a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md index a8b0a7025c..8851078960 100644 --- a/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md +++ b/src/synthetic-homotopy-theory/universal-property-suspensions-of-pointed-types.lagda.md @@ -9,6 +9,7 @@ module synthetic-homotopy-theory.universal-property-suspensions-of-pointed-types ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/trees/bases-directed-trees.lagda.md b/src/trees/bases-directed-trees.lagda.md index 2e96641277..c5c64f75d2 100644 --- a/src/trees/bases-directed-trees.lagda.md +++ b/src/trees/bases-directed-trees.lagda.md @@ -13,6 +13,8 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/trees/bases-enriched-directed-trees.lagda.md b/src/trees/bases-enriched-directed-trees.lagda.md index 6d2feee2cc..6415de0b55 100644 --- a/src/trees/bases-enriched-directed-trees.lagda.md +++ b/src/trees/bases-enriched-directed-trees.lagda.md @@ -10,6 +10,7 @@ module trees.bases-enriched-directed-trees where open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-coproduct-types diff --git a/src/trees/bounded-multisets.lagda.md b/src/trees/bounded-multisets.lagda.md index ceda35ae57..da84d060e6 100644 --- a/src/trees/bounded-multisets.lagda.md +++ b/src/trees/bounded-multisets.lagda.md @@ -10,6 +10,7 @@ module trees.bounded-multisets where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.existential-quantification open import foundation.propositions diff --git a/src/trees/combinator-directed-trees.lagda.md b/src/trees/combinator-directed-trees.lagda.md index 4d2862298f..ed2597b24a 100644 --- a/src/trees/combinator-directed-trees.lagda.md +++ b/src/trees/combinator-directed-trees.lagda.md @@ -12,6 +12,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/trees/directed-trees.lagda.md b/src/trees/directed-trees.lagda.md index 5c60f5b264..8a27a0c963 100644 --- a/src/trees/directed-trees.lagda.md +++ b/src/trees/directed-trees.lagda.md @@ -15,6 +15,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/trees/empty-multisets.lagda.md b/src/trees/empty-multisets.lagda.md index d31b3e8a6b..be9b34f19a 100644 --- a/src/trees/empty-multisets.lagda.md +++ b/src/trees/empty-multisets.lagda.md @@ -8,6 +8,7 @@ module trees.empty-multisets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.propositions diff --git a/src/trees/enriched-directed-trees.lagda.md b/src/trees/enriched-directed-trees.lagda.md index f17320ca15..ab7ba82a36 100644 --- a/src/trees/enriched-directed-trees.lagda.md +++ b/src/trees/enriched-directed-trees.lagda.md @@ -13,6 +13,8 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.homotopies diff --git a/src/trees/equivalences-directed-trees.lagda.md b/src/trees/equivalences-directed-trees.lagda.md index 5b7a6ffa00..57ddd72e36 100644 --- a/src/trees/equivalences-directed-trees.lagda.md +++ b/src/trees/equivalences-directed-trees.lagda.md @@ -12,6 +12,7 @@ open import foundation.binary-transport open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/trees/equivalences-enriched-directed-trees.lagda.md b/src/trees/equivalences-enriched-directed-trees.lagda.md index 410b7c1709..37f39e8369 100644 --- a/src/trees/equivalences-enriched-directed-trees.lagda.md +++ b/src/trees/equivalences-enriched-directed-trees.lagda.md @@ -11,6 +11,7 @@ open import foundation.commuting-squares-of-maps open import foundation.commuting-triangles-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-function-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/trees/extensional-w-types.lagda.md b/src/trees/extensional-w-types.lagda.md index 257d84375e..b40dcb2de8 100644 --- a/src/trees/extensional-w-types.lagda.md +++ b/src/trees/extensional-w-types.lagda.md @@ -10,6 +10,8 @@ module trees.extensional-w-types where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/trees/fibers-enriched-directed-trees.lagda.md b/src/trees/fibers-enriched-directed-trees.lagda.md index d6c2a7b325..80eace7236 100644 --- a/src/trees/fibers-enriched-directed-trees.lagda.md +++ b/src/trees/fibers-enriched-directed-trees.lagda.md @@ -9,6 +9,7 @@ module trees.fibers-enriched-directed-trees where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.identity-types open import foundation.torsorial-type-families diff --git a/src/trees/functoriality-combinator-directed-trees.lagda.md b/src/trees/functoriality-combinator-directed-trees.lagda.md index 62ecdf2b9c..2874e4cdaa 100644 --- a/src/trees/functoriality-combinator-directed-trees.lagda.md +++ b/src/trees/functoriality-combinator-directed-trees.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md b/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md index 12364a1b34..ed653ab8fc 100644 --- a/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md +++ b/src/trees/morphisms-algebras-polynomial-endofunctors.lagda.md @@ -10,6 +10,7 @@ module trees.morphisms-algebras-polynomial-endofunctors where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md index f6771ba67b..187fc56670 100644 --- a/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/morphisms-coalgebras-polynomial-endofunctors.lagda.md @@ -11,6 +11,7 @@ open import foundation.action-on-identifications-functions open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types open import foundation.fundamental-theorem-of-identity-types diff --git a/src/trees/morphisms-directed-trees.lagda.md b/src/trees/morphisms-directed-trees.lagda.md index 925111eb85..a5dbbe940c 100644 --- a/src/trees/morphisms-directed-trees.lagda.md +++ b/src/trees/morphisms-directed-trees.lagda.md @@ -10,6 +10,7 @@ module trees.morphisms-directed-trees where open import foundation.binary-transport open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-types diff --git a/src/trees/polynomial-endofunctors.lagda.md b/src/trees/polynomial-endofunctors.lagda.md index 793fbf9b59..eed1d536ca 100644 --- a/src/trees/polynomial-endofunctors.lagda.md +++ b/src/trees/polynomial-endofunctors.lagda.md @@ -9,6 +9,7 @@ module trees.polynomial-endofunctors where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/trees/raising-universe-levels-directed-trees.lagda.md b/src/trees/raising-universe-levels-directed-trees.lagda.md index 8f1e1ac294..cdaf4ca5a9 100644 --- a/src/trees/raising-universe-levels-directed-trees.lagda.md +++ b/src/trees/raising-universe-levels-directed-trees.lagda.md @@ -9,6 +9,7 @@ module trees.raising-universe-levels-directed-trees where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.raising-universe-levels open import foundation.universe-levels diff --git a/src/trees/ranks-of-elements-w-types.lagda.md b/src/trees/ranks-of-elements-w-types.lagda.md index 26e9e63740..ea0870e339 100644 --- a/src/trees/ranks-of-elements-w-types.lagda.md +++ b/src/trees/ranks-of-elements-w-types.lagda.md @@ -9,6 +9,7 @@ module trees.ranks-of-elements-w-types where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.existential-quantification open import foundation.identity-types diff --git a/src/trees/rooted-morphisms-directed-trees.lagda.md b/src/trees/rooted-morphisms-directed-trees.lagda.md index 81c9d5fc01..76ef5fba86 100644 --- a/src/trees/rooted-morphisms-directed-trees.lagda.md +++ b/src/trees/rooted-morphisms-directed-trees.lagda.md @@ -11,6 +11,8 @@ open import foundation.action-on-identifications-functions open import foundation.binary-transport open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md b/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md index f876ff518a..5fa28a0151 100644 --- a/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md +++ b/src/trees/rooted-morphisms-enriched-directed-trees.lagda.md @@ -8,6 +8,7 @@ module trees.rooted-morphisms-enriched-directed-trees where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.homotopies open import foundation.identity-types diff --git a/src/trees/rooted-quasitrees.lagda.md b/src/trees/rooted-quasitrees.lagda.md index 596e9e1061..33a6068908 100644 --- a/src/trees/rooted-quasitrees.lagda.md +++ b/src/trees/rooted-quasitrees.lagda.md @@ -9,6 +9,7 @@ module trees.rooted-quasitrees where ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.universe-levels open import graph-theory.trails-undirected-graphs diff --git a/src/trees/small-multisets.lagda.md b/src/trees/small-multisets.lagda.md index 6a8bc2b79f..dce94823f3 100644 --- a/src/trees/small-multisets.lagda.md +++ b/src/trees/small-multisets.lagda.md @@ -9,6 +9,7 @@ module trees.small-multisets where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md b/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md index 9184f6da42..2af81c2efc 100644 --- a/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md +++ b/src/trees/underlying-trees-elements-coalgebras-polynomial-endofunctors.lagda.md @@ -12,6 +12,8 @@ open import foundation.binary-transport open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/trees/underlying-trees-of-elements-of-w-types.lagda.md b/src/trees/underlying-trees-of-elements-of-w-types.lagda.md index bd9f754279..edbf940801 100644 --- a/src/trees/underlying-trees-of-elements-of-w-types.lagda.md +++ b/src/trees/underlying-trees-of-elements-of-w-types.lagda.md @@ -10,6 +10,8 @@ module trees.underlying-trees-of-elements-of-w-types where open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalence-extensionality open import foundation.equivalences diff --git a/src/trees/undirected-trees.lagda.md b/src/trees/undirected-trees.lagda.md index f60cce11cf..bd5054a204 100644 --- a/src/trees/undirected-trees.lagda.md +++ b/src/trees/undirected-trees.lagda.md @@ -14,6 +14,8 @@ open import foundation.contractible-types open import foundation.decidable-equality open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.identity-types open import foundation.mere-equality diff --git a/src/trees/w-type-of-natural-numbers.lagda.md b/src/trees/w-type-of-natural-numbers.lagda.md index 0d61f98e88..a9feae370a 100644 --- a/src/trees/w-type-of-natural-numbers.lagda.md +++ b/src/trees/w-type-of-natural-numbers.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-functions open import foundation.booleans open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-types diff --git a/src/trees/w-type-of-propositions.lagda.md b/src/trees/w-type-of-propositions.lagda.md index 8b460d8d29..0c8b029ec9 100644 --- a/src/trees/w-type-of-propositions.lagda.md +++ b/src/trees/w-type-of-propositions.lagda.md @@ -9,6 +9,7 @@ module trees.w-type-of-propositions where ```agda open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.propositional-extensionality open import foundation.propositions diff --git a/src/trees/w-types.lagda.md b/src/trees/w-types.lagda.md index 9e3ae175b9..21ee3b2a25 100644 --- a/src/trees/w-types.lagda.md +++ b/src/trees/w-types.lagda.md @@ -10,6 +10,7 @@ module trees.w-types where open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-products-truncated-types open import foundation.empty-types open import foundation.equivalences diff --git a/src/type-theories/dependent-type-theories.lagda.md b/src/type-theories/dependent-type-theories.lagda.md index 6f40eba0bc..1c09bb46cf 100644 --- a/src/type-theories/dependent-type-theories.lagda.md +++ b/src/type-theories/dependent-type-theories.lagda.md @@ -12,6 +12,7 @@ module type-theories.dependent-type-theories where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.homotopies diff --git a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md index eec01ce47a..7dee688b48 100644 --- a/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-decidable-subtypes.lagda.md @@ -17,6 +17,7 @@ open import foundation.decidable-equality open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/univalent-combinatorics/2-element-subtypes.lagda.md b/src/univalent-combinatorics/2-element-subtypes.lagda.md index 9c1bd2707d..b10fe6cd38 100644 --- a/src/univalent-combinatorics/2-element-subtypes.lagda.md +++ b/src/univalent-combinatorics/2-element-subtypes.lagda.md @@ -11,6 +11,8 @@ open import foundation.automorphisms open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.function-types diff --git a/src/univalent-combinatorics/2-element-types.lagda.md b/src/univalent-combinatorics/2-element-types.lagda.md index b44650d1ca..702cf0449e 100644 --- a/src/univalent-combinatorics/2-element-types.lagda.md +++ b/src/univalent-combinatorics/2-element-types.lagda.md @@ -18,6 +18,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.double-negation open import foundation.empty-types open import foundation.equivalence-extensionality diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index 7effe481d3..ad29a5ff2a 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -19,6 +19,8 @@ open import foundation.decidable-embeddings open import foundation.decidable-propositions open import foundation.decidable-subtypes open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.empty-types open import foundation.equivalences diff --git a/src/univalent-combinatorics/cartesian-product-types.lagda.md b/src/univalent-combinatorics/cartesian-product-types.lagda.md index 43dee54458..6dd2ffe8cb 100644 --- a/src/univalent-combinatorics/cartesian-product-types.lagda.md +++ b/src/univalent-combinatorics/cartesian-product-types.lagda.md @@ -14,6 +14,7 @@ open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.decidable-equality open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-cartesian-product-types diff --git a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md index 2dc4eea133..33adfc9922 100644 --- a/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/counting-decidable-subtypes.lagda.md @@ -16,6 +16,8 @@ open import foundation.coproduct-types open import foundation.decidable-embeddings open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.fibers-of-maps diff --git a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md index ce45d38d86..893e414561 100644 --- a/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/counting-dependent-pair-types.lagda.md @@ -18,6 +18,7 @@ open import foundation.coproduct-types open import foundation.decidable-equality open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.fibers-of-maps diff --git a/src/univalent-combinatorics/counting.lagda.md b/src/univalent-combinatorics/counting.lagda.md index b9c4fa6d19..1badcda52b 100644 --- a/src/univalent-combinatorics/counting.lagda.md +++ b/src/univalent-combinatorics/counting.lagda.md @@ -14,6 +14,8 @@ open import foundation.coproduct-types open import foundation.decidable-equality open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md b/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md index f1c5ab49c3..e1da80e9f0 100644 --- a/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md +++ b/src/univalent-combinatorics/cycle-prime-decomposition-natural-numbers.lagda.md @@ -19,6 +19,7 @@ open import foundation.action-on-identifications-functions open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.identity-types open import foundation.iterated-cartesian-product-types diff --git a/src/univalent-combinatorics/cyclic-finite-types.lagda.md b/src/univalent-combinatorics/cyclic-finite-types.lagda.md index da2741d64a..0e4a6941f9 100644 --- a/src/univalent-combinatorics/cyclic-finite-types.lagda.md +++ b/src/univalent-combinatorics/cyclic-finite-types.lagda.md @@ -20,6 +20,7 @@ open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types diff --git a/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md b/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md index 5f6cfff00c..900de88d03 100644 --- a/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md +++ b/src/univalent-combinatorics/decidable-dependent-function-types.lagda.md @@ -14,6 +14,7 @@ open import elementary-number-theory.natural-numbers open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.decidable-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md index 46f0521430..e4ef437ef5 100644 --- a/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md +++ b/src/univalent-combinatorics/decidable-equivalence-relations.lagda.md @@ -15,6 +15,7 @@ open import foundation.decidable-equality open import foundation.decidable-equivalence-relations open import foundation.decidable-relations open import foundation.decidable-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.equivalences open import foundation.function-types diff --git a/src/univalent-combinatorics/decidable-propositions.lagda.md b/src/univalent-combinatorics/decidable-propositions.lagda.md index c825d693f8..1243533287 100644 --- a/src/univalent-combinatorics/decidable-propositions.lagda.md +++ b/src/univalent-combinatorics/decidable-propositions.lagda.md @@ -15,6 +15,7 @@ open import foundation.coproduct-types open import foundation.decidable-equality open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.identity-types open import foundation.propositions diff --git a/src/univalent-combinatorics/decidable-subtypes.lagda.md b/src/univalent-combinatorics/decidable-subtypes.lagda.md index d7b83a688c..2e4cbaaf04 100644 --- a/src/univalent-combinatorics/decidable-subtypes.lagda.md +++ b/src/univalent-combinatorics/decidable-subtypes.lagda.md @@ -16,6 +16,7 @@ open import foundation.action-on-identifications-functions open import foundation.coproduct-types open import foundation.decidable-equality open import foundation.decidable-propositions +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.function-types open import foundation.identity-types diff --git a/src/univalent-combinatorics/dedekind-finite-sets.lagda.md b/src/univalent-combinatorics/dedekind-finite-sets.lagda.md index f3d73ff2db..6245f95fb6 100644 --- a/src/univalent-combinatorics/dedekind-finite-sets.lagda.md +++ b/src/univalent-combinatorics/dedekind-finite-sets.lagda.md @@ -8,6 +8,7 @@ module univalent-combinatorics.dedekind-finite-sets where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.propositions diff --git a/src/univalent-combinatorics/dependent-pair-types.lagda.md b/src/univalent-combinatorics/dependent-pair-types.lagda.md index ce7fef9510..a00f521bf4 100644 --- a/src/univalent-combinatorics/dependent-pair-types.lagda.md +++ b/src/univalent-combinatorics/dependent-pair-types.lagda.md @@ -11,6 +11,7 @@ open import foundation.dependent-pair-types public ```agda open import foundation.complements open import foundation.decidable-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalences diff --git a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md index 3eb65dbffb..df43f30e8f 100644 --- a/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/discrete-sigma-decompositions.lagda.md @@ -11,6 +11,8 @@ open import foundation.discrete-sigma-decompositions public ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.raising-universe-levels-unit-type diff --git a/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md b/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md index 64609a61a2..57498ee28b 100644 --- a/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md +++ b/src/univalent-combinatorics/distributivity-of-set-truncation-over-finite-products.lagda.md @@ -13,6 +13,7 @@ open import foundation.action-on-identifications-functions open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.dependent-universal-property-equivalences open import foundation.empty-types open import foundation.equivalences diff --git a/src/univalent-combinatorics/embeddings.lagda.md b/src/univalent-combinatorics/embeddings.lagda.md index e9776b2416..963c7454dd 100644 --- a/src/univalent-combinatorics/embeddings.lagda.md +++ b/src/univalent-combinatorics/embeddings.lagda.md @@ -15,6 +15,7 @@ open import foundation.coproduct-types open import foundation.decidable-embeddings open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.propositional-truncations diff --git a/src/univalent-combinatorics/equality-standard-finite-types.lagda.md b/src/univalent-combinatorics/equality-standard-finite-types.lagda.md index 637b3cf66a..c5d723201d 100644 --- a/src/univalent-combinatorics/equality-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/equality-standard-finite-types.lagda.md @@ -16,6 +16,8 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.discrete-types open import foundation.empty-types open import foundation.equivalences diff --git a/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md b/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md index b7044ed428..bb0dc4d012 100644 --- a/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/equivalences-standard-finite-types.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.exponentiation-natural-numbers open import elementary-number-theory.natural-numbers open import foundation.contractible-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.functoriality-cartesian-product-types open import foundation.type-arithmetic-empty-type diff --git a/src/univalent-combinatorics/ferrers-diagrams.lagda.md b/src/univalent-combinatorics/ferrers-diagrams.lagda.md index 034b26e3ad..5c1f722491 100644 --- a/src/univalent-combinatorics/ferrers-diagrams.lagda.md +++ b/src/univalent-combinatorics/ferrers-diagrams.lagda.md @@ -9,6 +9,7 @@ module univalent-combinatorics.ferrers-diagrams where ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-function-types open import foundation.equivalences open import foundation.fundamental-theorem-of-identity-types diff --git a/src/univalent-combinatorics/fibers-of-maps.lagda.md b/src/univalent-combinatorics/fibers-of-maps.lagda.md index 31ba87543e..15e292b04c 100644 --- a/src/univalent-combinatorics/fibers-of-maps.lagda.md +++ b/src/univalent-combinatorics/fibers-of-maps.lagda.md @@ -13,6 +13,7 @@ open import elementary-number-theory.natural-numbers open import elementary-number-theory.sums-of-natural-numbers open import foundation.decidable-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.functoriality-dependent-pair-types diff --git a/src/univalent-combinatorics/finite-types.lagda.md b/src/univalent-combinatorics/finite-types.lagda.md index ca162f16ce..2d1393831c 100644 --- a/src/univalent-combinatorics/finite-types.lagda.md +++ b/src/univalent-combinatorics/finite-types.lagda.md @@ -17,6 +17,8 @@ open import foundation.connected-components-universes open import foundation.contractible-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/univalent-combinatorics/finitely-many-connected-components.lagda.md b/src/univalent-combinatorics/finitely-many-connected-components.lagda.md index b2d49dc3a5..14a097a233 100644 --- a/src/univalent-combinatorics/finitely-many-connected-components.lagda.md +++ b/src/univalent-combinatorics/finitely-many-connected-components.lagda.md @@ -13,6 +13,8 @@ open import foundation.0-connected-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equivalences open import foundation.function-types diff --git a/src/univalent-combinatorics/finitely-presented-types.lagda.md b/src/univalent-combinatorics/finitely-presented-types.lagda.md index 6cc22a250a..ebcece7eb3 100644 --- a/src/univalent-combinatorics/finitely-presented-types.lagda.md +++ b/src/univalent-combinatorics/finitely-presented-types.lagda.md @@ -10,6 +10,7 @@ module univalent-combinatorics.finitely-presented-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.fibers-of-maps open import foundation.function-types diff --git a/src/univalent-combinatorics/inhabited-finite-types.lagda.md b/src/univalent-combinatorics/inhabited-finite-types.lagda.md index f6ad56cab3..3eb8693c2e 100644 --- a/src/univalent-combinatorics/inhabited-finite-types.lagda.md +++ b/src/univalent-combinatorics/inhabited-finite-types.lagda.md @@ -9,6 +9,7 @@ module univalent-combinatorics.inhabited-finite-types where ```agda open import elementary-number-theory.natural-numbers +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-function-types diff --git a/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md b/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md index 7de999ba15..e88e3a3eef 100644 --- a/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md +++ b/src/univalent-combinatorics/kuratowski-finite-sets.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.decidable-equality open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.existential-quantification open import foundation.propositional-truncations open import foundation.propositions diff --git a/src/univalent-combinatorics/locally-finite-types.lagda.md b/src/univalent-combinatorics/locally-finite-types.lagda.md index 273e1cd35b..6e8a9b8216 100644 --- a/src/univalent-combinatorics/locally-finite-types.lagda.md +++ b/src/univalent-combinatorics/locally-finite-types.lagda.md @@ -14,6 +14,8 @@ open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-equality +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.dependent-universal-property-equivalences open import foundation.empty-types open import foundation.equality-cartesian-product-types diff --git a/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md b/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md index f88ff5969a..c2cf1af773 100644 --- a/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md +++ b/src/univalent-combinatorics/main-classes-of-latin-hypercubes.lagda.md @@ -13,6 +13,7 @@ open import foundation.1-types open import foundation.contractible-types open import foundation.decidable-propositions open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.inhabited-types open import foundation.mere-equivalences open import foundation.products-unordered-tuples-of-types diff --git a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md index bd5ea5ce14..e15d22f6c8 100644 --- a/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md +++ b/src/univalent-combinatorics/orientations-complete-undirected-graph.lagda.md @@ -27,6 +27,7 @@ open import foundation.decidable-equivalence-relations open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.empty-types open import foundation.equality-dependent-pair-types open import foundation.equivalence-classes diff --git a/src/univalent-combinatorics/partitions.lagda.md b/src/univalent-combinatorics/partitions.lagda.md index 1d697a9f42..a8a74937f5 100644 --- a/src/univalent-combinatorics/partitions.lagda.md +++ b/src/univalent-combinatorics/partitions.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.binary-relations open import foundation.cartesian-product-types +open import foundation.dependent-products-propositions open import foundation.equality-cartesian-product-types open import foundation.equivalence-extensionality open import foundation.equivalence-relations diff --git a/src/univalent-combinatorics/pi-finite-types.lagda.md b/src/univalent-combinatorics/pi-finite-types.lagda.md index 5632fede24..b6b281f8b2 100644 --- a/src/univalent-combinatorics/pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/pi-finite-types.lagda.md @@ -10,6 +10,8 @@ module univalent-combinatorics.pi-finite-types where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions +open import foundation.dependent-products-truncated-types open import foundation.identity-types open import foundation.propositions open import foundation.set-truncations diff --git a/src/univalent-combinatorics/pigeonhole-principle.lagda.md b/src/univalent-combinatorics/pigeonhole-principle.lagda.md index 8c52386070..3e7b021e87 100644 --- a/src/univalent-combinatorics/pigeonhole-principle.lagda.md +++ b/src/univalent-combinatorics/pigeonhole-principle.lagda.md @@ -13,6 +13,7 @@ open import elementary-number-theory.strict-inequality-natural-numbers open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.empty-types open import foundation.equivalences diff --git a/src/univalent-combinatorics/ramsey-theory.lagda.md b/src/univalent-combinatorics/ramsey-theory.lagda.md index c5e0cc22ff..c2f61c1012 100644 --- a/src/univalent-combinatorics/ramsey-theory.lagda.md +++ b/src/univalent-combinatorics/ramsey-theory.lagda.md @@ -10,6 +10,7 @@ module univalent-combinatorics.ramsey-theory where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.function-types open import foundation.identity-types open import foundation.propositions diff --git a/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md b/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md index afd05cac1d..8d7f320c33 100644 --- a/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md +++ b/src/univalent-combinatorics/set-quotients-of-index-two.lagda.md @@ -14,6 +14,7 @@ open import foundation.commuting-squares-of-maps open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.embeddings open import foundation.empty-types open import foundation.equivalence-relations diff --git a/src/univalent-combinatorics/sigma-decompositions.lagda.md b/src/univalent-combinatorics/sigma-decompositions.lagda.md index 3fe2f92b9c..4fe1f23fe4 100644 --- a/src/univalent-combinatorics/sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/sigma-decompositions.lagda.md @@ -10,6 +10,7 @@ open import foundation.sigma-decompositions public ```agda open import foundation.cartesian-product-types +open import foundation.dependent-products-propositions open import foundation.dependent-universal-property-equivalences open import foundation.embeddings open import foundation.equivalences diff --git a/src/univalent-combinatorics/standard-finite-types.lagda.md b/src/univalent-combinatorics/standard-finite-types.lagda.md index 31d90d106c..1620ae6151 100644 --- a/src/univalent-combinatorics/standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/standard-finite-types.lagda.md @@ -18,6 +18,7 @@ open import foundation.contractible-types open import foundation.coproduct-types open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.embeddings open import foundation.empty-types open import foundation.equality-coproduct-types diff --git a/src/univalent-combinatorics/steiner-systems.lagda.md b/src/univalent-combinatorics/steiner-systems.lagda.md index 5c3a9d87d2..8333097e23 100644 --- a/src/univalent-combinatorics/steiner-systems.lagda.md +++ b/src/univalent-combinatorics/steiner-systems.lagda.md @@ -12,6 +12,7 @@ open import elementary-number-theory.natural-numbers open import foundation.contractible-types open import foundation.decidable-subtypes open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.universe-levels open import univalent-combinatorics.finite-types diff --git a/src/univalent-combinatorics/surjective-maps.lagda.md b/src/univalent-combinatorics/surjective-maps.lagda.md index 2ebd5851c5..282058ec81 100644 --- a/src/univalent-combinatorics/surjective-maps.lagda.md +++ b/src/univalent-combinatorics/surjective-maps.lagda.md @@ -16,6 +16,7 @@ open import foundation.decidable-embeddings open import foundation.decidable-equality open import foundation.decidable-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.logical-equivalences open import foundation.propositional-truncations diff --git a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md index 5816c35f0e..c18717d04f 100644 --- a/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md +++ b/src/univalent-combinatorics/trivial-sigma-decompositions.lagda.md @@ -11,6 +11,8 @@ open import foundation.trivial-sigma-decompositions public ```agda open import foundation.contractible-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.inhabited-types open import foundation.propositions diff --git a/src/univalent-combinatorics/type-duality.lagda.md b/src/univalent-combinatorics/type-duality.lagda.md index fc008806c9..0184e34620 100644 --- a/src/univalent-combinatorics/type-duality.lagda.md +++ b/src/univalent-combinatorics/type-duality.lagda.md @@ -11,6 +11,7 @@ open import foundation.type-duality public ```agda open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalences open import foundation.full-subtypes open import foundation.functoriality-dependent-function-types diff --git a/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md b/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md index f4335a963a..176ec92e4f 100644 --- a/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/unbounded-pi-finite-types.lagda.md @@ -15,6 +15,7 @@ open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.empty-types open import foundation.equality-coproduct-types open import foundation.equivalences diff --git a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md index 707c60a123..e1f0301667 100644 --- a/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/universal-property-standard-finite-types.lagda.md @@ -13,6 +13,7 @@ open import foundation.cartesian-product-types open import foundation.contractible-types open import foundation.coproduct-types open import foundation.dependent-pair-types +open import foundation.dependent-products-contractible-types open import foundation.equivalences open import foundation.function-extensionality open import foundation.function-types diff --git a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md index 63f9ba773a..07c8821913 100644 --- a/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md +++ b/src/univalent-combinatorics/untruncated-pi-finite-types.lagda.md @@ -16,6 +16,8 @@ open import foundation.coproduct-types open import foundation.decidable-propositions open import foundation.decidable-types open import foundation.dependent-identifications +open import foundation.dependent-products-contractible-types +open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.empty-types open import foundation.equality-coproduct-types diff --git a/src/universal-algebra/algebraic-theory-of-groups.lagda.md b/src/universal-algebra/algebraic-theory-of-groups.lagda.md index 719d008255..ead34c0c31 100644 --- a/src/universal-algebra/algebraic-theory-of-groups.lagda.md +++ b/src/universal-algebra/algebraic-theory-of-groups.lagda.md @@ -10,6 +10,7 @@ module universal-algebra.algebraic-theory-of-groups where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equality-dependent-pair-types open import foundation.equivalences open import foundation.function-extensionality diff --git a/src/universal-algebra/algebras-of-theories.lagda.md b/src/universal-algebra/algebras-of-theories.lagda.md index 3ae5fa65d3..ed9b36b787 100644 --- a/src/universal-algebra/algebras-of-theories.lagda.md +++ b/src/universal-algebra/algebras-of-theories.lagda.md @@ -8,6 +8,7 @@ module universal-algebra.algebras-of-theories where ```agda open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.identity-types open import foundation.propositions open import foundation.sets diff --git a/src/universal-algebra/congruences.lagda.md b/src/universal-algebra/congruences.lagda.md index d8951087da..241907f00e 100644 --- a/src/universal-algebra/congruences.lagda.md +++ b/src/universal-algebra/congruences.lagda.md @@ -11,6 +11,7 @@ open import elementary-number-theory.natural-numbers open import foundation.cartesian-product-types open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-relations open import foundation.propositions open import foundation.raising-universe-levels-unit-type diff --git a/src/universal-algebra/quotient-algebras.lagda.md b/src/universal-algebra/quotient-algebras.lagda.md index 94bfede7ee..dfb32f00fa 100644 --- a/src/universal-algebra/quotient-algebras.lagda.md +++ b/src/universal-algebra/quotient-algebras.lagda.md @@ -10,6 +10,7 @@ module universal-algebra.quotient-algebras where open import elementary-number-theory.natural-numbers open import foundation.dependent-pair-types +open import foundation.dependent-products-propositions open import foundation.equivalence-classes open import foundation.equivalence-relations open import foundation.equivalences From ee6b0e57f0d55dc2501d518ee119eb9477bbdae9 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Fri, 21 Mar 2025 14:04:16 +0000 Subject: [PATCH 32/39] wip unpostulate --- scripts/add_funext_parameter.py | 102 ++++++++++++------ .../function-extensionality.lagda.md | 31 +++--- 2 files changed, 85 insertions(+), 48 deletions(-) diff --git a/scripts/add_funext_parameter.py b/scripts/add_funext_parameter.py index 078f9f42f3..087cba2ad9 100644 --- a/scripts/add_funext_parameter.py +++ b/scripts/add_funext_parameter.py @@ -34,6 +34,9 @@ def modify_file_content(file_path, module_name, dependent_modules): with open(file_path, 'r', encoding='utf-8') as f: content = f.read() + # Check if this is a literate Agda Markdown file + is_markdown = file_path.endswith('.lagda.md') + # Find module declaration module_decl, module_id = find_module_declaration(content) if not module_decl: @@ -83,47 +86,82 @@ def modify_file_content(file_path, module_name, dependent_modules): modified_content = '\n'.join(updated_lines) # Modify imports of modules that depend on funext - for dep_module in dependent_modules: - # Find imports of this module - import_pattern = rf'open\s+import\s+{re.escape(dep_module)}(?:\s+[^\n]*)?(?:\n|$)' - for match in re.finditer(import_pattern, modified_content): + # If it's a Markdown file, we need to handle code blocks correctly + if is_markdown: + # Handle imports in code blocks properly + code_block_pattern = r'```agda\n(.*?)\n```' + def process_code_block(match): + code_content = match.group(1) + # Process imports within the code block + for dep_module in dependent_modules: + import_pattern = rf'open\s+import\s+{re.escape(dep_module)}(?:\s+[^\n]*)?(?:\n|$)' + for import_match in re.finditer(import_pattern, code_content): + import_stmt = import_match.group(0) + # Skip if already has funext + if "funext" in import_stmt: + continue + + # Ensure we don't duplicate "using" keyword + if "using" in import_stmt: + new_import = import_stmt.replace(dep_module, f"{dep_module} funext") + else: + # No existing parameters + new_import = import_stmt.rstrip() + " funext\n" + + code_content = code_content[:import_match.start()] + new_import + code_content[import_match.end():] + + # Also handle direct imports of function-extensionality + funext_direct_import_pattern = r'open\s+import\s+foundation\.function-extensionality\b(?!-axiom)' + for import_match in re.finditer(funext_direct_import_pattern, code_content, re.MULTILINE): + import_stmt = import_match.group(0) + if "funext" in import_stmt: + continue + + if "using" in import_stmt: + new_import = re.sub(r'(foundation\.function-extensionality)\b(?!-axiom)', r'\1 funext', import_stmt) + else: + new_import = import_stmt.rstrip() + " funext\n" + + code_content = code_content[:import_match.start()] + new_import + code_content[import_match.end():] + + return f"```agda\n{code_content}\n```" + + modified_content = re.sub(code_block_pattern, process_code_block, modified_content, flags=re.DOTALL) + else: + # Handle regular Agda files as before + for dep_module in dependent_modules: + # Find imports of this module + import_pattern = rf'open\s+import\s+{re.escape(dep_module)}(?:\s+[^\n]*)?(?:\n|$)' + for match in re.finditer(import_pattern, modified_content): + import_stmt = match.group(0) + # Skip if already has funext + if "funext" in import_stmt: + continue + + # Add funext parameter to the import + if import_stmt.strip().endswith(dep_module): + # No existing parameters + new_import = import_stmt.rstrip() + " funext\n" + else: + # Has other parameters, add funext + new_import = import_stmt.replace(dep_module, f"{dep_module} funext") + + modified_content = modified_content[:match.start()] + new_import + modified_content[match.end():] + + # Additionally, handle direct imports of foundation.function-extensionality + funext_direct_import_pattern = r'open\s+import\s+foundation\.function-extensionality\b(?!-axiom)' + for match in re.finditer(funext_direct_import_pattern, modified_content, re.MULTILINE): import_stmt = match.group(0) - # Skip if already has funext if "funext" in import_stmt: continue - # Add funext parameter to the import - if import_stmt.strip().endswith(dep_module): - # No existing parameters + if import_stmt.strip().endswith("foundation.function-extensionality"): new_import = import_stmt.rstrip() + " funext\n" else: - # Has other parameters, add funext - new_import = import_stmt.replace(dep_module, f"{dep_module} funext") + new_import = re.sub(r'(foundation\.function-extensionality)\b(?!-axiom)', r'\1 funext', import_stmt) modified_content = modified_content[:match.start()] + new_import + modified_content[match.end():] - # Additionally, handle direct imports of foundation.function-extensionality - # Make sure we only match the exact module name, not ones that start with it - funext_direct_import_pattern = r'open\s+import\s+foundation\.function-extensionality\b(?!-axiom)' - - # Use finditer with the MULTILINE flag to ensure we catch all instances - for match in re.finditer(funext_direct_import_pattern, modified_content, re.MULTILINE): - import_stmt = match.group(0) - # Skip if already has funext - if "funext" in import_stmt: - continue - - # Add funext parameter to the import - if import_stmt.strip().endswith("foundation.function-extensionality"): - # No existing parameters - new_import = import_stmt.rstrip() + " funext\n" - else: - # Has other parameters, add funext appropriately - # Use a more specific pattern to ensure we only replace the exact module name - new_import = re.sub(r'(foundation\.function-extensionality)\b(?!-axiom)', r'\1 funext', import_stmt) - - modified_content = modified_content[:match.start()] + new_import + modified_content[match.end():] - # Only return modified content if changes were made if modified_content != content: return modified_content diff --git a/src/foundation/function-extensionality.lagda.md b/src/foundation/function-extensionality.lagda.md index d26c3c48c8..b6ca9801f6 100644 --- a/src/foundation/function-extensionality.lagda.md +++ b/src/foundation/function-extensionality.lagda.md @@ -3,7 +3,10 @@ ```agda open import foundation.function-extensionality-axiom -module foundation.function-extensionality where +module + foundation.function-extensionality + (funext : function-extensionality) + where ```
Imports @@ -12,6 +15,7 @@ module foundation.function-extensionality where open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types +open import foundation.evaluation-functions open import foundation.implicit-function-types open import foundation.universe-levels @@ -78,23 +82,23 @@ module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} where - postulate - eq-htpy : f ~ g → f ＝ g + eq-htpy : f ~ g → f ＝ g + eq-htpy = map-inv-is-equiv (funext f g) + opaque is-section-eq-htpy : is-section htpy-eq eq-htpy + is-section-eq-htpy = is-section-map-inv-is-equiv (funext f g) - is-retraction-eq-htpy' : is-retraction htpy-eq eq-htpy + is-retraction-eq-htpy : is-retraction htpy-eq eq-htpy + is-retraction-eq-htpy = is-retraction-map-inv-is-equiv (funext f g) - coh-eq-htpy' : + coh-eq-htpy : coherence-is-coherently-invertible ( htpy-eq) ( eq-htpy) ( is-section-eq-htpy) - ( is-retraction-eq-htpy') - -funext : function-extensionality -funext f g = - is-equiv-is-invertible eq-htpy is-section-eq-htpy is-retraction-eq-htpy' + ( is-retraction-eq-htpy) + coh-eq-htpy = coherence-map-inv-is-equiv (funext f g) module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} @@ -107,12 +111,7 @@ module _ is-equiv-eq-htpy : (f g : (x : A) → B x) → is-equiv (eq-htpy {f = f} {g}) is-equiv-eq-htpy f g = - is-equiv-is-invertible htpy-eq is-retraction-eq-htpy' is-section-eq-htpy - - abstract - is-retraction-eq-htpy : - {f g : (x : A) → B x} → is-retraction (htpy-eq {f = f} {g}) eq-htpy - is-retraction-eq-htpy {f} {g} = is-retraction-map-inv-is-equiv (funext f g) + is-equiv-is-invertible htpy-eq is-retraction-eq-htpy is-section-eq-htpy eq-htpy-refl-htpy : (f : (x : A) → B x) → eq-htpy (refl-htpy {f = f}) ＝ refl From 12515058c2d7e5ec9160cef08cd5dc93fb77f48e Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 24 Mar 2025 18:39:01 +0000 Subject: [PATCH 33/39] hide scripts --- scripts/add_funext_parameter.py | 237 --------- scripts/build_definition_graph.py | 665 ------------------------- scripts/build_dependency_graph.py | 281 ----------- scripts/remove_unused_funext_import.py | 85 ---- 4 files changed, 1268 deletions(-) delete mode 100644 scripts/add_funext_parameter.py delete mode 100644 scripts/build_definition_graph.py delete mode 100644 scripts/build_dependency_graph.py delete mode 100644 scripts/remove_unused_funext_import.py diff --git a/scripts/add_funext_parameter.py b/scripts/add_funext_parameter.py deleted file mode 100644 index 087cba2ad9..0000000000 --- a/scripts/add_funext_parameter.py +++ /dev/null @@ -1,237 +0,0 @@ -#!/usr/bin/env python3 - -import os -import re -import argparse -from pathlib import Path -import shutil -import sys - -# Import the dependency graph functionality -from build_dependency_graph import compute_transitive_closure, build_dependency_graph - -FUNEXT_MODULE = "foundation.function-extensionality" -FUNEXT_IMPORT = "open import foundation.function-extensionality-axiom" -FUNEXT_PARAM = "(funext : function-extensionality)" - -def find_module_declaration(content): - """Find the main module declaration in a file.""" - # Match 'module name.of.module' potentially with parameters - module_pattern = r'^module\s+([^\s\(]+)(?:\s+[^\n]*)?(?:\n|$)' - match = re.search(module_pattern, content, re.MULTILINE) - if match: - return match.group(0), match.group(1) - return None, None - -def modify_file_content(file_path, module_name, dependent_modules): - """ - Modify the content of an Agda file to: - 1. Remove any existing function extensionality imports - 2. Add function extensionality import right before module declaration - 3. Add funext parameter to module declaration - 4. Add funext parameter to dependent imports - """ - with open(file_path, 'r', encoding='utf-8') as f: - content = f.read() - - # Check if this is a literate Agda Markdown file - is_markdown = file_path.endswith('.lagda.md') - - # Find module declaration - module_decl, module_id = find_module_declaration(content) - if not module_decl: - print(f"Warning: Could not find module declaration in {file_path}") - return None - - # Remove any existing function extensionality imports - modified_content = content - existing_import_pattern = rf'{re.escape(FUNEXT_IMPORT)}(?:\s*\n|\n)' - modified_content = re.sub(existing_import_pattern, '', modified_content) - - # If content changed, get updated module declaration - if modified_content != content: - print(f"Note: Removed existing function extensionality import in {file_path}") - module_decl, module_id = find_module_declaration(modified_content) - content = modified_content - - # Check if the module declaration already has funext parameter - has_funext_param = "funext" in module_decl - - # Add function extensionality import and update module declaration - lines = content.split('\n') - updated_lines = [] - module_line_found = False - - for line in lines: - # When we find the module declaration line - if not module_line_found and line.startswith('module '): - # Add the import before the module declaration - updated_lines.append(FUNEXT_IMPORT + '\n') - module_line_found = True - - # Add funext parameter to module declaration if needed - if not has_funext_param: - if "where" in line: - # If there's a 'where' clause, put parameters before it - updated_line = re.sub(r'(\s+where)', f" {FUNEXT_PARAM}\\1", line) - else: - # Otherwise, add at the end - updated_line = line.rstrip() + f" {FUNEXT_PARAM} where" - updated_lines.append(updated_line) - else: - updated_lines.append(line) - else: - updated_lines.append(line) - - modified_content = '\n'.join(updated_lines) - - # Modify imports of modules that depend on funext - # If it's a Markdown file, we need to handle code blocks correctly - if is_markdown: - # Handle imports in code blocks properly - code_block_pattern = r'```agda\n(.*?)\n```' - def process_code_block(match): - code_content = match.group(1) - # Process imports within the code block - for dep_module in dependent_modules: - import_pattern = rf'open\s+import\s+{re.escape(dep_module)}(?:\s+[^\n]*)?(?:\n|$)' - for import_match in re.finditer(import_pattern, code_content): - import_stmt = import_match.group(0) - # Skip if already has funext - if "funext" in import_stmt: - continue - - # Ensure we don't duplicate "using" keyword - if "using" in import_stmt: - new_import = import_stmt.replace(dep_module, f"{dep_module} funext") - else: - # No existing parameters - new_import = import_stmt.rstrip() + " funext\n" - - code_content = code_content[:import_match.start()] + new_import + code_content[import_match.end():] - - # Also handle direct imports of function-extensionality - funext_direct_import_pattern = r'open\s+import\s+foundation\.function-extensionality\b(?!-axiom)' - for import_match in re.finditer(funext_direct_import_pattern, code_content, re.MULTILINE): - import_stmt = import_match.group(0) - if "funext" in import_stmt: - continue - - if "using" in import_stmt: - new_import = re.sub(r'(foundation\.function-extensionality)\b(?!-axiom)', r'\1 funext', import_stmt) - else: - new_import = import_stmt.rstrip() + " funext\n" - - code_content = code_content[:import_match.start()] + new_import + code_content[import_match.end():] - - return f"```agda\n{code_content}\n```" - - modified_content = re.sub(code_block_pattern, process_code_block, modified_content, flags=re.DOTALL) - else: - # Handle regular Agda files as before - for dep_module in dependent_modules: - # Find imports of this module - import_pattern = rf'open\s+import\s+{re.escape(dep_module)}(?:\s+[^\n]*)?(?:\n|$)' - for match in re.finditer(import_pattern, modified_content): - import_stmt = match.group(0) - # Skip if already has funext - if "funext" in import_stmt: - continue - - # Add funext parameter to the import - if import_stmt.strip().endswith(dep_module): - # No existing parameters - new_import = import_stmt.rstrip() + " funext\n" - else: - # Has other parameters, add funext - new_import = import_stmt.replace(dep_module, f"{dep_module} funext") - - modified_content = modified_content[:match.start()] + new_import + modified_content[match.end():] - - # Additionally, handle direct imports of foundation.function-extensionality - funext_direct_import_pattern = r'open\s+import\s+foundation\.function-extensionality\b(?!-axiom)' - for match in re.finditer(funext_direct_import_pattern, modified_content, re.MULTILINE): - import_stmt = match.group(0) - if "funext" in import_stmt: - continue - - if import_stmt.strip().endswith("foundation.function-extensionality"): - new_import = import_stmt.rstrip() + " funext\n" - else: - new_import = re.sub(r'(foundation\.function-extensionality)\b(?!-axiom)', r'\1 funext', import_stmt) - - modified_content = modified_content[:match.start()] + new_import + modified_content[match.end():] - - # Only return modified content if changes were made - if modified_content != content: - return modified_content - else: - print(f"No changes needed for {file_path}") - return None - -def main(): - parser = argparse.ArgumentParser(description='Add function extensionality parameter to Agda modules') - parser.add_argument('root_dir', help='Root directory of the Agda library') - parser.add_argument('--dry-run', action='store_true', - help='Show what would be changed without making actual changes') - parser.add_argument('--backup', action='store_true', - help='Create backup files before modifying') - args = parser.parse_args() - - root_dir = args.root_dir - - print(f"Building dependency graph for {root_dir}...") - graph, module_to_file = build_dependency_graph(root_dir) - - print("Computing transitive closure of dependencies...") - transitive_graph = compute_transitive_closure(graph) - - # Find all modules that depend on foundation.function-extensionality - funext_dependent_modules = [] - for module, deps in transitive_graph.items(): - if FUNEXT_MODULE in deps: - funext_dependent_modules.append(module) - - print(f"Found {len(funext_dependent_modules)} modules that depend on {FUNEXT_MODULE}") - - # Create a mapping of each file to its dependent modules - file_dependent_modules = {} - for module in funext_dependent_modules: - if module in module_to_file: - file_path = module_to_file[module] - file_dependent_modules[file_path] = [ - dep for dep in graph.get(module, []) - if dep in funext_dependent_modules - ] - - # Process each file - modified_count = 0 - for file_path, dependent_modules in file_dependent_modules.items(): - module_name = next((m for m, f in module_to_file.items() if f == file_path), None) - if not module_name: - continue - - print(f"Processing {module_name} ({file_path})...") - modified_content = modify_file_content(file_path, module_name, dependent_modules) - - if modified_content: - if args.dry_run: - print(f"Would modify: {file_path}") - else: - if args.backup: - backup_path = f"{file_path}.bak" - shutil.copy2(file_path, backup_path) - print(f"Created backup: {backup_path}") - - with open(file_path, 'w', encoding='utf-8') as f: - f.write(modified_content) - print(f"Modified: {file_path}") - modified_count += 1 - - if args.dry_run: - print(f"\nDry run completed. {modified_count} files would be modified.") - else: - print(f"\nCompleted. Modified {modified_count} files.") - -if __name__ == "__main__": - main() diff --git a/scripts/build_definition_graph.py b/scripts/build_definition_graph.py deleted file mode 100644 index 85732c8a43..0000000000 --- a/scripts/build_definition_graph.py +++ /dev/null @@ -1,665 +0,0 @@ -#!/usr/bin/env python3 - -import os -import re -import argparse -import json -from collections import defaultdict, deque -from pathlib import Path - -# Import utils for Git-related functionality -import sys -import os.path -sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) -from scripts.utils import get_git_tracked_files - -def find_agda_files(root_dir): - """Find all Git-tracked Agda source files in the given directory tree.""" - # Get all Git-tracked files - git_tracked_files = get_git_tracked_files() - - # Filter to keep only Agda files that are tracked by Git - agda_files = [] - root_path = Path(root_dir).resolve() - - for file_path in git_tracked_files: - full_path = Path(file_path) - # Check if the file is in the specified root directory - if root_path in full_path.resolve().parents or root_path == full_path.resolve().parent: - if file_path.suffix == '.agda' or (file_path.suffix == '.md' and file_path.stem.endswith('.lagda')): - agda_files.append(str(file_path)) - - return agda_files - -def extract_module_name(file_path, root_dir): - """Extract the module name from a file path.""" - rel_path = os.path.relpath(file_path, root_dir) - if rel_path.endswith('.lagda.md'): - module_name = rel_path[:-9] - else: # .agda - module_name = rel_path[:-5] - module_name = module_name.replace('/', '.') - return module_name - -def extract_definitions(file_path): - """ - Extract all definitions from a file. - Returns a list of tuples (definition_name, line_number, line_content) - """ - # Define a blacklist of regex patterns for definition names to exclude - definition_blacklist_patterns = [ - r'^[a-zA-Z]$', # Single letter names - r'^l\d+$', # 'l' followed by a number - ] - - with open(file_path, 'r', encoding='utf-8') as f: - content = f.read() - - # Determine if this is a literate Agda file (.lagda.md) - is_literate_agda = file_path.endswith('.lagda.md') - - # For literate Agda files, extract only content within code blocks - if is_literate_agda: - # Extract Agda code blocks (```agda ... ```) - code_blocks = re.findall(r'```agda\n(.*?)```', content, re.DOTALL) - # Combine all code blocks into a single string with line numbers preserved - processed_lines = [] - line_num = 0 - for block in code_blocks: - block_lines = block.split('\n') - processed_lines.extend([(line_num + i, line) for i, line in enumerate(block_lines)]) - # Update line_num to account for the block and the delimiters - line_num += len(block_lines) + 2 # +2 for ```agda and ``` - else: - # For regular .agda files, process all lines - lines = content.split('\n') - processed_lines = [(i, line) for i, line in enumerate(lines)] - - # Look for lines of the form "identifier : type" - pattern = r'^\s*([^\s;{}()@"]+)\s+:(?=$|\s)' - - # Add pattern for data and record definitions - data_record_pattern = r'^\s*(data|record)\s*\n?\s+(\S+)(?:$|\!\}|[\s;{}()@"._])' - - definitions = [] - - # Process regular definitions - for line_num, line in processed_lines: - match = re.search(pattern, line) - if match: - definition_name = match.group(1) - # Skip if it's a comment line or matches a blacklist pattern - if not line.strip().startswith('--') and not any(re.match(pattern, definition_name) for pattern in definition_blacklist_patterns): - # Remove underscores from definition name - definition_name = definition_name.replace('_', '') - definitions.append((definition_name, line_num, line)) - - # Process data and record definitions - i = 0 - while i < len(processed_lines): - line_num, line = processed_lines[i] - - # Check for data or record declarations that might span multiple lines - if re.match(r'^\s*(data|record)\s*$', line): - # If the keyword is alone on a line, check the next line - if i + 1 < len(processed_lines): - next_line_num, next_line = processed_lines[i+1] - combined_line = line + ' ' + next_line - match = re.search(data_record_pattern, combined_line) - if match: - definition_name = match.group(2) - if not any(re.match(pattern, definition_name) for pattern in definition_blacklist_patterns): - definition_name = definition_name.replace('_', '') - definitions.append((definition_name, line_num, combined_line)) - else: - # Check for data or record declarations on the same line - match = re.search(data_record_pattern, line) - if match: - definition_name = match.group(2) - if not line.strip().startswith('--') and not any(re.match(pattern, definition_name) for pattern in definition_blacklist_patterns): - definition_name = definition_name.replace('_', '') - definitions.append((definition_name, line_num, line)) - - i += 1 - - return definitions - -def extract_definition_bodies(file_path, definitions): - """ - Extract the body of each definition. - Returns a dictionary mapping definition names to their bodies. - """ - with open(file_path, 'r', encoding='utf-8') as f: - content = f.read() - - # Determine if this is a literate Agda file (.lagda.md) - is_literate_agda = file_path.endswith('.lagda.md') - - # Process content depending on file type - if is_literate_agda: - # Extract Agda code blocks - code_blocks = re.findall(r'```agda\n(.*?)```', content, re.DOTALL) - # Create a mapping from line numbers in original file to line content - line_to_content = {} - line_num = 0 - for block in code_blocks: - block_lines = block.split('\n') - for i, line in enumerate(block_lines): - line_to_content[line_num + i] = line - line_num += len(block_lines) + 2 # +2 for ```agda and ``` - - # Create a list of (line_number, line) for all code blocks - lines = [] - for i in sorted(line_to_content.keys()): - lines.append((i, line_to_content[i])) - else: - # For regular .agda files, process all lines - lines = [(i, line) for i, line in enumerate(content.split('\n'))] - - definition_bodies = {} - - for i, (definition_name, def_line_num, _) in enumerate(definitions): - # Find the start of the body (the first top-level colon after the definition name) - body_start = None - - # Find the line index in our processed lines list that corresponds to the definition line - def_idx = None - for idx, (line_num, _) in enumerate(lines): - if line_num == def_line_num: - def_idx = idx - break - - if def_idx is None: - continue # Skip if we couldn't find the definition line - - # Look for the first top-level colon after the definition name - current_idx = def_idx - paren_level = 0 # Track the nesting level of parentheses - - while current_idx < len(lines) and body_start is None: - line_num, line = lines[current_idx] - - # Process character by character to track parentheses nesting - for char_idx, char in enumerate(line): - if char == '(': - paren_level += 1 - elif char == ')': - paren_level = max(0, paren_level - 1) # Ensure we don't go negative - elif char == ':' and paren_level == 0: - # Found a top-level colon - body_start = (current_idx, char_idx + 1) # Start after the colon - break - - current_idx += 1 - - if body_start is None: - continue # No body found or constructor/postulate without implementation - - # Find the end of the body (the next definition or end of code block) - body_end = None - if i < len(definitions) - 1: - next_def_idx = None - for idx, (line_num, _) in enumerate(lines): - if line_num == definitions[i + 1][1]: - next_def_idx = idx - break - if next_def_idx is not None: - body_end = (next_def_idx, 0) - - if body_end is None: - body_end = (len(lines), 0) # End of file - - # Extract the body - body = "" - if body_start[0] == body_end[0]: - # Body is on the same line - body = lines[body_start[0]][1][body_start[1]:body_end[1]] - else: - # Body spans multiple lines - body = lines[body_start[0]][1][body_start[1]:] - for j in range(body_start[0] + 1, body_end[0]): - if j < len(lines): - body += '\n' + lines[j][1] - if body_end[1] > 0 and body_end[0] < len(lines): - body += '\n' + lines[body_end[0]][1][:body_end[1]] - - definition_bodies[definition_name] = body - - return definition_bodies - -def build_definition_graph(root_dir): - """ - Build a dependency graph of definitions from all Git-tracked Agda files. - """ - agda_files = find_agda_files(root_dir) - - # Dictionary to store all definitions across all files - all_definitions = {} # Maps definition_name -> (module_name, file_path) - module_definitions = defaultdict(list) # Maps module_name -> list of def_names - all_definition_bodies = {} # Maps definition_name -> body - - print(f"Processing {len(agda_files)} Agda files...") - - # First pass: collect all definitions - for file_path in agda_files: - try: - module_name = extract_module_name(file_path, root_dir) - definitions = extract_definitions(file_path) - - for def_name, _, _ in definitions: - # Store with module name to avoid name collisions across modules - qualified_name = f"{module_name}.{def_name}" - all_definitions[qualified_name] = (module_name, file_path) - module_definitions[module_name].append(def_name) - except Exception as e: - print(f"Error processing definitions in {file_path}: {e}") - - print(f"Found {len(all_definitions)} unique qualified definitions") - - # Second pass: extract bodies and build the dependency graph - for file_path in agda_files: - try: - module_name = extract_module_name(file_path, root_dir) - definitions = extract_definitions(file_path) - definition_bodies = extract_definition_bodies(file_path, definitions) - - for def_name, body in definition_bodies.items(): - qualified_name = f"{module_name}.{def_name}" - all_definition_bodies[qualified_name] = body - except Exception as e: - print(f"Error processing definition bodies in {file_path}: {e}") - - # Build the dependency graph - graph = defaultdict(list) - - # Create a reverse lookup from bare definition name to qualified names - # This will help us find all possible qualified definitions for a given bare name - bare_to_qualified = defaultdict(list) - for qualified_name in all_definitions: - bare_name = qualified_name.split('.')[-1] - bare_to_qualified[bare_name].append(qualified_name) - - # Define a blacklist of regex patterns to ignore when finding dependencies - token_blacklist_patterns = [ - r'^[a-zA-Z]$', # Single letter names - r'^l\d+$', # 'l' followed by a number - ] - - # For each definition body, check if it contains references to other definitions - for def_name, body in all_definition_bodies.items(): - module_name = def_name.rsplit('.', 1)[0] # Extract module name from qualified definition name - bare_def_name = def_name.split('.')[-1] # Extract the bare definition name - - # Split the body into tokens (only identifiers, not qualified) - - # The regex uses lookbehind and lookahead to match identifiers surrounded by separators - # but only captures the identifier itself - tokens = [] - pattern = r"""(?:^|\{\!|\{-\#|[\s;{}()@"._])(?!'|--)([^\s;{}()@"._]+)(?:$|\!\}|[\s;{}()@"._])""" - matches = re.finditer(pattern, ' ' + body + ' ') # Add spaces to ensure boundary matching - for match in matches: - tokens.append(match.group(1)) - - # Track unique dependencies to avoid duplicates - unique_deps = set() - - # Check if any token matches a known definition name (ignore qualified parts) - for token in tokens: - # Remove underscores from the token for matching - clean_token = token.replace('_', '') - - # Skip tokens that are the definition itself - if clean_token == bare_def_name: - continue - - # Skip tokens that match any regex in the blacklist - if any(re.match(pattern, clean_token) for pattern in token_blacklist_patterns): - continue - - # Check if it's a reference to a definition in the same module first - if clean_token in module_definitions[module_name]: - qualified_token = f"{module_name}.{clean_token}" - unique_deps.add(qualified_token) - # Otherwise, it might be a reference to an imported definition - # For now, we'll just consider all possible matches to be conservative - elif clean_token in bare_to_qualified and len(bare_to_qualified[clean_token]) > 0: - # Add potential dependencies - # For simplicity and to avoid false positives with common names, - # we'll only consider it a dependency if there's exactly one definition with this name - if len(bare_to_qualified[clean_token]) == 1: - unique_deps.add(bare_to_qualified[clean_token][0]) - - # Add all unique dependencies to the graph - graph[def_name] = list(unique_deps) - - return graph, all_definitions - -def compute_transitive_closure(graph): - """ - Compute the transitive closure of the dependency graph. - Returns a new graph where each definition has a list of all its - direct and indirect dependencies. - """ - transitive_closure = defaultdict(set) - - # For each definition, perform BFS to find all dependencies - for definition in graph: - queue = deque(graph[definition]) - visited = set(graph[definition]) - - while queue: - dep = queue.popleft() - transitive_closure[definition].add(dep) - - # Add any dependencies of this dependency that we haven't seen yet - for next_dep in graph.get(dep, []): - if next_dep not in visited: - visited.add(next_dep) - queue.append(next_dep) - - # Convert sets back to lists for consistent output - return {definition: list(deps) for definition, deps in transitive_closure.items()} - -def export_to_dot(graph, output_file): - """Export the graph to DOT format for visualization with Graphviz.""" - with open(output_file, 'w') as f: - f.write('digraph Dependencies {\n') - f.write(' node [shape=box];\n') - - for definition, deps in graph.items(): - for dep in deps: - f.write(f' "{definition}" -> "{dep}";\n') - - f.write('}\n') - -def export_to_json(graph, output_file): - """Export the graph to JSON format.""" - with open(output_file, 'w') as f: - json.dump(graph, f, indent=2) - -def find_dependent_definitions(graph, target_definition): - """ - Find all definitions that depend on the target definition. - - If the target_definition is not fully qualified, it will match any definition - that ends with this name (i.e., any module's definition with this bare name). - """ - dependent_definitions = [] - - # Check if the target is a fully qualified name or just a bare name - is_qualified = '.' in target_definition - - for definition, dependencies in graph.items(): - if is_qualified: - # Direct match for fully qualified names - if target_definition in dependencies: - dependent_definitions.append(definition) - else: - # For bare names, check if any dependency ends with the target - for dep in dependencies: - if dep.endswith('.' + target_definition): - dependent_definitions.append(definition) - break - - return dependent_definitions - -def find_module_dependent_definitions(graph, all_definitions, module_name): - """ - Find all definitions that transitively depend on any definition in the specified module. - - Args: - graph: The dependency graph - all_definitions: Dictionary mapping qualified definition names to (module_name, file_path) - module_name: The name of the module to find dependents of - - Returns: - A list of definition names that depend on any definition in the module - """ - # Find all definitions in the target module - module_definitions = [] - for qualified_name, (def_module, _) in all_definitions.items(): - if def_module == module_name: - module_definitions.append(qualified_name) - - if not module_definitions: - return [] - - # Find all definitions that depend on any definition in the module - dependent_definitions = set() - for definition in module_definitions: - dependents = find_dependent_definitions(graph, definition) - dependent_definitions.update(dependents) - - return list(dependent_definitions) - -def find_module_direct_dependencies(graph, all_definitions, module_name): - """ - Find all modules that directly depend on any definition in the specified module. - - Args: - graph: The dependency graph - all_definitions: Dictionary mapping qualified definition names to (module_name, file_path) - module_name: The name of the module to find direct dependents of - - Returns: - A list of module names that directly depend on any definition in the specified module - """ - # Find all definitions in the target module - module_definitions = [] - for qualified_name, (def_module, _) in all_definitions.items(): - if def_module == module_name: - module_definitions.append(qualified_name) - - if not module_definitions: - return [] - - # Find all definitions that depend on any definition in the module - dependent_modules = set() - for source_def, dependencies in graph.items(): - source_module = source_def.rsplit('.', 1)[0] # Extract module name from qualified definition name - - # Skip if the source is the same module we're checking dependencies for - if source_module == module_name: - continue - - # Check if this definition depends on any definition from our target module - for dep in dependencies: - if any(dep == target_def for target_def in module_definitions): - dependent_modules.add(source_module) - break - - return list(dependent_modules) - -def main(): - parser = argparse.ArgumentParser(description='Build dependency graph of Agda definitions') - parser.add_argument('root_dir', help='Root directory of the Agda library') - parser.add_argument('--dot', help='Output file for DOT graph') - parser.add_argument('--json', help='Output file for JSON representation') - parser.add_argument('--transitive', action='store_true', - help='Compute transitive closure of dependencies') - parser.add_argument('--transitive-dot', help='Output file for transitive closure DOT graph') - parser.add_argument('--transitive-json', help='Output file for transitive closure JSON') - parser.add_argument('--top-dependent', type=int, default=10, - help='Print top N definitions with most dependencies (default: 10)') - parser.add_argument('--find-dependents', metavar='DEFINITION', - help='Find all definitions that depend on the specified definition') - parser.add_argument('--find-module-dependents', metavar='MODULE', - help='Find all definitions that depend on any definition in the specified module') - parser.add_argument('--find-module-deps', metavar='MODULE', - help='Find all modules that directly depend on any definition in the specified module') - parser.add_argument('--quiet', action='store_true', - help='Suppress informational output, only show requested results') - args = parser.parse_args() - - # If find_dependents, find_module_dependents, or find_module_deps is used, enable quiet mode by default - quiet_mode = args.quiet or ((args.find_dependents or args.find_module_dependents or args.find_module_deps) and - not any([args.transitive, args.dot, args.json, args.transitive_dot, args.transitive_json])) - - if not quiet_mode: - print(f"Analyzing Git-tracked Agda files in {args.root_dir}...") - - try: - graph, all_definitions = build_definition_graph(args.root_dir) - except Exception as e: - print(f"Error building definition graph: {e}") - return - - # No need for duplicate filtering as we're being more careful above - # Just keep the graph as is - - if not quiet_mode: - print(f"Found {len(graph)} tracked definitions with dependencies.") - total_deps = sum(len(deps) for deps in graph.values()) - print(f"Total dependencies: {total_deps}") - - if args.dot: - export_to_dot(graph, args.dot) - if not quiet_mode: - print(f"DOT graph exported to {args.dot}") - - if args.json: - export_to_json(graph, args.json) - if not quiet_mode: - print(f"JSON data exported to {args.json}") - - # Compute transitive closure if needed - transitive_graph = None - if args.transitive or args.transitive_dot or args.transitive_json or args.find_dependents or args.find_module_dependents: - if not quiet_mode: - print("Computing transitive closure of dependencies...") - transitive_graph = compute_transitive_closure(graph) - - if args.transitive_dot: - export_to_dot(transitive_graph, args.transitive_dot) - if not quiet_mode: - print(f"Transitive closure DOT graph exported to {args.transitive_dot}") - - if args.transitive_json: - export_to_json(transitive_graph, args.transitive_json) - if not quiet_mode: - print(f"Transitive closure JSON exported to {args.transitive_json}") - - if args.transitive and not (args.transitive_dot or args.transitive_json) and not quiet_mode: - # Print some statistics about the transitive closure - avg_deps = sum(len(deps) for deps in transitive_graph.values()) / len(transitive_graph) if transitive_graph else 0 - max_deps = max(len(deps) for deps in transitive_graph.values()) if transitive_graph else 0 - - print(f"\nTransitive closure statistics:") - print(f" Average dependencies per definition: {avg_deps:.2f}") - print(f" Maximum dependencies for a definition: {max_deps}") - - # Check for definitions that depend on a specific definition - if args.find_dependents: - if not transitive_graph: - if not quiet_mode: - print("Computing transitive closure of dependencies...") - transitive_graph = compute_transitive_closure(graph) - - dependent_definitions = find_dependent_definitions(transitive_graph, args.find_dependents) - - # If no results with the input as provided, check if we need to look for it as a bare name - if not dependent_definitions and '.' not in args.find_dependents: - # Print possible fully qualified names that match this bare name - matching_qualified_names = [] - for qualified_name in all_definitions: - if qualified_name.endswith('.' + args.find_dependents): - matching_qualified_names.append(qualified_name) - - if matching_qualified_names: - print(f"\nFound {len(matching_qualified_names)} definitions named '{args.find_dependents}':") - for name in sorted(matching_qualified_names): - print(f" {name}") - print(f"\nTry searching with a fully qualified name like '--find-dependents {matching_qualified_names[0]}'") - - print(f"\nDefinitions that depend on '{args.find_dependents}':") - print(f"Found {len(dependent_definitions)} dependent definitions") - - if dependent_definitions: - # Sort alphabetically for easier reading - for definition in sorted(dependent_definitions): - print(f" {definition}") - - # Optionally export to a file if requested - if args.json: - dependents_json = os.path.splitext(args.json)[0] + f"-dependents-of-{args.find_dependents.replace('.', '-')}.json" - with open(dependents_json, 'w') as f: - json.dump(dependent_definitions, f, indent=2) - print(f"Dependent definitions exported to {dependents_json}") - else: - print(" No definitions depend on this definition") - - # Check for definitions that depend on any definition in a module - if args.find_module_dependents: - if not transitive_graph: - if not quiet_mode: - print("Computing transitive closure of dependencies...") - transitive_graph = compute_transitive_closure(graph) - - module_dependent_definitions = find_module_dependent_definitions(transitive_graph, all_definitions, args.find_module_dependents) - - print(f"\nDefinitions that depend on module '{args.find_module_dependents}':") - print(f"Found {len(module_dependent_definitions)} dependent definitions") - - if module_dependent_definitions: - # Sort alphabetically for easier reading - for definition in sorted(module_dependent_definitions): - print(f" {definition}") - - # Optionally export to a file if requested - if args.json: - module_dependents_json = os.path.splitext(args.json)[0] + f"-dependents-of-module-{args.find_module_dependents.replace('.', '-')}.json" - with open(module_dependents_json, 'w') as f: - json.dump(module_dependent_definitions, f, indent=2) - print(f"Module dependent definitions exported to {module_dependents_json}") - else: - print(f" No definitions depend on any definition in module '{args.find_module_dependents}'") - - # Check for modules that directly depend on a module - if args.find_module_deps: - module_dependencies = find_module_direct_dependencies(graph, all_definitions, args.find_module_deps) - - print(f"\nModules that directly depend on module '{args.find_module_deps}':") - print(f"Found {len(module_dependencies)} dependent modules") - - if module_dependencies: - # Sort alphabetically for easier reading - for module in sorted(module_dependencies): - print(f" {module}") - - # Optionally export to a file if requested - if args.json: - module_deps_json = os.path.splitext(args.json)[0] + f"-modules-depend-on-{args.find_module_deps.replace('.', '-')}.json" - with open(module_deps_json, 'w') as f: - json.dump(module_dependencies, f, indent=2) - print(f"Module dependencies exported to {module_deps_json}") - else: - print(f" No modules directly depend on module '{args.find_module_deps}'") - - # Only print remaining statistics if not in quiet mode - if not quiet_mode: - # Print top definitions with most direct dependencies - direct_dep_count = {definition: len(deps) for definition, deps in graph.items()} - - if direct_dep_count: - print(f"\nTop {args.top_dependent} definitions with most direct dependencies:") - for i, (definition, count) in enumerate(sorted(direct_dep_count.items(), key=lambda x: x[1], reverse=True)[:args.top_dependent], 1): - print(f" {i}. {definition}: {count} direct dependencies") - else: - print("\nNo definitions found for direct dependency analysis.") - - if not any([args.dot, args.json, args.transitive, args.transitive_dot, args.transitive_json, args.find_dependents]): - # Calculate the most depended upon definitions - most_depended = defaultdict(int) - for _, deps in graph.items(): - for dep in deps: - most_depended[dep] += 1 - - if most_depended: - print("\nTop 10 most used definitions:") - for definition, count in sorted(most_depended.items(), key=lambda x: x[1], reverse=True)[:10]: - print(f" {definition}: {count} usages") - else: - print("\nNo definitions found for usage analysis.") - -if __name__ == "__main__": - main() diff --git a/scripts/build_dependency_graph.py b/scripts/build_dependency_graph.py deleted file mode 100644 index 6c6271c6d8..0000000000 --- a/scripts/build_dependency_graph.py +++ /dev/null @@ -1,281 +0,0 @@ -#!/usr/bin/env python3 - -import os -import re -import argparse -import json -from collections import defaultdict, deque -from pathlib import Path - -# Import utils for Git-related functionality -import sys -import os.path -sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) -from scripts.utils import get_git_tracked_files - -def find_agda_files(root_dir): - """Find all Git-tracked Agda source files in the given directory tree.""" - # Get all Git-tracked files - git_tracked_files = get_git_tracked_files() - - # Filter to keep only Agda files that are tracked by Git - agda_files = [] - root_path = Path(root_dir).resolve() - - for file_path in git_tracked_files: - full_path = Path(file_path) - # Check if the file is in the specified root directory - if root_path in full_path.resolve().parents or root_path == full_path.resolve().parent: - if file_path.suffix == '.agda' or (file_path.suffix == '.md' and file_path.stem.endswith('.lagda')): - agda_files.append(str(file_path)) - - return agda_files - -def extract_imports(file_path): - """Extract all module imports from a file.""" - with open(file_path, 'r', encoding='utf-8') as f: - content = f.read() - - # Pattern to match "open import module.name" - import_pattern = r'open\s+import\s+(\S+)' - - # Find all matches - imports = re.findall(import_pattern, content) - return imports - -def build_dependency_graph(root_dir): - """Build a dependency graph from all Git-tracked Agda files in the directory.""" - agda_files = find_agda_files(root_dir) - - # Map each file to its module name (derived from path) - file_to_module = {} - for file_path in agda_files: - # Convert file path to module name - rel_path = os.path.relpath(file_path, root_dir) - # Remove extension and replace / with . - if rel_path.endswith('.lagda.md'): - module_name = rel_path[:-9] - else: # .agda - module_name = rel_path[:-5] - module_name = module_name.replace('/', '.') - file_to_module[file_path] = module_name - - # Invert the mapping for lookup - module_to_file = {v: k for k, v in file_to_module.items()} - - # Build the dependency graph - graph = defaultdict(list) - for file_path in agda_files: - module_name = file_to_module[file_path] - imports = extract_imports(file_path) - for imported_module in imports: - graph[module_name].append(imported_module) - - return graph, module_to_file - -def compute_transitive_closure(graph): - """ - Compute the transitive closure of the dependency graph. - Returns a new graph where each module has a list of all its - direct and indirect dependencies. - """ - transitive_closure = defaultdict(set) - - # For each module, perform BFS to find all dependencies - for module in graph: - queue = deque(graph[module]) - visited = set(graph[module]) - - while queue: - dep = queue.popleft() - transitive_closure[module].add(dep) - - # Add any dependencies of this dependency that we haven't seen yet - for next_dep in graph.get(dep, []): - if next_dep not in visited: - visited.add(next_dep) - queue.append(next_dep) - - # Convert sets back to lists for consistent output - return {module: list(deps) for module, deps in transitive_closure.items()} - -def export_to_dot(graph, output_file): - """Export the graph to DOT format for visualization with Graphviz.""" - with open(output_file, 'w') as f: - f.write('digraph Dependencies {\n') - f.write(' node [shape=box];\n') - - for module, deps in graph.items(): - for dep in deps: - f.write(f' "{module}" -> "{dep}";\n') - - f.write('}\n') - -def export_to_json(graph, output_file): - """Export the graph to JSON format.""" - with open(output_file, 'w') as f: - json.dump(graph, f, indent=2) - -def find_dependent_modules(graph, target_module): - """ - Find all modules that depend on the target module. - Uses the transitive closure of the dependency graph. - - Args: - graph: The transitive closure of the dependency graph - target_module: The module to check dependencies for - - Returns: - A list of modules that depend on the target module - """ - dependent_modules = [] - for module, dependencies in graph.items(): - if target_module in dependencies: - dependent_modules.append(module) - return dependent_modules - -def main(): - parser = argparse.ArgumentParser(description='Build dependency graph of Agda modules') - parser.add_argument('root_dir', help='Root directory of the Agda library') - parser.add_argument('--dot', help='Output file for DOT graph') - parser.add_argument('--json', help='Output file for JSON representation') - parser.add_argument('--transitive', action='store_true', - help='Compute transitive closure of dependencies') - parser.add_argument('--transitive-dot', help='Output file for transitive closure DOT graph') - parser.add_argument('--transitive-json', help='Output file for transitive closure JSON') - parser.add_argument('--top-dependent', type=int, default=10, - help='Print top N modules with most dependencies (default: 10)') - parser.add_argument('--find-dependents', metavar='MODULE', - help='Find all modules that depend on the specified module') - parser.add_argument('--quiet', action='store_true', - help='Suppress informational output, only show requested results') - # Remove the --omit-top-level argument as we'll always do this - args = parser.parse_args() - - # If find_dependents is used, enable quiet mode by default unless explicitly overridden - quiet_mode = args.quiet or (args.find_dependents and not any([args.transitive, args.dot, args.json, args.transitive_dot, args.transitive_json])) - - if not quiet_mode: - print(f"Analyzing Git-tracked Agda files in {args.root_dir}...") - graph, module_to_file = build_dependency_graph(args.root_dir) - - if not quiet_mode: - print(f"Found {len(graph)} tracked modules with dependencies.") - - if args.dot: - export_to_dot(graph, args.dot) - if not quiet_mode: - print(f"DOT graph exported to {args.dot}") - - if args.json: - export_to_json(graph, args.json) - if not quiet_mode: - print(f"JSON data exported to {args.json}") - - # Compute transitive closure if needed - transitive_graph = None - if args.transitive or args.transitive_dot or args.transitive_json or args.find_dependents: - if not quiet_mode: - print("Computing transitive closure of dependencies...") - transitive_graph = compute_transitive_closure(graph) - - if args.transitive_dot: - export_to_dot(transitive_graph, args.transitive_dot) - if not quiet_mode: - print(f"Transitive closure DOT graph exported to {args.transitive_dot}") - - if args.transitive_json: - export_to_json(transitive_graph, args.transitive_json) - if not quiet_mode: - print(f"Transitive closure JSON exported to {args.transitive_json}") - - if args.transitive and not (args.transitive_dot or args.transitive_json) and not quiet_mode: - # Print some statistics about the transitive closure - avg_deps = sum(len(deps) for deps in transitive_graph.values()) / len(transitive_graph) if transitive_graph else 0 - max_deps = max(len(deps) for deps in transitive_graph.values()) if transitive_graph else 0 - - print(f"\nTransitive closure statistics:") - print(f" Average dependencies per module: {avg_deps:.2f}") - print(f" Maximum dependencies for a module: {max_deps}") - - # Find module with most dependencies (among non-top-level modules) - non_top_level_modules = {module: deps for module, deps in transitive_graph.items() if '.' in module} - if non_top_level_modules: - most_deps_module = max(non_top_level_modules.items(), key=lambda x: len(x[1])) - print(f" Module with most dependencies: {most_deps_module[0]} ({len(most_deps_module[1])} deps)") - - # Only print transitive dependency top lists if not in quiet mode - if not quiet_mode: - # Always filter out top-level modules - filtered_transitive_graph = {module: deps for module, deps in transitive_graph.items() - if '.' in module} - if filtered_transitive_graph: - # Only print this if we've actually filtered out modules - if len(transitive_graph) != len(filtered_transitive_graph): - print(f"Filtered out {len(transitive_graph) - len(filtered_transitive_graph)} top-level modules.") - - # Print top modules with most dependencies (transitive) - print(f"\nTop {args.top_dependent} modules with most dependencies (including transitive):") - sorted_modules = sorted(filtered_transitive_graph.items(), key=lambda x: len(x[1]), reverse=True) - for i, (module, deps) in enumerate(sorted_modules[:args.top_dependent], 1): - print(f" {i}. `{module}` {len(deps)} dependencies") - else: - print("\nNo non-top-level modules found for transitive analysis.") - - # Check for modules that depend on a specific module - if args.find_dependents: - if not transitive_graph: - if not quiet_mode: - print("Computing transitive closure of dependencies...") - transitive_graph = compute_transitive_closure(graph) - - dependent_modules = find_dependent_modules(transitive_graph, args.find_dependents) - - print(f"\nModules that depend on '{args.find_dependents}':") - print(f"Found {len(dependent_modules)} dependent modules") - - if dependent_modules: - # Sort alphabetically for easier reading - for module in sorted(dependent_modules): - print(f" {module}") - - # Optionally export to a file if requested - if args.json: - dependents_json = os.path.splitext(args.json)[0] + f"-dependents-of-{args.find_dependents.replace('.', '-')}.json" - with open(dependents_json, 'w') as f: - json.dump(dependent_modules, f, indent=2) - print(f"Dependent modules exported to {dependents_json}") - else: - print(" No modules depend on this module") - - # Only print remaining statistics if not in quiet mode - if not quiet_mode: - # Always filter out top-level modules for direct dependencies - filtered_graph = {module: deps for module, deps in graph.items() if '.' in module} - - if filtered_graph: - # Print modules with most direct dependencies - direct_dep_count = {module: len(deps) for module, deps in filtered_graph.items()} - print(f"\nTop {args.top_dependent} modules with most direct dependencies:") - for i, (module, count) in enumerate(sorted(direct_dep_count.items(), key=lambda x: x[1], reverse=True)[:args.top_dependent], 1): - print(f" {i}. {module}: {count} direct dependencies") - else: - print("\nNo non-top-level modules found for direct dependency analysis.") - - if not any([args.dot, args.json, args.transitive, args.transitive_dot, args.transitive_json, args.find_dependents]): - # Filter the imported modules count to only include non-top-level modules - most_imported = defaultdict(int) - for _, deps in graph.items(): - for dep in deps: - if '.' in dep: # Only count imports of non-top-level modules - most_imported[dep] += 1 - - if most_imported: - print("\nTop 10 most imported non-top-level modules:") - for module, count in sorted(most_imported.items(), key=lambda x: x[1], reverse=True)[:10]: - print(f" `{module}` {count} imports") - else: - print("\nNo non-top-level modules found for import analysis.") - -if __name__ == "__main__": - main() diff --git a/scripts/remove_unused_funext_import.py b/scripts/remove_unused_funext_import.py deleted file mode 100644 index ff05d8ab84..0000000000 --- a/scripts/remove_unused_funext_import.py +++ /dev/null @@ -1,85 +0,0 @@ -#!/usr/bin/env python3 - -import os -import re -import argparse -from pathlib import Path - -# Import utils for Git-related functionality -import sys -import os.path -sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) -from scripts.utils import get_git_tracked_files - -def find_agda_files(root_dir): - """Find all Git-tracked Agda source files in the given directory tree.""" - # Get all Git-tracked files - git_tracked_files = get_git_tracked_files() - - # Filter to keep only Agda files that are tracked by Git - agda_files = [] - root_path = Path(root_dir).resolve() - - for file_path in git_tracked_files: - full_path = Path(file_path) - # Check if the file is in the specified root directory - if root_path in full_path.resolve().parents or root_path == full_path.resolve().parent: - if file_path.suffix == '.agda' or (file_path.suffix == '.md' and file_path.stem.endswith('.lagda')): - agda_files.append(str(file_path)) - - return agda_files - -def process_file(file_path, dry_run=False): - """ - Check if the file contains the import line but doesn't use function extensionality. - Return True if the file was modified or would be modified. - """ - with open(file_path, 'r', encoding='utf-8') as f: - content = f.read() - - # Check if the file imports function-extensionality - target_import = "open import foundation.function-extensionality\n" - if target_import not in content: - return False - - # Check if the file uses either 'eq-htpy' or 'funext' - if 'eq-htpy' in content or 'funext' in content: - return False - - # The file has the import but doesn't appear to use it - if not dry_run: - # Remove the import line and write the file back - new_content = re.sub(f'^{re.escape(target_import)}', '', content, flags=re.MULTILINE) - with open(file_path, 'w', encoding='utf-8') as f: - f.write(new_content) - - return True - -def main(): - parser = argparse.ArgumentParser(description='Remove unused function-extensionality imports') - parser.add_argument('root_dir', help='Root directory of the Agda library') - parser.add_argument('--dry-run', action='store_true', - help='Only report files that would be modified without changing them') - args = parser.parse_args() - - print(f"Analyzing Git-tracked Agda files in {args.root_dir}...") - agda_files = find_agda_files(args.root_dir) - print(f"Found {len(agda_files)} tracked Agda files to check.") - - modified_files = [] - for file_path in agda_files: - if process_file(file_path, args.dry_run): - modified_files.append(file_path) - - if args.dry_run: - print(f"\nDry run: {len(modified_files)} files would be modified to remove unused imports.") - else: - print(f"\nModified {len(modified_files)} files to remove unused function-extensionality imports.") - - if modified_files: - print("\nModified files:") - for file_path in modified_files: - print(f" - {file_path}") - -if __name__ == "__main__": - main() From 5cd74a3eae15cd7a0a3f39afa22ad2a43523db18 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 24 Mar 2025 19:05:15 +0000 Subject: [PATCH 34/39] fix prose --- .../dependent-products-contractible-types.lagda.md | 4 ++-- src/foundation/dependent-products-propositions.lagda.md | 7 ++----- src/foundation/dependent-products-truncated-types.lagda.md | 6 ++---- src/foundation/raising-universe-levels-booleans.lagda.md | 7 +++---- src/foundation/raising-universe-levels-unit-type.lagda.md | 4 +++- 5 files changed, 12 insertions(+), 16 deletions(-) diff --git a/src/foundation/dependent-products-contractible-types.lagda.md b/src/foundation/dependent-products-contractible-types.lagda.md index 0cf967700c..da25f720c5 100644 --- a/src/foundation/dependent-products-contractible-types.lagda.md +++ b/src/foundation/dependent-products-contractible-types.lagda.md @@ -21,8 +21,8 @@ open import foundation-core.identity-types ## Idea -Contractible types are types that have, up to identification, exactly one -element. +Given a family of [contractible types](foundation-core.contractible-types.md) +`B : A → 𝒰`, then the dependent product `Π A B` is again contractible. ## Properties diff --git a/src/foundation/dependent-products-propositions.lagda.md b/src/foundation/dependent-products-propositions.lagda.md index 029f396e8a..fbb367cc9a 100644 --- a/src/foundation/dependent-products-propositions.lagda.md +++ b/src/foundation/dependent-products-propositions.lagda.md @@ -22,11 +22,8 @@ open import foundation-core.propositions ## Idea -A type is a {{#concept "proposition" Agda=is-prop}} if its -[identity types](foundation-core.identity-types.md) are -[contractible](foundation-core.contractible-types.md). This condition is -[equivalent](foundation-core.equivalences.md) to the condition that it has up to -identification at most one element. +Given a family of [propositions](foundation-core.propositions.md) `B : A → 𝒰`, +then the dependent product `Π A B` is again a proposition. ## Definitions diff --git a/src/foundation/dependent-products-truncated-types.lagda.md b/src/foundation/dependent-products-truncated-types.lagda.md index 52960698b7..1dde1aed0e 100644 --- a/src/foundation/dependent-products-truncated-types.lagda.md +++ b/src/foundation/dependent-products-truncated-types.lagda.md @@ -34,10 +34,8 @@ open import foundation-core.truncation-levels ## Idea -The truncatedness of a type is a measure of the complexity of its identity -types. The simplest case is a contractible type. This is the base case of the -inductive definition of truncatedness for types. A type is `k+1`-truncated if -its identity types are `k`-truncated. +Given a family of $n$-[truncated](foundation-core.truncated-types.md) +`B : A → 𝒰`, then the dependent product `Π A B` is again $n$-truncated. ## Properties diff --git a/src/foundation/raising-universe-levels-booleans.lagda.md b/src/foundation/raising-universe-levels-booleans.lagda.md index a94fd6c0e0..c22c66ddbc 100644 --- a/src/foundation/raising-universe-levels-booleans.lagda.md +++ b/src/foundation/raising-universe-levels-booleans.lagda.md @@ -18,10 +18,9 @@ open import foundation-core.equivalences ## Idea -The type of **booleans** is a -[2-element type](univalent-combinatorics.2-element-types.md) with elements -`true false : bool`, which is used for reasoning with -[decidable propositions](foundation-core.decidable-propositions.md). +We can [raise](foundation.raising-universe-levels.md) the type of +[booleans](foundation-core.booleans.md) to any +[universe](foundation.universe-levels.md). ## Definition diff --git a/src/foundation/raising-universe-levels-unit-type.lagda.md b/src/foundation/raising-universe-levels-unit-type.lagda.md index c8315fa606..bd7f6068a8 100644 --- a/src/foundation/raising-universe-levels-unit-type.lagda.md +++ b/src/foundation/raising-universe-levels-unit-type.lagda.md @@ -28,7 +28,9 @@ open import foundation-core.truncation-levels ## Idea -The **unit type** is a type inductively generated by a single point. +We can [raise](foundation.raising-universe-levels.md) the type of +[booleans](foundation-core.booleans.md) to any +[universe](foundation.universe-levels.md). ## Definition From 0e6f5f377168abfb3708801b47fb9a54d77a4704 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 24 Mar 2025 19:07:45 +0000 Subject: [PATCH 35/39] repostulate funext --- .../function-extensionality.lagda.md | 31 ++++++++++--------- 1 file changed, 16 insertions(+), 15 deletions(-) diff --git a/src/foundation/function-extensionality.lagda.md b/src/foundation/function-extensionality.lagda.md index b6ca9801f6..d26c3c48c8 100644 --- a/src/foundation/function-extensionality.lagda.md +++ b/src/foundation/function-extensionality.lagda.md @@ -3,10 +3,7 @@ ```agda open import foundation.function-extensionality-axiom -module - foundation.function-extensionality - (funext : function-extensionality) - where +module foundation.function-extensionality where ```
Imports @@ -15,7 +12,6 @@ module open import foundation.action-on-identifications-binary-functions open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.evaluation-functions open import foundation.implicit-function-types open import foundation.universe-levels @@ -82,23 +78,23 @@ module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} {f g : (x : A) → B x} where - eq-htpy : f ~ g → f ＝ g - eq-htpy = map-inv-is-equiv (funext f g) + postulate + eq-htpy : f ~ g → f ＝ g - opaque is-section-eq-htpy : is-section htpy-eq eq-htpy - is-section-eq-htpy = is-section-map-inv-is-equiv (funext f g) - is-retraction-eq-htpy : is-retraction htpy-eq eq-htpy - is-retraction-eq-htpy = is-retraction-map-inv-is-equiv (funext f g) + is-retraction-eq-htpy' : is-retraction htpy-eq eq-htpy - coh-eq-htpy : + coh-eq-htpy' : coherence-is-coherently-invertible ( htpy-eq) ( eq-htpy) ( is-section-eq-htpy) - ( is-retraction-eq-htpy) - coh-eq-htpy = coherence-map-inv-is-equiv (funext f g) + ( is-retraction-eq-htpy') + +funext : function-extensionality +funext f g = + is-equiv-is-invertible eq-htpy is-section-eq-htpy is-retraction-eq-htpy' module _ {l1 l2 : Level} {A : UU l1} {B : A → UU l2} @@ -111,7 +107,12 @@ module _ is-equiv-eq-htpy : (f g : (x : A) → B x) → is-equiv (eq-htpy {f = f} {g}) is-equiv-eq-htpy f g = - is-equiv-is-invertible htpy-eq is-retraction-eq-htpy is-section-eq-htpy + is-equiv-is-invertible htpy-eq is-retraction-eq-htpy' is-section-eq-htpy + + abstract + is-retraction-eq-htpy : + {f g : (x : A) → B x} → is-retraction (htpy-eq {f = f} {g}) eq-htpy + is-retraction-eq-htpy {f} {g} = is-retraction-map-inv-is-equiv (funext f g) eq-htpy-refl-htpy : (f : (x : A) → B x) → eq-htpy (refl-htpy {f = f}) ＝ refl From 49cc93e45c0be1cd2b0077f3afb47d6d18033a9a Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 24 Mar 2025 19:54:18 +0000 Subject: [PATCH 36/39] fix link concept --- src/foundation/logical-equivalences.lagda.md | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/foundation/logical-equivalences.lagda.md b/src/foundation/logical-equivalences.lagda.md index f95d0aacb7..7f76f93557 100644 --- a/src/foundation/logical-equivalences.lagda.md +++ b/src/foundation/logical-equivalences.lagda.md @@ -35,9 +35,9 @@ open import foundation-core.torsorial-type-families ## Idea -{{#concept "Logical equivalences" Disambiguation="of types" Agda=iff}} between -two types `A` and `B` consist of a map `A → B` and a map `B → A`. The type of -logical equivalences between types is the +{{#concept "Logical equivalences" Disambiguation="of types"}} between two types +`A` and `B` consist of a map `A → B` and a map `B → A`. The type of logical +equivalences between types is the [Curry–Howard interpretation](https://en.wikipedia.org/wiki/Curry–Howard_correspondence) of logical equivalences between [propositions](foundation-core.propositions.md). From 29957d077dd28a82398c6e23da18bf0cfbafca77 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 24 Mar 2025 20:16:24 +0000 Subject: [PATCH 37/39] `foundation-core.raising-universe-levels` --- .../copresheaf-categories.lagda.md | 3 +- ...inuous-maps-omega-complete-posets.lagda.md | 3 +- .../omega-continuous-maps-posets.lagda.md | 3 +- .../scott-continuous-maps-posets.lagda.md | 3 +- ...rtier-delooping-sign-homomorphism.lagda.md | 3 +- .../delooping-sign-homomorphism.lagda.md | 3 +- .../finite-type-groups.lagda.md | 3 +- ...mpson-delooping-sign-homomorphism.lagda.md | 3 +- .../transpositions.lagda.md | 3 +- src/foundation-core.lagda.md | 1 + .../raising-universe-levels.lagda.md | 128 ++++++++++++++++++ src/foundation-core/small-types.lagda.md | 2 +- src/foundation/category-of-sets.lagda.md | 2 +- .../connected-components-universes.lagda.md | 2 +- .../decidable-propositions.lagda.md | 2 +- src/foundation/decidable-types.lagda.md | 2 +- .../dependent-binomial-theorem.lagda.md | 2 +- src/foundation/empty-types.lagda.md | 2 +- .../families-over-telescopes.lagda.md | 3 +- .../multivariable-operations.lagda.md | 2 +- .../propositional-extensionality.lagda.md | 2 +- .../raising-universe-levels-booleans.lagda.md | 2 +- ...raising-universe-levels-unit-type.lagda.md | 2 +- .../raising-universe-levels.lagda.md | 109 +-------------- src/foundation/vectors-set-quotients.lagda.md | 2 +- .../large-higher-directed-graphs.lagda.md | 3 +- ...g-universe-levels-directed-graphs.lagda.md | 3 +- .../walks-directed-graphs.lagda.md | 3 +- src/group-theory/trivial-groups.lagda.md | 3 +- src/linear-algebra/vectors.lagda.md | 3 +- src/lists/equality-lists.lagda.md | 2 +- src/lists/lists-discrete-types.lagda.md | 3 +- ...roduction-to-homotopy-type-theory.lagda.md | 2 +- .../join-preserving-maps-posets.lagda.md | 3 +- .../supremum-preserving-maps-posets.lagda.md | 3 +- .../raise-modalities.lagda.md | 3 +- ...sing-universe-levels-real-numbers.lagda.md | 3 +- src/set-theory/countable-sets.lagda.md | 2 +- src/set-theory/cumulative-hierarchy.lagda.md | 3 +- .../infinite-cyclic-types.lagda.md | 3 +- .../universal-cover-circle.lagda.md | 3 +- ...ng-universe-levels-directed-trees.lagda.md | 3 +- src/trees/small-multisets.lagda.md | 3 +- src/trees/universal-multiset.lagda.md | 3 +- .../2-element-types.lagda.md | 3 +- .../binomial-types.lagda.md | 3 +- .../finite-types.lagda.md | 2 +- .../standard-finite-types.lagda.md | 3 +- 48 files changed, 205 insertions(+), 152 deletions(-) create mode 100644 src/foundation-core/raising-universe-levels.lagda.md diff --git a/src/category-theory/copresheaf-categories.lagda.md b/src/category-theory/copresheaf-categories.lagda.md index dcce328cf6..63d3374268 100644 --- a/src/category-theory/copresheaf-categories.lagda.md +++ b/src/category-theory/copresheaf-categories.lagda.md @@ -34,11 +34,12 @@ open import foundation.functoriality-cartesian-product-types open import foundation.homotopies open import foundation.identity-types open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.raising-universe-levels ```
diff --git a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md index c53ceea500..6c249799da 100644 --- a/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-omega-complete-posets.lagda.md @@ -28,13 +28,14 @@ open import foundation.homotopy-induction open import foundation.identity-types open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle open import foundation.surjective-maps open import foundation.torsorial-type-families open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import order-theory.join-preserving-maps-posets open import order-theory.least-upper-bounds-posets open import order-theory.order-preserving-maps-posets diff --git a/src/domain-theory/omega-continuous-maps-posets.lagda.md b/src/domain-theory/omega-continuous-maps-posets.lagda.md index 43b73432ad..add807a58c 100644 --- a/src/domain-theory/omega-continuous-maps-posets.lagda.md +++ b/src/domain-theory/omega-continuous-maps-posets.lagda.md @@ -26,13 +26,14 @@ open import foundation.homotopy-induction open import foundation.identity-types open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle open import foundation.surjective-maps open import foundation.torsorial-type-families open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import order-theory.join-preserving-maps-posets open import order-theory.least-upper-bounds-posets open import order-theory.order-preserving-maps-posets diff --git a/src/domain-theory/scott-continuous-maps-posets.lagda.md b/src/domain-theory/scott-continuous-maps-posets.lagda.md index f405401866..09d408c19f 100644 --- a/src/domain-theory/scott-continuous-maps-posets.lagda.md +++ b/src/domain-theory/scott-continuous-maps-posets.lagda.md @@ -23,7 +23,6 @@ open import foundation.homotopy-induction open import foundation.identity-types open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.small-types open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle @@ -31,6 +30,8 @@ open import foundation.surjective-maps open import foundation.torsorial-type-families open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import order-theory.least-upper-bounds-posets open import order-theory.order-preserving-maps-posets open import order-theory.posets diff --git a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md index e60eb8b932..36cf91f5e0 100644 --- a/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/cartier-delooping-sign-homomorphism.lagda.md @@ -28,12 +28,13 @@ open import foundation.identity-types open import foundation.mere-equivalences open import foundation.negation open import foundation.propositional-truncations -open import foundation.raising-universe-levels open import foundation.transport-along-identifications open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import group-theory.homomorphisms-concrete-groups open import group-theory.homomorphisms-groups open import group-theory.isomorphisms-groups diff --git a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md index 96b95761fd..e56ceda2d3 100644 --- a/src/finite-group-theory/delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/delooping-sign-homomorphism.lagda.md @@ -51,7 +51,6 @@ open import foundation.negated-equality open import foundation.negation open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.reflecting-maps-equivalence-relations open import foundation.sets open import foundation.transport-along-identifications @@ -63,6 +62,8 @@ open import foundation.universal-property-set-quotients open import foundation.universe-levels open import foundation.whiskering-identifications-concatenation +open import foundation-core.raising-universe-levels + open import group-theory.generating-sets-groups open import group-theory.groups open import group-theory.homomorphisms-concrete-groups diff --git a/src/finite-group-theory/finite-type-groups.lagda.md b/src/finite-group-theory/finite-type-groups.lagda.md index b4e0df3adb..3469c84dda 100644 --- a/src/finite-group-theory/finite-type-groups.lagda.md +++ b/src/finite-group-theory/finite-type-groups.lagda.md @@ -22,11 +22,12 @@ open import foundation.function-types open import foundation.identity-types open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.sets open import foundation.truncated-types open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import group-theory.concrete-groups open import group-theory.groups open import group-theory.homomorphisms-groups diff --git a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md index 8fb9e6fd97..53a2dee050 100644 --- a/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md +++ b/src/finite-group-theory/simpson-delooping-sign-homomorphism.lagda.md @@ -41,13 +41,14 @@ open import foundation.logical-equivalences open import foundation.mere-equivalences open import foundation.negation open import foundation.propositional-truncations -open import foundation.raising-universe-levels open import foundation.sets open import foundation.transport-along-identifications open import foundation.type-theoretic-principle-of-choice open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import group-theory.groups open import group-theory.homomorphisms-concrete-groups open import group-theory.homomorphisms-groups diff --git a/src/finite-group-theory/transpositions.lagda.md b/src/finite-group-theory/transpositions.lagda.md index 477adf32dd..7f7c3003ed 100644 --- a/src/finite-group-theory/transpositions.lagda.md +++ b/src/finite-group-theory/transpositions.lagda.md @@ -40,7 +40,6 @@ open import foundation.negated-equality open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.sets open import foundation.transport-along-identifications open import foundation.type-arithmetic-empty-type @@ -48,6 +47,8 @@ open import foundation.unit-type open import foundation.univalence open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import lists.concatenation-lists open import lists.functoriality-lists open import lists.lists diff --git a/src/foundation-core.lagda.md b/src/foundation-core.lagda.md index 17d58ece65..4a0a82d4dd 100644 --- a/src/foundation-core.lagda.md +++ b/src/foundation-core.lagda.md @@ -51,6 +51,7 @@ open import foundation-core.precomposition-functions public open import foundation-core.propositional-maps public open import foundation-core.propositions public open import foundation-core.pullbacks public +open import foundation-core.raising-universe-levels public open import foundation-core.retractions public open import foundation-core.retracts-of-types public open import foundation-core.sections public diff --git a/src/foundation-core/raising-universe-levels.lagda.md b/src/foundation-core/raising-universe-levels.lagda.md new file mode 100644 index 0000000000..15251fb47f --- /dev/null +++ b/src/foundation-core/raising-universe-levels.lagda.md @@ -0,0 +1,128 @@ +# Raising universe levels + +```agda +module foundation-core.raising-universe-levels where +``` + +
Imports + +```agda +open import foundation.action-on-identifications-functions +open import foundation.dependent-pair-types +open import foundation.universe-levels + +open import foundation-core.equivalences +open import foundation-core.function-types +open import foundation-core.homotopies +open import foundation-core.identity-types +open import foundation-core.propositions +open import foundation-core.sets +``` + +
+ +## Idea + +In Agda, types have a designated universe levels, and universes in Agda don't +overlap. Using `data` types we can construct for any type `A` of universe level +`l` an equivalent type in any higher universe. + +## Definition + +```agda +data raise (l : Level) {l1 : Level} (A : UU l1) : UU (l1 ⊔ l) where + map-raise : A → raise l A + +data raiseω {l1 : Level} (A : UU l1) : UUω where + map-raiseω : A → raiseω A +``` + +## Properties + +### Types are equivalent to their raised equivalents + +```agda +module _ + {l l1 : Level} {A : UU l1} + where + + map-inv-raise : raise l A → A + map-inv-raise (map-raise x) = x + + is-section-map-inv-raise : (map-raise ∘ map-inv-raise) ~ id + is-section-map-inv-raise (map-raise x) = refl + + is-retraction-map-inv-raise : (map-inv-raise ∘ map-raise) ~ id + is-retraction-map-inv-raise x = refl + + is-equiv-map-raise : is-equiv (map-raise {l} {l1} {A}) + is-equiv-map-raise = + is-equiv-is-invertible + map-inv-raise + is-section-map-inv-raise + is-retraction-map-inv-raise + +compute-raise : (l : Level) {l1 : Level} (A : UU l1) → A ≃ raise l A +pr1 (compute-raise l A) = map-raise +pr2 (compute-raise l A) = is-equiv-map-raise + +inv-compute-raise : (l : Level) {l1 : Level} (A : UU l1) → raise l A ≃ A +inv-compute-raise l A = inv-equiv (compute-raise l A) + +Raise : (l : Level) {l1 : Level} (A : UU l1) → Σ (UU (l1 ⊔ l)) (λ X → A ≃ X) +pr1 (Raise l A) = raise l A +pr2 (Raise l A) = compute-raise l A +``` + +### Raising universe levels of propositions + +```agda +raise-Prop : (l : Level) {l1 : Level} → Prop l1 → Prop (l ⊔ l1) +pr1 (raise-Prop l P) = raise l (type-Prop P) +pr2 (raise-Prop l P) = + is-prop-equiv' (compute-raise l (type-Prop P)) (is-prop-type-Prop P) +``` + +### Raising universe levels of sets + +```agda +raise-Set : (l : Level) {l1 : Level} → Set l1 → Set (l ⊔ l1) +pr1 (raise-Set l A) = raise l (type-Set A) +pr2 (raise-Set l A) = + is-set-equiv' (type-Set A) (compute-raise l (type-Set A)) (is-set-type-Set A) +``` + +### Raising equivalent types + +```agda +module _ + {l1 l2 : Level} (l3 l4 : Level) {A : UU l1} {B : UU l2} (e : A ≃ B) + where + + map-equiv-raise : raise l3 A → raise l4 B + map-equiv-raise (map-raise x) = map-raise (map-equiv e x) + + map-inv-equiv-raise : raise l4 B → raise l3 A + map-inv-equiv-raise (map-raise y) = map-raise (map-inv-equiv e y) + + is-section-map-inv-equiv-raise : + ( map-equiv-raise ∘ map-inv-equiv-raise) ~ id + is-section-map-inv-equiv-raise (map-raise y) = + ap map-raise (is-section-map-inv-equiv e y) + + is-retraction-map-inv-equiv-raise : + ( map-inv-equiv-raise ∘ map-equiv-raise) ~ id + is-retraction-map-inv-equiv-raise (map-raise x) = + ap map-raise (is-retraction-map-inv-equiv e x) + + is-equiv-map-equiv-raise : is-equiv map-equiv-raise + is-equiv-map-equiv-raise = + is-equiv-is-invertible + map-inv-equiv-raise + is-section-map-inv-equiv-raise + is-retraction-map-inv-equiv-raise + + equiv-raise : raise l3 A ≃ raise l4 B + pr1 equiv-raise = map-equiv-raise + pr2 equiv-raise = is-equiv-map-equiv-raise +``` diff --git a/src/foundation-core/small-types.lagda.md b/src/foundation-core/small-types.lagda.md index adb78b9475..9acc144795 100644 --- a/src/foundation-core/small-types.lagda.md +++ b/src/foundation-core/small-types.lagda.md @@ -14,7 +14,6 @@ open import foundation.functoriality-dependent-function-types open import foundation.logical-equivalences open import foundation.mere-equivalences open import foundation.propositional-truncations -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.transport-along-identifications open import foundation.type-arithmetic-dependent-pair-types @@ -29,6 +28,7 @@ open import foundation-core.coproduct-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.retractions open import foundation-core.sections ``` diff --git a/src/foundation/category-of-sets.lagda.md b/src/foundation/category-of-sets.lagda.md index 23f7b9be68..1d847f4316 100644 --- a/src/foundation/category-of-sets.lagda.md +++ b/src/foundation/category-of-sets.lagda.md @@ -27,7 +27,6 @@ open import foundation.function-types open import foundation.fundamental-theorem-of-identity-types open import foundation.identity-types open import foundation.isomorphisms-of-sets -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.retractions open import foundation.sections @@ -38,6 +37,7 @@ open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.functoriality-dependent-pair-types +open import foundation-core.raising-universe-levels ```
diff --git a/src/foundation/connected-components-universes.lagda.md b/src/foundation/connected-components-universes.lagda.md index 6e4a87e413..a4d4a7e90e 100644 --- a/src/foundation/connected-components-universes.lagda.md +++ b/src/foundation/connected-components-universes.lagda.md @@ -14,7 +14,6 @@ open import foundation.functoriality-propositional-truncation open import foundation.fundamental-theorem-of-identity-types open import foundation.mere-equivalences open import foundation.propositional-truncations -open import foundation.raising-universe-levels open import foundation.subtype-identity-principle open import foundation.subuniverses open import foundation.univalence @@ -23,6 +22,7 @@ open import foundation.universe-levels open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.identity-types +open import foundation-core.raising-universe-levels open import foundation-core.subtypes open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/decidable-propositions.lagda.md b/src/foundation/decidable-propositions.lagda.md index d2425e4573..a942804d38 100644 --- a/src/foundation/decidable-propositions.lagda.md +++ b/src/foundation/decidable-propositions.lagda.md @@ -22,7 +22,6 @@ open import foundation.negation open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-coproduct-types open import foundation.type-arithmetic-dependent-pair-types @@ -34,6 +33,7 @@ open import foundation-core.coproduct-types open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types +open import foundation-core.raising-universe-levels open import foundation-core.retracts-of-types open import foundation-core.sets open import foundation-core.small-types diff --git a/src/foundation/decidable-types.lagda.md b/src/foundation/decidable-types.lagda.md index 93bdd1707e..e61835a0b8 100644 --- a/src/foundation/decidable-types.lagda.md +++ b/src/foundation/decidable-types.lagda.md @@ -17,7 +17,6 @@ open import foundation.hilberts-epsilon-operators open import foundation.logical-equivalences open import foundation.negation open import foundation.propositional-truncations -open import foundation.raising-universe-levels open import foundation.retracts-of-types open import foundation.type-arithmetic-empty-type open import foundation.unit-type @@ -26,6 +25,7 @@ open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.function-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.retractions open import foundation-core.sections ``` diff --git a/src/foundation/dependent-binomial-theorem.lagda.md b/src/foundation/dependent-binomial-theorem.lagda.md index 8be54bea03..78ab7bbd20 100644 --- a/src/foundation/dependent-binomial-theorem.lagda.md +++ b/src/foundation/dependent-binomial-theorem.lagda.md @@ -15,7 +15,6 @@ open import foundation.dependent-products-contractible-types open import foundation.equality-dependent-pair-types open import foundation.functoriality-cartesian-product-types open import foundation.functoriality-dependent-function-types -open import foundation.raising-universe-levels open import foundation.transport-along-identifications open import foundation.universal-property-coproduct-types open import foundation.universal-property-dependent-pair-types @@ -27,6 +26,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.functoriality-dependent-pair-types open import foundation-core.homotopies +open import foundation-core.raising-universe-levels open import foundation-core.type-theoretic-principle-of-choice open import foundation-core.univalence diff --git a/src/foundation/empty-types.lagda.md b/src/foundation/empty-types.lagda.md index 28925f767f..08551072cb 100644 --- a/src/foundation/empty-types.lagda.md +++ b/src/foundation/empty-types.lagda.md @@ -14,7 +14,6 @@ open import foundation.dependent-products-propositions open import foundation.embeddings open import foundation.equivalences open import foundation.propositional-truncations -open import foundation.raising-universe-levels open import foundation.subuniverses open import foundation.univalence open import foundation.universe-levels @@ -23,6 +22,7 @@ open import foundation-core.contractible-types open import foundation-core.equality-dependent-pair-types open import foundation-core.function-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.sets open import foundation-core.truncated-types open import foundation-core.truncation-levels diff --git a/src/foundation/families-over-telescopes.lagda.md b/src/foundation/families-over-telescopes.lagda.md index a6a2844f56..7e36e446f0 100644 --- a/src/foundation/families-over-telescopes.lagda.md +++ b/src/foundation/families-over-telescopes.lagda.md @@ -9,9 +9,10 @@ module foundation.families-over-telescopes where ```agda open import elementary-number-theory.natural-numbers -open import foundation.raising-universe-levels open import foundation.telescopes open import foundation.universe-levels + +open import foundation-core.raising-universe-levels ```
diff --git a/src/foundation/multivariable-operations.lagda.md b/src/foundation/multivariable-operations.lagda.md index fd82bdc4d4..5da52c8b7a 100644 --- a/src/foundation/multivariable-operations.lagda.md +++ b/src/foundation/multivariable-operations.lagda.md @@ -12,7 +12,6 @@ open import elementary-number-theory.natural-numbers open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types open import foundation.equality-cartesian-product-types -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels @@ -23,6 +22,7 @@ open import foundation-core.equivalences open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types +open import foundation-core.raising-universe-levels open import linear-algebra.vectors ``` diff --git a/src/foundation/propositional-extensionality.lagda.md b/src/foundation/propositional-extensionality.lagda.md index 3d3e72c471..cbe65e5a9e 100644 --- a/src/foundation/propositional-extensionality.lagda.md +++ b/src/foundation/propositional-extensionality.lagda.md @@ -15,7 +15,6 @@ open import foundation.fundamental-theorem-of-identity-types open import foundation.logical-equivalences open import foundation.negation open import foundation.postcomposition-functions -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.subtype-identity-principle open import foundation.transport-along-identifications @@ -32,6 +31,7 @@ open import foundation-core.equivalences open import foundation-core.functoriality-dependent-pair-types open import foundation-core.identity-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.sets open import foundation-core.torsorial-type-families ``` diff --git a/src/foundation/raising-universe-levels-booleans.lagda.md b/src/foundation/raising-universe-levels-booleans.lagda.md index c22c66ddbc..3b47e71463 100644 --- a/src/foundation/raising-universe-levels-booleans.lagda.md +++ b/src/foundation/raising-universe-levels-booleans.lagda.md @@ -7,11 +7,11 @@ module foundation.raising-universe-levels-booleans where
Imports ```agda -open import foundation.raising-universe-levels open import foundation.universe-levels open import foundation-core.booleans open import foundation-core.equivalences +open import foundation-core.raising-universe-levels ```
diff --git a/src/foundation/raising-universe-levels-unit-type.lagda.md b/src/foundation/raising-universe-levels-unit-type.lagda.md index bd7f6068a8..403eb843ca 100644 --- a/src/foundation/raising-universe-levels-unit-type.lagda.md +++ b/src/foundation/raising-universe-levels-unit-type.lagda.md @@ -9,7 +9,6 @@ module foundation.raising-universe-levels-unit-type where ```agda open import foundation.action-on-identifications-functions open import foundation.dependent-pair-types -open import foundation.raising-universe-levels open import foundation.unit-type open import foundation.universe-levels @@ -18,6 +17,7 @@ open import foundation-core.contractible-types open import foundation-core.equivalences open import foundation-core.identity-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.retractions open import foundation-core.sets open import foundation-core.truncated-types diff --git a/src/foundation/raising-universe-levels.lagda.md b/src/foundation/raising-universe-levels.lagda.md index 052c944420..3c660be25b 100644 --- a/src/foundation/raising-universe-levels.lagda.md +++ b/src/foundation/raising-universe-levels.lagda.md @@ -2,6 +2,8 @@ ```agda module foundation.raising-universe-levels where + +open import foundation-core.raising-universe-levels public ```
Imports @@ -33,115 +35,8 @@ In Agda, types have a designated universe levels, and universes in Agda don't overlap. Using `data` types we can construct for any type `A` of universe level `l` an equivalent type in any higher universe. -## Definition - -```agda -data raise (l : Level) {l1 : Level} (A : UU l1) : UU (l1 ⊔ l) where - map-raise : A → raise l A - -data raiseω {l1 : Level} (A : UU l1) : UUω where - map-raiseω : A → raiseω A -``` - ## Properties -### Types are equivalent to their raised equivalents - -```agda -module _ - {l l1 : Level} {A : UU l1} - where - - map-inv-raise : raise l A → A - map-inv-raise (map-raise x) = x - - is-section-map-inv-raise : (map-raise ∘ map-inv-raise) ~ id - is-section-map-inv-raise (map-raise x) = refl - - is-retraction-map-inv-raise : (map-inv-raise ∘ map-raise) ~ id - is-retraction-map-inv-raise x = refl - - is-equiv-map-raise : is-equiv (map-raise {l} {l1} {A}) - is-equiv-map-raise = - is-equiv-is-invertible - map-inv-raise - is-section-map-inv-raise - is-retraction-map-inv-raise - -compute-raise : (l : Level) {l1 : Level} (A : UU l1) → A ≃ raise l A -pr1 (compute-raise l A) = map-raise -pr2 (compute-raise l A) = is-equiv-map-raise - -inv-compute-raise : (l : Level) {l1 : Level} (A : UU l1) → raise l A ≃ A -inv-compute-raise l A = inv-equiv (compute-raise l A) - -Raise : (l : Level) {l1 : Level} (A : UU l1) → Σ (UU (l1 ⊔ l)) (λ X → A ≃ X) -pr1 (Raise l A) = raise l A -pr2 (Raise l A) = compute-raise l A -``` - -### Raising universe levels of propositions - -```agda -raise-Prop : (l : Level) {l1 : Level} → Prop l1 → Prop (l ⊔ l1) -pr1 (raise-Prop l P) = raise l (type-Prop P) -pr2 (raise-Prop l P) = - is-prop-equiv' (compute-raise l (type-Prop P)) (is-prop-type-Prop P) -``` - -### Raising universe levels of sets - -```agda -raise-Set : (l : Level) {l1 : Level} → Set l1 → Set (l ⊔ l1) -pr1 (raise-Set l A) = raise l (type-Set A) -pr2 (raise-Set l A) = - is-set-equiv' (type-Set A) (compute-raise l (type-Set A)) (is-set-type-Set A) -``` - -### Raising universe levels of subtypes - -```agda -raise-subtype : - (l : Level) {l1 l2 : Level} {A : UU l1} → - subtype l2 A → subtype (l2 ⊔ l) A -raise-subtype l B x = raise-Prop l (B x) -``` - -### Raising equivalent types - -```agda -module _ - {l1 l2 : Level} (l3 l4 : Level) {A : UU l1} {B : UU l2} (e : A ≃ B) - where - - map-equiv-raise : raise l3 A → raise l4 B - map-equiv-raise (map-raise x) = map-raise (map-equiv e x) - - map-inv-equiv-raise : raise l4 B → raise l3 A - map-inv-equiv-raise (map-raise y) = map-raise (map-inv-equiv e y) - - is-section-map-inv-equiv-raise : - ( map-equiv-raise ∘ map-inv-equiv-raise) ~ id - is-section-map-inv-equiv-raise (map-raise y) = - ap map-raise (is-section-map-inv-equiv e y) - - is-retraction-map-inv-equiv-raise : - ( map-inv-equiv-raise ∘ map-equiv-raise) ~ id - is-retraction-map-inv-equiv-raise (map-raise x) = - ap map-raise (is-retraction-map-inv-equiv e x) - - is-equiv-map-equiv-raise : is-equiv map-equiv-raise - is-equiv-map-equiv-raise = - is-equiv-is-invertible - map-inv-equiv-raise - is-section-map-inv-equiv-raise - is-retraction-map-inv-equiv-raise - - equiv-raise : raise l3 A ≃ raise l4 B - pr1 equiv-raise = map-equiv-raise - pr2 equiv-raise = is-equiv-map-equiv-raise -``` - ### Raising universe levels from `l1` to `l ⊔ l1` is an embedding from `UU l1` to `UU (l ⊔ l1)` ```agda diff --git a/src/foundation/vectors-set-quotients.lagda.md b/src/foundation/vectors-set-quotients.lagda.md index d9652fc385..4436c4ecb8 100644 --- a/src/foundation/vectors-set-quotients.lagda.md +++ b/src/foundation/vectors-set-quotients.lagda.md @@ -19,7 +19,6 @@ open import foundation.function-extensionality open import foundation.function-extensionality-axiom open import foundation.multivariable-operations open import foundation.products-equivalence-relations -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.reflecting-maps-equivalence-relations open import foundation.set-quotients @@ -37,6 +36,7 @@ open import foundation-core.function-types open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.propositions +open import foundation-core.raising-universe-levels open import foundation-core.retractions open import foundation-core.sections diff --git a/src/graph-theory/large-higher-directed-graphs.lagda.md b/src/graph-theory/large-higher-directed-graphs.lagda.md index 6d805cf1a8..295f90798b 100644 --- a/src/graph-theory/large-higher-directed-graphs.lagda.md +++ b/src/graph-theory/large-higher-directed-graphs.lagda.md @@ -14,10 +14,11 @@ open import foundation.dependent-pair-types open import foundation.function-types open import foundation.identity-types open import foundation.large-binary-relations -open import foundation.raising-universe-levels open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import graph-theory.directed-graphs open import graph-theory.higher-directed-graphs ``` diff --git a/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md b/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md index ff763cffc0..7b166ec703 100644 --- a/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md +++ b/src/graph-theory/raising-universe-levels-directed-graphs.lagda.md @@ -9,9 +9,10 @@ module graph-theory.raising-universe-levels-directed-graphs where ```agda open import foundation.dependent-pair-types open import foundation.equivalences -open import foundation.raising-universe-levels open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import graph-theory.directed-graphs open import graph-theory.equivalences-directed-graphs open import graph-theory.walks-directed-graphs diff --git a/src/graph-theory/walks-directed-graphs.lagda.md b/src/graph-theory/walks-directed-graphs.lagda.md index 62dbd71950..8138dc122b 100644 --- a/src/graph-theory/walks-directed-graphs.lagda.md +++ b/src/graph-theory/walks-directed-graphs.lagda.md @@ -24,11 +24,12 @@ open import foundation.homotopies open import foundation.identity-types open import foundation.injective-maps open import foundation.negated-equality -open import foundation.raising-universe-levels open import foundation.torsorial-type-families open import foundation.transport-along-identifications open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import graph-theory.directed-graphs open import graph-theory.equivalences-directed-graphs open import graph-theory.morphisms-directed-graphs diff --git a/src/group-theory/trivial-groups.lagda.md b/src/group-theory/trivial-groups.lagda.md index b1a2bb41ae..bfc102a46f 100644 --- a/src/group-theory/trivial-groups.lagda.md +++ b/src/group-theory/trivial-groups.lagda.md @@ -15,11 +15,12 @@ open import foundation.fundamental-theorem-of-identity-types open import foundation.homotopies open import foundation.identity-types open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.structure-identity-principle open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import group-theory.abelian-groups open import group-theory.full-subgroups open import group-theory.groups diff --git a/src/linear-algebra/vectors.lagda.md b/src/linear-algebra/vectors.lagda.md index c4ad918758..32ee3b6fa0 100644 --- a/src/linear-algebra/vectors.lagda.md +++ b/src/linear-algebra/vectors.lagda.md @@ -23,7 +23,6 @@ open import foundation.function-extensionality-axiom open import foundation.function-types open import foundation.homotopies open import foundation.identity-types -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.transport-along-identifications @@ -33,6 +32,8 @@ open import foundation.unit-type open import foundation.universe-levels open import foundation.whiskering-higher-homotopies-composition +open import foundation-core.raising-universe-levels + open import univalent-combinatorics.involution-standard-finite-types open import univalent-combinatorics.standard-finite-types ``` diff --git a/src/lists/equality-lists.lagda.md b/src/lists/equality-lists.lagda.md index ddfac7ade4..f69a8625e8 100644 --- a/src/lists/equality-lists.lagda.md +++ b/src/lists/equality-lists.lagda.md @@ -23,7 +23,6 @@ open import foundation.equivalences open import foundation.function-types open import foundation.functoriality-dependent-pair-types open import foundation.negation -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.torsorial-type-families @@ -35,6 +34,7 @@ open import foundation.universe-levels open import foundation-core.homotopies open import foundation-core.identity-types open import foundation-core.maybe +open import foundation-core.raising-universe-levels open import lists.lists ``` diff --git a/src/lists/lists-discrete-types.lagda.md b/src/lists/lists-discrete-types.lagda.md index 64cecc520a..59dd7561d4 100644 --- a/src/lists/lists-discrete-types.lagda.md +++ b/src/lists/lists-discrete-types.lagda.md @@ -16,11 +16,12 @@ open import foundation.dependent-pair-types open import foundation.empty-types open import foundation.function-types open import foundation.identity-types -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import lists.equality-lists open import lists.lists ``` diff --git a/src/literature/introduction-to-homotopy-type-theory.lagda.md b/src/literature/introduction-to-homotopy-type-theory.lagda.md index 39b75e92c2..c802dce2bc 100644 --- a/src/literature/introduction-to-homotopy-type-theory.lagda.md +++ b/src/literature/introduction-to-homotopy-type-theory.lagda.md @@ -787,7 +787,7 @@ open import foundation.universe-levels using **Remark 6.2.4.** Inclusions into the successor universe. ```agda -open import foundation.raising-universe-levels using +open import foundation-core.raising-universe-levels using ( raise) _ : (l : Level) → UU l → UU (lsuc l) diff --git a/src/order-theory/join-preserving-maps-posets.lagda.md b/src/order-theory/join-preserving-maps-posets.lagda.md index 11d5cc44fb..cc4546d3ac 100644 --- a/src/order-theory/join-preserving-maps-posets.lagda.md +++ b/src/order-theory/join-preserving-maps-posets.lagda.md @@ -18,13 +18,14 @@ open import foundation.homotopies open import foundation.homotopy-induction open import foundation.identity-types open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.small-types open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle open import foundation.torsorial-type-families open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import order-theory.least-upper-bounds-posets open import order-theory.order-preserving-maps-posets open import order-theory.posets diff --git a/src/order-theory/supremum-preserving-maps-posets.lagda.md b/src/order-theory/supremum-preserving-maps-posets.lagda.md index eeda5fcfba..cb66d8a36a 100644 --- a/src/order-theory/supremum-preserving-maps-posets.lagda.md +++ b/src/order-theory/supremum-preserving-maps-posets.lagda.md @@ -18,13 +18,14 @@ open import foundation.homotopies open import foundation.homotopy-induction open import foundation.identity-types open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.small-types open import foundation.strictly-involutive-identity-types open import foundation.subtype-identity-principle open import foundation.torsorial-type-families open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import order-theory.join-preserving-maps-posets open import order-theory.least-upper-bounds-posets open import order-theory.order-preserving-maps-posets diff --git a/src/orthogonal-factorization-systems/raise-modalities.lagda.md b/src/orthogonal-factorization-systems/raise-modalities.lagda.md index 1f7569b41d..269d67950f 100644 --- a/src/orthogonal-factorization-systems/raise-modalities.lagda.md +++ b/src/orthogonal-factorization-systems/raise-modalities.lagda.md @@ -8,9 +8,10 @@ module orthogonal-factorization-systems.raise-modalities where ```agda open import foundation.function-types -open import foundation.raising-universe-levels open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import orthogonal-factorization-systems.modal-operators open import orthogonal-factorization-systems.types-local-at-maps open import orthogonal-factorization-systems.uniquely-eliminating-modalities diff --git a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md index 422760c592..627f6b08de 100644 --- a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md +++ b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md @@ -21,10 +21,11 @@ open import foundation.identity-types open import foundation.inhabited-subtypes open import foundation.logical-equivalences open import foundation.negation -open import foundation.raising-universe-levels open import foundation.subtypes open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import logic.functoriality-existential-quantification open import real-numbers.dedekind-real-numbers diff --git a/src/set-theory/countable-sets.lagda.md b/src/set-theory/countable-sets.lagda.md index 6b2a4cf4d7..982fc80390 100644 --- a/src/set-theory/countable-sets.lagda.md +++ b/src/set-theory/countable-sets.lagda.md @@ -32,7 +32,6 @@ open import foundation.negated-equality open import foundation.negation open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.retracts-of-types open import foundation.sets open import foundation.shifting-sequences @@ -43,6 +42,7 @@ open import foundation.universe-levels open import foundation-core.cartesian-product-types open import foundation-core.fibers-of-maps open import foundation-core.identity-types +open import foundation-core.raising-universe-levels open import univalent-combinatorics.standard-finite-types ``` diff --git a/src/set-theory/cumulative-hierarchy.lagda.md b/src/set-theory/cumulative-hierarchy.lagda.md index c4e25f4da1..902df4741c 100644 --- a/src/set-theory/cumulative-hierarchy.lagda.md +++ b/src/set-theory/cumulative-hierarchy.lagda.md @@ -27,7 +27,6 @@ open import foundation.negation open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-booleans open import foundation.raising-universe-levels-unit-type open import foundation.sets @@ -35,6 +34,8 @@ open import foundation.transport-along-identifications open import foundation.truncated-types open import foundation.unit-type open import foundation.universe-levels + +open import foundation-core.raising-universe-levels ```
diff --git a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md index 3c499aa004..6540c13dfb 100644 --- a/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md +++ b/src/synthetic-homotopy-theory/infinite-cyclic-types.lagda.md @@ -27,11 +27,12 @@ open import foundation.homotopies open import foundation.identity-types open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.torsorial-type-families open import foundation.type-arithmetic-dependent-pair-types open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import structured-types.equivalences-types-equipped-with-endomorphisms open import structured-types.initial-pointed-type-equipped-with-automorphism open import structured-types.mere-equivalences-types-equipped-with-endomorphisms diff --git a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md index 0b7e16571f..cfed6ad47e 100644 --- a/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md +++ b/src/synthetic-homotopy-theory/universal-cover-circle.lagda.md @@ -34,7 +34,6 @@ open import foundation.injective-maps open import foundation.negated-equality open import foundation.negation open import foundation.precomposition-dependent-functions -open import foundation.raising-universe-levels open import foundation.sets open import foundation.torsorial-type-families open import foundation.transport-along-identifications @@ -42,6 +41,8 @@ open import foundation.truncated-types open import foundation.truncation-levels open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import synthetic-homotopy-theory.descent-circle open import synthetic-homotopy-theory.free-loops open import synthetic-homotopy-theory.loop-spaces diff --git a/src/trees/raising-universe-levels-directed-trees.lagda.md b/src/trees/raising-universe-levels-directed-trees.lagda.md index cdaf4ca5a9..00591d1102 100644 --- a/src/trees/raising-universe-levels-directed-trees.lagda.md +++ b/src/trees/raising-universe-levels-directed-trees.lagda.md @@ -11,9 +11,10 @@ open import foundation.contractible-types open import foundation.dependent-pair-types open import foundation.dependent-products-contractible-types open import foundation.equivalences -open import foundation.raising-universe-levels open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import graph-theory.directed-graphs open import graph-theory.raising-universe-levels-directed-graphs open import graph-theory.walks-directed-graphs diff --git a/src/trees/small-multisets.lagda.md b/src/trees/small-multisets.lagda.md index dce94823f3..7ce5c004dd 100644 --- a/src/trees/small-multisets.lagda.md +++ b/src/trees/small-multisets.lagda.md @@ -17,13 +17,14 @@ open import foundation.functoriality-dependent-pair-types open import foundation.homotopies open import foundation.identity-types open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.small-types open import foundation.subtypes open import foundation.transport-along-identifications open import foundation.univalence open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import trees.multisets open import trees.w-types ``` diff --git a/src/trees/universal-multiset.lagda.md b/src/trees/universal-multiset.lagda.md index 954321d15a..e347a35a1f 100644 --- a/src/trees/universal-multiset.lagda.md +++ b/src/trees/universal-multiset.lagda.md @@ -10,12 +10,13 @@ module trees.universal-multiset where open import foundation.dependent-pair-types open import foundation.equivalences open import foundation.identity-types -open import foundation.raising-universe-levels open import foundation.small-types open import foundation.small-universes open import foundation.transport-along-identifications open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import trees.functoriality-w-types open import trees.multisets open import trees.small-multisets diff --git a/src/univalent-combinatorics/2-element-types.lagda.md b/src/univalent-combinatorics/2-element-types.lagda.md index 702cf0449e..b58564f62c 100644 --- a/src/univalent-combinatorics/2-element-types.lagda.md +++ b/src/univalent-combinatorics/2-element-types.lagda.md @@ -38,7 +38,6 @@ open import foundation.negated-equality open import foundation.negation open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.sets open import foundation.subuniverses open import foundation.torsorial-type-families @@ -51,6 +50,8 @@ open import foundation.unit-type open import foundation.universal-property-identity-systems open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import univalent-combinatorics.equality-standard-finite-types open import univalent-combinatorics.equivalences open import univalent-combinatorics.finite-types diff --git a/src/univalent-combinatorics/binomial-types.lagda.md b/src/univalent-combinatorics/binomial-types.lagda.md index ad29a5ff2a..9595430e57 100644 --- a/src/univalent-combinatorics/binomial-types.lagda.md +++ b/src/univalent-combinatorics/binomial-types.lagda.md @@ -38,7 +38,6 @@ open import foundation.postcomposition-functions open import foundation.propositional-extensionality open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.type-arithmetic-cartesian-product-types open import foundation.type-arithmetic-coproduct-types @@ -51,6 +50,8 @@ open import foundation.universal-property-equivalences open import foundation.universal-property-maybe open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import univalent-combinatorics.coproduct-types open import univalent-combinatorics.finite-types open import univalent-combinatorics.standard-finite-types diff --git a/src/univalent-combinatorics/finite-types.lagda.md b/src/univalent-combinatorics/finite-types.lagda.md index 2d1393831c..705affe740 100644 --- a/src/univalent-combinatorics/finite-types.lagda.md +++ b/src/univalent-combinatorics/finite-types.lagda.md @@ -31,7 +31,6 @@ open import foundation.logical-equivalences open import foundation.mere-equivalences open import foundation.propositional-truncations open import foundation.propositions -open import foundation.raising-universe-levels open import foundation.raising-universe-levels-unit-type open import foundation.sets open import foundation.subtypes @@ -43,6 +42,7 @@ open import foundation.unit-type open import foundation.univalence open import foundation.universe-levels +open import foundation-core.raising-universe-levels open import foundation-core.torsorial-type-families open import univalent-combinatorics.counting diff --git a/src/univalent-combinatorics/standard-finite-types.lagda.md b/src/univalent-combinatorics/standard-finite-types.lagda.md index 1620ae6151..57830d99dc 100644 --- a/src/univalent-combinatorics/standard-finite-types.lagda.md +++ b/src/univalent-combinatorics/standard-finite-types.lagda.md @@ -33,13 +33,14 @@ open import foundation.negated-equality open import foundation.negation open import foundation.noncontractible-types open import foundation.preunivalent-type-families -open import foundation.raising-universe-levels open import foundation.retractions open import foundation.sets open import foundation.transport-along-identifications open import foundation.unit-type open import foundation.universe-levels +open import foundation-core.raising-universe-levels + open import structured-types.types-equipped-with-endomorphisms ``` From f4f6ce2de841fa9ba0a2acf2eb815e1d50958916 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Mon, 24 Mar 2025 20:44:35 +0000 Subject: [PATCH 38/39] restore lemma raising universe levels --- src/foundation/raising-universe-levels.lagda.md | 9 +++++++++ .../raising-universe-levels-real-numbers.lagda.md | 3 +-- 2 files changed, 10 insertions(+), 2 deletions(-) diff --git a/src/foundation/raising-universe-levels.lagda.md b/src/foundation/raising-universe-levels.lagda.md index 3c660be25b..f2dc4d44aa 100644 --- a/src/foundation/raising-universe-levels.lagda.md +++ b/src/foundation/raising-universe-levels.lagda.md @@ -37,6 +37,15 @@ overlap. Using `data` types we can construct for any type `A` of universe level ## Properties +### Raising universe levels of subtypes + +```agda +raise-subtype : + (l : Level) {l1 l2 : Level} {A : UU l1} → + subtype l2 A → subtype (l2 ⊔ l) A +raise-subtype l B x = raise-Prop l (B x) +``` + ### Raising universe levels from `l1` to `l ⊔ l1` is an embedding from `UU l1` to `UU (l ⊔ l1)` ```agda diff --git a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md index 627f6b08de..422760c592 100644 --- a/src/real-numbers/raising-universe-levels-real-numbers.lagda.md +++ b/src/real-numbers/raising-universe-levels-real-numbers.lagda.md @@ -21,11 +21,10 @@ open import foundation.identity-types open import foundation.inhabited-subtypes open import foundation.logical-equivalences open import foundation.negation +open import foundation.raising-universe-levels open import foundation.subtypes open import foundation.universe-levels -open import foundation-core.raising-universe-levels - open import logic.functoriality-existential-quantification open import real-numbers.dedekind-real-numbers From 119269ba8150fa1dd7b43b794fa3ba61fed97a24 Mon Sep 17 00:00:00 2001 From: Fredrik Bakke Date: Tue, 22 Apr 2025 20:09:36 +0100 Subject: [PATCH 39/39] Update remove_unused_imports.py --- scripts/remove_unused_imports.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/scripts/remove_unused_imports.py b/scripts/remove_unused_imports.py index 14ad2f055f..c1c56aaa4c 100755 --- a/scripts/remove_unused_imports.py +++ b/scripts/remove_unused_imports.py @@ -115,7 +115,7 @@ def filter_agda_files(f): return utils.is_agda_file(pathlib.Path(f)) and os.path temp_dir = 'temp' status = 0 - agda_options = '--without-K --exact-split --no-import-sorts --auto-inline --no-caching -WnoPatternShadowsConstructor' + agda_options = '--without-K --exact-split --no-import-sorts --auto-inline --no-caching' temp_root = os.path.join(root, temp_dir) shutil.rmtree(temp_root, ignore_errors=True)